Submitted to Operations Research
manuscript XX
A General Attraction Model and Sales-based Linear
Program for Network Revenue Management under
Customer Choice
Guillermo Gallego
Department of Industrial Engienering and Operations Research, Columbia University, New York, NY 10027,
[email protected]
Richard Ratliff and Sergey Shebalov
Research Group, Sabre Holdings, Southlake, TX 76092, [email protected]
This paper addresses two concerns with the state of the art in network revenue management with dependent
demands. The first concern is that the basic attraction model (BAM), of which the multinomial logit (MNL)
model is a special case, tends to overestimate demand recapture in practice. The second concern is that the
choice based deterministic linear program, currently in use to derive heuristics for the stochastic network
revenue management problem, has an exponential number of variables. We introduce a generalized attraction
model (GAM) that allows for partial demand dependencies ranging from the BAM to the independent
demand model (IDM). We also provide an axiomatic justification for the GAM and a method to estimate its
parameters. As a choice model, the GAM is of practical interest because of its flexibility to adjust product-
specific recapture. Our second contribution is a new formulation called the Sales Based Linear Program
(SBLP) that works for the GAM. This formulation avoids the exponential number of variables in the earlier
choice-based network RM approaches, and is essentially the same size as the well known LP formulation
for the IDM. The SBLP should be of interest to revenue managers because it makes choice-based network
RM problems tractable to solve. In addition, the SBLP formulation yields new insights into the assortment
problem that arises when capacities are infinite. Together these two contributions move forward the state of
the art for network revenue management under customer choice and competition.
Key words : pricing, choice models, network revenue management, dependent demands, O&D, upsell,
recapture
1. Introduction
One of the leading areas of research in revenue management (RM) has been incorporating demand
dependencies into forecasting and optimization models. Developing effective models for suppliers
to estimate how consumer demand is redirected as the set of available products changes is critical
1
Gallego, Ratliff, and Shebalov: A General Choice Model and Network RM Optimization
2 Article submitted to Operations Research; manuscript no. XX
in determining the revenue maximizing set of products and prices to offer for sale in industries
where RM is used. These industries include airlines, hotels, and car rental companies, but the issue
of how customers select among different offerings is also important in transportation, retailing and
healthcare. Several terms are used in industry to describe different types of demand dependen-
cies. If all products are available for sale, we observe ...
Assignment 2 Organisms in Your BiomeIn this assignment, you wil.docxsherni1
Assignment 2: Organisms in Your Biome
In this assignment, you will create a Microsoft PowerPoint presentation that exhibits the different organisms in your current biome.
Include the following in your presentation:
· Describe Your Own Environment
Consider the natural environment or biome found in the geographic area where you currently live. For example, if you live in the Midwest, the natural biome for this area is the grassland. If you live in Alaska you are likely to live in either the tundra or the boreal forest. Describe the main features of the biome found in your geographic area. Include features such as the environment (moisture, temperature) and any topographic features that would influence the climate (mountains, large bodies of water, etc.).
· Identify Ten Organisms
Make a list identifying at least ten organisms—at least five plants and five animals—that live in your biome, and describe how these organisms interact with one another. For example, is the relationship competitive or symbiotic?
· Describe Each Organism and its Environmental Needs
In the speaker notes section in your presentation, briefly describe these ten organisms and the type of conditions—that is, moisture, warm temperatures, or a type of plant—they need in order to survive. Be sure to include the interactions between these organisms and the resources they need to survive. You may wish to use various tools available in Microsoft PowerPoint to visually depict these relationships.
· Hypothesis of a New Environment
Consider a situation where the temperature of the climate was to increase by an average of ten degrees Celsius. Address the following:
· How would these organisms survive if the temperature warmed up this much?
· Would they stay or move to a more suitable environment?
· Would a new species move in?
· How would migratory species be impacted?
· What would happen to your biome?
Now, consider if your biome changes with the temperature shift. Address the following:
· What types of plants and animals do you think would live there?
· What will happen to the rarer species? Will they cease to exist?
· Identify five plants and five animals that you feel would inhabit this warmer area.
· Describe this new ecosystem and the new interactions that will most likely exist.
· Additional Topics to Include
· How would environmental management practices change in your area?
· Would this drastic shift in temperature impact culture and society in your area?
· Would you still choose to live in this area after a drastic shift in temperature? Give reasons to support your answer.
Use pictures from the Internet to represent your chosen species, and give credit to these Web sites. Support your statements with 3–5 credible sources. Use the last slide of your presentation as a reference slide.
Develop a 10–15-slide presentation in Microsoft PowerPoint format. Apply APA standards to citation of sources. Use the following file naming convention: LastnameFirstInitial_M3_A ...
Thesis - Mechanizing optimization of warehouses by implementation of machine ...Shrikant Samarth
Task: As Research Project is part of a postgraduate course it is also required that students employ and
develop their research knowledge and skills in an applied fashion. The Research Project must
involve the identification, generation, or collation of relevant primary or secondary data and the
ability to analyze them in a meaningful and critical manner.
Approach: Data was taken from a working organization to resolve the issue regarding the space optimization of the warehouse which results into losses to the company.
Findings: Ada boosting algorithm works best for identification of the blowout products beforehand which would help warehouse manager to apply strategies on the products which would take time to sell. So that, the losses associated to such products can be avoided.
Tools: Python programming, Excel visualizations, Overleaf latex
This document summarizes a study on surge pricing in transportation network economies. It begins by explaining how dynamic pricing allows prices to change quickly based on demand without significant costs. Dynamic pricing is common in sharing economies and industries with digital sales. The transportation industry, including ridesharing services, uses dynamic pricing where prices surge to match supply and demand. However, consumers have complained about excessive surge pricing in some cases. The document aims to analyze surge pricing as a potential case of excessive pricing and how authorities should regulate dynamic prices. It provides background on dynamic pricing applications and benefits across industries before focusing on its use and effects in the transportation sector.
This document proposes applying boosting techniques to attraction-based demand models that are popular in pricing optimization. It formulates a multinomial likelihood for a semiparametric demand choice model (DCM) where product utility is specified without a fixed functional form. Gradient boosting is used to maximize the likelihood and estimate the nonparametric utility functions. The boosted tree-based approach flexibly models utility as a sum of trees, addressing limitations of existing DCMs like non-stationary demand and nonlinear attribute effects.
Pareto optimality refers to an allocation of resources where it is not possible to make one person better off without making another person worse off. A perfectly competitive market can achieve a Pareto optimal allocation of resources. In game theory, a Pareto optimal outcome is one where no player can be better off without making another player worse off. Multi-objective optimization involves simultaneously optimizing two or more conflicting objectives subject to constraints. Evolutionary algorithms are commonly used to approximate the entire Pareto front of optimal solutions in a single run.
More on https://highlyscalable.wordpress.com/
Data Mining Problems in Retail is an analytical report that studies how retailers can make sense of their
data by adopting advanced data analysis and optimization techniques that enable automated decision
making in the area of marketing and pricing. The report analyzes dozens of practical case studies and
research reports and presents a systematic view on the problem.
We hope that this article will be useful for data scientists, marketing specialists, and business analysts
who are looking beyond the basic statistical and data mining techniques to build comprehensive
data-driven business optimization processes and solutions.
A proposal for an econometric analysis of switching costs in the software ind...haramaya university
This proposal aims to empirically analyze switching costs in the software industry using a hedonic pricing model. It will study the supply chain management software market, where significant switching costs exist due to integration requirements, business process changes, training needs, and maintenance costs. The proposal has three goals: 1) provide a detailed taxonomy of switching cost types; 2) estimate the magnitude of switching costs on price; 3) deduce implications for competitive strategies. It will test hypotheses about how switching costs influence pricing and firm behavior. Project-level data on customer budgets and vendor contracts will be collected from 1991-2003 to estimate switching costs and their impact on SAP's prices as both an entrant and incumbent in the market.
IRJET- Credit Profile of E-Commerce CustomerIRJET Journal
This document proposes using RFM (Recency, Frequency, Monetary) variables and advanced k-means clustering to create positive and negative credit profiles for e-commerce customers. This will help minimize losses by identifying genuine versus fraudulent customers. The methodology calculates credit scores based on RFM and other factors. Advanced k-means clustering is then used to segment customers into clusters like excellent, good, average, and worst. Customers in different clusters will receive different benefits or restrictions based on their predicted reliability. The goal is to reduce losses from unwanted cancellations while retaining high value customers.
Assignment 2 Organisms in Your BiomeIn this assignment, you wil.docxsherni1
Assignment 2: Organisms in Your Biome
In this assignment, you will create a Microsoft PowerPoint presentation that exhibits the different organisms in your current biome.
Include the following in your presentation:
· Describe Your Own Environment
Consider the natural environment or biome found in the geographic area where you currently live. For example, if you live in the Midwest, the natural biome for this area is the grassland. If you live in Alaska you are likely to live in either the tundra or the boreal forest. Describe the main features of the biome found in your geographic area. Include features such as the environment (moisture, temperature) and any topographic features that would influence the climate (mountains, large bodies of water, etc.).
· Identify Ten Organisms
Make a list identifying at least ten organisms—at least five plants and five animals—that live in your biome, and describe how these organisms interact with one another. For example, is the relationship competitive or symbiotic?
· Describe Each Organism and its Environmental Needs
In the speaker notes section in your presentation, briefly describe these ten organisms and the type of conditions—that is, moisture, warm temperatures, or a type of plant—they need in order to survive. Be sure to include the interactions between these organisms and the resources they need to survive. You may wish to use various tools available in Microsoft PowerPoint to visually depict these relationships.
· Hypothesis of a New Environment
Consider a situation where the temperature of the climate was to increase by an average of ten degrees Celsius. Address the following:
· How would these organisms survive if the temperature warmed up this much?
· Would they stay or move to a more suitable environment?
· Would a new species move in?
· How would migratory species be impacted?
· What would happen to your biome?
Now, consider if your biome changes with the temperature shift. Address the following:
· What types of plants and animals do you think would live there?
· What will happen to the rarer species? Will they cease to exist?
· Identify five plants and five animals that you feel would inhabit this warmer area.
· Describe this new ecosystem and the new interactions that will most likely exist.
· Additional Topics to Include
· How would environmental management practices change in your area?
· Would this drastic shift in temperature impact culture and society in your area?
· Would you still choose to live in this area after a drastic shift in temperature? Give reasons to support your answer.
Use pictures from the Internet to represent your chosen species, and give credit to these Web sites. Support your statements with 3–5 credible sources. Use the last slide of your presentation as a reference slide.
Develop a 10–15-slide presentation in Microsoft PowerPoint format. Apply APA standards to citation of sources. Use the following file naming convention: LastnameFirstInitial_M3_A ...
Thesis - Mechanizing optimization of warehouses by implementation of machine ...Shrikant Samarth
Task: As Research Project is part of a postgraduate course it is also required that students employ and
develop their research knowledge and skills in an applied fashion. The Research Project must
involve the identification, generation, or collation of relevant primary or secondary data and the
ability to analyze them in a meaningful and critical manner.
Approach: Data was taken from a working organization to resolve the issue regarding the space optimization of the warehouse which results into losses to the company.
Findings: Ada boosting algorithm works best for identification of the blowout products beforehand which would help warehouse manager to apply strategies on the products which would take time to sell. So that, the losses associated to such products can be avoided.
Tools: Python programming, Excel visualizations, Overleaf latex
This document summarizes a study on surge pricing in transportation network economies. It begins by explaining how dynamic pricing allows prices to change quickly based on demand without significant costs. Dynamic pricing is common in sharing economies and industries with digital sales. The transportation industry, including ridesharing services, uses dynamic pricing where prices surge to match supply and demand. However, consumers have complained about excessive surge pricing in some cases. The document aims to analyze surge pricing as a potential case of excessive pricing and how authorities should regulate dynamic prices. It provides background on dynamic pricing applications and benefits across industries before focusing on its use and effects in the transportation sector.
This document proposes applying boosting techniques to attraction-based demand models that are popular in pricing optimization. It formulates a multinomial likelihood for a semiparametric demand choice model (DCM) where product utility is specified without a fixed functional form. Gradient boosting is used to maximize the likelihood and estimate the nonparametric utility functions. The boosted tree-based approach flexibly models utility as a sum of trees, addressing limitations of existing DCMs like non-stationary demand and nonlinear attribute effects.
Pareto optimality refers to an allocation of resources where it is not possible to make one person better off without making another person worse off. A perfectly competitive market can achieve a Pareto optimal allocation of resources. In game theory, a Pareto optimal outcome is one where no player can be better off without making another player worse off. Multi-objective optimization involves simultaneously optimizing two or more conflicting objectives subject to constraints. Evolutionary algorithms are commonly used to approximate the entire Pareto front of optimal solutions in a single run.
More on https://highlyscalable.wordpress.com/
Data Mining Problems in Retail is an analytical report that studies how retailers can make sense of their
data by adopting advanced data analysis and optimization techniques that enable automated decision
making in the area of marketing and pricing. The report analyzes dozens of practical case studies and
research reports and presents a systematic view on the problem.
We hope that this article will be useful for data scientists, marketing specialists, and business analysts
who are looking beyond the basic statistical and data mining techniques to build comprehensive
data-driven business optimization processes and solutions.
A proposal for an econometric analysis of switching costs in the software ind...haramaya university
This proposal aims to empirically analyze switching costs in the software industry using a hedonic pricing model. It will study the supply chain management software market, where significant switching costs exist due to integration requirements, business process changes, training needs, and maintenance costs. The proposal has three goals: 1) provide a detailed taxonomy of switching cost types; 2) estimate the magnitude of switching costs on price; 3) deduce implications for competitive strategies. It will test hypotheses about how switching costs influence pricing and firm behavior. Project-level data on customer budgets and vendor contracts will be collected from 1991-2003 to estimate switching costs and their impact on SAP's prices as both an entrant and incumbent in the market.
IRJET- Credit Profile of E-Commerce CustomerIRJET Journal
This document proposes using RFM (Recency, Frequency, Monetary) variables and advanced k-means clustering to create positive and negative credit profiles for e-commerce customers. This will help minimize losses by identifying genuine versus fraudulent customers. The methodology calculates credit scores based on RFM and other factors. Advanced k-means clustering is then used to segment customers into clusters like excellent, good, average, and worst. Customers in different clusters will receive different benefits or restrictions based on their predicted reliability. The goal is to reduce losses from unwanted cancellations while retaining high value customers.
A Comparative Study Of Machine Learning Algorithms For Industry-Specific Frei...Karla Long
This document describes a study that compares machine learning algorithms to traditional regression for generating freight models by industry. Researchers evaluated 7 machine learning algorithms and ordinary least squares regression on freight generation data for 45 industries. Models were selected individually for each industry based on statistically significant improvements in error reduction compared to ordinary least squares. Results showed machine learning algorithms reduced root mean square error by around 30% over 80% of the time compared to ordinary least squares regression. The study suggests using machine learning algorithms can improve accuracy of industry-specific freight generation models.
Airline Network Design And Fleet Assignment Using Logit-Based Dynamic Demand...James Heller
This document discusses airline network design and fleet assignment while considering dynamic demand. It uses a logit-based model to capture demand as a function of the supply offered, rather than a static parameter. This adds complexity over previous models. The paper aims to integrate network design and fleet assignment stages while accounting for demand-supply interactions and competition. It presents a nonlinear model, which is transformed into a linear one and solved using an example to illustrate the approach.
CURRENT RESEARCH ON REVERSE AUCTIONS: PART II -IMPLEMENTATION ISSUES ASSOCIAT...ijmvsc
This article serves as the second part in a two-part series that provides an overview of the reverse auction concept, building on the best research in the field of supply chain management. In this instalment, we look at the concerns involved in making reverse auctions work in practice – the implementation issues. Frist, we look at when reverse auctions should – and should not – be utilized by a buying organization. We then examine the decision rules that should be used in determining which of the competing suppliers wins the reverse auction. Next, we look at the best research available as to how the use of reverse auctions impacts the buyer-seller relationship. Finally, we examine what is in essence a “make or buy” decision in regards to whether the purchasing organization should run an auction in-house or make use of the services of a third-party “market maker.
Churn in the Telecommunications Industryskewdlogix
Strategic Business Analysis Capstone Project Telecommunications Churn Management
Churn is a significant problem that costs telecommunications companies billions of dollars through lost revenue. Now that the market is more mature, the only way for a company to grow is to take their competitors customers. This issue
combined with the greater choice that consumers have gained means that any adverse touch point with a consumer can result in a lost customer.
Multi-commodity ETRM’s are becoming too expensive to implement, and maintain ...CTRM Center
Since ETRM software was first introduced around 20-years ago, developers have continually sought to move from developing solutions designed to support specific commodities such as crude oil, natural gas, and electric power, to building solutions that catered for multiple energy commodities. In part, their objective was to reduce costs – specifically integration costs, but without a doubt, part of the objective was self-serving, as this also allowed them to broaden the appeal of their software to a larger and more lucrative market.
CONSIGNMENT INVENTORY SIMULATION MODEL FOR SINGLE VENDOR-MULTI BUYERS IN A SU...IAEME Publication
The focus on the studies of supply chain management has been increasing in
recent years among academics as well as practitioners. In this paper, we present an
extendable multi agent supply chain simulation model for consignment stock inventory
model for a single vendor - multiple buyers. The simulation study dealt the
quantitative measures of performance of consignment stock model with respect to
number of shipments, delay deliveries, number of shipments shifted due to partial
information sharing, average inventory levels of buyer and vendor and joint total
economic cost (JTEC) as key performance parameters. Flexsim V3.0 a discrete event
simulation software is used for simulating the model.
CONSIGNMENT INVENTORY SIMULATION MODEL FOR SINGLE VENDOR-MULTI BUYERS IN A SU...IAEME Publication
The document describes a simulation model of a consignment inventory system for a single vendor and multiple buyers. The simulation model is developed using Flexsim software and evaluates key performance metrics like total cost, inventory levels, shipments, and fill rate. Three models are simulated: one without delays, one with delivery delays, and one with partial information sharing between vendor and buyer. Results show that total cost increases with more buyers but information sharing reduces costs the most, especially for multiple buyers. The number of shipments and delays decreases with information sharing while fill rate increases.
Adoption of Vendor Managed Inventory Practices on Supply Chain Performance in...AkashSharma618775
This document discusses a study on the adoption of vendor managed inventory practices on supply chain performance in selected automobile industries in Nairobi County, Kenya. The study aims to determine the role of supplier demand visibility, communication mechanisms, inventory decisions, and replenishment decisions on supply chain management performance. The document provides background on vendor managed inventory and outlines the research objectives, questions, significance, scope, and methodology. It discusses the theoretical framework, conceptual framework, research design, target population, sampling techniques, and data collection instruments used in the study.
Is freemium a viable pricing strategy for cloud services?Izam Ryan
An in-depth study of the application of freemium pricing practice in the cloud services space that Amazon EC2, Google Compute Engine, Microsoft Azure and Rackshare compete in.
