Draft Two:
This report looks at one approach to the standard scheduling problem by constructing a model for use by high schools and small colleges/universities. This iteration of the model builds up an integer programming optimization model, aiming to maximize credit hours following constraints: 1) required class hours per course-week; 2) instructor preference for teaching-free days; 3) restricting group-room assignments to Integer: (0,1); 4) restricting number of instructors per group-room to Integer:(0,1); and other constraints. The model searches through two thousand variable fields: 1) ten instructors; with potential to occupy: 2) eight group-room assignments; over 3) five potential course time slots per day; over five days each week – vis. 10 X 8 X 5 X 5. But the model has capability beyond the two thousand variables. For instance, if the system limits a department teaching hours to two time slots per day (or different days), the system could accommodate several departments to minimize scheduling conflicts while maximizing satisfaction for instructors and students.
This project uses the robust solver mechanism in OpenSolver, an open source project developed by Andrew Mason in the Department of Engineering Science at the University of Auckland. The standard solver issued with Microsoft Excel is limited to only 200 variable fields. The OpenSolver mechanism does not impose artificial limits to the number of potential variable fields.
Sca a sine cosine algorithm for solving optimization problemslaxmanLaxman03209
The document proposes a new population-based optimization algorithm called the Sine Cosine Algorithm (SCA) for solving optimization problems. SCA creates multiple random initial solutions and uses sine and cosine functions to fluctuate the solutions outward or toward the best solution, emphasizing exploration and exploitation. The performance of SCA is evaluated on test functions, qualitative metrics, and by optimizing the cross-section of an aircraft wing, showing it can effectively explore, avoid local optima, converge to the global optimum, and solve real problems with constraints.
LNCS 5050 - Bilevel Optimization and Machine Learningbutest
This document discusses using bilevel optimization and machine learning techniques to improve model selection in machine learning problems. It proposes framing machine learning model selection as a bilevel optimization problem, where the inner level problems involve optimizing models on training data and the outer level problem selects hyperparameters to minimize error on test data. This bilevel framing allows for systematic optimization of hyperparameters and enables novel machine learning approaches. The document illustrates the approach for support vector regression, formulating model selection as a Stackelberg game and solving the resulting mathematical program with equilibrium constraints.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
BINARY SINE COSINE ALGORITHMS FOR FEATURE SELECTION FROM MEDICAL DATAacijjournal
A well-constructed classification model highly depends on input feature subsets from a dataset, which may contain redundant, irrelevant, or noisy features. This challenge can be worse while dealing with medical datasets. The main aim of feature selection as a pre-processing task is to eliminate these features and select the most effective ones. In the literature, metaheuristic algorithms show a successful performance to find optimal feature subsets. In this paper, two binary metaheuristic algorithms named S-shaped binary Sine Cosine Algorithm (SBSCA) and V-shaped binary Sine Cosine Algorithm (VBSCA) are proposed for feature selection from the medical data. In these algorithms, the search space remains continuous, while a binary position vector is generated by two transfer functions S-shaped and V-shaped for each solution. The proposed algorithms are compared with four latest binary optimization algorithms over five medical datasets from the UCI repository. The experimental results confirm that using both bSCA variants enhance the accuracy of classification on these medical datasets compared to four other algorithms.
This document reviews applications of evolutionary multiobjective optimization (EMO) techniques in production research. It summarizes EMO applications in several areas of production research, including scheduling, production planning and control, cellular manufacturing, flexible manufacturing systems, and assembly-line optimization. The review finds that EMO techniques have been successfully applied to optimization problems in these areas and provide a number of non-dominated solutions. However, future research opportunities remain, such as improved integration of EMO with other metaheuristics and consideration of additional objectives.
An Iterative Model as a Tool in Optimal Allocation of Resources in University...Dr. Amarjeet Singh
In this paper, a study was carried out to aid in
adequate allocation of resources in the College of Natural
Sciences, TYZ University (not real name because of ethical
issue). Questionnaires were administered to the highranking officials of one the Colleges, College of Pure and
Applied Sciences, to examine how resources were allocated
for three consecutive sessions(the sessions were 2009/2010,
2010/2011 and 2011/2012),then used the data gathered and
analysed to generate contributory inputs for the three basic
outputs (variables)formed for the purpose of the study.
These variables are: 1
x
represents the quality of graduates
produced;
2
x
stands for research papers, Seminars,
Journals articles etc. published by faculties and
3
x
denotes service delivery within the three sessions under study.
Simplex Method of Linear Programming was used to solve
the model formulated.
Automatically Estimating Software Effort and Cost using Computing Intelligenc...cscpconf
In the IT industry, precisely estimate the effort of each software project the development cost
and schedule are count for much to the software company. So precisely estimation of man
power seems to be getting more important. In the past time, the IT companies estimate the work
effort of man power by human experts, using statistics method. However, the outcomes are
always unsatisfying the management level. Recently it becomes an interesting topic if computing
intelligence techniques can do better in this field. This research uses some computing
intelligence techniques, such as Pearson product-moment correlation coefficient method and
one-way ANOVA method to select key factors, and K-Means clustering algorithm to do project
clustering, to estimate the software project effort. The experimental result show that using
computing intelligence techniques to estimate the software project effort can get more precise
and more effective estimation than using traditional human experts did
IMPROVED WORKLOAD BALANCING OF THE SCHEDULING JOBS WITH THE RELEASE DATES IN ...IJCSEA Journal
This paper presents the identical parallel machine’s scheduling problem when the jobs are submitted over time. This problem consists of assigning N various jobs to M identical parallel machines to reduce the workload imponderables among the different machines. We generalized the mixed-integer linear programming approach to decrease the workload imbalance between the different machines, and that is done by converting the problem to the mathematical model. The studied cases are presented for different problems, and it indicates to an online system, and this system does not know the arrival times of the jobs before and reduce Makespan criterion is not well appropriate to describe the utilization for this online problem. The obtained results proved good solutions for the scheduling problem compared with standard algorithms.
Sca a sine cosine algorithm for solving optimization problemslaxmanLaxman03209
The document proposes a new population-based optimization algorithm called the Sine Cosine Algorithm (SCA) for solving optimization problems. SCA creates multiple random initial solutions and uses sine and cosine functions to fluctuate the solutions outward or toward the best solution, emphasizing exploration and exploitation. The performance of SCA is evaluated on test functions, qualitative metrics, and by optimizing the cross-section of an aircraft wing, showing it can effectively explore, avoid local optima, converge to the global optimum, and solve real problems with constraints.
LNCS 5050 - Bilevel Optimization and Machine Learningbutest
This document discusses using bilevel optimization and machine learning techniques to improve model selection in machine learning problems. It proposes framing machine learning model selection as a bilevel optimization problem, where the inner level problems involve optimizing models on training data and the outer level problem selects hyperparameters to minimize error on test data. This bilevel framing allows for systematic optimization of hyperparameters and enables novel machine learning approaches. The document illustrates the approach for support vector regression, formulating model selection as a Stackelberg game and solving the resulting mathematical program with equilibrium constraints.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
BINARY SINE COSINE ALGORITHMS FOR FEATURE SELECTION FROM MEDICAL DATAacijjournal
A well-constructed classification model highly depends on input feature subsets from a dataset, which may contain redundant, irrelevant, or noisy features. This challenge can be worse while dealing with medical datasets. The main aim of feature selection as a pre-processing task is to eliminate these features and select the most effective ones. In the literature, metaheuristic algorithms show a successful performance to find optimal feature subsets. In this paper, two binary metaheuristic algorithms named S-shaped binary Sine Cosine Algorithm (SBSCA) and V-shaped binary Sine Cosine Algorithm (VBSCA) are proposed for feature selection from the medical data. In these algorithms, the search space remains continuous, while a binary position vector is generated by two transfer functions S-shaped and V-shaped for each solution. The proposed algorithms are compared with four latest binary optimization algorithms over five medical datasets from the UCI repository. The experimental results confirm that using both bSCA variants enhance the accuracy of classification on these medical datasets compared to four other algorithms.
This document reviews applications of evolutionary multiobjective optimization (EMO) techniques in production research. It summarizes EMO applications in several areas of production research, including scheduling, production planning and control, cellular manufacturing, flexible manufacturing systems, and assembly-line optimization. The review finds that EMO techniques have been successfully applied to optimization problems in these areas and provide a number of non-dominated solutions. However, future research opportunities remain, such as improved integration of EMO with other metaheuristics and consideration of additional objectives.
An Iterative Model as a Tool in Optimal Allocation of Resources in University...Dr. Amarjeet Singh
In this paper, a study was carried out to aid in
adequate allocation of resources in the College of Natural
Sciences, TYZ University (not real name because of ethical
issue). Questionnaires were administered to the highranking officials of one the Colleges, College of Pure and
Applied Sciences, to examine how resources were allocated
for three consecutive sessions(the sessions were 2009/2010,
2010/2011 and 2011/2012),then used the data gathered and
analysed to generate contributory inputs for the three basic
outputs (variables)formed for the purpose of the study.
These variables are: 1
x
represents the quality of graduates
produced;
2
x
stands for research papers, Seminars,
Journals articles etc. published by faculties and
3
x
denotes service delivery within the three sessions under study.
Simplex Method of Linear Programming was used to solve
the model formulated.
Automatically Estimating Software Effort and Cost using Computing Intelligenc...cscpconf
In the IT industry, precisely estimate the effort of each software project the development cost
and schedule are count for much to the software company. So precisely estimation of man
power seems to be getting more important. In the past time, the IT companies estimate the work
effort of man power by human experts, using statistics method. However, the outcomes are
always unsatisfying the management level. Recently it becomes an interesting topic if computing
intelligence techniques can do better in this field. This research uses some computing
intelligence techniques, such as Pearson product-moment correlation coefficient method and
one-way ANOVA method to select key factors, and K-Means clustering algorithm to do project
clustering, to estimate the software project effort. The experimental result show that using
computing intelligence techniques to estimate the software project effort can get more precise
and more effective estimation than using traditional human experts did
IMPROVED WORKLOAD BALANCING OF THE SCHEDULING JOBS WITH THE RELEASE DATES IN ...IJCSEA Journal
This paper presents the identical parallel machine’s scheduling problem when the jobs are submitted over time. This problem consists of assigning N various jobs to M identical parallel machines to reduce the workload imponderables among the different machines. We generalized the mixed-integer linear programming approach to decrease the workload imbalance between the different machines, and that is done by converting the problem to the mathematical model. The studied cases are presented for different problems, and it indicates to an online system, and this system does not know the arrival times of the jobs before and reduce Makespan criterion is not well appropriate to describe the utilization for this online problem. The obtained results proved good solutions for the scheduling problem compared with standard algorithms.
Optimization Problems Solved by Different Platforms Say Optimum Tool Box (Mat...IRJET Journal
The document discusses using MATLAB and Excel Solver to solve optimization problems in engineering. It provides examples of using these tools to solve linear programming problems, including a purchasing optimization problem maximizing profits. Nonlinear programming problems are also demonstrated, such as quadratic and least squares problems. The key benefits of MATLAB and Excel Solver for optimization problems are their ease of use without requiring an in-depth understanding of mathematical algorithms. They allow students and researchers to efficiently model and solve a variety of optimization problems.