Submitted in partial fulfilment of the requirements of the Imperial MBA degree and the Diploma of Imperial College London. I was awarded a Distinction for this Pricing Strategy elective.
Excluding appendixes: 2,497 words
Assortment Planning And Inventory Decisions Under A Locational Choice ModelAndrea Porter
This document summarizes a research paper about assortment planning and inventory management for retailers using a locational choice model of consumer demand. The paper analyzes optimal product variety, location, and inventory decisions under both static and dynamic substitution scenarios. Key findings include: 1) Under static substitution, products are equally spaced so there is no substitution between them. 2) Dynamic substitution provides more variety and locates products closer together to benefit from substitution. 3) The optimal assortment may not include the most popular product due to demand fragmentation.
The Club War Case Study Report by Sachin mathews Sachin Mathews
The objective of this study is to analyse Sam’s club and their current inefficiencies and provide suggestions to Mr.Jim who heads the reengineering team that can help his team formulate appropriate supply chain strategies in order to achieve lowest possible cost and attain greater competitive advantage. The paper provides a background of the current situation faced by club where the current inefficiencies are discussed and possible recommendations are then suggested.
CONSIGNMENT INVENTORY SIMULATION MODEL FOR SINGLE VENDOR- MULTI BUYERSIAEME Publication
The focus on the studies of supply chain management has been increasing in
recent years among academics as well as practitioners. In this paper, we present an
extendable multi agent supply chain simulation model for consignment stock inventory
model for a single vendor - multiple buyers. The simulation study dealt the
quantitative measures of performance of consignment stock model with respect to
number of shipments, delay deliveries, number of shipments shifted due to partial
information sharing, average inventory levels of buyer and vendor and joint total
economic cost (JTEC) as key performance parameters. Flexsim V3.0 a discrete event
simulation software is used for simulating the model
At various levels of decomposition we can
analysed the supply chain problem. At the first level problem
of supply chain management which is consist of many sub
problems as product design, customer services, logistic
management and others. We can define all the problems as
general and in specific way. These problems come at various
vertical direction of problem decomposition and these are
related with one particular issue for example inventory
management. Other way general problems are horizontal; they
deal with problems which require solving multiple specific
problems for example, ensuring customer service problems
from sales area as well as logistics.
Pricing Optimization using Machine LearningIRJET Journal
This document discusses using machine learning algorithms to optimize pricing. Specifically:
1. It reviews previous research applying machine learning to price prediction and optimization in various industries like e-commerce, real estate, and insurance. Methods discussed include linear regression, clustering, random forests, and integer linear programming.
2. It then introduces using machine learning like regression trees and random forests to forecast demand and maximize revenue by setting optimal prices. Variables like holidays, promotions, and inventory are considered.
3. The goal of the paper is to develop a pricing algorithm that can predict and optimize daily prices in response to changing demand using machine learning techniques. Outcomes will demonstrate machine learning's ability to optimize pricing.
A study on the chain restaurants dynamic negotiation games of the optimizatio...ijcsit
In the era of meager profit, production costs often become an important factor affecting SMEs’ operating
conditions, and how to effectively reduce production costs has become an issue of in-depth consideration
for the business owners. Especially, the food and beverage (F&B) industry cannot accurately predict the
demand. It many cause demand forecast fall and excess or insufficient inventory pressure. Companies of
the F&B industry may be even unable to meet immediate customer needs. They are faced great challenges
in quick response and inventory pressure. This study carried out the product inventory model analysis of
the most recent year’s sales data of the fresh food materials for chain restaurants in a supply chain region
with raw material suppliers and demanders. Moreover, this study adopted the multi-agent dynamic strategy
game to establish the joint procurement decision model negotiation algorithm for analysis and verification
by simulation cases to achieve the design of dynamic negotiation optimization mechanism for the joint
procurement of food materials. Coupled with supply chain management 3C theory for food material
inventory management, we developed the optimization method for determining the order quantities of the
chain restaurants. For product demand forecast, we applied the commonality model, production and
delivery capacity model, and the model of consumption and replenishment based on market demand
changes in categorization and development. Moreover, with the existence of dependencies between product
demands as the demand forecast basis, we determined the appropriate inventory model accordingly.
. Facility location is an important problem faced by companies in many industries. Finding an optimal
location for facilities and determining their size involves the consideration of many factors, including proximity to customers and suppliers, availability of skilled employees and support services, and cost-related factors, for
example, construction or leasing costs, utility costs, taxes, availability of support services, and others. The demand of the surrounding region plays an important role in location decisions. A high population density may not necessarily cause a proportional demand for products or services. The demography of a region could dictate the demand
for products, and this, in turn, affects a facility’s size and location. The location of a company’s competitors also affects the location of that company’s facilities. Another important aspect in facility location modeling is that many models focus on current demand and do not adequately consider future demand. However, while making location
decisions in an industry in decline, carefully and accurately considering future demand is especially important, and the question in focus is whether to shrink or close down certain facilities with the objective of keeping a certain market share or maximizing profit, especially in a competitive environment. This paper develops a model which enables companies to select sites for their businesses according to their
strategy. The model analyzes the strategic position of the company and forms a guideline for the decision. It investigates which facilities should be closed, (re)opened, shrunk, or expanded. If facilities are to shrink or expand,
the model also determines their new capacities. It depicts the impact on market share and accounts for the costs of closure and reopening. A number of papers deal with location theory and its applications, but few have been written for modeling a competitive environment in the case of declining demand. Existing papers in this area of research are mostly static in nature, do not offer multi-period approaches, nor do they incorporate the behavior of competitors in the market. To demonstrate the validity of the model, it is first solved using a small problem set – three facilities, three demand locations, and three periods – in LINGO solver. To get a better understanding of the model’s behavior, several additional scenarios were constructed. First, the number of demand locations was extended to 10. Our findings show that the model presented provides an extension of existing facility location models that can be applied to a variety of location problems in commercial and industry sectors that need to make their decisions considering future periods and competitors. The developed heuristic shows multiple options for solving the problem, including their advantages and disadvantages, respectively. The Java code and LINGO fragments thus developed can be used to provide easy access to related problems.
Clustering Prediction Techniques in Defining and Predicting Customers Defecti...IJECEIAES
With the growth of the e-commerce sector, customers have more choices, a fact which encourages them to divide their purchases amongst several ecommerce sites and compare their competitors‟ products, yet this increases high risks of churning. A review of the literature on customer churning models reveals that no prior research had considered both partial and total defection in non-contractual online environments. Instead, they focused either on a total or partial defect. This study proposes a customer churn prediction model in an e-commerce context, wherein a clustering phase is based on the integration of the k-means method and the Length-RecencyFrequency-Monetary (LRFM) model. This phase is employed to define churn followed by a multi-class prediction phase based on three classification techniques: Simple decision tree, Artificial neural networks and Decision tree ensemble, in which the dependent variable classifies a particular customer into a customer continuing loyal buying patterns (Non-churned), a partial defector (Partially-churned), and a total defector (Totally-churned). Macroaveraging measures including average accuracy, macro-average of Precision, Recall, and F-1 are used to evaluate classifiers‟ performance on 10-fold cross validation. Using real data from an online store, the results show the efficiency of decision tree ensemble model over the other models in identifying both future partial and total defection.
A Model of Manufacturer-Driven Governing Mechanisms and Distributor PerformanceRuss Merz, Ph.D.
Drawing from relational exchange, dependence, and agency theories the authors explain that it is not only the type of governing mechanisms but also the proper sequencing of them that improves a manufacturer-distributor relationship and performance. Dependence affected relationship continuity positively. Monitoring affected the second order relational norm construct, comprising information sharing and flexibility, positively. Relational norm positively affected relationship continuity. Dependence, relationship continuity, monitoring, and relational norm affected distributor performance positively.
The changes required in the IT project plan for Telecomm Ltd would.docxmattinsonjanel
The changes required in the IT project plan for Telecomm Ltd would entail specific variation in the platforms used in the initial implementation plan. Initially, the three projects that were planned for implementation included; the installation of business intelligence platform, the implementation of Statistical Analysis System software technology, and the creation of an effectively network infrastructure. In this case, the changes would include an addition of an ERP software to ensure the performance of the workforce within the Telecomms Ltd employees.
ERP is an effectively coordinated information technology system that would ensure the company’s performance is enhanced. To understand how the implementation of a coordinated IT system offers a competitive advantage of a firm, it is essential to acknowledge three core reasons for the failure of information technology related projects as commonly cited by IT managers. In this case, IT managers cite the three reasons as; poor planning or management, change in business objectives and goals during the implementation process of a project, and lack of proper management support completion (Houston, 2011). Also, in the majority of completed projects, technology is usually deployed in a vacuum; hence users resist it. The implementation of coordinated information technology systems, such as ERP would provide an ultimate solution to the three reasons for failure, and thus would give Telecomms Ltd a competitive advantage in the already competitive market. Since the implementation of systems like ERP directly provides solution to common problems that act as drawbacks regarding the competitiveness of firm, it is, therefore, evident that its use place Telecomms Ltd above its rival companies in the market share (Wallace & Kremzar, 2001).
The use ERP, which is a reliable coordinated IT system entails three distinctive implementation strategies that a firm can choose depending on its specific needs. The changes in the projects would be as follows: The three implementation strategies are independently capable of providing a relatively competitive advantage for many companies. These strategies are: big bang, phased rollout, and parallel adoption. In the big bang implementation strategy, happens in a single instance, whereby all the users are moved to a new system on a designated (Wallace & Kremzar, 2001). The phased rollout implementation on the other hand usually involves a changeover in several phases, and it is executed in an extended period. In this case, the users move onto the new system in a series of steps (Houston, 2011). Lastly, the parallel adoption implementation strategy allows both legacy and the new ERP system to run at the same time. It is also essential to note that users in this strategy get to learn the new system while still working on the old system (Wallace & Kremzar, 2001). The three strategies effectively change the information system of Telecomms Ltd tremendously such that it positiv ...
The Catholic University of America Metropolitan School of .docxmattinsonjanel
The Catholic University of America
Metropolitan School of Professional Studies
Course Syllabus
THE CATHOLIC UNIVERSITY OF AMERICA
Metropolitan School of Professional Studies
MBU 514 and MBU 315 Leadership Foundations
Fall 2015
Credits: 3
Classroom: Online
Dates: August 31, 2015 to December 14, 2015
Instructor:
Dr. Jacquie Hamp
Email: [email protected]
Twitter: @drjacquie
Telephone: 202 215 8117 cell
Office Hours: By Appointment
Dr. Jacquie Hamp is an educator, coach and consultant with particular expertise in leadership development, organizational development and human resources development strategy. From 2006 to 2015 she held the position as the Senior Director of Leadership Development for Goodwill Industries International in Rockville, Maryland. Dr. Hamp was responsible for the design and execution of leadership development programs and activities for all levels of the 4 billion dollar social enterprise network of Goodwill Industries across 165 independent local agencies. Jacquie is also a part time Associate Professor at George Washington University teaching at the graduate level and she is an adjunct professor at Catholic University of America, teaching leadership theory in the Masters Program.
Jacquie has a Master of Science degree in Human Resources Development Administration from Barry University. She holds a Doctor of Education degree in Human and Organizational Learning from the Graduate School of Education and Human Development at George Washington University. Jacquie has received a certificate in Executive Coaching from Georgetown University, a certificate in the Practice of Teaching Leadership from Harvard University and holds the national certification of Senior Professional in Human Resources (SPHR).
Jacquie has been invited to speak at conferences in the United States and the United Kingdom on the topic of how women learn through transformative experiences and techniques for effective leadership development in the social enterprise sector. She is a member of the Society of Human Resource Management (SHRM) and the International Leadership Association (ILA). In 2011 Dr. Hamp was awarded the Strategic Alignment Award by the Human Resources Leadership Association of Washington DC for her work in the redesign of the Goodwill Industries International leadership programs in order to meet the strategic goals of the organization.
Course Description: Surveys, compares, and contrasts contemporary theories of leadership, providing students the opportunity to assess their own leadership competencies and how they fit in with models of leadership. Students also discuss current literature, media coverage, and case studies on leadership issues.
Instructional Methods This course is based on the following adult learning concepts:
1. Learning is done by the learners, who are encouraged to achieve the overall course objectives through individual learning styles that meet their personal learning needs. ...
More Related Content
Similar to Submitted to Operations Researchmanuscript XXA General A.docx
A Comparative Study Of Machine Learning Algorithms For Industry-Specific Frei...Karla Long
This document describes a study that compares machine learning algorithms to traditional regression for generating freight models by industry. Researchers evaluated 7 machine learning algorithms and ordinary least squares regression on freight generation data for 45 industries. Models were selected individually for each industry based on statistically significant improvements in error reduction compared to ordinary least squares. Results showed machine learning algorithms reduced root mean square error by around 30% over 80% of the time compared to ordinary least squares regression. The study suggests using machine learning algorithms can improve accuracy of industry-specific freight generation models.
Airline Network Design And Fleet Assignment Using Logit-Based Dynamic Demand...James Heller
This document discusses airline network design and fleet assignment while considering dynamic demand. It uses a logit-based model to capture demand as a function of the supply offered, rather than a static parameter. This adds complexity over previous models. The paper aims to integrate network design and fleet assignment stages while accounting for demand-supply interactions and competition. It presents a nonlinear model, which is transformed into a linear one and solved using an example to illustrate the approach.
CURRENT RESEARCH ON REVERSE AUCTIONS: PART II -IMPLEMENTATION ISSUES ASSOCIAT...ijmvsc
This article serves as the second part in a two-part series that provides an overview of the reverse auction concept, building on the best research in the field of supply chain management. In this instalment, we look at the concerns involved in making reverse auctions work in practice – the implementation issues. Frist, we look at when reverse auctions should – and should not – be utilized by a buying organization. We then examine the decision rules that should be used in determining which of the competing suppliers wins the reverse auction. Next, we look at the best research available as to how the use of reverse auctions impacts the buyer-seller relationship. Finally, we examine what is in essence a “make or buy” decision in regards to whether the purchasing organization should run an auction in-house or make use of the services of a third-party “market maker.
Churn in the Telecommunications Industryskewdlogix
Strategic Business Analysis Capstone Project Telecommunications Churn Management
Churn is a significant problem that costs telecommunications companies billions of dollars through lost revenue. Now that the market is more mature, the only way for a company to grow is to take their competitors customers. This issue
combined with the greater choice that consumers have gained means that any adverse touch point with a consumer can result in a lost customer.
Multi-commodity ETRM’s are becoming too expensive to implement, and maintain ...CTRM Center
Since ETRM software was first introduced around 20-years ago, developers have continually sought to move from developing solutions designed to support specific commodities such as crude oil, natural gas, and electric power, to building solutions that catered for multiple energy commodities. In part, their objective was to reduce costs – specifically integration costs, but without a doubt, part of the objective was self-serving, as this also allowed them to broaden the appeal of their software to a larger and more lucrative market.
CONSIGNMENT INVENTORY SIMULATION MODEL FOR SINGLE VENDOR-MULTI BUYERS IN A SU...IAEME Publication
The focus on the studies of supply chain management has been increasing in
recent years among academics as well as practitioners. In this paper, we present an
extendable multi agent supply chain simulation model for consignment stock inventory
model for a single vendor - multiple buyers. The simulation study dealt the
quantitative measures of performance of consignment stock model with respect to
number of shipments, delay deliveries, number of shipments shifted due to partial
information sharing, average inventory levels of buyer and vendor and joint total
economic cost (JTEC) as key performance parameters. Flexsim V3.0 a discrete event
simulation software is used for simulating the model.
CONSIGNMENT INVENTORY SIMULATION MODEL FOR SINGLE VENDOR-MULTI BUYERS IN A SU...IAEME Publication
The document describes a simulation model of a consignment inventory system for a single vendor and multiple buyers. The simulation model is developed using Flexsim software and evaluates key performance metrics like total cost, inventory levels, shipments, and fill rate. Three models are simulated: one without delays, one with delivery delays, and one with partial information sharing between vendor and buyer. Results show that total cost increases with more buyers but information sharing reduces costs the most, especially for multiple buyers. The number of shipments and delays decreases with information sharing while fill rate increases.
Adoption of Vendor Managed Inventory Practices on Supply Chain Performance in...AkashSharma618775
This document discusses a study on the adoption of vendor managed inventory practices on supply chain performance in selected automobile industries in Nairobi County, Kenya. The study aims to determine the role of supplier demand visibility, communication mechanisms, inventory decisions, and replenishment decisions on supply chain management performance. The document provides background on vendor managed inventory and outlines the research objectives, questions, significance, scope, and methodology. It discusses the theoretical framework, conceptual framework, research design, target population, sampling techniques, and data collection instruments used in the study.
Is freemium a viable pricing strategy for cloud services?Izam Ryan
An in-depth study of the application of freemium pricing practice in the cloud services space that Amazon EC2, Google Compute Engine, Microsoft Azure and Rackshare compete in.
Submitted in partial fulfilment of the requirements of the Imperial MBA degree and the Diploma of Imperial College London. I was awarded a Distinction for this Pricing Strategy elective.
Excluding appendixes: 2,497 words
Assortment Planning And Inventory Decisions Under A Locational Choice ModelAndrea Porter
This document summarizes a research paper about assortment planning and inventory management for retailers using a locational choice model of consumer demand. The paper analyzes optimal product variety, location, and inventory decisions under both static and dynamic substitution scenarios. Key findings include: 1) Under static substitution, products are equally spaced so there is no substitution between them. 2) Dynamic substitution provides more variety and locates products closer together to benefit from substitution. 3) The optimal assortment may not include the most popular product due to demand fragmentation.
The Club War Case Study Report by Sachin mathews Sachin Mathews
The objective of this study is to analyse Sam’s club and their current inefficiencies and provide suggestions to Mr.Jim who heads the reengineering team that can help his team formulate appropriate supply chain strategies in order to achieve lowest possible cost and attain greater competitive advantage. The paper provides a background of the current situation faced by club where the current inefficiencies are discussed and possible recommendations are then suggested.
CONSIGNMENT INVENTORY SIMULATION MODEL FOR SINGLE VENDOR- MULTI BUYERSIAEME Publication
The focus on the studies of supply chain management has been increasing in
recent years among academics as well as practitioners. In this paper, we present an
extendable multi agent supply chain simulation model for consignment stock inventory
model for a single vendor - multiple buyers. The simulation study dealt the
quantitative measures of performance of consignment stock model with respect to
number of shipments, delay deliveries, number of shipments shifted due to partial
information sharing, average inventory levels of buyer and vendor and joint total
economic cost (JTEC) as key performance parameters. Flexsim V3.0 a discrete event
simulation software is used for simulating the model
At various levels of decomposition we can
analysed the supply chain problem. At the first level problem
of supply chain management which is consist of many sub
problems as product design, customer services, logistic
management and others. We can define all the problems as
general and in specific way. These problems come at various
vertical direction of problem decomposition and these are
related with one particular issue for example inventory
management. Other way general problems are horizontal; they
deal with problems which require solving multiple specific
problems for example, ensuring customer service problems
from sales area as well as logistics.
Pricing Optimization using Machine LearningIRJET Journal
This document discusses using machine learning algorithms to optimize pricing. Specifically:
1. It reviews previous research applying machine learning to price prediction and optimization in various industries like e-commerce, real estate, and insurance. Methods discussed include linear regression, clustering, random forests, and integer linear programming.
2. It then introduces using machine learning like regression trees and random forests to forecast demand and maximize revenue by setting optimal prices. Variables like holidays, promotions, and inventory are considered.
3. The goal of the paper is to develop a pricing algorithm that can predict and optimize daily prices in response to changing demand using machine learning techniques. Outcomes will demonstrate machine learning's ability to optimize pricing.
A study on the chain restaurants dynamic negotiation games of the optimizatio...ijcsit
In the era of meager profit, production costs often become an important factor affecting SMEs’ operating
conditions, and how to effectively reduce production costs has become an issue of in-depth consideration
for the business owners. Especially, the food and beverage (F&B) industry cannot accurately predict the
demand. It many cause demand forecast fall and excess or insufficient inventory pressure. Companies of
the F&B industry may be even unable to meet immediate customer needs. They are faced great challenges
in quick response and inventory pressure. This study carried out the product inventory model analysis of
the most recent year’s sales data of the fresh food materials for chain restaurants in a supply chain region
with raw material suppliers and demanders. Moreover, this study adopted the multi-agent dynamic strategy
game to establish the joint procurement decision model negotiation algorithm for analysis and verification
by simulation cases to achieve the design of dynamic negotiation optimization mechanism for the joint
procurement of food materials. Coupled with supply chain management 3C theory for food material
inventory management, we developed the optimization method for determining the order quantities of the
chain restaurants. For product demand forecast, we applied the commonality model, production and
delivery capacity model, and the model of consumption and replenishment based on market demand
changes in categorization and development. Moreover, with the existence of dependencies between product
demands as the demand forecast basis, we determined the appropriate inventory model accordingly.
. Facility location is an important problem faced by companies in many industries. Finding an optimal
location for facilities and determining their size involves the consideration of many factors, including proximity to customers and suppliers, availability of skilled employees and support services, and cost-related factors, for
example, construction or leasing costs, utility costs, taxes, availability of support services, and others. The demand of the surrounding region plays an important role in location decisions. A high population density may not necessarily cause a proportional demand for products or services. The demography of a region could dictate the demand
for products, and this, in turn, affects a facility’s size and location. The location of a company’s competitors also affects the location of that company’s facilities. Another important aspect in facility location modeling is that many models focus on current demand and do not adequately consider future demand. However, while making location
decisions in an industry in decline, carefully and accurately considering future demand is especially important, and the question in focus is whether to shrink or close down certain facilities with the objective of keeping a certain market share or maximizing profit, especially in a competitive environment. This paper develops a model which enables companies to select sites for their businesses according to their
strategy. The model analyzes the strategic position of the company and forms a guideline for the decision. It investigates which facilities should be closed, (re)opened, shrunk, or expanded. If facilities are to shrink or expand,
the model also determines their new capacities. It depicts the impact on market share and accounts for the costs of closure and reopening. A number of papers deal with location theory and its applications, but few have been written for modeling a competitive environment in the case of declining demand. Existing papers in this area of research are mostly static in nature, do not offer multi-period approaches, nor do they incorporate the behavior of competitors in the market. To demonstrate the validity of the model, it is first solved using a small problem set – three facilities, three demand locations, and three periods – in LINGO solver. To get a better understanding of the model’s behavior, several additional scenarios were constructed. First, the number of demand locations was extended to 10. Our findings show that the model presented provides an extension of existing facility location models that can be applied to a variety of location problems in commercial and industry sectors that need to make their decisions considering future periods and competitors. The developed heuristic shows multiple options for solving the problem, including their advantages and disadvantages, respectively. The Java code and LINGO fragments thus developed can be used to provide easy access to related problems.
Clustering Prediction Techniques in Defining and Predicting Customers Defecti...IJECEIAES
With the growth of the e-commerce sector, customers have more choices, a fact which encourages them to divide their purchases amongst several ecommerce sites and compare their competitors‟ products, yet this increases high risks of churning. A review of the literature on customer churning models reveals that no prior research had considered both partial and total defection in non-contractual online environments. Instead, they focused either on a total or partial defect. This study proposes a customer churn prediction model in an e-commerce context, wherein a clustering phase is based on the integration of the k-means method and the Length-RecencyFrequency-Monetary (LRFM) model. This phase is employed to define churn followed by a multi-class prediction phase based on three classification techniques: Simple decision tree, Artificial neural networks and Decision tree ensemble, in which the dependent variable classifies a particular customer into a customer continuing loyal buying patterns (Non-churned), a partial defector (Partially-churned), and a total defector (Totally-churned). Macroaveraging measures including average accuracy, macro-average of Precision, Recall, and F-1 are used to evaluate classifiers‟ performance on 10-fold cross validation. Using real data from an online store, the results show the efficiency of decision tree ensemble model over the other models in identifying both future partial and total defection.
A Model of Manufacturer-Driven Governing Mechanisms and Distributor PerformanceRuss Merz, Ph.D.
Drawing from relational exchange, dependence, and agency theories the authors explain that it is not only the type of governing mechanisms but also the proper sequencing of them that improves a manufacturer-distributor relationship and performance. Dependence affected relationship continuity positively. Monitoring affected the second order relational norm construct, comprising information sharing and flexibility, positively. Relational norm positively affected relationship continuity. Dependence, relationship continuity, monitoring, and relational norm affected distributor performance positively.
Similar to Submitted to Operations Researchmanuscript XXA General A.docx (20)
The changes required in the IT project plan for Telecomm Ltd would.docxmattinsonjanel
The changes required in the IT project plan for Telecomm Ltd would entail specific variation in the platforms used in the initial implementation plan. Initially, the three projects that were planned for implementation included; the installation of business intelligence platform, the implementation of Statistical Analysis System software technology, and the creation of an effectively network infrastructure. In this case, the changes would include an addition of an ERP software to ensure the performance of the workforce within the Telecomms Ltd employees.
ERP is an effectively coordinated information technology system that would ensure the company’s performance is enhanced. To understand how the implementation of a coordinated IT system offers a competitive advantage of a firm, it is essential to acknowledge three core reasons for the failure of information technology related projects as commonly cited by IT managers. In this case, IT managers cite the three reasons as; poor planning or management, change in business objectives and goals during the implementation process of a project, and lack of proper management support completion (Houston, 2011). Also, in the majority of completed projects, technology is usually deployed in a vacuum; hence users resist it. The implementation of coordinated information technology systems, such as ERP would provide an ultimate solution to the three reasons for failure, and thus would give Telecomms Ltd a competitive advantage in the already competitive market. Since the implementation of systems like ERP directly provides solution to common problems that act as drawbacks regarding the competitiveness of firm, it is, therefore, evident that its use place Telecomms Ltd above its rival companies in the market share (Wallace & Kremzar, 2001).
The use ERP, which is a reliable coordinated IT system entails three distinctive implementation strategies that a firm can choose depending on its specific needs. The changes in the projects would be as follows: The three implementation strategies are independently capable of providing a relatively competitive advantage for many companies. These strategies are: big bang, phased rollout, and parallel adoption. In the big bang implementation strategy, happens in a single instance, whereby all the users are moved to a new system on a designated (Wallace & Kremzar, 2001). The phased rollout implementation on the other hand usually involves a changeover in several phases, and it is executed in an extended period. In this case, the users move onto the new system in a series of steps (Houston, 2011). Lastly, the parallel adoption implementation strategy allows both legacy and the new ERP system to run at the same time. It is also essential to note that users in this strategy get to learn the new system while still working on the old system (Wallace & Kremzar, 2001). The three strategies effectively change the information system of Telecomms Ltd tremendously such that it positiv ...
The Catholic University of America Metropolitan School of .docxmattinsonjanel
The Catholic University of America
Metropolitan School of Professional Studies
Course Syllabus
THE CATHOLIC UNIVERSITY OF AMERICA
Metropolitan School of Professional Studies
MBU 514 and MBU 315 Leadership Foundations
Fall 2015
Credits: 3
Classroom: Online
Dates: August 31, 2015 to December 14, 2015
Instructor:
Dr. Jacquie Hamp
Email: [email protected]
Twitter: @drjacquie
Telephone: 202 215 8117 cell
Office Hours: By Appointment
Dr. Jacquie Hamp is an educator, coach and consultant with particular expertise in leadership development, organizational development and human resources development strategy. From 2006 to 2015 she held the position as the Senior Director of Leadership Development for Goodwill Industries International in Rockville, Maryland. Dr. Hamp was responsible for the design and execution of leadership development programs and activities for all levels of the 4 billion dollar social enterprise network of Goodwill Industries across 165 independent local agencies. Jacquie is also a part time Associate Professor at George Washington University teaching at the graduate level and she is an adjunct professor at Catholic University of America, teaching leadership theory in the Masters Program.
Jacquie has a Master of Science degree in Human Resources Development Administration from Barry University. She holds a Doctor of Education degree in Human and Organizational Learning from the Graduate School of Education and Human Development at George Washington University. Jacquie has received a certificate in Executive Coaching from Georgetown University, a certificate in the Practice of Teaching Leadership from Harvard University and holds the national certification of Senior Professional in Human Resources (SPHR).
Jacquie has been invited to speak at conferences in the United States and the United Kingdom on the topic of how women learn through transformative experiences and techniques for effective leadership development in the social enterprise sector. She is a member of the Society of Human Resource Management (SHRM) and the International Leadership Association (ILA). In 2011 Dr. Hamp was awarded the Strategic Alignment Award by the Human Resources Leadership Association of Washington DC for her work in the redesign of the Goodwill Industries International leadership programs in order to meet the strategic goals of the organization.
Course Description: Surveys, compares, and contrasts contemporary theories of leadership, providing students the opportunity to assess their own leadership competencies and how they fit in with models of leadership. Students also discuss current literature, media coverage, and case studies on leadership issues.
Instructional Methods This course is based on the following adult learning concepts:
1. Learning is done by the learners, who are encouraged to achieve the overall course objectives through individual learning styles that meet their personal learning needs. ...
The Case of Frank and Judy. During the past few years Frank an.docxmattinsonjanel
The Case of Frank and Judy.
During the past few years Frank and Judy have experienced many conflicts in their marriage. Although they have made attempts to resolve their problems by themselves, they have finally decided to seek the help of a professional marriage counselor. Even though they have been thinking about divorce with increasing frequency, they still have some hope that they can achieve a satisfactory marriage.
Three couples counselors, each holding a different set of values pertaining to marriage and the family, describe their approach to working with Frank and Judy. As you read these responses, think about the degree to which each represents what you might say and do if you were counseling this couple.
· Counselor A. This counselor believes it is not her place to bring her values pertaining to the family into the sessions. She is fully aware of her biases regarding marriage and divorce, but she does not impose them or expose them in all cases. Her primary interest is to help Frank and Judy discover what is best for them as individuals 459460and as a couple. She sees it as unethical to push her clients toward a definite course of action, and she lets them know that her job is to help them be honest with themselves.
·
· What are your reactions to this counselor's approach?
· ▪ What values of yours could interfere with your work with Frank and Judy?
Counselor B. This counselor has been married three times herself. Although she believes in marriage, she is quick to maintain that far too many couples stay in their marriages and suffer unnecessarily. She explores with Judy and Frank the conflicts that they bring to the sessions. The counselor's interventions are leading them in the direction of divorce as the desired course of action, especially after they express this as an option. She suggests a trial separation and states her willingness to counsel them individually, with some joint sessions. When Frank brings up his guilt and reluctance to divorce because of the welfare of the children, the counselor confronts him with the harm that is being done to them by a destructive marriage. She tells him that it is too much of a burden to put on the children to keep the family together.
· ▪ What, if any, ethical issues do you see in this case? Is this counselor exposing or imposing her values?
· ▪ Do you think this person should be a marriage counselor, given her bias?
· ▪ What interventions made by the counselor do you agree with? What are your areas of disagreement?
Counselor C. At the first session this counselor states his belief in the preservation of marriage and the family. He believes that many couples give up too soon in the face of difficulty. He says that most couples have unrealistically high expectations of what constitutes a “happy marriage.” The counselor lets it be known that his experience continues to teach him that divorce rarely solves any problems but instead creates new problems that are often worse. The counsel ...
The Case of MikeChapter 5 • Common Theoretical Counseling Perspe.docxmattinsonjanel
The Case of Mike
Chapter 5 • Common Theoretical Counseling Perspectives 135
Mike is a 20-year-old male who has just recently been released from jail. Mike is technically on probation for car theft, though he has been involved in crime to a much greater extent. Mike has been identified as a cocaine user and has been suspected, though not convicted, for dealing cocaine. Mike has been tested for drugs by his probation department and was found positive for cocaine. The county has mandated that Mike receive drug counseling but the drug counselor has referred Mike to your office because the drug counselor suspects that Mike has issues beyond simple drug addiction. In fact, the drug counselor’s notes suggest that Mike has Narcissistic personality disorder. Mike seems to have little regard for the feelings of others. Coupled with this is his complete sensitivity to the comments of others. In fact, his prior fiancé has broken off her relationship with him due to what she calls his “constant need for admiration and attention. He is completely self-centered.” After talking with Mike, you quickly find that he has no close friends. As he talks about people who have been close to him, he discounts them for one imperfection or another. These imperfections are all considered severe enough to warrant dismissing the person entirely. Mike makes a point of noting how many have betrayed their loyalty to him or have otherwise failed to give him the credit that he deserves. When asked about getting caught in the auto theft, he remarks that “well my dumb partner got me out of a hot situation by driving me out in a stolen get-a-way car.” (Word on the street has it that Mike was involved in a sour drug deal and was unlikely to have made it out alive if not for his partner.) Mike adds, “you know, I plan everything out perfectly, but you just cannot rely on anybody . . . if you want it done right, do it yourself.” Mike recently has been involved with another woman (unknown to his prior fiancé) who has become pregnant. When she told Mike he said “tough, you can go get an abortionor something, it isn’t like we were in love or something.” Then he laughed at her and toldher to go find some other guy who would shack up with her. Incidentally, Mike is a very attractive man and he likes to point that out on occasion. “Yeah, I was going to be a male model in L. A.,but my agent did not know what he was doing . . . could never get things settled out right . . . so I had to fire him.” Mike is very popular with women and has had a constant string of failed relationships due to what he calls “their inability to keep things exciting.” As Mike puts it “hey, I am too smart for this stuff. These people around me, they don’t deserve the good dummies. But me, well I know how to run things and get over on people. And I am not about to let these dummies get in my way. I got it all figured out . . . see?”
Effective Small Business Management: An Entrepreneurial Approach 9th Edition, 2009 IS ...
THE CHRONICLE OF HIGHER EDUCATIONNovember 8, 2002 -- vol. 49, .docxmattinsonjanel
THE CHRONICLE OF HIGHER EDUCATION
November 8, 2002 -- vol. 49, no. 11, p. B7
The Dangerous Myth of Grade Inflation
By Alfie Kohn
Grade inflation got started ... in the late '60s and early '70s.... The grades that faculty members now give ... deserve to be a scandal.
--Professor Harvey Mansfield, Harvard University, 2001
Grades A and B are sometimes given too readily -- Grade A for work of no very high merit, and Grade B for work not far above mediocrity. ... One of the chief obstacles to raising the standards of the degree is the readiness with which insincere students gain passable grades by sham work.
--Report of the Committee on Raising the Standard, Harvard University, 1894
Complaints about grade inflation have been around for a very long time. Every so often a fresh flurry of publicity pushes the issue to the foreground again, the latest example being a series of articles in The Boston Globe last year that disclosed -- in a tone normally reserved for the discovery of entrenched corruption in state government -- that a lot of students at Harvard were receiving A's and being graduated with honors.
The fact that people were offering the same complaints more than a century ago puts the latest bout of harrumphing in perspective, not unlike those quotations about the disgraceful values of the younger generation that turn out to be hundreds of years old. The long history of indignation also pretty well derails any attempts to place the blame for higher grades on a residue of bleeding-heart liberal professors hired in the '60s. (Unless, of course, there was a similar countercultural phenomenon in the 1860s.)
Yet on campuses across America today, academe's usual requirements for supporting data and reasoned analysis have been suspended for some reason where this issue is concerned. It is largely accepted on faith that grade inflation -- an upward shift in students' grade-point averages without a similar rise in achievement -- exists, and that it is a bad thing. Meanwhile, the truly substantive issues surrounding grades and motivation have been obscured or ignored.
The fact is that it is hard to substantiate even the simple claim that grades have been rising. Depending on the time period we're talking about, that claim may well be false. In their book When Hope and Fear Collide (Jossey-Bass, 1998), Arthur Levine and Jeanette Cureton tell us that more undergraduates in 1993 reported receiving A's (and fewer reported receiving grades of C or below) compared with their counterparts in 1969 and 1976 surveys. Unfortunately, self-reports are notoriously unreliable, and the numbers become even more dubious when only a self-selected, and possibly unrepresentative, segment bothers to return the questionnaires. (One out of three failed to do so in 1993; no information is offered about the return rates in the earlier surveys.)
To get a more accurate picture of whether grades have changed over the years, one needs to look at official student tran ...
The chart is a guide rather than an absolute – feel free to modify.docxmattinsonjanel
The chart is a guide rather than an absolute – feel free to modify or adjust it as need to fit the specific ideas that you are developing.
Area: SALES
Specific Change Plans for Functional Areas
Capability Being Addressed
This can be pulled from the strategic proposal recommended in Part 2B
How do the recommended changes (details provided below) help improve the capability?
This is a logic "double check". Be sure you can show how the changes recommended below improve the capability and help address the product and market focus and add to accomplishment of the value proposition
Details of Specific Changes:
Proposed Changes in Resources
Proposed Changes to Management
Preferences
Proposed Changes to Organizational
Processes
Detailed Change Plans
(Lay out here the specifics of all recommended changes for this area. Modify the layout as necessary to account for the changes being recommended)
Proposed Change
Timing
Costs
On going impact on budget
On going impact on revenue
Wiki
Template
Part-‐2:
Gaps,
Issues
and
New
Strategy
BUSI
4940
–
Business
Policy
1
THE ENVIRONMENT/INDUSTRY
1. Drivers of change
Key drivers of change begin with the availability of substitute products. Many
other
companies can easily provide a substitute and the firm will have to find a way to
stand
out among them. Next would be the ability to differentiate yourself among other
firms
that pose a threat in the industry. Last, the political sector. The the federal, state,
and local governments could all shape the way healthcare is everywhere.
2. Key survival factors
Key survival factors would include making the firm stand out above the rest in the
industry and creating a name for itself. Second would be making sure there is a
broad
network of providers available for the customers. Giving the customer options
will
make the customer happy. Providing excellent customer service is key to any
firm in
the industry.