This document provides an overview of Data Envelopment Analysis (DEA), a technique for evaluating the relative efficiencies of decision making units that may have multiple inputs and outputs. It discusses the assumptions and formulations of DEA models, including input-oriented and output-oriented linear programming models. Examples are provided to illustrate DEA applications for banks, supply chains, and clothing shops. The document also compares constant returns to scale and variable returns to scale DEA models and references key papers on the development of DEA.
Computational Aptitude of Handheld Calculatormathsmasters
A Manuscript entitled "Computational Aptitude of Handheld Calculator" can be found at:
This is useful for solving problems in:
Thermodynamics, Mass and Heat Transfer, Engineering Analysis, Accounting and Economics and so on. It has been found useful in Undergraduate and Post graduate level courses. Kindly share with your younger ones.
This document discusses optimization in power systems. Optimization aims to find the maximum and minimum values of functions, and can be used to optimize various systems including power networks, transportation, and more. In power systems specifically, optimization becomes important as systems grow larger and more complex over time due to increasing demand. Optimization techniques can save power utilities hundreds of millions annually through reduced fuel costs and improved reliability while meeting environmental standards. The key goals of optimization in power systems are minimizing generation costs and maximizing social welfare while satisfying operational constraints.
1) The document discusses Data Envelopment Analysis (DEA), a linear programming technique used to evaluate the efficiency of decision-making units like organizations. DEA can handle multiple inputs and outputs to measure efficiency relative to best practices.
2) Transportation problems, which aim to minimize costs in transporting goods from origins to destinations, can be formulated as linear programs and solved using techniques like the simplex method. Initial basic feasible solutions are found using methods like the Northwest Corner Rule.
3) The document provides an example of using DEA and transportation problem solving methods to optimize the allocation of milk transportation from dairy plants to distribution centers to minimize costs.
Download Complete Material - https://www.instamojo.com/prashanth_ns/
This Data Structures and Algorithms contain 15 Units and each Unit contains 60 to 80 slides in it.
Contents…
• Introduction
• Algorithm Analysis
• Asymptotic Notation
• Foundational Data Structures
• Data Types and Abstraction
• Stacks, Queues and Deques
• Ordered Lists and Sorted Lists
• Hashing, Hash Tables and Scatter Tables
• Trees and Search Trees
• Heaps and Priority Queues
• Sets, Multi-sets and Partitions
• Dynamic Storage Allocation: The Other Kind of Heap
• Algorithmic Patterns and Problem Solvers
• Sorting Algorithms and Sorters
• Graphs and Graph Algorithms
• Class Hierarchy Diagrams
• Character Codes
A Comparison between FPPSO and B&B Algorithm for Solving Integer Programming ...Editor IJCATR
This document summarizes and compares two algorithms for solving integer programming problems: branch and bound (B&B) and an improved version of the flower pollination algorithm combined with particle swarm optimization (FPPSO). B&B is commonly used but has high computational costs, while FPPSO is able to obtain optimal results faster than traditional methods like B&B. The FPPSO combines the flower pollination algorithm with particle swarm optimization to improve search accuracy for integer programming problems.
IRJET- Solving Supply Chain Network Design Problem using Center of Gravit...IRJET Journal
This document discusses using a gravity location model to solve a supply chain network design problem for pump manufacturing companies. Specifically, it summarizes using a gravity model to identify optimal geographic locations for new warehouses. The model considers transportation costs from suppliers and to markets to minimize total costs. The authors apply the model to collect geographic data from 4 pump companies and determine new warehouse locations for each that reduce transportation costs and times.
SIMULATION-BASED OPTIMIZATION USING SIMULATED ANNEALING FOR OPTIMAL EQUIPMENT...Sudhendu Rai
The paper describes a software toolkit that enables the data-driven simulation-based optimization of print shops It enables quick modeling of complex print production environments under the cellular production framework. The software toolkit automates several steps of the modeling process by taking declarative inputs from the end-user and then automatically generating complex simulation models that are used to determine improved design and operating points. This paper describes the addition of another layer of automation consisting of simulation-based optimization using simulated-annealing that enables automated search of a large number of design alternatives in the presence of operational constraints to determine a cost-optimal solution. The results of the application of this approach to a real-world problem are also described.
This document discusses functions and their applications. It begins with an introduction that defines a function as a rule that maps an input number to a unique output number. It then provides examples of functions. It discusses applications of functions in real world contexts like tracking location over time. It also discusses applications in computer science and software engineering. Finally, it concludes that polynomials are an important topic in mathematics and provides references and websites for further information.
This document provides economic projections for various commodities from 2015 to 2026, including changes in price, volume, export value, and other metrics. It includes projections for coal, copper concentrate, iron ore, crude oil, zinc ore, non-money gold, calcite, molybdenum, washed cashmere, combed cashmere, and total mineral contributions. For each commodity, it shows the projected annual percentage change in price and volume, as well as total export value. The projections contain values for mean price changes, standard deviation of price changes, and other statistical indicators.
This is the working draft of my original and current research paper reviewing correlations between gold and silver prices and the 90-day forward Mongolian Tugrik : $US foreign exchange rate. The paper suggests that Mongolia is currently on a gold standard. (All rights reserved.)
This chart plots the 90-pay prior Moving Average price of Gold, 90-days prior to the Mongolian Tugrik spot price. In other words, it plots the average gold price from 180 to 90 pays prior of the day's gold price. The regression fit is perhaps too close to be coincidental, with an R-Value (Pearson Correlation) of 0.97 .
This document describes a Monte Carlo analysis of stakeholder interests in the Oyu Tolgoi minerals project in Mongolia. It constructs probabilistic models to forecast copper and gold prices, project revenue and cash flow over 35 years for the project. The analysis estimates the discounted cash flow and net present value for stakeholders, including the Government of Mongolia, Rio Tinto, and Turquoise Hill Resources. The models indicate the government will likely secure over 73% of projected cash flows from the project through royalties, taxes and equity.
The GMIT Biodiesel Project aims to produce biodiesel from waste vegetable oil on a non-profit basis. The project focuses on chemical and mechanical engineering processes involved in biodiesel production, conducting production experiments, and analyzing related costs, safety procedures, and economic feasibility. If successful, the project could provide an alternative fuel source while reducing pollution and waste through recycling used cooking oil.
The document analyzes Mongolia's falling foreign exchange rate from 2012-2016. It examines the relationship between Mongolia's exchange rate and gold prices over time using statistical analysis and charts. It finds their exchange rate has a strong correlation with average past prices of gold, silver, and copper over the previous 90 days. Using this relationship, it creates a regression model that predicts Mongolia's exchange rate 90 days in advance with 96% accuracy based on historic mineral prices. It suggests this model could help Mongolia better predict and manage its macroeconomic environment.
Financial Analysis of Oyu Tolgoi Presented to: OPPORTUNITIES & CHALLENGES: THE CHANGING FACE OF 21ST CENTURY MONGOLIA: AN INTERDISCIPLINARY INTERNATIONAL SYMPOSIUM (IDIS 2014)
Biogen Idec is a leading biotechnology firm that has experienced strong growth through niche pharmaceutical products. However, an analyst's model projects the stock is overvalued given limitations on sustained high growth rates as markets become saturated and competitors increase efforts. The model finds a 73% probability the stock is fairly priced between $180-300 but only 5.25% above $300. The analyst advises taking profits and waiting for new product approvals and guidance.
This document reviews options for Mongolia-based MCS-APB Tiger Brewery to dispose of or utilize brewers spent grains (BSG) in an economic and environmentally-friendly manner. It analyzes both minimal capital investment options like donating or composting BSG, as well as more capital-intensive options like installing biogas production infrastructure. The three most viable options are identified as: 1) Producing methane for energy recovery through anaerobic digestion, 2) Selling or donating BSG to livestock farmers, and 3) Installing a cogeneration facility to produce steam and electricity from BSG. Financial analysis of capital-intensive options like using BSG to produce steam/power
The document provides a feasibility and financial study for a proposed biodiesel production laboratory project at the German-Mongolian Institute for Resources and Technology (GMIT). It discusses the worldwide and local biodiesel industries, analyzes the costs associated with establishing a small-scale biodiesel production facility, and models the financial viability of the proposed GMIT Biodiesel Project. The study concludes that under favorable pricing conditions, the project can sustain itself financially and provide educational benefits to students while also producing value for the local community through recycling of waste vegetable oil into biodiesel and other products.
The operation research book that involves all units including the lpp problems, integer programming problem, queuing theory, simulation Monte Carlo and more is covered in this digital material.
Optimization Problems Solved by Different Platforms Say Optimum Tool Box (Mat...IRJET Journal
The document discusses using MATLAB and Excel Solver to solve optimization problems in engineering. It provides examples of using these tools to solve linear programming problems, including a purchasing optimization problem maximizing profits. Nonlinear programming problems are also demonstrated, such as quadratic and least squares problems. The key benefits of MATLAB and Excel Solver for optimization problems are their ease of use without requiring an in-depth understanding of mathematical algorithms. They allow students and researchers to efficiently model and solve a variety of optimization problems.
This document provides an overview of Data Envelopment Analysis (DEA), a technique for evaluating the relative efficiencies of decision making units that may have multiple inputs and outputs. It discusses the assumptions and formulations of DEA models, including input-oriented and output-oriented linear programming models. Examples are provided to illustrate DEA applications for banks, supply chains, and clothing shops. The document also compares constant returns to scale and variable returns to scale DEA models and references key papers on the development of DEA.
Computational Aptitude of Handheld Calculatormathsmasters
A Manuscript entitled "Computational Aptitude of Handheld Calculator" can be found at:
This is useful for solving problems in:
Thermodynamics, Mass and Heat Transfer, Engineering Analysis, Accounting and Economics and so on. It has been found useful in Undergraduate and Post graduate level courses. Kindly share with your younger ones.
This document discusses optimization in power systems. Optimization aims to find the maximum and minimum values of functions, and can be used to optimize various systems including power networks, transportation, and more. In power systems specifically, optimization becomes important as systems grow larger and more complex over time due to increasing demand. Optimization techniques can save power utilities hundreds of millions annually through reduced fuel costs and improved reliability while meeting environmental standards. The key goals of optimization in power systems are minimizing generation costs and maximizing social welfare while satisfying operational constraints.
1) The document discusses Data Envelopment Analysis (DEA), a linear programming technique used to evaluate the efficiency of decision-making units like organizations. DEA can handle multiple inputs and outputs to measure efficiency relative to best practices.
2) Transportation problems, which aim to minimize costs in transporting goods from origins to destinations, can be formulated as linear programs and solved using techniques like the simplex method. Initial basic feasible solutions are found using methods like the Northwest Corner Rule.
3) The document provides an example of using DEA and transportation problem solving methods to optimize the allocation of milk transportation from dairy plants to distribution centers to minimize costs.
Download Complete Material - https://www.instamojo.com/prashanth_ns/
This Data Structures and Algorithms contain 15 Units and each Unit contains 60 to 80 slides in it.