3. Product/Market and Value Proposition possibilities
Maintaining the use of heavy discounts will keep Careington in the competitive
market. They also concentrate on constantly innovating technology to make
sure that
they have the latest devices to offer their customers. To have high value proposition, Careington
will need to show their costumers that they can believe in them and trust them to
do the right thing. Showing the customers that they can always be on top of the
latest
technology and new age products will help build trust with the customers.
STRATEGY OF THE FIRM
1. Goals
Striving to promote the health and well being of their clients by continuing to
provide
low cost health care solutions. A lot of this concentration is on clients that cannot
afford health care very easily or that a ...
The Challenge of Choosing FoodFor this forum, please read http.docxmattinsonjanel
The Challenge of Choosing Food:
For this forum, please read: https://www.washingtonpost.com/lifestyle/food/no-food-is-healthy-not-even-kale/2016/01/15/4a5c2d24-ba52-11e5-829c-26ffb874a18d_story.html?postshare=3401453180639248&tid=ss_fb-bottom
The article is from the Washington Post, January 17, 2016, by Michael Ruhlmanentitled: "No Food is Healthy, Not even Kale."
Based on your reading in the textbook share the following information with your classmates:
(1) To what degree to you agree with article, "No Food is Healthy, Not even Kale." Do semantics count? Should we focus on foods that are described as nourishing (nutrient-dense) instead of foods described as healthy because the word "healthy" is a "bankrupt" word? Explain and refer to information from the article.
(2) Based on the article and the textbook reading (review pages 9-30), how challenging is it for you to choose nutritious foods that promote health? What factors drive your food choices? Explain to your classmates.
(3) What do you think is the biggest concern we face health-wise in the US today?
(4) What are some obstacles as to why we may not be eating as well as we would like to?
Please complete all questions, if you have any question let me knowv
Test file, (Do not modify it)
// $> javac -cp .:junit-cs211.jar ProperQueueTests.java #compile
// $> java -cp .:junit-cs211.jar ProperQueueTests #run tests
//
// On windows replace : with ; (colon with semicolon)
// $> javac -cp .;junit-cs211.jar ProperQueueTests.java #compile
// $> java -cp .;junit-cs211.jar ProperQueueTests #run tests
import org.junit.*;
import static org.junit.Assert.*;
import java.util.*;
public class ProperQueueTests {
public static void main(String args[]){
org.junit.runner.JUnitCore.main("ProperQueueTests");
}
/*
building queues:
- build small empty queue. (2)
- build larger empty queue. (11)
- build length-zero queue. (0)
*/
@Test(timeout=1000) public void ProperQueue_makeQueue_1(){
String expected = "";
ProperQueue q = new ProperQueue(2);
String actual = q.toString();
assertEquals(2, q.getCapacity());
assertEquals(expected, actual);
}
@Test(timeout=1000) public void ProperQueue_makeQueue_2(){
String expected = "";
ProperQueue q = new ProperQueue(11);
String actual = q.toString();
assertEquals(11, q.getCapacity());
assertEquals(expected, actual);
}
@Test(timeout=1000) public void Queue_makeQueue_3(){
String expected = "";
ProperQueue q = new ProperQueue(0);
String actual = q.toString();
assertEquals(0, q.getCapacity());
assertEquals(expected, actual);
}
/*
add/offer tests.
- add a single value to a short queue.
- fill up a small queue.
- over-add to a queue and witness it struggle.
- add many but don't finish filling a queue.
- make size-zero queue, adds fail, check it's still empty.
*/
@Test(timeout=1000) public void ProperQueue_add_1(){
String expecte ...
The Civil Rights Movement
Dr. James Patterson
Black Civil Rights Movement
Basic denial of civil rights (review)
Segregation in society
Inferior schools
Job discrimination
Political disenfranchisement
Over ½ lived below poverty level
Unemployment double national ave.
Ghettoes: gangs, drugs, substandard housing, crime
Early Victories
WWII egalitarianism and backlash against German racism
Jackie Robinson integrated professional baseball—1947
Desegregation of the armed forces ordered by president Truman—1948
Marian Anderson performed at the New York Metropolitan Opera House—1955
Increased interest in civil rights a result of Cold War propaganda
Brown v. Board of Education
1954 – Topeka, Kansas
Linda Brown: filed suit to attend a neighborhood school
“Separate educational institutions are inherently unequal.”
Overturned Plessy v. Ferguson
Court says: integrate "with all deliberate speed.”
What did this mean?
Linda Brown and Family
Circumvention of Brown v. Board of Education Ruling
White supremacist parents feared racial mixing and attempted to block black enrollment.
Ignored the integration issue
Token integration
Segregation through standardized placement tests
Segregation through private schools
Stalling through legal action
By 1964, 10 years after the Brown case, only 1% of black children attended truly integrated schools.
Little Rock High School
1957 courts order integration in Little Rock
9 black students enrolled.
Governor called out militia to block it.
Mobs replaced militia after recall.
Eisenhower ordered federal troops to protect the students.
Daily harassment
Courageous black students persevered.
Montgomery Bus Boycott
1955--Rosa Parks arrested for not giving up seat to white man
Boycott of bus system led by Martin Luther King, Jr.:
Walking, church busses, car pools, bicycles
Bus lines caught in the middle
Rosa Parks being Booked
Supreme Court ruled bus companies must integrate.
Inspired other protests:
Sit-ins, wade-ins, kneel-ins
Woolworth’s lunch counter
Montgomery Bus Boycott
Martin Luther King, Jr.
Martin Luther King, Jr.
Non-Violent
Influenced by Ghandi
“The blood may flow, but it must be our blood, not that of the white man.”
“Lord, we ain’t what we oughta be. We ain’t what we wanna be. We ain’t what we gonna be. But thank God, we ain’t what we was.”
Freedom Riders
Activists traveled from city to city to ignite the protest.
Bull Conner:
in Montgomery
Dogs
Whips
Water hoses
Cattle prods
Television
Public backlash
Civil Rights March (AL. 1965)
1963 - Washington, D.C. "I have a Dream“—200,000 Attended
Civil Rights Legislation
1964 - Civil Rights Act
1964 - 24th Amendment
Abolished Poll Tax
1965 Voting Rights Act
Affirmative action
Int ...
The Churchill CentreReturn to Full GraphicsThe Churchi.docxmattinsonjanel
The Churchill Centre
Return to Full Graphics
The Churchill Centre | Calendar | Churchill Facts | Speeches & Quotations | Publications and Resources |
News | Join The Centre! | Churchill Stores | Contact Us | Links | Search
Their Finest Hour
Sir Winston Churchill > Speeches & Quotations > Speeches
June 18, 1940
House of Commons
I spoke the other day of the colossal military disaster which occurred when the French High Command
failed to withdraw the northern Armies from Belgium at the moment when they knew that the French front
was decisively broken at Sedan and on the Meuse. This delay entailed the loss of fifteen or sixteen French
divisions and threw out of action for the critical period the whole of the British Expeditionary Force. Our
Army and 120,000 French troops were indeed rescued by the British Navy from Dunkirk but only with the
loss of their cannon, vehicles and modern equipment. This loss inevitably took some weeks to repair, and in
the first two of those weeks the battle in France has been lost. When we consider the heroic resistance
made by the French Army against heavy odds in this battle, the enormous losses inflicted upon the enemy
and the evident exhaustion of the enemy, it may well be the thought that these 25 divisions of the
best-trained and best-equipped troops might have turned the scale. However, General Weygand had to fight
without them. Only three British divisions or their equivalent were able to stand in the line with their French
comrades. They have suffered severely, but they have fought well. We sent every man we could to France
as fast as we could re-equip and transport their formations.
I am not reciting these facts for the purpose of recrimination. That I judge to be utterly futile and even
harmful. We cannot afford it. I recite them in order to explain why it was we did not have, as we could have
had, between twelve and fourteen British divisions fighting in the line in this great battle instead of only
three. Now I put all this aside. I put it on the shelf, from which the historians, when they have time, will
select their documents to tell their stories. We have to think of the future and not of the past. This also
applies in a small way to our own affairs at home. There are many who would hold an inquest in the House
of Commons on the conduct of the Governments-and of Parliaments, for they are in it, too-during the years
which led up to this catastrophe. They seek to indict those who were responsible for the guidance of our
affairs. This also would be a foolish and pernicious process. There are too many in it. Let each man search
his conscience and search his speeches. I frequently search mine.
Of this I am quite sure, that if we open a quarrel between the past and the present, we shall find that we
have lost the future. Therefore, I cannot accept the drawing of any distinctions between Members of the
present Government. It was formed at a moment of crisis in order to unite a ...
The Categorical Imperative (selections taken from The Foundati.docxmattinsonjanel
The Categorical Imperative (selections taken from The Foundations of the Metaphysics of
Morals)
Preface
As my concern here is with moral philosophy, I limit the question suggested to this:
Whether it is not of the utmost necessity to construct a pure thing which is only empirical and
which belongs to anthropology? for that such a philosophy must be possible is evident from the
common idea of duty and of the moral laws. Everyone must admit that if a law is to have moral
force, i.e., to be the basis of an obligation, it must carry with it absolute necessity; that, for
example, the precept, "Thou shalt not lie," is not valid for men alone, as if other rational beings
had no need to observe it; and so with all the other moral laws properly so called; that, therefore,
the basis of obligation must not be sought in the nature of man, or in the circumstances in the
world in which he is placed, but a priori simply in the conception of pure reason; and although
any other precept which is founded on principles of mere experience may be in certain respects
universal, yet in as far as it rests even in the least degree on an empirical basis, perhaps only as to
a motive, such a precept, while it may be a practical rule, can never be called a moral law…
What is the “Good Will?”
NOTHING can possibly be conceived in the world, or even out of it, which can be called
good, without qualification, except a good will. Intelligence, wit, judgement, and the other
talents of the mind, however they may be named, or courage, resolution, perseverance, as
qualities of temperament, are undoubtedly good and desirable in many respects; but these gifts of
nature may also become extremely bad and mischievous if the will which is to make use of them,
and which, therefore, constitutes what is called character, is not good. It is the same with the
gifts of fortune. Power, riches, honour, even health, and the general well-being and contentment
with one's condition which is called happiness, inspire pride, and often presumption, if there is
not a good will to correct the influence of these on the mind, and with this also to rectify the
whole principle of acting and adapt it to its end. The sight of a being who is not adorned with a
single feature of a pure and good will, enjoying unbroken prosperity, can never give pleasure to
an impartial rational spectator. Thus a good will appears to constitute the indispensable condition
even of being worthy of happiness.
There are even some qualities which are of service to this good will itself and may
facilitate its action, yet which have no intrinsic unconditional value, but always presuppose a
good will, and this qualifies the esteem that we justly have for them and does not permit us to
regard them as absolutely good. Moderation in the affections and passions, self-control, and calm
deliberation are not only good in many respects, but even seem to constitute part of th ...
The cave represents how we are trained to think, fell or act accor.docxmattinsonjanel
The cave represents how we are trained to think, fell or act according to society, following our own way and not the way intended for us. The shadows are merely a reflection of what they perceived to be reality instead of an illusion. The prisoners are trapped in society, each one of us who choose to stay trapped in our own way. The man that escapes is the person who no longer is a slave to society and can see the difference between reality and illusion. The day light can be compared to God’s will. When you don’t follow the plan that has been laid out for you by God, than you are trapped and you will only see illusions or reflections of reality. Escaping and choosing to go into “the light,” or following the will of God, only then can you be set free from your prison.
When looking at a piece of art, a painting, for example, at first glance the painting can appear to be something other what it is intended to be (reality). This reminds me of those pictures that everyone sees on social media, the picture that has circles all over it. When you look at the picture it appears that the circles are moving, but in reality the circles do not move at all. So art can more or less be perceived as more of an illusion.
An example of the picture can be seen here http://www.dailyhaha.com/_pics/movie_circles_illusion.jpg
Accepting illusion as reality happens a lot more times than we probably think. Anything that we see on T.V., Social Media, internet, or even dating, can all be perceived as an illusion at some point. Take dating for example; how a person acts on a date is most likely not how they would act to someone they have known for a while (illusion). Not all people pretend to be something different but in many cases they do. Recognizing what you failed to see after the initial first date and thereafter is how you would know what you first seen was just simply an illusion and therefore not reality, unless of course in reality they are simply a fake person I suppose. Following this pattern makes you realize most people do not appear to be who they are. A good “first impression” doesn’t necessarily mean much when thinking about illusions vs reality, because that’s all the “first impression” is in fact more or less an illusion.
People live in shadows because they fail to recognize reality and choose to continue to believe in illusions. With the growth of Social media, more and more people are falling victim to what things appear to be and will stay in the dark (cave). We as a society are imprisoned by what we see and read through news channels and social media. We will believe anything that comes across CNN or any news station (not fox news though) and let them make up our mind for us. People comment on any shooting victims and assume the cop was in the wrong and is racist, in reality that is not always the case.
It’s interesting to think in terms of appearance vs reality when viewing not only art, but the world. Not taking things for what they appear to ...
The Case Superior Foods Corporation Faces a ChallengeOn his way.docxmattinsonjanel
The Case: Superior Foods Corporation Faces a Challenge
On his way to the plant office, Jason Starnes passed by the production line where hundreds of gloved, uniformed workers were packing sausages and processed meats for shipment to grocery stores around the world.
Jason's company, Superior Foods Corporation, based in Wichita, Kansas, employed 30,000 people in eight countries and had beef and pork processing plants in Arkansas, California, Milwaukee, and Nebraska City. Since a landmark United States–Japan trade agreement signed in 1988, markets had opened up for major exports of American beef, now representing 10 percent of U.S. production. Products called “variety meats”—including intestines, hearts, brains, and tongues—were very much in demand for export to international markets.
Jason was in Nebraska City to talk with the plant manager, Ben Schroeder, about the U.S. outbreak of bovine spongiform encephalopathy (mad cow disease) and its impact on the plant. On December 23, 2011, the U.S. Department of Agriculture had announced that bovine spongiform encephalopathy had been discovered in a Holstein cow in Washington State. The global reaction was swift: Seven countries imposed either total or partial bans on the importation of U.S. beef, and thousands of people were chatting about it on blogs and social networking sites. Superior had moved quickly to intercept a container load of frozen Asian-bound beef from its shipping port in Los Angeles, and all other shipments were on hold.
After walking into Ben's office, Jason sat down across from him and said, “Ben, your plant has been a top producer of variety meats for Superior, and we have appreciated all your hard work out here. Unfortunately, it looks like we need to limit production for a while—at least three months, or until the bans get relaxed. I know Senator Nelson is working hard to get the bans lifted. In the meantime, we need to shut down production and lay off about 25 percent of your workers. I know it is going to be difficult, and I'm hoping we can work out a way to communicate this to your employees.”
...
The Case You can choose to discuss relativism in view of one .docxmattinsonjanel
The Case:
You can choose to discuss relativism in view of one of the following two cases:
The Case:
· Start by giving a brief explanation of relativism (200 words).
· what is the difference between ethical & cultural relativism. Then discuss, in view of relativism, how we can reconcile the apparent conflict between the need for enforcement of human rights standards with the need for protection of cultural diversity. (400 words).
...
The Case Study of Jim, Week Six The body or text (i.e., not rest.docxmattinsonjanel
The Case Study of Jim, Week Six
The body or text (i.e., not restating the question in your answer, not including your references or your signature) of your initial response should be at least 300 words of text to be considered substantive. You will see a red U for initial responses that are not at least 300 words. Note: your initial response to this required discussion will not count toward participation
The Case Study of Jim, Week 6
Title of Activity: In class discussion of the case study of Jim, Week Six
Objective: Review the concepts of the case study in Ch.13 of Personality and then relate Jim’s case to the theorists discussed during the week. In addition, summarize the entire case study.
1. Read “The Case of Jim” in Ch. 13 of Personality.
2. Discuss the case. This week, discussion should focus on social-cognitive theory.
3. Provide a summary of the entire case.
THE CASE OF JIM Twenty years ago Jim was assessed from various theoretical points of view: psychoanalytic, phenomenological, personal construct, and trait.
At the time, social-cognitive theory was just beginning to evolve, and thus he was not considered from this standpoint. Later, however, it was possible to gather at least some data from this theoretical standpoint as well. Although comparisons with earlier data may be problematic because of the time lapse, we can gain at least some insight into Jim’s personality from this theoretical point of view. We do so by considering
Jim’s goals, reinforcers he experiences, and his self-efficacy beliefs.
Jim was asked about his goals for the immediate future and for the long-range future. He felt that his immediate and long-term goals were pretty much the same: (1) getting to know his son and being a good parent, (2) becoming more accepting and less critical of his wife and others, and (3) feeling good about his professional work as a consultant.
Generally he feels that there is a good chance of achieving these goals but is guarded in that estimate, with some uncertainty about just how much he will be able to “get out of myself” and thereby be more able to give to his wife and child.
Jim also was asked about positive and aversive reinforcers, things that were important to him that he found rewarding or unpleasant.
Concerning positive reinforcers, Jim reported that money was “a biggie.”
In addition he emphasized time with loved ones, the glamour of going to an opening night, and generally going to the theater or movies.
He had a difficult time thinking of aversive reinforcers. He described writing as a struggle and then noted, “I’m having trouble with this.”
Jim also discussed another social-cognitive variable: his competencies or skills (both intellectual and social). He reported that he considered himself to be very bright and functioning at a very high intellectual level. He felt that he writes well from the standpoint of a clear, organized presentation, but he had not written anything that is innovative or creative. Ji ...
The Case of Missing Boots Made in ItalyYou can lead a shipper to.docxmattinsonjanel
The Case of Missing Boots Made in Italy
You can lead a shipper to the water, but if the horse does not want to drink…
Vocabulary:
Shipper: In commercial trade, the person who gives goods to a shipping company to be transported to a foreign destination; in export transactions, it is usually the exporter. Do not confuse the shipper with the shipping company or carrier.
Consignee: The person who is ultimately receiving the goods, generally the buyer or importer. Sometimes these people will designate a “notify party” to be notified when the goods arrive in the port of entry, so that customs clearance can be arranged and the goods picked up for further domestic transport.
Carrier: A company that transports goods (sometimes referred to as a “shipping company” or a “freight company”).
Forwarder (or “freight forwarder”): A forwarder is like a travel agent for cargo – forwarders organize the transport of your goods from departure to destination, and charge a fee for their services. There are many different kinds of forwarders. There are firms that act as both forwarders and carriers. Sometimes forwarders will have relationships with a whole string of carriers and other forwarders, so that the shipper only deals with the forwarder but in the end the goods are actually carrier by a series of independent transport companies.
NVOCC: Non-vessel operating common carrier. A “common carrier” in the legal terminology refers to a carrier who has accepted the additional legal burdens imposed on a company that regularly carries goods for a fee (as opposed to someone with a truck who might agree to help you out just this once because you’re in trouble).
Container: Large standard-sized metal boxes for transporting merchandise; you see them on the back of trucks, or stacked up outside of ports like Lego toys, or on top of large ocean-going container ships. The capacity of container vessels is measured in TEU (twenty-foot equivalent units; containers generally measure 20 or 40 feet long; large vessels can now carry in excess of 4,000 TEU). There are different kinds of containers for different purposes. For example, refrigerated containers (for transporting meat or fruit, for example) are called “reefers,” so be careful where you use this term.
Consolidator: When large companies ship a lot of goods, they are usually able to fill entire containers. However, shippers who ship smaller amounts (like the shipper in the example below), often have their goods “stuffed” (the industry term) along with other goods into the same container; hence, they are “consolidated.” Some firms specialize in consolidating various shipments from different shippers, these are “consolidators.” A load which requires consolidation is a “LCL” or less-than-full-container load, as opposed to a “FCL” – full-container-load.
Marine Insurance: This is a common term for cargo insurance for international shipments, even in cases where much of the transport is NOT by sea; “marine insurance ...
The Cardiovascular SystemNSCI281 Version 51University of .docxmattinsonjanel
The Cardiovascular System
NSCI/281 Version 5
1
University of Phoenix Material
The Cardiovascular System
Exercise 9.6: Cardiovascular System—Thorax, Arteries, Anterior View
Layer 1 (p. 470)
A. .
B. .
C. .
D. .
E. .
F. .
G. .
H. .
Layer 2 (p. 470)
A. .
B. .
C. .
D. .
E. .
F. .
G. .
H. .
I. .
J. .
Layer 3 (p. 471)
A. .
B. .
C. .
D. .
E. .
F. .
G. .
H. .
I. .
J. .
Layer 4 (pp. 471-472)
A. .
B. .
C. .
D. .
E. .
F. .
G. .
H. .
I. .
J. .
K. .
L. .
M. .
N. .
O. .
P. .
Q. .
R. .
S. .
T. .
U. .
V. .
W. .
Layer 5 (p. 472)
A. .
B. .
C. .
D. .
E. .
F. .
G. .
H. .
I. .
J. .
K. .
Layer 6 (pp. 472-473)
A. .
B. .
C. .
D. .
E. .
F. .
G. .
H. .
I. .
J. .
K. .
L. .
M. .
N. .
O. .
P. .
Q. .
R. .
S. .
T. .
U. .
V. .
W. .
X. .
Exercise 9.7a: Imaging—Aortic Arch
A. .
B. .
C. .
D. .
E. .
F. .
G. .
H. .
I. .
J. .
K. .
L. .
M. .
N. .
O. .
P. .
Q. .
R. .
S. .
T. .
U. .
V. .
W. .
X. .
Y. .
Z. .
AA. .
Exercise 9.7b: Imaging—Aortic Arch
A. .
B. .
C. .
D. .
E. .
F. .
G. .
H. .
I. .
J. .
K. .
L. .
M. .
N. .
O. .
P. .
Q. .
R. .
S. .
T. .
U. .
Exercise 9.8: Cardiovascular System—Thorax, Veins, Anterior View
Layer 2 (pp. 474-475)
A. .
B. .
C. .
D. .
E. .
F. .
G. .
H. .
I. .
J. .
Layer 3 (p. 475)
A. .
B. .
C. .
D. .
E. .
F. .
G. .
H. .
I. .
J. .
Layer 4 (p. 476)
A. .
B. .
C. .
D. .
E. .
F. .
G. .
H. .
I. .
J. .
K. .
L. .
M. .
N. .
O. .
P. .
Q. .
R. .
S. .
T. .
U. .
V. .
W. .
Layer 5 (pp. 476-477)
A. .
B. .
C. .
D. .
E. .
F. .
G. .
H. .
I. .
J. .
Layer 6 (p. 476)
A. .
B. .
C. .
D. .
E. .
F. .
G. .
H. .
I. .
J. .
K. .
L. .
M. .
N. .
O. .
P. .
Q. .
R. .
S. .
Animation: Pulmonary and Systemic Circulation
After viewing the animation, answer these questions:
1. Name the two divisions of the cardiovascular system.
2. What are the destinations of these two circuits?
3. In the systemic circulation, where does gas exchange occur?
4. In the pulmonary circulation, where does gas exchange occur?
5. Name the blood vessels that carry oxygen-rich blood to the heart. How many are there? Where do they terminate?
Exercise 9.9: Imaging—Thorax
A. .
B. .
C. .
D. .
E. .
F. .
G. .
H. .
I. .
J. .
K. .
In Review
1. What is the name for the fibrous sac that encloses the heart?
2. Name the lymphatic organ that is large in children but atrophies during adolescence.
3. Name the bilobed endocrine gland located lateral to the trachea and larynx.
4. How do large arteries supply blood to body structures?
5. Name the large vessel that conveys oxygen-poor blood from the right ventricle of the heart.
6. Name the two branches of the blood vessel mentioned in question 5 that convey oxygen-poor blood to the lungs.
7. Name the blunt tip of the left ventricle.
8. What is the carotid sheath? What structures are found within it?
9. What is the serous pericardium?
10. Name the structure that ...
The Cardiovascular SystemNSCI281 Version 55University of .docxmattinsonjanel
The Cardiovascular System
NSCI/281 Version 5
5
University of Phoenix Material
The Cardiovascular System
Exercise 9.6: Cardiovascular System—Thorax, Arteries, Anterior View
Layer 1 (p. 470)
A. .
B. .
C. .
D. .
E. .
F. .
G. .
H. .
Layer 2 (p. 470)
A. .
B. .
C. .
D. .
E. .
F. .
G. .
H. .
I. .
J. .
Layer 3 (p. 471)
A. .
B. .
C. .
D. .
E. .
F. .
G. .
H. .
I. .
J. .
Layer 4 (pp. 471-472)
A. .
B. .
C. .
D. .
E. .
F. .
G. .
H. .
I. .
J. .
K. .
L. .
M. .
N. .
O. .
P. .
Q. .
R. .
S. .
T. .
U. .
V. .
W. .
Layer 5 (p. 472)
A. .
B. .
C. .
D. .
E. .
F. .
G. .
H. .
I. .
J. .
K. .
Layer 6 (pp. 472-473)
A. .
B. .
C. .
D. .
E. .
F. .
G. .
H. .
I. .
J. .
K. .
L. .
M. .
N. .
O. .
P. .
Q. .
R. .
S. .
T. .
U. .
V. .
W. .
X. .
Exercise 9.7a: Imaging—Aortic Arch
A. .
B. .
C. .
D. .
E. .
F. .
G. .
H. .
I. .
J. .
K. .
L. .
M. .
N. .
O. .
P. .
Q. .
R. .
S. .
T. .
U. .
V. .
W. .
X. .
Y. .
Z. .
AA. .
Exercise 9.7b: Imaging—Aortic Arch
A. .
B. .
C. .
D. .
E. .
F. .
G. .
H. .
I. .
J. .
K. .
L. .
M. .
N. .
O. .
P. .
Q. .
R. .
S. .
T. .
U. .
Exercise 9.8: Cardiovascular System—Thorax, Veins, Anterior View
Layer 2 (pp. 474-475)
A. .
B. .
C. .
D. .
E. .
F. .
G. .
H. .
I. .
J. .
Layer 3 (p. 475)
A. .
B. .
C. .
D. .
E. .
F. .
G. .
H. .
I. .
J. .
Layer 4 (p. 476)
A. .
B. .
C. .
D. .
E. .
F. .
G. .
H. .
I. .
J. .
K. .
L. .
M. .
N. .
O. .
P. .
Q. .
R. .
S. .
T. .
U. .
V. .
W. .
Layer 5 (pp. 476-477)
A. .
B. .
C. .
D. .
E. .
F. .
G. .
H. .
I. .
J. .
Layer 6 (p. 476)
A. .
B. .
C. .
D. .
E. .
F. .
G. .
H. .
I. .
J. .
K. .
L. .
M. .
N. .
O. .
P. .
Q. .
R. .
S. .
Animation: Pulmonary and Systemic Circulation
After viewing the animation, answer these questions:
1. Name the two divisions of the cardiovascular system.
2. What are the destinations of these two circuits?
3. In the systemic circulation, where does gas exchange occur?
4. In the pulmonary circulation, where does gas exchange occur?
5. Name the blood vessels that carry oxygen-rich blood to the heart. How many are there? Where do they terminate?
Exercise 9.9: Imaging—Thorax
A. .
B. .
C. .
D. .
E. .
F. .
G. .
H. .
I. .
J. .
K. .
In Review
1. What is the name for the fibrous sac that encloses the heart?
2. Name the lymphatic organ that is large in children but atrophies during adolescence.
3. Name the bilobed endocrine gland located lateral to the trachea and larynx.
4. How do large arteries supply blood to body structures?
5. Name the large vessel that conveys oxygen-poor blood from the right ventricle of the heart.
6. Name the two branches of the blood vessel mentioned in question 5 that convey oxygen-poor blood to the lungs.
7. Name the blunt tip of the left ventricle.
8. What is the carotid sheath? What structures are found within it?
9. What is the serous pericardium?
10. Name the structure that ...
The British Airways Swipe Card Debacle case study;On Friday, Jul.docxmattinsonjanel
The British Airways Swipe Card Debacle case study;
On Friday, July 18, 2003, British Airways staff in Terminals 1 and 4 at London’s busy Heathrow Airport held a 24 hour wildcat strike. The strike was not officially sanctioned by the trade unions but was spontaneous action by over 250 check in staff who walked out at 4 pm. The wildcat strike occurred at the start of a peak holiday season weekend which led to chaotic scenes at Heathrow. Some 60 departure flights were grounded and over 10,000 passengers left stranded. The situation was heralded as the worst industrial situation BA had faced since 1997 when a strike was called by its cabin crew. BA response was to cancel its services from both terminals, apologize for the disruption and ask those who were due to fly not to go to the airport as they would be unable to service them. BA also set up a tent outside Heathrow to provide refreshments and police were called in to manage the crow. BA was criticized by many American visitors who were trying to fly back to the US for not providing them with sufficient information about what was going on. Staff returned to work on Saturday evening but the effects of the strike flowed on through the weekend. By Monday morning July 21, BA reported that Heathrow was still extremely busy. There is still a large backlog of more than 1000 passengers from services cancelled over the weekend. We are doing everything we can to get these passengers away in the next couple of days. As a result of the strike BA lost around 40 million and its reputation was severely dented. The strike also came at a time when BA was still recovering from other environmental jolts such as 9/11 the Iraqi war, SARS, and inroads on its markets from budget airlines. Afterwards BA revealed that it lost over 100,000 customers a result of the dispute.
BA staff were protesting the introduction of a system for electronic clocking in that would record when they started and finished work for the day. Staff were concerned that the system would enable managers to manipulate their working patterns and shift hours. The clocking in system was one small part of a broader restructuring program in BA, titled the Future Size and Shape recovery program. Over the previous two years this had led to approximately 13,000 or almost one in four jobs, being cut within the airline. As The Economist noted, the side effects of these cuts were emerging with delayed departures resulting from a shortage of ground staff at Gatwick and a high rate of sickness causing the airline to hire in aircraft and crew to fill gaps. Rising absenteeism is a sure sign of stress in an organization that is contracting. For BA management introduction of the swipe card system was a way of modernizing BA and improving the efficient use of staff and resources. As one BA official was quoted as saying We needed to simplify things and bring in the best system to manage people. For staff it was seen as a prelude to a radical shakeup in working ...
The Case Abstract Accuracy International (AI) is a s.docxmattinsonjanel
The Case
Abstract
Accuracy International (AI) is a specialist British firearms manufacturer based in Portsmouth,
Hampshire, England and best known for producing the Accuracy International Arctic Warfare
series of precision sniper rifles. The company was established in 1978 by British Olympic shooting
gold medallist Malcolm Cooper, MBE (1947–2001), Sarah Cooper, Martin Kay, and the designers
of the weapons, Dave Walls and Dave Craig. All were highly skilled international or national target
shooters. Accuracy International's high-accuracy sniper rifles are in use with many military units
and police departments around the world. Accuracy International went into liquidation in 2005, and
was bought by a British consortium including the original design team of Dave Walls and Dave
Craig.
Earlier this year, AI's computer network was hit by a data stealing malware which cost thousands of
pounds to recover from. Also last year there have been a couple of incidents of industrial
espionage, involving staff who were later sacked and prosecuted.
As part of an ongoing covert investigation, the head of Security at AI (DG) has hired you to
conduct a forensic investigation on an image of a USB device. The USB device, it is a non-
company issued device, allegedly belonging to an employee Christian Macleod, a consultant and
technical manager at AI for more than six years.
Case details
Christian’s manager, David Bolton, is the regional manager and head of R&D and has been
working at AI for the last three years. David initiated this fact finding covert investigation which is
conducted with the support of the head of Security at AI.
The USB device in question allegedly was removed from Christian's workstation at AI while he
was out of the office for lunch, the device was imaged and then it was plugged in back into
Christian's workstation. You have been provided with a copy of that image (the original copy is at
the moment secure in a secure locker at the security department).
You have been told by DG that Dave was alarmed by some of the work practices of Christian and
that prompted him to start this investigation by contacting the Head of Security at AI. According to
Dave, Christian would bring in devices such as his iPod and his iPhone and he would often plug
these into his workstation. There is no policy against personal music devices and there is no
BYOD policy but there is a strict policy against copying corporate data is any personal device. The
company's policy states that such data is not to be stored unencrypted, on unauthorised, non
company approved devices. According to DG, Dave has reasons to believe that an earlier malware
infection incident at AI had its origins in one of Christian's personal devices.
Supporting information
1. You need to be aware that Dave and Christian do not get along as they had a few verbal exchanges
in the last year. Christian has filled in a ...
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
How to Fix the Import Error in the Odoo 17Celine George
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
How to Add Chatter in the odoo 17 ERP ModuleCeline George
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
Leveraging Generative AI to Drive Nonprofit InnovationTechSoup
In this webinar, participants learned how to utilize Generative AI to streamline operations and elevate member engagement. Amazon Web Service experts provided a customer specific use cases and dived into low/no-code tools that are quick and easy to deploy through Amazon Web Service (AWS.)
Leveraging Generative AI to Drive Nonprofit Innovation
Submitted to Operations Researchmanuscript XXA General A.docx
1. Submitted to Operations Research
manuscript XX
A General Attraction Model and Sales-based Linear
Program for Network Revenue Management under
Customer Choice
Guillermo Gallego
Department of Industrial Engienering and Operations Research,
Columbia University, New York, NY 10027,
[email protected]
Richard Ratliff and Sergey Shebalov
Research Group, Sabre Holdings, Southlake, TX 76092,
[email protected]
This paper addresses two concerns with the state of the art in
network revenue management with dependent
demands. The first concern is that the basic attraction model
(BAM), of which the multinomial logit (MNL)
model is a special case, tends to overestimate demand recapture
in practice. The second concern is that the
choice based deterministic linear program, currently in use to
derive heuristics for the stochastic network
revenue management problem, has an exponential number of
variables. We introduce a generalized attraction
model (GAM) that allows for partial demand dependencies
2. ranging from the BAM to the independent
demand model (IDM). We also provide an axiomatic
justification for the GAM and a method to estimate its
parameters. As a choice model, the GAM is of practical interest
because of its flexibility to adjust product-
specific recapture. Our second contribution is a new formulation
called the Sales Based Linear Program
(SBLP) that works for the GAM. This formulation avoids the
exponential number of variables in the earlier
choice-based network RM approaches, and is essentially the
same size as the well known LP formulation
for the IDM. The SBLP should be of interest to revenue
managers because it makes choice-based network
RM problems tractable to solve. In addition, the SBLP
formulation yields new insights into the assortment
problem that arises when capacities are infinite. Together these
two contributions move forward the state of
the art for network revenue management under customer choice
and competition.
Key words : pricing, choice models, network revenue
management, dependent demands, O&D, upsell,
recapture
1. Introduction
3. One of the leading areas of research in revenue management
(RM) has been incorporating demand
dependencies into forecasting and optimization models.
Developing effective models for suppliers
to estimate how consumer demand is redirected as the set of
available products changes is critical
1
Gallego, Ratliff, and Shebalov: A General Choice Model and
Network RM Optimization
2 Article submitted to Operations Research; manuscript no. XX
in determining the revenue maximizing set of products and
prices to offer for sale in industries
where RM is used. These industries include airlines, hotels, and
car rental companies, but the issue
of how customers select among different offerings is also
important in transportation, retailing and
healthcare. Several terms are used in industry to describe
different types of demand dependen-
cies. If all products are available for sale, we observe the first-
choice, or natural, demand, for each
of the products. However, when a product is unavailable, its
first-choice demand is redirected to
other available alternatives (including the ‘no-purchase’
4. alternative). From a supplier’s perspective,
this turned away demand for a product can result in two
possible outcomes: ‘spill’ or ‘recapture’.
Spill refers to redirected demand that is lost to competition or
to the no-purchase alternative, and
recapture refers to redirected demand that results in the sale of
a different available product. Depen-
dent demand RM models lead to improved revenue performance
because they consider recaptured
demand that would otherwise be ignored using traditional RM
methods that assume independent
demands. The work presented in this paper provides a practical
mechanism to incorporate both
of these effects into the network RM optimization process
through use of customer-choice models
(including methods to estimate the model parameters in the
presence of competition).
An early motivation for studying demand dependencies was
concerned with incorporating a
special type of recapture known as ‘upsell demand’ in single
resource RM problems. Upsell is
recapture from closed discount fare classes into open, higher
valued ones that consume the same
capacity (called ‘same-flight upsell’ in the airline industry).
5. More specifically, there was a perceived
need to model the probability that a customer would buy up to a
higher fare class if his preferred fare
was not available. The inability to account for upsell demand
makes the widely used independent
demand model (IDM) too pessimistic, resulting in too much
inventory offered at lower fares and
in a phenomenon known as ‘revenue spiral down’; see Cooper et
al. (2006). To our knowledge, the
first authors to account for upsell potential in the context of
single resource RM were Brumelle
et al. (1990) who worked out implicit formulas for the two fare
class problem. A static heuristic
was proposed by Belobaba and Weatherford (1996), who made
fare adjustments while keeping
the assumption of independent demands. Talluri and van Ryzin
(2004) develop the first stochastic
Gallego, Ratliff, and Shebalov: A General Choice Model and
Network RM Optimization
Article submitted to Operations Research; manuscript no. XX 3
dynamic programming formulation for choice-based, dependent
demand for the single resource case.
Gallego, Ratliff and Li (2009) developed heuristics that
6. combined fare adjustments with dependent
demand structure for multiple fares that worked nearly as well
as solving the dynamic program of
Talluri and van Ryzin (2004). Their work suggest that
considering same-flight upsell has significant
revenue impact, leading to improvements ranging from 3-6%.