Contents…
• Introduction
• Algorithm Analysis
• Asymptotic Notation
• Foundational Data Structures
• Data Types and Abstraction
• Stacks, Queues and Deques
• Ordered Lists and Sorted Lists
• Hashing, Hash Tables and Scatter Tables
• Trees and Search Trees
• Heaps and Priority Queues
• Sets, Multi-sets and Partitions
• Dynamic Storage Allocation: The Other Kind of Heap
• Algorithmic Patterns and Problem Solvers
• Sorting Algorithms and Sorters
• Graphs and Graph Algorithms
• Class Hierarchy Diagrams
• Character Codes
A Comparison between FPPSO and B&B Algorithm for Solving Integer Programming ...Editor IJCATR
This document summarizes and compares two algorithms for solving integer programming problems: branch and bound (B&B) and an improved version of the flower pollination algorithm combined with particle swarm optimization (FPPSO). B&B is commonly used but has high computational costs, while FPPSO is able to obtain optimal results faster than traditional methods like B&B. The FPPSO combines the flower pollination algorithm with particle swarm optimization to improve search accuracy for integer programming problems.
IRJET- Solving Supply Chain Network Design Problem using Center of Gravit...IRJET Journal
This document discusses using a gravity location model to solve a supply chain network design problem for pump manufacturing companies. Specifically, it summarizes using a gravity model to identify optimal geographic locations for new warehouses. The model considers transportation costs from suppliers and to markets to minimize total costs. The authors apply the model to collect geographic data from 4 pump companies and determine new warehouse locations for each that reduce transportation costs and times.
SIMULATION-BASED OPTIMIZATION USING SIMULATED ANNEALING FOR OPTIMAL EQUIPMENT...Sudhendu Rai
The paper describes a software toolkit that enables the data-driven simulation-based optimization of print shops It enables quick modeling of complex print production environments under the cellular production framework. The software toolkit automates several steps of the modeling process by taking declarative inputs from the end-user and then automatically generating complex simulation models that are used to determine improved design and operating points. This paper describes the addition of another layer of automation consisting of simulation-based optimization using simulated-annealing that enables automated search of a large number of design alternatives in the presence of operational constraints to determine a cost-optimal solution. The results of the application of this approach to a real-world problem are also described.
This document discusses functions and their applications. It begins with an introduction that defines a function as a rule that maps an input number to a unique output number. It then provides examples of functions. It discusses applications of functions in real world contexts like tracking location over time. It also discusses applications in computer science and software engineering. Finally, it concludes that polynomials are an important topic in mathematics and provides references and websites for further information.
This document provides economic projections for various commodities from 2015 to 2026, including changes in price, volume, export value, and other metrics. It includes projections for coal, copper concentrate, iron ore, crude oil, zinc ore, non-money gold, calcite, molybdenum, washed cashmere, combed cashmere, and total mineral contributions. For each commodity, it shows the projected annual percentage change in price and volume, as well as total export value. The projections contain values for mean price changes, standard deviation of price changes, and other statistical indicators.
This is the working draft of my original and current research paper reviewing correlations between gold and silver prices and the 90-day forward Mongolian Tugrik : $US foreign exchange rate. The paper suggests that Mongolia is currently on a gold standard. (All rights reserved.)
This chart plots the 90-pay prior Moving Average price of Gold, 90-days prior to the Mongolian Tugrik spot price. In other words, it plots the average gold price from 180 to 90 pays prior of the day's gold price. The regression fit is perhaps too close to be coincidental, with an R-Value (Pearson Correlation) of 0.97 .
This document describes a Monte Carlo analysis of stakeholder interests in the Oyu Tolgoi minerals project in Mongolia. It constructs probabilistic models to forecast copper and gold prices, project revenue and cash flow over 35 years for the project. The analysis estimates the discounted cash flow and net present value for stakeholders, including the Government of Mongolia, Rio Tinto, and Turquoise Hill Resources. The models indicate the government will likely secure over 73% of projected cash flows from the project through royalties, taxes and equity.
The GMIT Biodiesel Project aims to produce biodiesel from waste vegetable oil on a non-profit basis. The project focuses on chemical and mechanical engineering processes involved in biodiesel production, conducting production experiments, and analyzing related costs, safety procedures, and economic feasibility. If successful, the project could provide an alternative fuel source while reducing pollution and waste through recycling used cooking oil.
The document analyzes Mongolia's falling foreign exchange rate from 2012-2016. It examines the relationship between Mongolia's exchange rate and gold prices over time using statistical analysis and charts. It finds their exchange rate has a strong correlation with average past prices of gold, silver, and copper over the previous 90 days. Using this relationship, it creates a regression model that predicts Mongolia's exchange rate 90 days in advance with 96% accuracy based on historic mineral prices. It suggests this model could help Mongolia better predict and manage its macroeconomic environment.
Financial Analysis of Oyu Tolgoi Presented to: OPPORTUNITIES & CHALLENGES: THE CHANGING FACE OF 21ST CENTURY MONGOLIA: AN INTERDISCIPLINARY INTERNATIONAL SYMPOSIUM (IDIS 2014)
Biogen Idec is a leading biotechnology firm that has experienced strong growth through niche pharmaceutical products. However, an analyst's model projects the stock is overvalued given limitations on sustained high growth rates as markets become saturated and competitors increase efforts. The model finds a 73% probability the stock is fairly priced between $180-300 but only 5.25% above $300. The analyst advises taking profits and waiting for new product approvals and guidance.
This document reviews options for Mongolia-based MCS-APB Tiger Brewery to dispose of or utilize brewers spent grains (BSG) in an economic and environmentally-friendly manner. It analyzes both minimal capital investment options like donating or composting BSG, as well as more capital-intensive options like installing biogas production infrastructure. The three most viable options are identified as: 1) Producing methane for energy recovery through anaerobic digestion, 2) Selling or donating BSG to livestock farmers, and 3) Installing a cogeneration facility to produce steam and electricity from BSG. Financial analysis of capital-intensive options like using BSG to produce steam/power
The document provides a feasibility and financial study for a proposed biodiesel production laboratory project at the German-Mongolian Institute for Resources and Technology (GMIT). It discusses the worldwide and local biodiesel industries, analyzes the costs associated with establishing a small-scale biodiesel production facility, and models the financial viability of the proposed GMIT Biodiesel Project. The study concludes that under favorable pricing conditions, the project can sustain itself financially and provide educational benefits to students while also producing value for the local community through recycling of waste vegetable oil into biodiesel and other products.
The operation research book that involves all units including the lpp problems, integer programming problem, queuing theory, simulation Monte Carlo and more is covered in this digital material.
Dear students get fully solved SMU MBA Fall 2014 assignments
Send your semester & Specialization name to our mail id :
“ help.mbaassignments@gmail.com ”
or
Call us at : 08263069601
A weighted-sum-technique-for-the-joint-optimization-of-performance-and-power-...Cemal Ardil
The document presents a self-adaptive weighted sum technique for jointly optimizing performance and power consumption in data centers. It formulates the problem as a multi-objective optimization to minimize total power consumption and task completion time. The proposed technique adapts weights during optimization to better explore non-convex regions of the solution space, unlike traditional weighted sum methods. It was tested on data from a satellite control network and showed improved results over greedy heuristics and competitive performance against optimal solutions for smaller problems.
Dear students get fully solved SMU MBA Fall 2014 assignments
Send your semester & Specialization name to our mail id :
“ help.mbaassignments@gmail.com ”
or
Call us at : 08263069601
(Prefer mailing. Call in emergency )
Computational optimization, modelling and simulation: Recent advances and ove...Xin-She Yang
This document summarizes recent advances in computational optimization, modeling, and simulation. It discusses how optimization is important for engineering design and industrial applications to maximize profits and minimize costs. Metaheuristic algorithms and surrogate-based optimization techniques are becoming widely used for complex optimization problems. The workshop accepted papers that applied optimization, modeling, and simulation to diverse areas like production planning, mixed-integer programming, electromagnetics, and reliability analysis. Overall computational optimization and modeling have broad applications and continued research is needed in areas like metaheuristic convergence and surrogate modeling methods.
This document discusses linear programming and transportation problems. It provides definitions and applications of linear programming, including choice of investments, product mix selection, and design problems. Transportation problems are defined as using linear programming to determine the minimum cost of transporting a commodity from multiple origins to various destinations, given supply and demand constraints. Several examples of transportation problems and their least cost solutions are provided.
The document summarizes key concepts regarding linear programming problems. It discusses:
1. Linear programming problems aim to optimize an objective function subject to constraints. They can model many practical operations research problems.
2. The document provides an example problem of determining production levels to maximize profit. It demonstrates formulating the problem as a mathematical model and solving it graphically and with the simplex method.
3. The simplex method solves linear programming problems by examining vertex points of the feasible solution space. It involves setting up the problem in standard form and using minimum ratio and pivot element calculations to systematically search for an optimal solution.
The document discusses linear programming and its applications. It begins by defining linear programming and its key characteristics like objectives, constraints, and decision variables. It then provides examples of how linear programming is used in various industries like manufacturing, retail, delivery routing, and machine learning to optimize objectives like profit, efficiency, and costs. Specific techniques like graphical method and solving LP problems in tabular form are also summarized.
This document introduces a linear programming problem involving the production of two new products, Product 1 and Product 2, at the Wyndor Glass Co. The objective is to determine the production rates of each product that will maximize total weekly profit, subject to the limited production capacities of Plants 1-3. Plant 1 can produce 4 batches of Product 1 per week, Plant 2 can produce 6 batches of Product 2 per week, and Plant 3 has capacity for 18 total hours across Products 1 and 2. The mathematical model aims to maximize profit (Z) which is defined as 3x1 + 5x2, where x1 and x2 are the decision variables representing the production rates of each product, subject to the plant capacity constraints.
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
This document provides an overview of a faculty development program on operations management focusing on supply chain analytics. It discusses the origin and evolution of supply chain management. It also defines different types of analytics including data analytics and big data analytics. The document outlines various decision science models such as quantitative, qualitative, simulation-based, and advanced models. It provides examples of applications of decision science in various organizations. Finally, it introduces linear programming techniques for prescriptive analytics and provides an example linear programming model to maximize profit from production.
1) The document discusses definitions and characteristics of operations research (OR). It provides definitions of OR from several leaders and pioneers in the field that describe OR as applying scientific methods to optimize complex systems.
2) Key characteristics of OR mentioned are that it takes a team approach using quantitative techniques, aims to help executives make optimal decisions, relies on mathematical models, and uses computers to analyze models.
3) Limitations of OR discussed include that it is time-consuming, practitioners may lack industrial experience, and solutions can be difficult to communicate to non-technical executives. Linear programming is introduced as a prominent OR technique.
The document discusses linear programming and its key concepts. It begins by defining linear programming as using a mathematical model to allocate scarce resources to maximize profit or minimize cost. It then provides the steps to solve linear programming problems: [1] identify the problem as solvable by LP, [2] formulate a mathematical model, [3] solve the model, and [4] implement the solution. The document also discusses modeling techniques like defining decision variables, objective functions, and constraints. It provides examples of LP formulations and solutions using both graphical and algebraic methods. Finally, it discusses special issues that can arise like infeasible, unbounded, and redundant solutions or the existence of multiple optimal solutions.