For network models, in addition to upsell, it is also important to
consider ‘cross-flight recapture’
that occurs when a customer’s preferred choice is unavailable,
and he selects to purchase a fare
on a different flight instead of buying up to a higher fare on the
same flight. Authors that have
tried to estimate upsell and recapture effects include Andersson
(1998), Ja et al. (2001), and Ratliff
et al. (2008). In markets in which there are multiple flight
departures, recapture rates typically
range between 15-55%; see Ja et al. (2001). Other authors have
dealt with the topic of demand
estimation from historical sales and availability data. The most
recent methods use maximum like-
lihood estimation techniques to estimate primary demands and
market flight alternative selection
probabilities (including both same-flight upsell and cross-flight
recapture); for details, see Vulcano
7. et al. (2012), Meterelliyoz (2009) and Newman, Garrow,
Ferguson and Jacobs (2010).
Most of the optimization work in network revenue management
with dependent demands is based
on formulating and solving large scale linear programs that are
then used as the basis to develop
heuristics for the stochastic network revenue management
(SNRM) problem; e.g. see Bront et al.
(2009), Fiig et al. (2010), Gallego et al. (2004), Kunnumkal and
Topaloglu (2010), Kunnumkal
and Topaloglu (2008), Liu and van Ryzin (2008), and Zhang and
Adelman (2009). Note that
preliminary versions of Fiig et al. (2010) were discussed as
early as 2005, and the method is one
of the earliest practical heuristics for incorporating dependent
demands into SNRM optimization.
However, as described in section 5.4, the applicability of the
approach requires severe assumptions
and is restricted to certain special cases and fundamentally
differs from the discrete choice models
described in this paper.
Our paper makes two main contributions. The first contribution
is to discrete choice modeling
8. and should be of interest both to people working on RM, as well
as to others with an interest
Gallego, Ratliff, and Shebalov: A General Choice Model and
Network RM Optimization
4 Article submitted to Operations Research; manuscript no. XX
in discrete choice modeling. The second contribution is the
development of a tractable network
optimization formulation for dependent demands under the
aforementioned discrete choice model.
Our first contribution is a response to known limitations of the
multinomial choice model (MNL)
which is often used to handle demand dependencies. The MNL
developed by McFadden (1974) is a
random utility model based on independent Gumbel errors, and
a special case of the basic attraction
model (BAM) developed axiomatically by Luce (1959). The
BAM states that the demand for a
product is the ratio of the attractiveness of the product divided
by the sum of the attractiveness
of the available products (including a no purchase alternative).
This means that closing a product
will result in spill, and a portion of the spill is recaptured by
other available products in proportion
9. to their attraction values. In practice, we have seen situations
where the BAM overestimates or
misallocates recapture probabilities. In a sense, one could say
that the BAM tends to be too
optimistic about recapture. In contrast, the independent demand
model (IDM) assumes that all
demand for a product is lost when the product is not available
for sale. It is fair to say, therefore,
that the IDM is too pessimistic about recapture as all demand
spills to the no-purchase alternative.
To address these limitations, we develop a generalized
attraction model (GAM) that is better at
handling recapture than either the BAM or the IDM. In essence,
the GAM adds flexibility in
modeling spill and recapture by making the attractiveness of the
no-purchase alternative a function
of the products not offered. As we shall see, the GAM includes
both the BAM and the IDM as
special cases. We justify the GAM axiomatically by
generalizing one of the Luce Axioms to better
control for the portion of the demand that is recaptured by other
products. We show that the GAM
also arises as a limiting case of the nested logit (NL) model
where the offerings within each nest
10. are perfectly correlated. In its full generality, the GAM has
about twice as many parameters than
the BAM. However, a parsimonious version is also presented
that has only one more parameter
than the BAM.
We adapt and enhance the Expectation-Maximization algorithm
(henceforth EM algorithm)
developed by Vulcano et al. (2012) for the BAM to estimate the
parameters for the GAM , with
the estimates becoming better if the firm knows its market share
when it offers all products. The
Gallego, Ratliff, and Shebalov: A General Choice Model and
Network RM Optimization
Article submitted to Operations Research; manuscript no. XX 5
estimation requires only data from the products offered by the
firm and the corresponding selections
made by customers.
Our second main contribution is the development of a new
formulation for the network revenue
management problem under the GAM. This formulation avoids
the exponential number of variables
in the Choice Based Linear Program (CBLP) that was designed
originally for the BAM; see Gallego
11. et al. (2004). In the CBLP, the exponential number of variables
arises because a variable is needed to
capture the amount of time each subset of products is offered
during the sales horizon. The number
of products itself is usually very large; for example, in airlines,
it is the number of origin-destination
fares (ODFs), and the number of subsets is two raised to the
number of ODFs for each market
segment. This forces the use of column generation in the CBLP
and makes resolving frequently
or solving for randomly generated demands impractical. We
propose an alternative formulation
called the sales based linear program (SBLP), which we show is
equivalent to the CBLP not only
under the BAM but also under the GAM. Due to a unique
combination of demand balancing and
scaling constraints, the new formulation, has a linear rather than
exponential number of variables
and constraints. This provides important practical advantages
because the SBLP allows for direct
solution without the need for large-scale column generation
techniques. We also show how to
recover the solution to the CBLP from the SBLP. We show,
moreover, that the solution to the
12. SBLP is a nested collection of offered sets together with the
optimal proportion of time to offer
each set. The smallest of these subsets is the core, consisting of
products that are always offered.
Larger subsets typically contain lower-revenue products that are
only offered part of the time.
Offering these subsets from the largest to the smallest in the
suggested portions of the time over
the sales horizon provides a heuristic to the stochastic version
of the problem. Moreover, the ease
with which we can compute the optimal offered sets from the
SBLP formulation allow us to resolve
the problem frequently and update the offer sets. In addition,
other heuristics proposed by the
research community, e.g., Bront et al. (2009), Kunnumkal and
Topaloglu (2010), Kunnumkal and
Topaloglu (2008), Liu and van Ryzin (2008), Talluri (2012),
and Zhang and Adelman (2009), can
benefit from the ability to quickly solve large scale versions of
the CBLP and SBLP formulations.
Gallego, Ratliff, and Shebalov: A General Choice Model and
Network RM Optimization
6 Article submitted to Operations Research; manuscript no. XX
13. The solution to the SBLP also provides managerial insights into
the assortment problem (a special
case that arises when capacities are infinite).
The remainder of this paper is organized as follows. In §2 we
present the GAM as well as
two justifications for the model. We then present an
expectation-maximization (E-M) algorithm
to estimate its parameters. In §3 we present the stochastic,
choice based, network revenue
management problem. The choice based linear program is
reviewed in section §4. The new,
sales based linear program is presented in §5 as well as
examples that illustrate the use of the
formulation. The infinite capacity case gives rise to the
assortment problem and is studied in §6.
Our conclusions and directions for future research are in §7.
2. Generalized Attraction Model
For several decades, most revenue management systems
operated under the simplest type of cus-
tomer choice process known as the independent demand model
(IDM). Under the IDM, demand for
any given product is independent of the availability of other
products being offered. So if a vendor
14. is out-of-stock for a particular product (or it is otherwise
unavailable for sale), then that demand
is simply lost (to the no-purchase alternative); there is no
possibility of the vendor recapturing
any of those sales to alternate products because the demands are
treated as independent. Many
practitioners recognized that ignoring such demand interactions
lacked realism, but efforts to incor-
porate upsell heuristics into RM optimization processes were
hampered by practical difficulties in
estimating upsell rates. It was widely feared that, without a
rigorous foundation for estimating
upsell, the use of such heuristics could lead to an overprotection
bias in the inventory controls (and
consequent revenue losses). By the late 1990’s, progress on
dependent demand estimation methods
began to be made. van Ryzin, Talluri and Mahajan (1999)
presented excellent arguments for the
integration of discrete choice models into RM optimization
processes, and initial efforts to apply
this approach focused on the multinomial logit model (MNL)
which is a special case of the basic
attraction model (BAM) discussed next.
15. Gallego, Ratliff, and Shebalov: A General Choice Model and
Network RM Optimization
Article submitted to Operations Research; manuscript no. XX 7
Under the BAM, the probability that a customer selects product
j ∈ S when set S ⊂ N =
{1,.. .,n} is offered, is given by
πj(S) =
vj
v0 + V (S)
, (1)
where V (S) =
∑
j∈ S vj. The vj values are measures of the attractiveness of the
different choices,
embodied in the MNL model as exponentiated utilities (vj = e
ρuj for utilities uj where ρ > 0 is a
parameter that is inversely related to the variance of the Gumbel
distribution). The no-purchase
alternative is denoted by j = 0, and π0(S) is the probability that
a customer will prefer not to
purchase when the offer set is S. One could more formally write
πj(S+) instead of πj(S) since
the customer is really selecting from S+. However, we will
16. refrain from this formalism and follow
the convention of writing πj(S) to mean πj(S+). Also, unless
otherwise stated, S ⊂ N and the
probabilities πj(S) refer to a particular vendor. In discrete
choice models, a single vendor is often
implicitly implied. However, in some of our discussions below,
we will allow for multiple vendors.
In the case of multiple vendors, the probabilities πj(S) j ∈ S,
will depend on the offerings of other
vendors.
There is considerable empirical evidence that the BAM may be
optimistic in estimating recapture
probabilities. The BAM assumes that even if a customer prefers
j /∈ S+, he must select among
k∈ S+. This ignores the possibility that the customer may look
for products j /∈ S+ elsewhere or at
a later time. As an example, suppose that a customer prefers a
certain wine, and the store does not
have it. The customer may then either buy one of the wines in
the store, leave without purchasing,
or go to another store and look for the wine he wants. The BAM
precludes the last possibility; it
implicitly assumes that the search cost for an alternative source
of product j /∈ S+ is infinity.
17. We will propose a generalization of the BAM , called the
General Attraction Model (GAM) to
better deal with the consequences of not offering a product.
Before presenting a formal definition
of the GAM, we will present a simple example and will revisit
the red-bus, blue-bus paradox (Ben-
Akiva and Lerman (1994)). Suppose there are two products with
attraction values v1 = v2 = v0 = 1.
Under the BAM, πk({1,2}) = 1/3 for k = 0,1,2. Eliminating
choice 2 results in πk({1}) = 50% for
Gallego, Ratliff, and Shebalov: A General Choice Model and
Network RM Optimization
8 Article submitted to Operations Research; manuscript no. XX
k = 0,1, so one half of the demand for product 2 is recaptured
by product 1. Suppose, however,
that product 2 is available across town and that the customer’s
attraction for product 2 from the
alternative source is w2 = 0.5. Then his choice set, when
product 2 is not offered, is in reality
S = {1,2′} with 2′ representing product 2 in the alternative
location with shadow attraction w2.
A customer can now select between the no-purchase alternative
(v0 = 1), product 1 (v1 = 1), and
18. product 2’ (w2 = 0.5), so the probabilities of purchase from the
store offering only product 1 are
now
π0({1}) =
1.5
2.5
= 60%, π1({1}) =
1
2.5
= 40%.
By including 2’ as a latent alternative, the probability of
choosing product 1 has decreased from
50% under the BAM to 40%. However, this probability is still
higher than that of the independent
demand model (IDM) which is 33.3%. So the GAM allows us to
obtain estimates that are in-between
the BAM and the IDM by considering product specific shadow
attractions. This formulation may
also help with inter-temporal choices, where a choice j /∈ S+
may become available at a later time.
In this case wj is the shadow attraction of choice j discounted
by time and the risk that it may
not be available in the future. Notice that this formulation is
19. different from what results if we use
the traditional approach of viewing a product and location as a
bundle. Indeed, including product
2’ with attraction w2 = 0.5, results in choice set {1,2,2′} for the
customer when the vendor offers
assortment {1,2}. This results in π1({1,2,2′}) = 1/3.5 6= 1/3.
The problem with this approach, in
terms of the MNL, is that an independent Gumbel random
variable is drawn to determine the
random utility of product 2’.
Under the red-bus, blue-bus paradox, a person has a choice
between driving a car and taking
either a red or blue bus (it is implicitly assumed that both buses
have ample capacity and depart
at the same time). Let v1 represent the direct attractiveness of
driving a car and let v2,w2 repre-
sent, respectively, the attraction and the shadow attraction of
the two buses. If w2 = v2 then the
probabilities are unchanged if one of the buses is removed (as
one intuitively expects because there
are essentially zero search costs in finding a comparable bus).
The model with w2 = 0 represents
20. Gallego, Ratliff, and Shebalov: A General Choice Model and
Network RM Optimization
Article submitted to Operations Research; manuscript no. XX 9
the case where there is no second bus. The common way to deal
with the paradox is to use a nested
logit (NL) model. Under the NL model used to resolve the
paradox, a person first selects a mode
of transportation and then one of the offerings within each
mode. We are able to avoid the use of
the NL model, but as we shall see later, our model can be
viewed as a limit of a NL model.
To formally define the GAM let S
̄ = {j ∈ N : j /∈ S} be the
complement of S in N = {1,.. .,n}.
In addition to the attraction values vj, there are shadow
attraction values wj ∈ [0,vj],j ∈ N such
that for any subset S ⊂N
πj(S) =
vj
v0 + W(S
̄ ) + V (S)
j ∈ S, (2)
where for any R ⊂ N, W(R) =
∑
j∈ R wj. Consequently, the no-purchase probability is given by
π0(S) = (v0 + W(S
̄ ))/(v0 + W(S
̄ ) + V (S)). In essence, the
21. attraction value of the no-purchase
alternative has been modified to be v0 + W(S
̄ ).
An alternative, perhaps simpler, way of presenting the GAM by
using the following transforma-
tion: ṽ0 = v0 + W(N) and ṽj = vj −wj,j ∈N. For S ∈N, let Ṽ (S)
=
∑
j∈S ṽj. With this notation
the GAM becomes:
πj(S) =
vj
ṽ0 + Ṽ (S)
∀ j ∈ S and π0(S) = 1−πS(S). (3)
where πS(S) =
∑
j∈S πj(S). Notice that all choice probabilities are non-negative
as long as ṽj =
vj −wj ≥ 0 and ṽ0 = v0 +
∑
j∈ N wj > 0, which holds when v0 > 0 and wj ∈ [0,vj] for all j
∈ N.
The case wk = 0,k ∈N recovers the BAM, because ṽ0 = v0 and
ṽj = vj,j ∈ N. In contrast, the
22. case wk = vk,k ∈N, results in ṽ0 + Ṽ (S) = v0 + V (N) for all
offered sets S ⊂N. The probability
πj(S), of selecting product j is independent of the set S
containing j, resulting in the independent
demand model (IDM).
The parsimonious formulation P-GAM is given by wj = θvj ∀ j
∈ N for θ ∈ [0,1] can serve to
test H0 : θ = 0 vs H1 : θ > 0 to see whether the BAM applies or
to test H0 : θ = 1 against H1 : θ < 1,
to see whether the IDM applies. If either of these tests fail, then
a GAM maybe a better fit to the
data.
Gallego, Ratliff, and Shebalov: A General Choice Model and
Network RM Optimization
10 Article submitted to Operations Research; manuscript no.
XX
We provide two justifications for the GAM. The first
justification is Axiomatic. The second
is a limiting case of the nested logit (NL) model. Readers who
are not interested in the formal
derivation of the GAM can skip to section 2.4 for a method to
estimate the GAM parameters.
2.1. Axiomatic Justification
23. Luce (1959) proposed two choice axioms. To describe the
axioms under the assumption that the
no-purchase alternative is always available we will use the
notation πS+ (T) =
∑
j∈ S+
πj(T) for all
S ∈T and will use set difference notation T −S = T ∩ S
̄ to
represent the elements of T that are
not in S. The Luce axioms are given by :
• Axiom 1: If πi({i}) ∈ (0,1) for all i∈ T, then for any R⊂S+, S
⊂T
πR(T) = πR(S)πS+ (T).
• Axiom 2: If πi({i}) = 0 for some i∈ T, then for any S ⊂T such
that i∈ S
πS(T) = πS−{i}(T −{i}).
The most celebrated consequence of the Luce Axioms, due to
Luce (1959), is that πi(S) satisfies
the Luce Axioms if and only if there exist attraction values vj,j
∈ N+ such that equation (1) holds.
Since its original publication, the paper Luce (1959) has been
cited thousands of times. Among
the most famous citations, we find the already mentioned paper
24. by McFadden (1974) that shows
that the only random utility model that is consistent with the
BAM is the one with independent
Gumbel errors. An early paper by Debreu (1960), criticizes the
Luce model as it suffers from the so
called independence of irrelevant alternatives (IIA). The IIA
states the relative preference between
two alternatives does not change as additional alternatives are
added to the choice set. Debreu,
however, suggests that the addition of an alternative to an
offered set hurts alternatives that are
similar to the added alternative more than those that are
dissimilar to it. To illustrate this, Debreu
provides an example that is a precursor to the red-bus, blue-bus
paradox based on the choice
between three records: a suite by Debussy, and two different
recordings of the same Beethoven
Gallego, Ratliff, and Shebalov: A General Choice Model and
Network RM Optimization
Article submitted to Operations Research; manuscript no. XX
11
symphony. Another famous paper by Tversky (1972), criticizes
both the Luce model as well as all
25. random utility models that assume independent utilities for their
inability to deal with the IIA.
Tversky offers the elimination by aspects theory as a way to
cope with the IIA. Others, such as n
Domenich and McFadden (1975) and Williams (1977), have
turned to the nested logit (NL) model
as an alternative way of dealing with the IIA. Under a nested
logit model, for example, a person
will first chose between modes of transportation (car or bus)
before selecting a particular car or
bus color.
To our knowledge no one has altered the Luce Axioms with the
explicit goal of modifying the
recapture probabilities. Yellott (1977), however, gives a
characterization of the Luce model by an
axiom which he called invariance under uniform expansion of
the choice set, which is weaker than
Luce’s Axiom but implies Luce’s Axiom when the choice model
is assumed to be an independent
random utility model. The reader is also refereed to Dagsvik
(1983), who expands Yellott’s ideas
to choices made over time.
Notice that Axiom 1 holds trivially for R = ∅ since π∅ (S) = 0
for all S ⊂N. For ∅ 6= R⊂S the
26. formula can be written as the ratio of the demand captured by R
when we add T −S to S. The
ratio is given by
πR(T)
πR(S)
= πS+ (T) = 1−πT−S(T),
and is independent of R⊂S. Our goal is to generalize Axiom 1
so that the ratio remains indepen-
dent of R⊂S but in such a way that we have more control over
the proportion of the demand that
goes to T −S. This suggests the following generalization of
Axiom 1.
• Axiom 1’: If πi({i}) ∈ (0,1) for all i∈ T, then for any ∅ 6=
R⊂S ⊂T
πR(T)
πR(S)
= 1−
∑
j∈ T−S
(1−θj)πj(T)
for some set of values θj ∈ [0,1],j ∈ N.
We will call the set of Axioms 1’ and 2 the Generalized Luce
27. Axioms (GLA). We can think of
θj ∈ [0,1] as a relative measure of the competitiveness of
product j in the market place. The next
Gallego, Ratliff, and Shebalov: A General Choice Model and
Network RM Optimization
12 Article submitted to Operations Research; manuscript no.
XX
result states that a choice model satisfies the GLA if and only if
it is a GAM and links θj to the
ratio of wj to vj.
Theorem 1. A choice model πi(S) satisfies the GLA if and only
if it is of the GAM form. More-
over, wj = θjvj for all j ∈ N.
A proof of this theorem may be found in the Appendix. Notice
that it is tempting to relax the
constraint wj ≥ 0 as long as ṽ0 > 0. However, this relaxation
would lead to a violation of Axiom 2.
2.2. GAM as Limit of Nested Logit Model under Competition
We now show that the GAM also arises as the limit of the
nested logit (NL) model. The NL model
was originally proposed in Domenich and McFadden (1975),
and later refined in McFadden (1978),
28. where it is shown that it belongs to the class of Generalized
Extreme Value (GEV) family of models.
Under the nested choice model, customers first select a nest and
then an offering within the nest.
The nests may correspond to product categories and the
offerings within a nest may correspond
to different variants of the product category. As an example, the
product categories may be the
different modes of transportation (car vs. bus) and the variants
may be the different alternatives
for each mode of transportation (e.g., the blue and the red
buses). As an alternative, a product
category may consist of a single product, and the variants may
be different offerings of the same
product by different vendors. We are interested in the case
where the random utility of the different
variants of a product category are highly correlated. The NL
model, allows for correlations for
variants in nest i through the dissimilarity parameter γi. Indeed,
if ρi is the correlation between
the random utilities of nest i offerings, then γi =
√
1−ρi is the dissimilarity parameter for the nest.
The case γi = 1 corresponds to uncorrelated products, and to a
29. BAM. The MNL is the special case
where the idiosyncratic part of the utilities are independent and
identically distributed Gumbel
random variables.
Consider now a NL model where the nests correspond to
individual products offered in the
market. Customers first select a product, and then one of the
vendors offering the selected product.
Gallego, Ratliff, and Shebalov: A General Choice Model and
Network RM Optimization
Article submitted to Operations Research; manuscript no. XX
13
Let Ok be the set of vendors offering product k, Sl be the set of
products offered by vendor l, and
vkl be the attraction value of product k offered by vendor l.
Under the NL model, the probability
that a customer selects product i∈ Sj is given by
πi(Sj) =
(∑
l∈ Oi
v
1/γi
il
30. )γi
v0 +
∑
k
(∑
l∈ Ok
v
1/γk
kl
)γk v1/γiij∑
l∈ Oi
v
1/γi
il
, (4)
where the first term is the probability that product i is selected
and the second term the probability
that vendor j is selected. Many authors, e.g., Greene (1984), use
what is know as the non-normalized
nested models where vij’s are not raised to the power 1/γi. This
is sometimes done for convenience
by simply redefining vkl ←v
1/γk
kl . There is no danger in using this transformation as long as
the γ’s
31. are fixed. However, the normalized model presented here is
consistent with random utility models,
see Train (2002), and we use the explicit formulation because
we will be taking limits as the γ’s
go to zero.
It is easy to see that πi(Sj) is a BAM for each vendor j, when γi
= 1 for all i. This case can be
viewed as a random utility model, where an independent
Gumbel random variable is associated with
each product and each vendor. Consider now the case where γi ↓
0 for all i. At γi = 0, the random
utilities of the different offerings of product i are perfectly and
positively correlated. This makes
sense when the products are identical and price and location are
the only things differentiating
vendors. When these differences are captured by the
deterministic part of the utility, then a single
Gumbel random variable is associated with each product. In the
limit, customers select among
available products and then buy from the most attractive
vendor. If several vendors offer the same
attraction value, then customers select randomly among such
vendors. The next result shows that
32. a GAM arises for each vendor, as γi ↓ 0 for all i.
Theorem 2. The limit of (4) as γi ↓ 0 for all i is a GAM. More
precisely, there are attraction
values akj, ãkj ∈ [0,akj], and ã0j ≥ 0, such that the discrete
choice model for vendor j is given by
πi(Sj) =
aij
ã0j +
∑
k∈ Sj
ãkj
∀ i∈ Sj.
Gallego, Ratliff, and Shebalov: A General Choice Model and
Network RM Optimization
14 Article submitted to Operations Research; manuscript no.
XX
This shows that if customers first select the product and then
the vendor, then the NL choice
model becomes a GAM for each vendor as the dissimilarity
parameters are driven down to zero.
The proof of this result is in the Appendix. Theorem 2 justifies
using a GAM when some or all
of the products offered by a vendor are also offered by other
33. vendors, and customers have a good
idea of the price and convenience of buying from different
vendors. The model may also be a
reasonable approximation when products in a nest are close
substitutes, e.g., when the correlations
are high but not equal to one. Although we have cast the
justification as a model that arises from
external competition, the GAM also arises as the limit of a NL
model where a firm has multiple
versions of products in a nest. At the limit, customers select the
product with the highest attraction
within each nest. Removing the product with the highest
attraction from a nest shifts part of the
demand to the product with the second highest attraction , and
part to the no-purchase alternative.
Consequently a GAM of this form can be used in Revenue
Management to model buy up behavior
when there are no fences, and customers either buy the lowest
available fare for each product or
do not purchase.
2.3. Limitation and Heuristic Uses of the GAM
One limitation of the GAM as we propose it is that, in practice,
the attraction and shadow attrac-
34. tion values may depend on a set of covariates that may be
customer or product specific. This can be
dealt with either by assuming a latent class model on the
population of customers or by assuming
a customer specific random set of coefficients to capture the
impact of the covariates. This results
in a mixture of GAMs. The issues also arise when using the
BAM. In practice, often a single BAM
is used to try to capture the choice probabilities of customers
that may come from different market
segments. This stretches both models, as this should really be
handled by adding market segments.
However the GAM can cope much better with this situation as
the following example illustrates.
Example 1: Suppose there are two stores (denoted l), and each
store attracts half of the
population. We will assume that there are two products (denoted
k) and that the GAM parameters
vlk and wlk for the two stores are as given in Table 1:
Gallego, Ratliff, and Shebalov: A General Choice Model and
Network RM Optimization
Article submitted to Operations Research; manuscript no. XX
15
35. v10 v11 v12 v20 v21 v22
w11 w12 w21 w22
1 1 1 1 0.9 0.9
0.9 0.8 0.8 0.7
Table 1 Attraction Values (v,w)
With this type of information we can use the GAM to compute
choice probabilities πj(S) that
a customer will purchase product j ∈ S from Store 1 when Store
1 offers set S, and Store 2 offers
set R = {1,2}. Suppose Store 1 has observed selection
probabilities for different offer sets S as
provided in Table 2:
S π0(S) π1(S) π2(S)
∅ 100% 0% 0%
{1} 82.1% 17.9% 0%
{2} 82.8% 0.0% 17.2%
{1,2} 66.7% 16.7% 16.7%
Table 2 Observed πj (S,R) for R = {1,2}
To estimate these choice probabilities using a single market
GAM we found the values of
vk,wk,k = 1,2 with v0 = 1 that minimizes the sum of squared
errors of the predicted probabilities.
This results in the GAM model: v0 = 1, v1 = v2 = 0.25, w1 =
0.20 and w2 = 0.15. This model per-
36. fectly recovers the probabilities in Table 2. However, when
limited to the BAM, the largest error
is 1.97% in estimating π0({1,2}).
This improved ability to fit the data comes at a cost because the
GAM requires estimating w in
addition to v. As we will see in the next section, it is possible to
estimate the v and w from the
store’s offer sets and sales data. We will assume, as in any
estimation of discrete choice modeling,
that the same choice model prevails over the collected data set.
If this is not the case, then the
estimation should be done over a subset of the data where this
assumption holds. As such, we do
not require information about what the competitors are offering,
only that their offer sets do not
vary over the data set. This is an implicit assumption made
when estimating any discrete choice
model. The output of the estimation provides the store manager
an indication of which products
face more competition by looking at the resulting estimates of
the ratios θi = wi/vi. Over time,
Gallego, Ratliff, and Shebalov: A General Choice Model and
Network RM Optimization
37. 16 Article submitted to Operations Research; manuscript no.
XX
a firm can estimate parametric or full GAM models that take
into account what competitors are
offering and then update their choice models dynamically
depending on what the competition is
doing.
2.4. GAM Estimation and Examples
It is possible to estimate the parameters of the GAM by refining
and extending the Expectation
Maximization method developed by VvRR (Vulcano et al.
(2012)) for the BAM. Readers not
interested in estimation can skip to Section 3. We assume that
demands in periods t = 1,.. .,T arise
from a GAM with parameters v and w and arrival rates λt = λ
for t = 1,.. .,T . The homogeneity
of the arrival rates is not crucial. In fact the method described
here can be extended to the case
where the arrival rates are governed by co-variates such as the
day of the week, seasonality index,
and indicator variables of demand drivers such as conferences,
concerts or other events that can
influence demand. Our main purpose here is show that it is
possible to estimate demands fairly
38. accurately. The data are given by the offer sets St ⊂N and the
realized sales zt ⊂Zn+, excluding the
unobserved value of the customers who chose the no-purchase
alternative, for t = 1,.. .,T . VvRR
assume that the market share s = πN(N), when all products are
offered, is known. While we do
not make this assumption here, we do present results with and
without knowledge of s.
VvRR update estimates of v by estimating demands for each of
the products in N when some of
them are not offered. To see how this is done, consider a
generic period with offer set S ⊂N,S 6= N
and realized sales vector Z = z. Let Xj be the demand for
product j if set N instead of S was
offered. We will estimate Xj conditioned on Z = z. Consider
first the case j /∈ S. Since Xj is
Poisson with parameter λπj(N), substituting the MLE estimate λ̂
= e
′z/πS(S) of λ we obtain the
estimate X
̂ j = λ̂πj(N) =
πj (N)
πS (S)
e′z. We could use a similar estimate for products j ∈ S but this
would
39. disregard the information zj. For example, if zj = 0 then we
know that the realization of Xj was
zero as customers had product j available for sale. We can think
of Xj, conditioned on (S,z) as a
binomial random variable with parameters zj and probability of
selection πj(N)/πj(S). In other
words, each of the zj customers that selected j when S was
available, would have selected j anyway
Gallego, Ratliff, and Shebalov: A General Choice Model and
Network RM Optimization
Article submitted to Operations Research; manuscript no. XX
17
with probability πj(N)/πj(S). Then X
̂ j =
πj (N)
πj (S)
zj is just the expectation of the binomial. Notice
that X
̂ [1,n] =
∑m
i=1
X
̂ j =
e′z
πS (S)
πN(N) = λ̂s. We can find X
̂ 0 by treating it as j /∈ S resulting in
40. X
̂ 0 =
π0(N)
πS (S)
e′z = λ̂(1−s). We summarize the results in the following
proposition:
Proposition 1. (VvRR extended to the GAM): If j ∈ S then
X
̂ j =
πj(N)
πj(S)
zj.
If j /∈ S or j = 0 we have
X
̂ j =
πj(N)
πS(S)
e′z.
Moreover, X
̂ [1,n] =
∑
j∈N X
̂ j =
πN (N)
πS (S)
e′z.
VvRR use the formulas for the BAM to estimate the parameters
λ,v1,.. .,vn under the assump-
tion that the share s = v(N)/(1 + v(N)) is known. From this they
41. use an E-M method to iterate
between estimating the X
̂ js given a vector v and then optimizing
the likelihood function over v
given the observations. The MLE has a closed form solution so
the updates are given by v̂ j = X
̂ j/X
̂ 0
for all j ∈N, where X
̂ 0 = rX
̂ [1,n] and r = 1/s−1. VvRR use
results in Wu (1983) to show that
the method converges. We now propose a refinement of the
VvRR method that can significantly
reduce the estimation errors.
Using data (St,zt),t = 1... ,T, VvRR obtain estimates X
̂ tj that are
then averaged over the T
observations for each j. In effect, this amounts to pooling
estimators from the different sets by
giving each period the same weight. When pooling estimators it
is convenient to take into account
the variance of the estimators and give more weight to sets with
smaller variance. Indeed, if we
have T different unbiased estimators of the same unknown
parameter, each with variance σ2t , then
giving weights proportional to the inverse of the variance
minimizes the variance of the pooled
estimator. Notice that the variance of X
̂ tj is proportional to
1/πj(St) if j ∈ St and proportional to
42. 1/πSt (St) otherwise. Let atj = πj(St) if j ∈ St and atj = πSt (St)
if j /∈ St. We can select the set the
weights for product j as
ωtj =
atj∑T
s=1
asj
.
Gallego, Ratliff, and Shebalov: A General Choice Model and
Network RM Optimization
18 Article submitted to Operations Research; manuscript no.
XX
Our numerical experiments suggests that using this weighting
scheme reduces the variance of the
estimators by about 4%.
To extend the procedure to the GAM we combine ideas of the
EM method based on MLEs and
least squares (LS). It is also possible to refine the estimates by
using iterative re-weighted least
squares (Green (1984) and Rubin (1983)) but our computational
experience shows that there is
little benefit from doing this. To initialize the estimation we use
formulas for the expected sales
43. under St,t = 1,. ..,T for arbitrary parameters λ,v and w. More
precisely, we estimate E[Ztj] by
λπj(St) = λ
vj
v0 + V (S) + W(S
̄ )
j ∈ St, t∈ {1,.. .,T}.
We then minimize the sum of squared errors between estimated
and observed sales (zts):
T∑
t=1
∑
i∈ St
[
λ
vj
v0 + V (S) + W(S
̄ )
−zti
]2
,
subject to the constraints 0 ≤ w ≤ v and λ ≥ 0. This is equivalent
to maximizing the likelihood
function ignoring the unobserved values of the no-purchase
alternative zt0.
This gives us an initial estimate λ(0),v(0),w(0) and an initial
44. estimate of the market share s(0) =
v(0)(N)/(1 + v(0)(N)). Let r(0) = 1/s(0) − 1. If s is known then
we add the constraint v(N) = r =
1/s−1. Given estimates of v(k) and w(k) the procedure works as
follows:
E-step: Estimate the first choice demands X
̂
(k)
tj and then aggregate over time using the current
estimate of the weights α
(k)
tj to produce X
̂
(k)
j =
∑T
t=1
X
̂
(k)
tj α
(k)
tj and X
̂
(k)
0 = r
(k)X
̂ (k)[1,n] and update
the estimates of v by
45. v
(k+1)
j =
X
̂
(k)
j
X
(k)
0
j ∈ N.
M-step: Feed v(k+1) together with arbitrary λ and w to estimate
sales under St,t = 1,.. .,T and
minimize the sum of squared errors between observed and
expected sales over λ and w subject to
w≤v(k+1) and non-negativity constraint to obtain updates
λ(k+1), w(k+1) and s(k+1).
The proof of convergence is a combination of the arguments in
Wu, as in VvRR, and the fact
that the least squared errors problem is a convex minimization
problem. The case when s is known
Gallego, Ratliff, and Shebalov: A General Choice Model and
Network RM Optimization
Article submitted to Operations Research; manuscript no. XX
19
46. works exactly as above, except that we do not need to update
this parameter. The M-step can be
done by solving the score equations:
∑
t∈ Ai
πi(St)[e
′zt + λπ0(St)]−
∑
t∈ Ai
zti = 0 i = 1,.. .,n,
∑
t/∈ Ai
π̂i(St)[e
′zt + λπ0(St)]−λ
∑
t/∈ Ai
π̂i(St) = 0 i = 1,.. .,n.
and
T∑
t=1
πSt (St)−
T∑
t=1
e′zt/λ = 0,
47. where Ai is the set of periods where product i is offered and
π̂i(St) =
vi
1 + V (St) + W(S
̄ t)
t /∈ Ai.
This is a system of up to 2n + 1 equations on 2n + 1 unknowns.
Attempting to solve the score
equations directly or through re-weighted least squares does not
materially improve the estimates
relative to the least square procedure described above.
We now present three examples to illustrate how the procedure
works in three different cases:
1) w = 0 corresponding to the BAM, 2) w = θv corresponding to
the (parsimonious) p-GAM, and
3) 0 6= w≤v corresponding to the GAM. These examples are
based on Example 1 in VvRR. The
examples involve five products and 15 periods where the set N
= {1,2,3,4,5} was offered in four
periods, set {2,3,4,5} was offered in two periods, while sets
{3,4,5},{4,5} and {5} were each
offered in three periods. Notice that product 5 is always offered
making it impossible to estimate
w5. On the other hand, estimates of w5 would not be needed
48. unless the firm planned to not offer
product 5.
In their paper, VvRR present the estimation results for a
specific realization of sales zt,t =
1,.. .,T = 15 corresponding to the 15 offer sets St,t = 1,. ..,15.
We instead generate 500 simulated
instances of sales, each over 15 periods, and then compute our
estimates for each of the 500
simulations. We report the mean and standard deviation of λ, v
and either θ or w over the 500
Gallego, Ratliff, and Shebalov: A General Choice Model and
Network RM Optimization
20 Article submitted to Operations Research; manuscript no.
XX
simulations. We feel these summary statistics are more
indicative of the ability of the method
to estimate the parameters. We report results when s (historical
market share) is assumed to be
known, as in Vulcano et al. (2012), and some results for the
case when s is unknown (see 1. in the
endnotes).
Estimates of the model parameters tend to be quite accurate
when s is known and the estimation
49. of λ and v become more accurate when w 6= 0. The results for s
unknown tend to be accurate when
w = 0 but severely biased when w 6= 0. The bias is positive for
v and w and negative for λ. Since it is
possible to have biased estimates of the parameters but accurate
estimates of demands, we measure
how close the estimated demands λ̂π̂i(S) = λ̂
v̂ i
1+v̂ (S)+ŵ(S
̄ )
i∈ S, S ⊂N are from the true expected
demands λπi(S), i∈ S, S ⊂N and also how close the estimated
demands λ̂π̂i(St) i∈ St,t = 1,.. .,T
are from sales zti,i∈ St,t = 1,.. .,T . These measures are reported,
respectively, as the Model Mean
Squared Error (M-MSE ) and the traditional Mean Squared
Error (MSE) between the estimates
and the data. Surprisingly the results with unknown s, although
strongly biased in terms of the
model parameters, often produce M-MSEs and MSEs that are
similar to the corresponding values
when s is known.
Example 2 (BAM) In the original VvRR example, the true value
of w is 0. The estimates with
50. s known and s unknown as well as the true values of the
parameters are given in Table 3.
s λ v1 v2 v3 v4 v5
known 50.27 0.988 0.700 0400 0.200 0.050
unknown 51.26 1.212 0.818 0.449 0.219 0.053
true 50.00 1.000 0.700 0.400 0.200 0.050
Table 3 Estimated values of λ and v with s known
The MSE and the M-MSE were respectively 247.50 and 58.44,
for both the case of s known and
unknown.