The document discusses linear programming and its key concepts. It begins by defining linear programming as using a mathematical model to allocate scarce resources to maximize profit or minimize cost. It then provides the steps to solve linear programming problems: [1] identify the problem as solvable by LP, [2] formulate a mathematical model, [3] solve the model, and [4] implement the solution. The document also discusses modeling techniques like defining decision variables, objective functions, and constraints. It provides examples of LP formulations and solutions using both graphical and algebraic methods. Finally, it discusses special issues that can arise like infeasible, unbounded, and redundant solutions or the existence of multiple optimal solutions.
Lecture 2 Basic Concepts of Optimal Design and Optimization Techniques final1...Khalil Alhatab
This document provides an overview of optimization techniques and the process of formulating an optimal design problem. It begins with introducing optimization and defining it as finding the best solution under given circumstances by optimizing an objective function. It then contrasts conventional versus optimal design processes and discusses classifying optimization problems based on constraints, variables, objectives, and other factors. The document concludes by outlining the five steps to formulate an optimal design problem: project description, data collection, defining design variables, establishing an optimization criterion or objective function, and specifying constraints.
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This document provides an overview of linear programming problems (LPP). It discusses the key components of linear programming models including objectives, decision variables, constraints, and parameters. It also covers formulation of LPP, graphical and simplex solution methods, duality, and post-optimality analysis. Various applications of linear programming in areas like production, marketing, finance, and personnel management are also highlighted. An example problem on determining optimal product mix given resource constraints is presented to illustrate linear programming formulation.
This document outlines a course on mathematics for economists. It introduces linear programming techniques for solving constrained and unconstrained optimization problems. The course objectives are to learn how to formulate and solve linear programming problems using graphical and simplex methods, test for linear dependence and convexity/concavity, and solve nonlinear programming problems, differential equations, and difference equations as applied to economics. Sample problems are provided to demonstrate how to formulate linear programming problems in the standard way, specifying the objective, decision variables, constraints, and developing the objective function.
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a. Observe the critical path diagram. Why are there two arrows pointing to task F? b. Why is the critical path shown as A-B-E-G-I? How is the critical path defined? c. What would happen if activity F was revised to take 4 days instead of 2days?
Beharry, Lyndon Mw: Oyu Tolgoi article appears on page 251 (247 in the PDF file)
International Minerals Processing Conference Ulaanbaatar Mongolia 2016
Lancaster Colony Corporation is one of my favorite equities: Stable, stable, stable.
Lancaster Colony is my *GoTo* example for teaching Corporate Finance. In my limited estimation, Lancaster is one of the few, most visible publicly-traded American companies boasting clean financials, little or no debt, excellent corporate governance, and a balanced executive pay schedule. You cannot get more wholesome than Lancaster. The very name suggests Amish lifestyle, thrift and savings, and quality home-spun products. I've been following Lancaster since I was an MBA candidate in 1995.
I updated my Excel Monte Carlo valuation workbook with Lancaster financials since 2018 to provide a more current Equity Value range. But this conservative analysis propels the firm's pro-forma at a mere 0.00% growth rate in revenue - so it is a low-ball estimate based on the close of books June 30, 2021. I expect LANC will release its 2022 10K late in the week beginning Monday 22 August 2022. Once I review the more current financials, I will complete a valuation with an alternative growth schedule.
Lancaster Colony is based in Ohio, a state with poison pill legislation within the State Code. Lancaster is also closely held and thinly traded. Hence, LANC is virtually immune from hostile takeover.
2022-07-28
I present the final draft of my professional valuation of Lockheed Martin Corporation Equity per Share. I spent some hours cleaning up the prose (mostly light editing). I checked the citations, added "C-5" to Lockheed's notable creations, and worked to tighten up the grammar. As always, subsequent readings will inevitably reveal typographical and grammatical errors, but in general, this report is complete.
I welcome any suggestions or complaints. Feedback always helps me improve my writing and my analysis.
(I will be transitioning to work on a write-up on Gilead Sciences starting next week. From time to time I like to brush up on my biochemistry, molecular biology, and Phase Trial Studies.)
I present the second draft of my professional valuation of Lockheed Martin Corporation Equity per Share. I am satisfied with the variables, the cashflow projections, and the discounting; so this item does carry my estimate of LMT's present valuation.
I worked on the History (p. 2) and the WACC calculations (did some Excel coding after I found a slight Drop down menu / VLookup error) and I finalized the recommendations pp. 6, 7, & 10.
I hope my readers enjoy it as much as I am enjoying producing it!
I am eager to share this report on Lockheed's Monte Carlo Equity Valuation. I have been working on this write-up for Lockheed Martin and I think I am in striking range of completion, so I am sharing the first draft. I hope to round out the PESTLE and Porter Analysis this week and clean up the text, so look forward to a final draft during the first or second week of August.
This Monte Carlo multi-iteration DCF Model returns a fair value for Kraft Heinz: $35.496 . The static Model returns a valuation of $34.388 . These models are conservative estimates projecting zero growth forward using cost factors pulled from the mean of the prior 15 years with a coefficient of variability of the cost factors equal to 10%. Kraft Heinz Company pays a dividend yield of 4.20% ay July 22, 2022.
KHC: Kraft Heinz Company came up on the screen I had completed earlier in the week on Tuesday, and it has been one of my favorites for many years (from before the divestiture of certain assets to Mondelez. Kraft is a textbook example of a stable U.S. entity which made a successful transition to multinational operations through purposefully introducing itself to various foreign markets, and also through astute trades and/or investments into food companies abroad. Kraft has significant presence in Europe, Asia, and Latin America; and a growing presence in Africa.
The Kraft Heinz Company, together with its subsidiaries, manufactures and markets food and beverage products in the United States, Canada, the United Kingdom, and internationally. Its products include condiments and sauces, cheese and dairy products, meals, meats, refreshment beverages, coffee, and other grocery products. The company also offers dressings, healthy snacks, and other categories; and spices and other seasonings. It sells its products through its own sales organizations, as well as through independent brokers, agents, and distributors to chain, wholesale, cooperative and independent grocery accounts, convenience stores, drug stores, value stores, bakeries, pharmacies, mass merchants, club stores, and foodservice distributors and institutions, including hotels, restaurants, hospitals, health care facilities, and government agencies; and online through various e-commerce platforms and retailers. The company was formerly known as H.J. Heinz Holding Corporation and changed its name to The Kraft Heinz Company in July 2015. The Kraft Heinz Company was founded in 1869 and is headquartered in Pittsburgh, Pennsylvania. (FY: 2021-12-25)
GILD 2021 10K: Gilead Sciences, Inc. is a biopharmaceutical company that has pursued and achieved breakthroughs in medicine for more than three decades. In 2021, the firm's primary revenue drivers originate with medications designed to combat HIV, AIDs and its symptoms. Gilead has also produced medications for combatting coronavirus disease 2019 (“COVID-19”). The firm also researches and manufactures medications treating liver disease. The firm serves the international market and has a vibrant and active pipeline of R&D, and potential offerings in various stages of testing and/or awaiting regulatory approval. (FY: 2021-12-31)
These Monte Carlo DCF and Static DCF analyses hold revenue growth to 0.00% (no growth) while modeling the income statement cost components following 15-year historic means and a coefficient of variability of 10%. (Many analysts are forecasting retracting revenue of between 1.0% and 2.5% for the foreseeable years.) Even at no growth of revenue, Monte Carlo analysis returns excellent and stable valuations for Gilead with a lower bound of approximately $43.70 and an upper bound of about $96.80 . In addition Gilead pays a healthy dividend yielding 4.66% at its current trading price of $66.
This analyst will expend some additional effort reviewing the firm's Phase Trial Clinical studies and pipeline for FDA and/or EU approval. Those qualitative reports will follow in the coming month.
I spent the morning updating BBBY: Bed Bath and Beyond. Crazy SGA volatility coupled with Covid quarantines to cripple this long-time Brick & Mortar household goods brand. The firm has some culture *problems*. Notably, stores were traditionally free to run themselves, carrying product lines local management surmised the local community cherished. Hence, there were never any true scale economies in purchasing inventory. Other problems include over-reliance on brick and mortar stores to the detriment of internet marketing; an *early/long-time* history of coupons which never expired; *early/long-time* history of "free" shipping; and other things.
On the plus side, BBBY owns much of its real property and has long-term leases on other holdings. These valuable items are still booked at acquisition costs (c. 1970s-80s real property values) and would generate substantial returns if the firm would transition to a more robust online presence and lease out much of its brick and mortar network. Only time will tell; if, that is, the firm is able to weather the next likely terrible 24 months of horrendous sales...
Monte Carlo DCF projections reflect HUGE volatility. At 0.00% revenue growth, the model returns a range of valuation from a low of -$260.02 (yes, that is a negative number) and up to a maximum of +$256. I had reviewed BBBY way back in 2019, and I think that SWOT analysis is still useful, so I tacked it onto this quantitative analytical summary.
Bed Bath & Beyond Inc., together with its subsidiaries, operates a chain of retail stores. It sells a range of domestics merchandise, including bed linens and related items, bath items, and kitchen textiles; and home furnishings, such as kitchen and tabletop items, fine tabletop, basic housewares, general home furnishings, consumables, and various juvenile products. As of February 26, 2022, the company had 953 stores, which included 771 Bed Bath & Beyond stores in 50 states, the District of Columbia, Puerto Rico, and Canada; 130 buybuy BABY stores in 37 states and Canada; and 52 stores in 6 states under the names Harmon, Harmon Face Values or Face Values. It also offers products through various Websites and applications comprising bedbathandbeyond.com, bedbathandbeyond.ca, harmondiscount.com, facevalues.com, buybuybaby.com, buybuybaby.ca, and decorist.com. In addition, the company operates Decorist, an online interior design platform that provides personalized home design services. Bed Bath & Beyond Inc. was incorporated in 1971 and is headquartered in Union, New Jersey.
Post 2000s, Oil and Gas company valuations are particularly problematic. On the one hand, they still service the bulk of humanity's energy demands. In fact, it is oil, gas, shale, and coal which provide the bulk of the energy used to manufacture Green Energy infrastructure (turbines, solar, hydro, and even geo-thermal) - and fossil fuels will continue to dominate the energy produced for the manufacture of Green Energy technology for decades to come.
But on the other hand, we all know that humanity must move away from fossil fuels and Developed World nation-states all have varying degrees of regulations requiring phasing out fossil fuel use and technology within this century. Less Developed Countries (LDCs) are beginning to leap-frog, totally bypassing fossil fuel energy infrastructure and directly embracing Green Energy production (infrastructure constructed in Developed World and BRIC (mainly China) using fossil fuel energy).
Furthermore, shale oil (fracking) has empowered U.S. and Canada with enough surplus to become net exporters of oil, and this plays havoc with world oil pricing (notwithstanding the current situation of high prices with the ongoing war in Ukraine). So ... revenue growth rates, Capital Expenditures, even Depreciation Schedules all become difficult to model.