Example 3 (P-GAM) For this example v is the same as above
but w = θv with θ = 0.20. The
results are given in Table 4. Notice that the estimate of θ is
more accurate for the case of s unknown.
Clearly the estimated values with s known are much closer to
the actual values. However, the fit
to the model and to data for the case of s unknown is similar to
the case of s known. Indeed, the
Gallego, Ratliff, and Shebalov: A General Choice Model and
Network RM Optimization
Article submitted to Operations Research; manuscript no. XX
21
s λ v1 v2 v3 v4 v5 θ
known 50.12 0.988 0.702 0.397 0.201 0.051 0.238
51. unknown 4.390 0.111 0.079 0.062 0.035 0.014 0.219
true 50.00 1.000 0.700 0.400 0.200 0.050 0.200
Table 4 Estimated values of λ,v and θ with s known
MSE and the M-MSE were respectively 226.2 and 50.37 for the
case of s known and 228.54 and
53.84, respectively, for the case of s unknown. This suggests
that the parameter values that can be
far from the true parameters and yet have a sufficiently close fit
to the model and to the data.
Example 4 (GAM) For this example λ and v are as above, and w
= (0.25,0.35,0.15,0.05,0.05).
The results are given in Table 5.
s λ v1 v2 v3 v4 v5 w1 w2 w3 w4 w5
known 50.19 0.994 0.700 0.404 0.202 0.051 0.321 0.288 0.186
0.106 0.010
true 50.00 1.000 0.700 0.400 0.200 0.050 0.250 0.350 0.150
0.050 0.050
Table 5 Estimated values of λ,v and w with s known and
unknown
Notice that the estimated values of λ and v for the case of v
known are better under the GAM
than for the case w = 0 or w = θv. The MSE and M-MSE are
respectively 204.71 and 48.56 for the
case of s known. The estimates of the parameters are severely
biased when s is unknown so are not
52. reported. However, the MSE and M-MSE were respectively,
203.70 and 54.33, a surprisingly good
fit to data. This again suggests that there is a ridge of parameter
values that fit the data and the
model well.
3. Stochastic Revenue Management over a Network
In this section we present the formulation for the stochastic
revenue management over a network.
We will assume that there are L customer market segments and
that customers in a particular
market segment are interested in a specific set of itineraries and
fares (see 2. in the endnotes) from
a set of origins to one or more destinations. For example, a
market segment could be morning
flights from New York to San Francisco that are less than $500,
or all flights from New York
City to the Mexican Caribbean. Notice that there may be
multiple fares with different restrictions
associated with each itinerary. At any time the set of origin-
destination-fares (ODFs) offered for
Gallego, Ratliff, and Shebalov: A General Choice Model and
Network RM Optimization
53. 22 Article submitted to Operations Research; manuscript no.
XX
sale to market segment l is a subset Sl ⊂Nl,l∈ L = {1,.. .,L}
where Nl is the consideration set for
market segment l∈ L with associated fares plk, for each product
k in nest Nl. If the consideration
sets are non-overlapping over the market segments then there is
no need to add further restrictions
to the offered sets. This is also true when consideration sets
overlap if the capacity provider is free
to independently decide what fares to offer in each market. As
an example, round-trips from the
US to Asia are sold both in Asia and the US. If the carrier can
charge different fares depending
on whether the customer buys the fare in the US or in Asia, then
no further restrictions are
needed. Otherwise, he needs to impose restrictions so that the
same set of products is offered in
both markets. One way to handle this is to post a single offer set
S at a time, so then use the
projection subsets Sl = S ∩Nl for all markets l that are
constrained to offers the same price for
offered fares. Customers in market segment l select from Sl and
the no-purchase alternative. We
54. will abuse notation slightly and write πlk(Sl) to denote the
probability of selecting product k∈ Sl+
from market segment l. For convenience we define πlk(Sl) = 0 if
k /∈ Sl+.
The state of the system will be denoted by (t,x) where t is the
time-to-go and x is an m-
dimensional vector representing remaining inventories. The
initial state is (T,c) where T is the
length of the horizon and c is the initial inventory capacity. For
ease of exposition we will assume
that customers arrive to market segment l as a Poisson process
with time homogeneous rate λl.
We will denote by J(t,x) the maximum expected revenues that
can be obtained from state (t,x).
The Hamilton-Jacobi-Bellman (HJB) equation is given by
∂J(t,x)
∂t
=
∑
l∈ L
λl max
Sl⊂Nl
∑
k∈ Sl
55. πlk(Sl) (plk −∆lkJ(t,x)) (5)
where ∆lkJ(t,x) = J(t,x)−J(t,x−Alk), where Alk is the vector of
resources consumed by k∈ Nl
(e.g. flight legs on a connecting itinerary class). The boundary
conditions are J(0,x) = 0 and
J(t,0) = 0. Talluri and van Ryzin (2004) developed the first
stochastic, choice-based, dependent
demand model for the single resource case in discrete time. The
first choice-based, network
formulation is due to Gallego et al. (2004).
Gallego, Ratliff, and Shebalov: A General Choice Model and
Network RM Optimization
Article submitted to Operations Research; manuscript no. XX
23
4. The Choice Based Linear Program
An upper bound J̄ (T,c) on the value function J(T,c) can be
obtained by solving a deterministic
linear program. The justification for the bound can be obtained
by using approximate dynamic
programming with affine functions.
We now introduce additional notation to write the linear
program with value function J̄ (T,c) ≥
56. J(T,c). Let πl(Sl) be the nl = |Nl|-dimensional vector with
components πlk(Sl),k ∈ Nl. Clearly
πl(Sl) has zeros for all k /∈ Sl. The vector πl(Sl) gives us the
probability of sale for each fare in Nl
per customer when we offer set Sl. Let rl(Sl) = p
′
lπl(Sl) =
∑
k∈ Nl
plkπlk(Sl) be the revenue rate per
customer associated with offering set Sl ⊂Nl where pl =
(plk)k∈ Nl is the fare vector for segment
l∈ L. Notice that πl(∅ ) = 0 ∈ <nl and rl(∅ ) = 0 ∈ <. Let Alπl(Sl)
be the consumption rate associated
with offering set Sl ⊂Nl where Al is a matrix with columns Alj
associated with ODF j ∈ Nl.
The choice based deterministic linear program (CBLP) for this
model can be written as
J̄ (T,c) = max
∑
l∈ LλlT
∑
Sl⊂Nl
rl(Sl)αl(Sl)
57. subject to
∑
l∈ LλlT
∑
Sl⊂Nl
Alπl(Sl)αl(Sl) ≤c∑
Sl⊂Nl
αl(Sl) = 1 l∈ L
αl(Sl) ≥ 0 Sl ⊂Nl l∈ L.
(6)
The decision variables are αl(Sl),Sl ⊂ Nl,l ∈ L which represent
the proportion of time that set
Sl ⊂Nl is used. The case of non-homogeneous arrival rates can
be handled by replacing λlT by∫ T
0
λlsds. There are
∑
l∈ L 2
nl decision variables. Gallego et al. (2004) showed that J(T,c) ≤
J̄ (T,c)
and proposed an efficient column generation algorithm for a
class of attraction models that
includes the BAM. This formulation has been used and analyzed
by other researchers including
58. Bront et al. (2009), Kunnumkal and Topaloglu (2010),
Kunnumkal and Topaloglu (2008), Liu and
van Ryzin (2008) and Zhang and Adelman (2009).
5. The Sales Based Linear Program for the GAM
In this section we will present a linear program that is
equivalent to the CBLP for the GAM, but
is much smaller in size (essentially the same size as the well
known IDM) and easier to solve (as
Gallego, Ratliff, and Shebalov: A General Choice Model and
Network RM Optimization
24 Article submitted to Operations Research; manuscript no.
XX
it avoids the need for column generation). The new formulation
is called the sales based linear
program (SBLP) because the decision variables are sales
quantities. The number of variables in
the formulation is
∑
l∈ L(nl + 1), where xlk,k = 0,1.. .,nl,l∈ L represents the sales of
product k in
market segment l. Let the aggregate market demand for segment
l be denoted by Λl = λlT,l∈ L
(or
59. ∫ T
0
λlsds if the arrival rates are time varying) inclusive of the no-
purchase alternative. With
this notation the formulation of the SBLP is given by:
R(T,c)= max
∑
l∈ L
∑
k∈ Nl
plkxlk
subject to
capacity :
∑
l∈ L
∑
k∈ Nl
Alkxlk ≤ c
balance :
ṽl0
vl0
xl0 +
∑
k∈ Nl
60. ṽlk
vlk
xlk = Λl l∈ L
scale :
xlk
vlk
− xl0
vl0
≤ 0 k∈ Nl l∈ L
non-negativity: xlk ≥ 0 k∈ Nl l∈ L
(7)
Theorem 3. If each market segment πlj(Sl) is of the GAM form
(2) then J̄ (T,c) = R(T,c).
We demonstrate the equivalence of the CBLP and SBLP
formulations by showing that the SBLP
is a relaxation of the CBLP and then proving that the dual of the
SBLP is a relaxation of the dual
of the CBLP. Full details of this proof may be found in the
Appendix.
The intuition behind the SBLP formulation is as follows. Our
decision variables represent the
amount of inventory to allocate for sales across ODFs for
different market segments. The objective
is to maximize revenues. Three types of constraints are
required. The capacity constraints limit
61. the sum of the allocations. The balance constraints ensure that
the sale allocations are in certain
hyperplanes, so when some service classes are closed for sale,
the demands for the remaining open
service classes (including the null alternative) changes
dependently; they must be modified to offset
the amount of the closed demands. The scale constraints operate
on the principle that demands
are rescaled depending on both the availability and the
attractiveness of other items in the choice
set.
The decision variables xl0 play an important role in the SBLP.
Since the null alternative has
positive attractiveness and is always available, the dependent
demand for any service class is
Gallego, Ratliff, and Shebalov: A General Choice Model and
Network RM Optimization
Article submitted to Operations Research; manuscript no. XX
25
upper bounded based on its size relative to the null alternative.
The scale constraints imply that
xlk/vlk ≤ xl0/vl0. Therefore, the scale constraints favor a large
value of xl0. On the other hand,
62. the balance constraint can be written as
∑
k∈N ṽlkxlk/vlk ≤ Λl − ṽl0xl0/vl0, favoring a small value
of xl0. The LP solves for this tradeoff taking into account the
objective function and the capacity
constraint. We will have more to say about xl0 in the absence of
capacity constraints in Section 6.
The combination of the balance and scale constraints ensures
that GAM properties are compactly
represented in the optimizer and that the correct ratios are
maintained between the sizes of each
of the open alternatives.
For the BAM the demand balance constraint simplifies to xl0 +
∑
k∈ Nl
xlk = Λl. For the inde-
pendent demand case, ṽl0 = vl0 +
∑
k∈ Nl
vlk and ṽlk = 0 for k∈ Nl. The balance constraint reduces
to xl0 = (vl0/ṽl0)Λl, and the scale constraint becomes xlk ≤
(vlk/ṽl0)Λl,k ∈ Nl, so clearly xl0 +∑
k∈ Nl
63. xlk ≤ Λl.
We remark that the CBLP and therefore the SBLP can be
extended to multi-stage problems
since the inventory dynamics are linear. This allows for
different choice models of the GAM family
to be used in different periods and is the typical approach in
practice.
5.1. Recovering the
Solution
for the CBLP
So we have learned that the SBLP problem is much easier to
solve and provides the same revenue
performance as the CBLP. However, there are some
circumstances (described later in this section)
in which it is more desirable to use the CBLP solution. The
reader may wonder whether it is
possible to recover the solution to the CBLP from the solution
to the SBLP. In other words, is it
64. possible to obtain a collection of offer sets {S : α(S) > 0} that
solves the CBLP from the solution
xlk,k ∈ Nl,l ∈ L of the SBLP? The answer is yes, and the method
presented here for the GAM
is inspired by Topaloglu et al. (2011) who used our SBLP
formulation and presented a method
to recover the solution to the CBLP for the BAM. When used
with the GAM, recovering the
CBLP solution is important because solutions in terms of
assortments tend to be more robust then
solutions in terms of sales. Indeed, our experience is that when
GAM parameters are estimated,
Gallego, Ratliff, and Shebalov: A General Choice Model and
Network RM Optimization
26 Article submitted to Operations Research; manuscript no.
XX
65. the solution in terms of sales can be fairly far from the solution
with known parameters, whereas
the solution in terms of assortments tends to be much closer.
In this section we will show how to obtain the solution of the
CBLP from the SBLP and will also
show that for each market segment the offered sets are nested in
the sense that there exist subsets
Slk increasing in k with positive weights. The products in the
smallest set are core products that
are always offered. Larger sets contain additional products that
are only offered part of the time.
The sorting of the products is not by revenues, but by the ratio
of xlk/vlk for all k∈ Nl ∪ {0} for
each l∈ L. We then form the sets Sl0 = ∅ and Slk = {1,. ..,k} for
k = 1,.. .,nl, where nl = |Nl| is
the cardinality of Nl. For k = 0,1,.. .,nl, let
66. αl(Slk) =
(
xlk
vlk
−
xl,k+1
vl,k+1
)
Ṽ (Slk)
Λl
,
where for convenience we define xl,nl+1/vl,nl+1 = 0. Set αl(Sl)
= 0 for all Sl ⊂Nl not in the col-
lection Sl0,Sl1,.. .,Slnl . It is then easy to verify that αl(Sl) ≥ 0,
that
∑
Sl⊂Nl
αl(Sl) = 1, and that∑
67. Sl⊂Nl
αl(Sl)πlk(Sl) = xlk. Applying this to the CBLP we can
immediately see that all constraints
are satisfied, and the objective function coincides with that of
the SBLP. Notice that for each
market segment the offered sets are nested Sl0 ⊂Sl1 ⊂ .. .⊂Slnl
, and that set Slk is offered for a
positive fraction of time if and only if xlk/vlk > xl,k+1/vl,k+1.
Unlike the BAM and the IDM, the
sorting order of products under the GAM is not necessarily
revenue ordered. This is because fares
that face more competition (wlj close to vlj) are more likely to
be offered even if their corresponding
fares are low.
5.2. Bounds and Numerical Examples
In this section we present two results that relate the solutions to
68. the extreme cases w = 0 and w = v
to the case 0 ≤w≤v. The proofs of the propositions are in the
Appendix.
The reader may wonder whether the solution that assumes wj =
0 for all j ∈ N is feasible when
wj ∈ (0,vj) j ∈ N . The following proposition confirms and
generalizes this idea.
Gallego, Ratliff, and Shebalov: A General Choice Model and
Network RM Optimization
Article submitted to Operations Research; manuscript no. XX
27
Proposition 2. Suppose that αl(Sl),Sl ⊂ Nl,l ∈ L is a solution to
the CBLP for the GAM for
fixed vlk,k ∈ Nl+,l∈ L and wlk ∈ [0,vlk],k ∈ Nl,l∈ L. Then
αl(Sl),Sl ⊂Nl,l∈ L is a feasible, but
suboptimal, solution for all GAM models with w′lk ∈
69. (wlk,vlk],k∈ Nl,l∈ L.
An easy consequence of this proposition is that if αl(Sl),l ∈ L is
an optimal solution for the
CBLP under the BAM, then it is also a feasible, but suboptimal,
solution for all GAMs with
wk ∈ (0,vk]. This implies that the solution to the BAM is a
lower bound on the revenue for the
GAM with wk ∈ (0,vk] for all k.
As mentioned in the introduction, the IDM underestimates
demand recapture. As such optimal
solutions for the SBLP under the IDM are feasible but
suboptimal solutions for the GAM. The
following proposition generalizes this notion.
Proposition 3. Suppose that xlk,k ∈ Nl,l∈ L is an optimal
solution to the SBLP for the GAM
for fixed vlk,k∈ Nl+ and wlk ∈ [0,vlk],k∈ Nl,l∈ L. Then
70. xlk,k∈ Nl+,l∈ L is a feasible solution for
all GAM models with w′lk ∈ [0,wlk],k∈ Nl,l∈ L with the same
objective function value.
An immediate corollary is that if xlk,k ∈ Nl,l∈ L is an optimal
solution to the SBLP under the
independent demand model then it is also a feasible solution for
the GAM with wk ∈ [0,vk] with
the same revenue as the IDM. This implies that the solution to
the IDM is another lower bound
on the GAM with wk ∈ [0,vk] for all k.
Example 5: The following example problem was originally
reported in Liu and van Ryzin (2008).
There are three flights AB,BC and AC. All customers depart
from A with destinations to either
B or C. The relevant itineraries are therefore AB,ABC and AC.
For each of these itineraries
71. there are two fares (high and low) and three market segments.
Market segment 1 are customers
who travel to B. Market segment 2 are customers who travel to
C but only at a high fare. Market
segment 3 are customers who travel to C but only at the low
fare. The six fares as well as vlj,j ∈ Nl
and vl0 for l = 1,2,3 are given in Table 6. The arrivals are
uniformly distributed over a horizon of
T = 15, and the expected market sizes are Λ1 = 6,Λ2 = 9,Λ3 =
15 and that capacity c = (10,5,5)
for flights AB, BC and AC.
Gallego, Ratliff, and Shebalov: A General Choice Model and
Network RM Optimization
28 Article submitted to Operations Research; manuscript no.
XX
1 2 3 4 5 6 0
72. Products ACH ABCH ABH ACL ABCL ABL Null
Fares $1,200 $800 $600 $800 $500 $300
(AB,v1j) 5 8 2
(AChigh,v2j) 10 5 5
(AClow,v3j) 5 10 10
Table 6 Market Segment and Attraction Values v
In this example we will consider the parsimonious p-GAM
model wlj = θvlj for all j ∈ Nl,l ∈
{1,2,3} for values of θ ∈ [0,1]. We will assume that the vlj
values are known for all j ∈ Nl,l ∈
{1,2,3}, but the BAM and the IDM use the extreme values θ = 0
and θ = 1, while the GAM uses
the correct value of θ. This situation may arise if the model is
calibrated based on sales when all
products are offered, e.g., Sl = Nl for all l∈ {1,2,3}. The
objective here is to study the robustness
73. of using the BAM and the IDM to the p-GAM for values of θ ∈
(0,1). The situation where the
parameters are calibrated from data that includes recapture will
be presented in the next example.
The solution to the CBLP for the BAM is given by α({1,2,3}) =
60%, α({1,2,3,5}) = 23.3% and
α({1,2,3,4,5}) = 16.7% with α(S) = 0 for all other subsets of
products. Equivalently, the solution
spends 18, 7 and 5 units of time, respectively, offering sets
{1,2,3}, {1,2,3,5} and {1,2,3,4,5}. The
solution results in $11,546.43 in revenues (see 3. in the
endnotes). By Proposition 2, the solution
α({1,2,3}) = 60%, α({1,2,3,5}) = 23.3%, α({1,2,3,4,5}) = 16.7%
is feasible for all θ∈ (0,1] with a
lower objective function value. The corresponding SBLP
solution is shown in Table 7 and provides
the same revenue outcome as the CBLP.