This analysis uses a modest forward 12.50% revenue growth rate (normal distribution; coefficient of variability 10%), with cost structure parameters taking the mean of 15-Yr historic patterns (high standard deviations, though); and a U.S. tax loading of 17% accommodating U.S. federal subsidies and favoritism to American Petroleum Institute lobby.
Bear in mind, though, that the Revenue Growth rate could go negative on a dime, as it had done in the 2010s, when oil and gas retracted and spent next to nothing on Capital Expenditure and discovery.
So, yeah. Fossil Fuel producers: oil and gas (not so much coal) are very difficult to value in this climate.
These variables produce a low range of potential value for Devon Energy Corporation. The obvious workaround would be to broaden the coefficient of variability for the Revenue growth rate and cost parameters. But this option is not attractive because, while more accurately mimicking true-to-life historical volatility in asset pricing, it would produce too broad a range of scenario valuation as to be of any practical use. So this instant valuation produces a rather low valuation estimate, indeed.
3M is interesting. It is a multinational conglomerate with production and sales ranging from household goods to medical devices. The numerical analysis is straightforward. But the trick AND the excitement of valuing these types of companies is that it forces the analyst to learn about the various production methods and markets for disparate ranges of products and look at the company as a true portfolio of cash-generating assets - the various productions - while analyzing and rating the risks of all of those different markets.
I first looked at 3M back in 2016, and then - apparently I have never looked at it since, because the Excel file in my Equity Valuation folders has not been revised in five or six years.
Well, it got some treatment today.
This is an econometrics analysis of quantitative data for 3M. I will review some qualitative data in the coming weeks, but based on the numbers, it looks really good. I included 10 iterations of the 1 Million steps to the Monte Carlo DCF. Enjoy.
I valued Biogen back in 2014 for an old friend, and I have looked in on it sporadically over the years. I did not like it back in the 2010s because it had too many competing therapies for multiple schlerosis (from my 2014 report here https://www.slideshare.net/LMBeharry/biib-reportlmbenterprises-59573190):
"• Several of the product offerings address multiple sclerosis, and these pharma products will likely begin cannibalizing each other within the intermediate term. The analyst believes that this cannibalization will curtail growth within the MS product line within the next 18 to 24 months."
and
"• The firm has submitted hemophilia agents, Factor VIII and Factor IX to the US FDA for regulatory review, anticipating marketing approval in 2014-2015. As these hemophilia products are administered orally, analysts expect sales to grow robustly indeed. (i.e. more doctors will prescribe the treatment as it circumvents costly and frequent recurrent need of infusion of clotting factor). Statistics indicate that roughly 20,000 US residents suffer with hemophilia. A market of 20,000 patients is not a growth sector."
Note that I have not kept up with its pipeline, nor its successes/failures at clinical trial. This printout is solely an exercise in econometric analysis using its historical cost structure to derive an equity valuation.
If you are curious about its current research endeavors, I provide the link for clinical trials here (already sorted for Biogen): https://clinicaltrials.gov/ct2/results?cond=&term=Biogen&cntry=&state=&city=&dist=
This document appears to be a resume or CV for Lyndon Beharry. It includes his educational background, including a Master's in Business Administration and some law school education. It also outlines his extensive professional experience in business, education, and non-profit work over nearly 30 years. This includes experience teaching in Mongolia and managing projects there. The CV highlights his skills in areas like financial modeling, education, and technical writing. Recommendation letters from previous employers in Mongolia praise his teaching abilities and contributions to their organizations.
Exelon Corporation is America's largest utility company, powering over 10 million customers across 6 regulated utility companies. In 2021, Exelon announced plans to separate into two publicly traded companies - Exelon Utilities which will include the regulated utilities, and Exelon Generation which will include competitive power generation and customer-facing energy businesses. The document provides an overview of Exelon's business history, financial performance, and challenges relating to competition and environmental regulation.
Impartiality as per ISO /IEC 17025:2017 StandardMuhammadJazib15
This document provides basic guidelines for imparitallity requirement of ISO 17025. It defines in detial how it is met and wiudhwdih jdhsjdhwudjwkdbjwkdddddddddddkkkkkkkkkkkkkkkkkkkkkkkwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwioiiiiiiiiiiiii uwwwwwwwwwwwwwwwwhe wiqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq gbbbbbbbbbbbbb owdjjjjjjjjjjjjjjjjjjjj widhi owqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq uwdhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhwqiiiiiiiiiiiiiiiiiiiiiiiiiiiiw0pooooojjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjj whhhhhhhhhhh wheeeeeeee wihieiiiiii wihe
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Determination of Equivalent Circuit parameters and performance characteristic...pvpriya2
Includes the testing of induction motor to draw the circle diagram of induction motor with step wise procedure and calculation for the same. Also explains the working and application of Induction generator
Digital Twins Computer Networking Paper Presentation.pptxaryanpankaj78
A Digital Twin in computer networking is a virtual representation of a physical network, used to simulate, analyze, and optimize network performance and reliability. It leverages real-time data to enhance network management, predict issues, and improve decision-making processes.
We have designed & manufacture the Lubi Valves LBF series type of Butterfly Valves for General Utility Water applications as well as for HVAC applications.
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Null Bangalore | Pentesters Approach to AWS IAMDivyanshu
#Abstract:
- Learn more about the real-world methods for auditing AWS IAM (Identity and Access Management) as a pentester. So let us proceed with a brief discussion of IAM as well as some typical misconfigurations and their potential exploits in order to reinforce the understanding of IAM security best practices.
- Gain actionable insights into AWS IAM policies and roles, using hands on approach.
#Prerequisites:
- Basic understanding of AWS services and architecture
- Familiarity with cloud security concepts
- Experience using the AWS Management Console or AWS CLI.
- For hands on lab create account on [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
# Scenario Covered:
- Basics of IAM in AWS
- Implementing IAM Policies with Least Privilege to Manage S3 Bucket
- Objective: Create an S3 bucket with least privilege IAM policy and validate access.
- Steps:
- Create S3 bucket.
- Attach least privilege policy to IAM user.
- Validate access.
- Exploiting IAM PassRole Misconfiguration
-Allows a user to pass a specific IAM role to an AWS service (ec2), typically used for service access delegation. Then exploit PassRole Misconfiguration granting unauthorized access to sensitive resources.
- Objective: Demonstrate how a PassRole misconfiguration can grant unauthorized access.
- Steps:
- Allow user to pass IAM role to EC2.
- Exploit misconfiguration for unauthorized access.
- Access sensitive resources.
- Exploiting IAM AssumeRole Misconfiguration with Overly Permissive Role
- An overly permissive IAM role configuration can lead to privilege escalation by creating a role with administrative privileges and allow a user to assume this role.
- Objective: Show how overly permissive IAM roles can lead to privilege escalation.
- Steps:
- Create role with administrative privileges.
- Allow user to assume the role.
- Perform administrative actions.
- Differentiation between PassRole vs AssumeRole
Try at [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
2. EXECUTIVE SUMMARY
Businesses routinely suffer inefficiencies and managers often suffer stress responding to scheduling issues. While many
software providers sell solutions catered to different types of enterprise: Schools and Universities, Hospitals, Factories, and
other organizations involving labor shift-work; off-the-shelf solutions are notoriously expensive, and sometimes malfunction
due to the inability of the underlying personal computer architecture to handle the range of variables within the model.
This report looks at one approach to the standard scheduling problem by constructing a model for use
by high schools and small colleges/universities. This iteration of the model builds up an integer
programming optimization model, aiming to maximize credit hours following constraints: 1) required
class hours per course-week; 2) instructor preference for teaching-free days; 3) restricting group-room
assignments to Integer: (0,1); 4) restricting number of instructors per group-room to Integer:(0,1); and
other constraints. The model searches through two thousand variable fields: 1) ten instructors; with
potential to occupy: 2) eight group-room assignments; over 3) five potential course time slots per day;
over 4) five days each week – viz. 10 X 8 X 5 X 5.
But the model has capability beyond the two thousand variables. For instance, if the system limits a
department teaching hours to two time slots per day (or different days), the system could
accommodate several departments to minimize scheduling conflicts while maximizing satisfaction for
instructors and students.
This project uses the robust solver mechanism in OpenSolver, an open source project developed by
Andrew Mason in the Department of Engineering Science at the University of Auckland. The
standard solver issued with Microsoft Excel is limited to only 200 variable fields. The OpenSolver
mechanism does not impose artificial limits to the number of potential variable fields.
EXECUTIVE SUMMARY Scheduling Optimization | 2015-11-20_Scheduler.docx |
11/24/2015 10:29
AM
3. CONTENTS | Page 2 of 33
Table of Contents
EXECUTIVE SUMMARY.......................................................................................................................................................................................................................1
A REVIEW OF THE STANDARD OPTIMIZATION ROUTINES..................................................................................................................................................3
THE STANDARD SCHEDULING PROBLEM .................................................................................................................................................................................4
THIS INSTANT SCHEDULING MODEL.........................................................................................................................................................................................5
THE MODEL’S CONSTRAINTS .......................................................................................................................................................................................................6
THE BENEFITS OF THE MODEL...................................................................................................................................................................................................9
OTHER MATERIAL01......................................................................................................................................................................................................................10
OTHER MATERIAL03 .....................................................................................................................................................................................................................12
OTHER MATERIAL04 .....................................................................................................................................................................................................................13
APPENDICES .....................................................................................................................................................................................................................................14
APPENDIX I: OPENSOLVER – OPEN SOURCE OPTIMIZATION FOR EXCEL...................................................................................................................15
APPENDIX II:....................................................................................................................................................................................................................................26
APPENDIX III:..................................................................................................................................................................................................................................27
APPENDIX IV:...................................................................................................................................................................................................................................28
APPENDIX V:.....................................................................................................................................................................................................................................29
APPENDIX VI:...................................................................................................................................................................................................................................30
REFERENCES.....................................................................................................................................................................................................................................A
CONTENTS Scheduling Optimization | 2015-11-20_Scheduler.docx | 11/24/2015 10:29 AM
4. A REVIEW OF STANDARD OPTIMIZATION ROUTINES | Page 3 of 33
A REVIEW OF THE STANDARD OPTIMIZATION ROUTINES
Since the beginnings of human civilization, governments and other authorities have been vexed with
issues concerning optimization of resources: Maximize benefit and reduce cost. The military forces of
ancient empires, for example, continually aimed to improve scheduling of forces and transport of
equipment, food, and fodder. Scheduling logistics, in other words, was and remains paramount for
survival on the march to battle; and superior scheduling in logistics and assignment of tasks remains
decisive in battle, in business, and in other socio-economic endeavor.
Modern mathematics theory has made great strides in computing optimization routines within the two
major fields of Linear Programming and Integer
Programming. Linear programming (LP; also called linear
optimization) seeks the best outcome (such as maximum
profit or lowest cost) in a mathematical model whose
requirements are represented by linear relationships.1
Similarly, Integer Programming seeks an optimum solution
in which some or all of the variables are restricted to be
integers. In many settings the term refers to integer linear
programming (ILP), in which the objective function and the
constraints (other than the integer constraints) are linear.2
The introduction of the personal computer in the late 1970’s
brought optimization routines into the domain of non-
academic persons. MatLab, Microsoft Excel, Palisades Risk
Optimizer, and other software packages bring the discipline into the range of anyone with the
discipline to learn the theory and some rudimentary mathematic formulae to outline the optimization
model and constraints.
Linear and Integer Optimization algorithms must translate a real-world situation into a mathematical
model. For instance:
XYZ building supply Company has two locations. Two customers submit orders for 3/4-inch
plywood. Customer A requests fifty sheets and Customer B needs seventy sheets.
XYZ’s east-side warehouse stores inventory of eighty sheets; its west-side warehouse has forty-five
sheets. Delivery costs per sheet: $0.50 from the eastern warehouse to Customer A, $0.60 from the
eastern warehouse to Customer B, $0.40 from the western warehouse to Customer A, and $0.55
from the western warehouse to Customer B. The equation: C = 0.5Ae + 0.6Be + 0.4Aw + 0.55Bw3
shipped from east warehouse to Customer A: Ae
shipped from west warehouse to Customer A: Aw
shipped from east warehouse to Customer B: Be
shipped from west warehouse to Customer B: Bw
Finally, the tandem of optimization formula and constraint defines a range of potential solutions,
typically a polyhedron. If one is testing for a local minimum point, subject to constraints, one views
the polyhedron as convex. Conversely, if seeking a maximum point, one views the polyhedron as
concave. Integer optimization routines are a variant of linear programming, but with the added
constraint that the feasible region must only offer integer values of solutions, typically binary 0 or 1.
Algorithms which optimize scheduling of persons, machines, or equipment follow the Integer
Optimization binary 0 or 1 model.
1 From: https://en.wikipedia.org/wiki/Linear_programming
2 From: https://en.wikipedia.org/wiki/Integer_programming
3 From http://www.purplemath.com/modules/linprog5.htm
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5. THE STANDARD SCHEDULING PROBLEM | Page 4 of 33
THE STANDARD SCHEDULING PROBLEM
In general, workplace scheduling problems evolve out of the nurse scheduling problem, an
optimization query aiming to assign shifts to workers subject to a range of constraints: a) which shift
(i.e. day shift, night shift, early morning shift, swing shift); b) number of hours worked per day; c)
number of days worked per week; d) maximum number of hours per week; e) employee preference
for rest days; f) employee preference for room; etc. Similarly, job shop scheduling involves
optimization of job assignment, contingent upon resource availability during particular daily intervals:
the system requires n jobs J1, J2, ..., Jn of varying sizes, scheduled on m identical machines, while
minimizing the time duration of the entirety.
This instant Course Scheduling routine aims to combine the nurse schedule optimization and the job
shop optimization algorithms, where the worker schedule optimizer aims to maximize satisfaction
following worker preferences for shifts, room assignments, and non-teaching days; and the job-shop
optimizer seeks to maximize usage of room-group resources, subject to minimizing room conflicts
and total hours, subject to satisfying requirements for contact hours.
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6. THIS INSTANT SCHEDULING MODEL | Page 5 of 33
THIS INSTANT SCHEDULING MODEL
This instant scheduling optimizer constructs a relatively simple model to assist schools schedule course
group and room assignments. The optimizer aims to:
1. minimize group-room conflicts;
2. maximize instructor satisfaction for preference for room and time; and
3. satisfy constraints for credit hours.
The developer built this optimizer using Microsoft Excel. Microsoft Excel is the current-day standard
for business spreadsheet and finance; but increasingly is applied to science and engineering regimens.
And even though the standard Excel Solver optimization routine limits variable assignments to an
arbitrary 200 potential fields, OpenSolver is Excel friendly, and OpenSolver imposes no artificial
constraints to variable fields. The combination of Excel and OpenSolver provides a robust and low-
cost alternative for creating optimization routines of great design complexity, along the extreme ranges
of functionality.
In overview, this scheduling model links student Groups to certain Rooms; hence – a Preparatory
Group One might be linked to a Room 101. This structure aims to satisfy instructor preference for
Room. And this structure also imposes a barrier to whether the Preparatory Group One could
potentially be scheduled twice during the same time slot. Bear in mind: the schedule shows availability
of all rooms at each time. Hence, during the final phase of scheduling, it is quite simple to adjust a
room assignment for the given group to another open room. But for simplicity in initial calculation,
the algorithm restricts each Group to a certain room.
Secondly, the model permits the scheduler to honor instructor preferences for non-teach days, to
satisfy such requirements as outside seminars, applied research, faculty conferences, office hours, and
other matters. At present, the user must input the constraint directly within the solver constraint
profile.
Lastly, the model aims to satisfy all of the following criteria:
1. Maximize total teaching hours per week, subject to the required inputs;
2. Restrict Group-Room use to 0 or 1 per time slot. In other words, no two Groups may occupy
the same room at the same time slot;
3. Restrict Instructor-Room use to 0 or 1 per time slot. In other words, no two Instructors may
occupy the same room at the same time slot;
4. Maximize Instructor satisfaction for non-teach days;
5. Restrict daily teaching periods to some limit: 1, 2, or 3 class periods per Instructor day
(obviously to maximize Instructor preference, but also to avoid stress and burn-out);
6. Minimize the potential for errors, and usage of time for administrators involved with
scheduling.
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7. THE MODEL’S CONSTRAINTS | Page 6 of 33
THE MODEL’S CONSTRAINTS
The functional worksheet Schedule Solver contains a comment description in cell E2:
This is the functional Solver worksheet. The user must input the course information on Schedule
Inputs Worksheet, and run the Solver routine here.
Set the following parameters manually, with course credit hours. {The system will automatically
draw class assignments by teacher from Schedule Inputs Worksheet. Type in total weekly
time slots for each course assignment (i.e. 2, 3, or 4 for each class assignment)}:
$E$87:$L87
$E$92:$L92
$E$97:$L97
$E$102:$L102
$E$107:$L107
$E$112:$L112
$E$117:$L117
$E$122:$L122
$E$127:$L127
$E$132:$L132
then run Solver under the following parameters:
Set $BD$21 to Max {Possible class hours subject to constraint}
Changing $E$10:$AR$59 {{Run the Macro CTRL +SHIFT R from Schedule Inputs Worksheet
to clear the range}
Subject to constraints:
Instructor Days Off {Set these constraints according to Instructor/Facility Requirements} For
Example:
$CC$12=0
$CD$11=0
$CE$10=0
Set the schedule to Integer "0" (not occupied) or "1" (occupied) :
$E$10:$AR$59<=1
$E$10:$AR$59=OR(0,1)
$E$10:$AR$59=Integer
Set Instructor Classes per Week to Max allowed:
$BD$10:$BD$119 = $BE$10:$BE$19
$BD$10:$BD$19>=$BF10:$BF$19
$BQ$10:$BU$59<=1
$CC$10:$CG$19<=$CH$6
Constrain each Room to Maximum one Instructor Group per Time Slot
$E$76:AZ$80<=1
Set classes Taught to Classes Required
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8. THE MODEL’S CONSTRAINTS | Page 7 of 33
$E$86:$L$86=$E$87:$L$87
$E$91:$L91=$E$92:$L92
$E$96:$L96=$E$97:$L$97
$E$101:$L$101=$E$102:$L$102
$E$106:$L$106=$E$107:$L$107
$E$111:$L$111=$E$112:$L$112
$E$116:$L$116=$E$117:$L$117
$E$121:$L$121=$E$122:$L$122
$E$126:$L$126=$E$127:$L$127
$E$131:$L$131=$E$132:$L$132
THE SPECIFICS
The user must input all course and teacher data within the worksheet =Schedule Inputs!. Teacher
information ($C$7:$D$16), list of available rooms ($L$7:$L$14), and course information By Teacher
and Group-Room ($R$7:$S$166), and Student Group Names ($U$7; $U$9, $U$11, $U$13, $U$15,
$U$17, $U$19, $U$21)
Though this iteration of the Optimization model accommodates only 8 possible Group-Room
assignments, one may stretch the functionality by 1) limiting the number of Rooms available for these
8 Groups; 2) constraining days or times available for these Groups; or a combination. Hence, by
limiting these groups to a certain four rooms, for example; or by scheduling another set of groups
within another set of rooms, it is easy to Optimize for larger assortments of groups (viz. by rooms
allocated by Department, or by major field of study, for example – with certain time slots allocated for
overlap, in the event of electives).
This model creates matrices for each of ten potential instructor sets including within the worksheet
=Schedule Solver!:
1. A list of each of ten potential Teachers;
2. Occupying one of 8 rooms for each of six potential working days;
a. Monday: Columns $E:$L
b. Tuesday: Columns $M:$T
c. Wednesday: Columns $U:$AB
d. Thursday: Columns $AC:$AJ
e. Friday: Columns $AK:$AR
f. Saturday: Columns $AS:$AZ
3. Over each of five time slots each for each teacher-day
a. Teacher 01: Rows $10:$14
b. Teacher 02: Rows $15:$19
c. Teacher 03: Rows $20:$24
d. Teacher 04: Rows $25:$29
e. Teacher 05: Rows $30:$34
f. Teacher 06: Rows $35:$39
g. Teacher 07: Rows $40:$44
h. Teacher 08: Rows $45:$49
i. Teacher 09: Rows $50:$54
j. Teacher 10: Rows $55:$59
4. Sums of Group-Room per Teacher-Day
a. Teacher 01: =Sum(E14:E19) and etc.
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9. THE MODEL’S CONSTRAINTS | Page 8 of 33
5. The Integer Optimization seeks to isolate the Integer Value (0,1) across each Teacher-Room
time slot matrix so that Weekly Group-Room time slots Per Teacher-Room is equivalent to
the required hours per Group-Room course; in other words
a. Teacher 01 $E$86:$N$86
b. Teacher 02 $E$91:$N$91
c. Teacher 03 $E$96:$N$96
d. Teacher 04 $E$101:$N$101
e. Teacher 05 $E$106:$N$106
f. Teacher 06 $E$111:$N$111
g. Teacher 07 $E$116:$N$116
h. Teacher 08 $E$121:$N$121
i. Teacher 09 $E$126:$N$126
j. Teacher 10 $E$131:$N$131
1. Where, for instance, $E$86 defines the constraint for weekly
Teacher-Room time slots per Group-Room course
=+SUM(E10,E15,E20,E25,E30,E35,E40,E45,E50,E55) and etc.
a. Must equal $E$87 (Required time-slots per Course Week);
6. Additional Matrix: $E$63:$AZ$72 calculates Teacher-Room occupancy by day {i.e.
=+SUM(E10:E14), and etc.};
7. Additional Matrix: $E$76:$AZ$80 calculates Teacher-Room and Group-Room occupancy by
hour {i.e. =+SUM(E10,E15,E20,E25,E30,E35,E40,E45,E50,E55), and etc.}; Constrain each
point to Integer (0,1) so that only One Teacher and only One Group may occupy any given
room any time slot;
8. Additional Matrix: $CC$10:$CH$19 defines the constraint for Teacher preference for non-
teach days: {Monday, Teacher 01 =SUM(E10:L14), and etc.}
9. Additional Matrix: $BD$9:$BD$18 defines the time slots taught per week by teacher {Teacher
01 =+SUM(E10:AZ14), and etc.}
10. The Optimization routine aims to maximize total Teacher Hours Taught each week: $BD$21,
while satisfying the defined constraints;
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10. THE BENEFITS OF THE MODEL | Page 9 of 33
THE BENEFITS OF THE MODEL
This scheduler model should reduce time constraints to administrators in scheduling Group-Room
assignments for studies. In addition, the model should provide sufficient leeway for the user to satisfy
many Instructor preferences for room and times. Lastly, the model offers sufficient flexibility for the
user to schedule special study days, including after hours and Saturdays.
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11. OTHER MATERIAL01 | Page 10 of 33
OTHER MATERIAL01
Blah blah blah.
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12. OTHER MATERIAL02 | Page 11 of 33
OTHER MATERIAL02
Blah blah blah.
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13. OTHER MATERIAL03 | Page 12 of 33
OTHER MATERIAL03
Blah…Blah…Blah
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14. OTHER MATERIAL04 | Page 13 of 33
OTHER MATERIAL04
Blah blah blah.
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15. APPENDICES | Page 14 of 33
APPENDICES
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16. APPENDIX I: OPEN SOLVER: OPEN SOURCE OPTIMIZATION FOR EXCEL| Page 15 of 33
APPENDIX I: OPENSOLVER – OPEN SOURCE OPTIMIZATION FOR EXCEL
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17. OpenSolver:
Open Source Optimisation for Excel
www.opensolver.org
Andrew J Mason
Department of Engineering Science
University of Auckland
New Zealand
a.mason@auckland.ac.nz
Iain Dunning
Department of Engineering Science
University of Auckland
New Zealand
Abstract
We have developed an open source Excel add-in, known as OpenSolver, that allows
linear and integer programming models developed in Excel to be solved using the
COIN-OR CBC solver. This paper describes OpenSolver‟s development and features.
Key words: OpenSolver, Open Source, Excel, Solver, Add-in, COIN-OR, CBC.
1 Introduction
Microsoft Excel (Wikipedia, 2010) contains a built-in optimisation tool known as
Solver (Frontline, 2010). Solver is developed by Frontline Systems, who provide the
software to Microsoft. Using Solver, a user can develop a spreadsheet optimisation
model and then solve it to find an optimal solution. Many introductory optimisation
courses use Solver and Excel to introduce students to modelling and optimisation.
Unfortunately, when students apply their optimisation skills to real-world problems,
they often discover that the size of problem Solver can optimise is artificially limited to
no more than 200 decision variables (Solver Limits, 2010), and that they need to
upgrade Solver to one of Frontline‟s more expensive products, such as Premium Solver.
(Beta versions of the latest Excel version, Excel 2010, have a smaller variable limit
(Dunning 2010); the current variable limit in shipping versions of Excel 2010 has not
been confirmed.)
We have recently been involved in the development of a large staff scheduling
model. This model was developed as part of a consultancy exercise where it was
important that the model could be used and scrutinised by a range of different users.
Satisfying this requirement using commercial products would have been logistically
difficult and expensive.
For a number of years, a group known as COIN-OR (Computational Infrastructure
for OR) (COIN-OR, 2010) have been developing and promoting open source
optimisation software, including the linear/integer programming optimiser known as
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18. CBC (CBC, 2010). While typically not as fast as its commercial equivalents, the COIN-
OR software has gained a reputation for quality and reliability and is now widely used in
industrial applications.
The combination of Excel and COIN-OR is a compelling one, and appeared to be a
perfect solution for our large staff scheduling model. Unfortunately, we were unable to
find any software that allowed Excel spreadsheet models to be solved using any of the
COIN-OR optimisers. A decision was taken to develop such software to progress the
scheduling project. This decision eventually led to the development of OpenSolver, a
freely available Excel add-in that allows existing spreadsheet linear and integer
programming models to be solved using the COIN-OR CBC optimiser
2 Solver Operation
We start by briefly describing how optimisation models are built using Solver. Readers
familiar with Solver may wish to skip this section.
A typical linear programming model is shown in Figure 1. The decision variables are
given in cells C2:E2. Cell G4 defines the objective function using a „sumproduct‟
formula defined in terms of the decision variables and the objective coefficients in cells
C4:E4. Each of the constraints are defined in terms of a constraint left hand side (LHS)
in G6:G9 and right hand side (RHS) in I6:I9. Note that the „min‟ in B4 and the
constraint relations in H6:H9 are for display purposes only, and are not used by Solver.
Figure 1: A typical spreadsheet optimization model. Many models do not follow
this layout, but instead ‘hide’ the model inside the spreadsheet formulae.
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19. Figure 2 shows how this model is set up using Solver. The decision variables,
objective function cell and constraint left and right hand side cells must all be specified
by the user within Solver. Note that a constraint can either consist of two multi-cell
ranges of the same dimension, such as A4:A8 >= B4:B8, or a multi-cell range and a
constant or single-cell range such as A4:A8 <= 8. Integer and binary restrictions on the
variables can also be specified using constraints.
Figure 2: Solver setup for the model above.
The means by which Solver stores a model does not appear to be documented.
However, a Google search eventually uncovered a comment that Solver uses hidden
named ranges (see, e.g., Walkenbach 2010). The Excel Name Manager add-in (Pieterse,
2010), developed by Jan Karel Pieterse of Decision Models UK, was then used to reveal
this hidden data. The names used by Solver are documented in Appendix 1. OpenSolver
uses these named ranges to determine the decision variables, the objective function and
LHS and RHS ranges of each constraint.
3 Constructing a Model from Excel Ranges
We wish to analyse the spreadsheet data to build an optimisation model which has
equations of the form:
Min/max c1x1+c2x2+... cnxn
Subject to a11x1+a12x2+... a1nxn ≤/=/≥ b1
a21x1+a22x2+... a2nxn ≤/=/≥ b2
...
am1x1+am2x2+... amnxn ≤/=/≥ bm
x1, x2, ..., xn >= 0
Assuming the model is linear, then the Excel data can be thought of as defining an
objective function given by
Obj(x) = c0+c1x1+c2x2+...cnxn
where x=(x1, x2, ..., xn) are the decision variable values, Obj(x) is the objective function
cell value, and c0 is a constant. Similarly, each constraint equation i is defined in Excel
by
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20. LHSi(x) ≤/=/≥ RHSi(x) LHSi(x) - RHSi(x) ≤/=/≥ 0, i=1, 2, ..., m
where LHSi(x) and RHSi(x) are the cell values for the LHS and RHS of constraint i
respectively given decision variable values x. Because Solver allows both LHSi(x) and
RHSi(x) to be expressions, we assume that both of these are linear functions of the
decision variables. Thus, we have
ai1x1+ai2x2+...ainxn- bi = LHSi(x) - RHSi(x), i=1, 2, ..., m.
OpenSolver determines the coefficients for the objective function and constraints
through numerical differentiation. First, all the decision variables are set to zero,
x=x0
=(0,0,...,0) giving:
c0=Obj(x0
)
bi = RHSi(x0
) - LHSi(x0
), i=1, 2, ..., m
Then, each variable xj is set to 1 in turn, giving decision variables values x=xj
, where
xj
=(x1
j
, x2
j
, ..., xn
j
) is a unit vector with the single non-zero element xj
j
=1. Then, the
spreadsheet is recalculated, and the change in the objective and LHS and RHS of each
constraint recorded. This allows us to calculate the following coefficients:
cj = Obj(xj
)-c0
aij = LHS(xj
)-RHS(xj
)+bi, i=1, 2, ..., m
This process assumes that these equations are indeed all linear. OpenSolver does not
currently check this, but will do so in a future release.
The speed of this process is set by the speed at which Excel can re-calculate the
spreadsheet. As an example, the large staff scheduling model discussed earlier has 532
variables and 1909 constraints, and took 22s to build (and just 1 second to solve) on an
Intel Core-2 Duo 2.66GHz laptop. There are a number of different Excel calculation
options available, such as just recalculating individual cells or recalculating the full
worksheet or workbook. OpenSolver currently does a full workbook recalculation as the
other options did not appear to give any faster results.
In our model form above, we have specified that the decision variables are all non-
negative. This assumption is also made by the COIN-OR CBC solver we use. To ensure
this is the case, OpenSolver requires the user to set Solver‟s “Assume Non-Negative”
option. OpenSolver cannot currently solve models for which this is not the case.
OpenSolver also requires that Solver‟s “Assume Linear Model” is set.
4 Integration with COIN-OR CBC Solver
OpenSolver uses the COIN-OR CBC linear/integer programming solver to generate its
solutions. While this solver can be called directly as a DLL, OpenSolver adopts the
simpler process of writing a „.lp‟ file that contains the model definition and then calling
the command line version of CBC with this file as an input argument. CBC then
produces an output file which is read back by OpenSolver. If a solution has been found,
OpenSolver uses this to set the values of the decision variable cells. Any infeasibility or
unboundedness, or early termination caused by time limits, is reported using a dialog.
Solver provides the user with a number of solution options. Of these, the “Max
Time” option is passed to CBC (using the CBC parameter “-seconds”), and the
“Tolerance” option is passed (using “-ratioGap”) to set the percentage tolerance required
for CBC integer solutions. Other CBC options can be set by creating a two column
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21. range named “OpenSolver_CBCParameters”on the spreadsheet that contains CBC
parameter names and values.
If the “Show Iteration Results” option is set, OpenSolver displays the CBC
command line window while CBC is running. (OpenSolver does not provide the step-
by-step functionality that this option enables in Solver.)
5 Excel Integration and User Interface
OpenSolver is coded in Visual Basic for Applications and runs as an Excel add-in. The
add-in presents the user with new OpenSolver controls using the standard ribbon
interface. These OpenSolver buttons and menus are shown in Figure 3 and Figure 4.
Figure 3: OpenSolver’s buttons and menu appear in Excel's Data ribbon.
Figure 4: OpenSolver’s menu gives access to its more advanced options.
OpenSolver is downloaded as a single .zip file which when expanded gives a folder
containing the CBC files and the OpenSolver.xlam add-in. Double clicking
OpenSolver.xlam loads OpenSolver and adds the new OpenSolver buttons and menu to
Excel. OpenSolver then remains available until Excel is quit. If required, the
OpenSolver and CBC files can be copied to the appropriate Office folder to ensure
OpenSolver is available every time Excel is launched. Note that no installation program
needs to be run to install either OpenSolver or CBC.
6 Performance
We have found OpenSolver‟s performance to be similar or better than Solver‟s. CBC
appears to be a more modern optimizer than Solver‟s, and so gives much improved
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22. performance on some difficult problems. For example, large knapsack problems which
take hours with Solver are solved instantly using OpenSolver, thanks to the newer
techniques such as problem strengthening and preprocessing used by CBC.
7 Model Visualisation
To view an optimisation model developed using the built-in Solver, the user needs to
check both the equations on the spreadsheet and the model formulation as entered into
Solver. This separation between the equations and the model form makes checking and
debugging difficult. OpenSolver provides a novel solution to this in the form of direct
model visualisation on the spreadsheet. As Figure 5 shows, OpenSolver can annotate a
spreadsheet to display a model as follows:
• The objective cell is highlighted and labelled min or max
• The adjustable cells are shaded. Binary and integer decision variable cells are
labelled „b‟ and „i‟ respectively.
• Each constraint is highlighted, and its sense (≥,≤, or =) shown (using a „>‟, „<‟ or
„=‟ respectively).
We have found this model visualisation to be very useful for checking large models, and
believe it will be very useful debugging tool for students learning to use Solver.
Figure 5: OpenSolver can display an optimisation model directly on the
spreadsheet. The screenshot on the left shows OpenSolver’s highlighting for the
model given earlier, while the screenshot on the right illustrates OpenSolver’s
highlighting for several other common model representations.
8 Automatic Model Construction
The original design of OpenSolver envisaged the continued use of Solver to build (but
not solve) the optimisation models. However, we have developed additional
functionality that allows OpenSolver to build Solver-compatible models itself without
requiring any user-interaction with Solver. Our approach builds on the philosophy that
the model should be fully documented on the spreadsheet. Thus, we require that the
spreadsheet identifies the objective sense (using the keyword „min‟ or „max‟ or variants
of these), and gives the sense (>=,<=, or =) of each constraint. Our example problem
shown in Figure 1 satisfies these requirements. In our teaching, we have always
recommended this model layout as good practice, and note that many textbooks follow a
similar approach. Our keyword-based approach creates only a minimal additional
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23. burden for the user but, by allowing the model construction process to be automated,
delivers what we consider to be a significantly improved modelling experience.
To identify the model, OpenSolver starts by searching for a cell containing the text
`min‟ or „max‟ (or variants on these). It then searches the cells in the vicinity of this
min/max cell to find a cell containing a formula (giving preference to any cell
containing a „sumproduct‟ formula); if one is found, this is assumed to define the
objective function. The user is then asked to confirm that this is the objective function
cell, or manually set or change the objective function cell.
After identifying the objective function cell, OpenSolver then tries to locate the
decision variables. Because the objective function depends on the decision variable
cells, these decision cells must be contained in the set of the objective function‟s
„precedent‟ cells (i.e. the cells referred to by the objective function formula, either
directly or indirectly through other intermediate cells). However, if a sumproduct is
used, for example, these precedents will also contain the objective function coefficients.
OpenSolver attempts to distinguish between decision variables and objective function
coefficients by looking at the number of dependent cells. An objective function
coefficient will typically only have one dependent cell, being the objective function cell.
However, decision variables will have many dependents as they feature in both the
objective function cell and in the constraint cells. Thus, OpenSolver examines each
objective function precedent cell, and keeps as decision variables those cells with more
than 1 successor. The resultant set of decision variables is presented to the user to
confirm or change.
The next step is to identify any binary or integer restrictions on the decision
variables. These are assumed to be indicated in the spreadsheet by the text „binary‟ or
„integer‟ (and variants of these) entered in the cell beneath any restricted decision
variable.
The final requirement is to determine the constraints. OpenSolver considers all cells
(except for the objective function cell) that are successors of the decision variables, and
searches in the vicinity of each of these for one of the symbols „<=‟, „<‟, „=‟, „>=‟, or
„>‟. A constraint is created for each occurrence of these symbols.
As shown in , OpenSolver allows the user to correct mistakes made when
determining the objective function cell, the decision variable cells, and/or any binary or
integer restrictions on these cells. Errors in the constraints currently need to be corrected
using Solver. Once the model has been confirmed (and/or corrected) by the user, it is
constructed and stored using the standard Solver named ranges, and thus can be solved
using Solver or OpenSolver. It can also be edited using Solver. Testing on a range of
spreadsheet models has shown that the auto-model algorithms work correctly for
commonly taught model layouts including tabular models such as transportation.
The AutoModel feature has been developed by Iain Dunning, a student in the
Engineering Science department at the University of Auckland
9 Advanced Features
OpenSolver offers a number of features for advanced users, including:
The ability to easily solve an LP relaxation,
Interaction with the CBC solver via the command line,
Faster running using „Quick Solve‟ when repeatedly solving the same
problem with a succession of different right hand sides, and
Viewing of the .lp problem file and CBC‟s solution file
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24. Note that our large scheduling problem had to be solved repeatedly for 52 different right
hand side values. The Quick Solve feature was developed to remove the need to
repeatedly analyse the spreadsheet to determine the model coefficients. Using Quick
Solve reduced the scheduling problem‟s run times for from one hour to one minute.
Figure 6: The auto-model dialog, shown here for the model in Figure 1, guides the
user through the model building steps, allowing them to correct any mistakes made
by OpenSolver’s auto-model algorithms.
10 User Feedback
As at 10 November 2010, OpenSolver has been downloaded over 750 times since 16
July 2010. Since 20 June 2010, the OpenSolver web site, www.opensolver.org, has
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25. served over 6000 page views to over 1800 visitors. Much of this interest can be
attributed to OpenSolver being featured on Mike Trick‟s OR blog (Trick, 2010) and
mentioned on the “IEOR Tools” website (Larry, 2010). It is difficult to determine how
OpenSolver is being used, but a comment by Joel Sokol from Georgia Tech on the
OpenSolver web site describes one use of OpenSolver as follows:
Thanks, Andrew! I’m using OpenSolver on a project I’m doing for a Major League
Baseball team, and it’s exactly what I needed. It lets the team use their preferred
platform, creates and solves their LPs very quickly, and doesn’t constrain them with any
variable limits. Thanks again! - Joel Sokol, August 11, 2010
11 Conclusions
We have shown that it is possible to leverage the COIN-OR software to provide users
with a new open source option for delivering spreadsheet-based operations research
solutions. While our software is compatible with Solver, it also provides novel tools for
visualising and building spreadsheet models that we hope will benefit both students and
practitioners.
References
CBC, 8 November 2010, https://projects.coin-or.org/Cbc
COIN-OR, 8 November 2010, www.coin-or.org
Dunning, I., personal communication, August 2010
FrontLine, 8 November 2010, www.solver.org
Larry, 7 July 2010, http://industrialengineertools.blogspot.com/2010/07/open-source-
solver-for-excel.html
Pieterse, J.K., 6 November 2010, http://www.jkp-ads.com/officemarketplacenm-en.asp
Solver Limits, 8 November 2010, http://www.solver.com/suppstdsizelim.htm
Trick, M., 7 July 2010, http://mat.tepper.cmu.edu/blog/?p=1167
Walkenbach, J., “Excel 2010 Formulas”, p75, Wiley Publishing, Indiana, 2010, online
on 7 November 2010 at Google Books.
Wikipedia, “Microsoft Excel”, 7 November 2010,
http://en.wikipedia.org/wiki/Microsoft_Excel
Appendix 1: Solver’s internal model representation under Excel 2010
and earlier versions. (This is a partial listing for Excel 2010.)
Name1
Interpretation Example Values2
solver_lhs1,
solver_lhs2, ...5
A range defining the left hand side of
constraints 1, 2, ...,
=Sheet1!$G$6:$G$7
=Sheet1!$G$8
solver_rhs1,
solver_rhs2, ...5
The right hand side of constraints 1, 2, ...
defined by either a range or a constant value
or one of the keywords: integer, binary
=Sheet1!$I$6:$I$7
=7
solver_rel1,
solver_rel2, ...5
The nature of the constraint, being one of
the following integer values: 1: <=, 2: =,
3: >=, 4: integer, 5: binary
=1
=binary
solver_num5
The number of constraints. =2
solver_adj A range defining the decision variables
(termed adjustable cells)
=Sheet1!$C$2:$E$2
Proceedings of the 45th
Annual Conference of the ORSNZ, November 2010
189
26. solver_lin3,7
1 if the user has ticked “Assume linear
model”, 2 if this is unchecked.
=1
=2
solver_neg3
1 if the user has ticked “Assume non-
negative”, 2 if this is unchecked.
=1
=2
solver_nwt Solver‟s “Search” option value,
1=”Newton”, 2=”Conjugate”
=1
solver_pre Solver‟s “Precision” option value =0.000001
solver_cvg Solver‟s “Convergence” option value =0.0001
solver_drv Solver‟s “Derivative” option value,
1=”Forward”, 2=”Central”
=1
solver_est Solver‟s “Estimates” option value,
1=”Tangent”, 2=”Quadratic”
=1
solver_itr Solver‟s “Iterations” option value, the
maximum number of iterations (branch and
bound nodes?) Solver can run for before the
user is alerted
=100
solver_scl Solver‟s “Use Automatic Scaling” option
value, 1=true, 2=false
=2
solver_sho8
Solver‟s “Show Iteration Results” option
value, 1=true, 2=false
=2
solver_tim Solver‟s “Max time” option value, the
maximum number of seconds Solver can
run for before the user is alerted
=100
solver_tol Solver‟s “Tolerance” option value, stored as
a fraction and displayed to the user as a
percentage value.
=0.05
solver_typ Objective sense, as in “Set target cell to”:
1=”Max”, 2=”Min”, 3=”Value of”
=2
solver_val If solver_typ=3, this gives the target value
for the objective function.
=0
solver_ver8
Solver version.(=3 in Excel 2010) =3
solver_eng8
Engine. 1=Nonlinear, 2=Simplex,
3=Evolutionary
=2
Notes:
1: The name is local to the sheet, and so is prefixed by the sheet name, e.g.
Sheet1!solver_lhs1.
2: The value always begins with an “=”, e.g. “=2” or “=Sheet1!$C$2:$E$2”
3: Models built using older versions of Solver may not have this defined.
4: Some values may be missing. For example, a model can be defined that has no
decision variables.
5: solver_num may be less than the apparent number of constraints. This occurs when
constraints are deleted because Solver does not delete the unused solver_lhs,
solver_rhs and solver_rel names.
6: References such as =Sheet1!#REF! can occur in the current model if cells have been
deleted. These are detected by OpenSolver.
7: Excel 2010 removes the “Assume linear model” option, and instead asks the user to
choose the specific solver (linear solver, non-linear solver or genetic algorithm).
8: Not defined in versions before Excel 2010
Proceedings of the 45th
Annual Conference of the ORSNZ, November 2010
190
27. APPENDIX II: | Page 26 of 33
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28. APPENDIX III: | Page 27 of 33
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29. APPENDIX IV: | Page 28 of 33
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30. APPENDIX V: | Page 29 of 33
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31. APPENDIX VI: | Page 30 of 33
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32. REFERENCES | PAGE A
REFERENCES
Mason, A.J., “OpenSolver – An Open Source Add-in to Solve Linear and Integer Progammes in Excel”, Operations
Research Proceedings 2011, eds. Klatte, Diethard, Lüthi, Hans-Jakob, Schmedders, Karl, Springer Berlin Heidelberg
pp 401-406, 2012, http://dx.doi.org/10.1007/978-3-642-29210-1_64, http://opensolver.org
.
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33. REFERENCES | PAGE B
GRAPHICS:
TBD
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