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Business Analytics: Methods, Models,
and Decisions
Third Edition, Global Edition
Chapter 1
Introduction to
Business Analytics
Copyright © 2021 Pearson Education Ltd.
Copyright © 2021 Pearson Education Ltd. Slide - 2
Business Analytics
(Business) Analytics is the use of:
• data,
• information technology,
• statistical analysis,
• quantitative methods, and
• mathematical or computer-based models
to help managers gain improved insight about their
business operations and make better, fact-based
decisions.
Copyright © 2021 Pearson Education Ltd. Slide - 3
Examples of Applications
• Pricing
– setting prices for consumer and industrial goods, government
contracts, and maintenance contracts
• Customer segmentation
– identifying and targeting key customer groups in retail,
insurance, and credit card industries
• Merchandising
– determining brands to buy, quantities, and allocations
• Location
– finding the best location for bank branches and ATMs, or where
to service industrial equipment
Copyright © 2021 Pearson Education Ltd. Slide - 4
Examples of Applications (continued)
• Supply Chain Design
– determining the best sourcing and transportation options and
finding the best delivery routes
• Staffing
– ensuring appropriate staffing levels and capabilities, and hiring
the right people
• Health care
– scheduling operating rooms to improve utilization, improving
patient flow and waiting times, purchasing supplies, and
predicting health risk factors
Copyright © 2021 Pearson Education Ltd. Slide - 5
Impacts of Analytics
• Benefits
– …reduced costs, better risk management, faster
decisions, better productivity and enhanced bottom-line
performance such as profitability and customer
satisfaction.
• Challenges
– …lack of understanding of how to use analytics,
competing business priorities, insufficient analytical
skills, difficulty in getting good data and sharing
information, and not understanding the benefits versus
perceived costs of analytics studies.
Copyright © 2021 Pearson Education Ltd. Slide - 6
Evolution of Business Analytics
• Analytic Foundations
– Business Intelligence (BI)
– Information Systems (IS)
– Statistics
– Operations Research/Management Science
(OR/MS)
Copyright © 2021 Pearson Education Ltd. Slide - 7
Evolution of Business Analytics
• Modern Business Analytic
– Data mining
– Simulation and risk analysis
– Decision Support Systems (DSS)
– Visualization
Copyright © 2021 Pearson Education Ltd. Slide - 8
A Visual Perspective of Business
Analytics
Copyright © 2021 Pearson Education Ltd. Slide - 9
Software Support and Spreadsheet
Technology
• Commercial software
– IBM Cognos Express
– SAS Analytics
– Tableau
• Spreadsheets
– Widely used
– Effective for manipulating data and developing and
solving models
– Support powerful commercial add-ons
– Facilitate communication of results
Copyright © 2021 Pearson Education Ltd. Slide - 10
Software Used in This Book
• Primary Spreadsheet Software
– Excel 2016 for Windows
– Excel 2016 for Mac
• Optional Software
– StatCrunch (Technology Help sections)
– Analytic Solver (online supplements)
Copyright © 2021 Pearson Education Ltd. Slide - 11
Descriptive, Predictive, and
Prescriptive Analytics
• Descriptive analytics: the use of data to
understand past and current business performance
and make informed decisions
• Predictive analytics: predict the future by
examining historical data, detecting patterns or
relationships in these data, and then extrapolating
these relationships forward in time.
• Prescriptive analytics: identify the best
alternatives to minimize or maximize some
objective
Copyright © 2021 Pearson Education Ltd. Slide - 12
Example 1.1: Retail Markdown
Decisions
• Most department stores clear seasonal inventory
by reducing prices.
• Key question: When to reduce the price and by
how much to maximize revenue?
• Potential applications of analytics in retail:
– Descriptive analytics: examine historical data for similar
– Predictive analytics: predict sales based on price
– Prescriptive analytics: find the best sets of pricing and
advertising to maximize sales revenue
products (prices, units sold, advertising …)
Copyright © 2021 Pearson Education Ltd. Slide - 13
Data for Business Analytics
• Data: numbers or textual data that are collected
through some type of measurement process
• Information: result of analyzing data; that is,
extracting meaning from data to support evaluation
and decision making
Copyright © 2021 Pearson Education Ltd. Slide - 14
Examples of Data Sources and Uses
• Annual reports
• Accounting audits
• Financial profitability analysis
• Economic trends
• Marketing research
• Operations management performance
• Human resource measurements
• Web behavior
– page views, visitor’s country, time of view, length of time, origin
and destination paths, products they searched for and viewed,
products purchased, what reviews they read, and many others
Copyright © 2021 Pearson Education Ltd. Slide - 15
Big Data
• Big data refers to massive amounts of business data
(volume) from a wide variety of sources (variety), much of
which is available in real time (velocity), and much of
which is uncertain or unpredictable (veracity).
• “The effective use of big data has the potential to
transform economies, delivering a new wave of
productivity growth and consumer surplus. Using big data
will become a key basis of competition for existing
companies, and will create new competitors who are able
to attract employees that have the critical skills for a big
data world.” - McKinsey Global Institute, 2011
Copyright © 2021 Pearson Education Ltd. Slide - 16
Data Reliability and Validity
• Reliability - data are accurate and consistent.
• Validity - data correctly measures what it is
supposed to measure.
Copyright © 2021 Pearson Education Ltd. Slide - 17
Data Reliability and Validity Examples
A tire pressure gage that consistently reads
several pounds of pressure below the true value is
not reliable, although it is valid because it does
measure tire pressure.
Copyright © 2021 Pearson Education Ltd. Slide - 18
Data Reliability and Validity Examples
The number of calls to a customer service desk
might be counted correctly each day (and thus
is a reliable measure) but not valid if it is used
to assess customer dissatisfaction, as many
calls may be simple queries.
Copyright © 2021 Pearson Education Ltd. Slide - 19
Data Reliability and Validity Examples
A survey question that asks a customer to rate the
quality of the food in a restaurant may be neither
reliable (because different customers may have
conflicting perceptions) nor valid (if the intent is to
measure customer satisfaction, as satisfaction
generally includes other elements of service
besides food).
Copyright © 2021 Pearson Education Ltd. Slide - 20
Models in Business Analytics
• Model - an abstraction or representation of a real
system, idea, or object.
– Captures the most important features
– Can be a written or verbal description, a visual
representation, a mathematical formula, or a
spreadsheet.
Copyright © 2021 Pearson Education Ltd. Slide - 21
Example 1.2: Three Forms of a
Model
The sales of a new product, such as a first-generation iPad
or 3D television, often follow a common pattern.
1. Verbal description: The rate of sales starts small as
early adopters begin to evaluate a new product and then
begins to grow at an increasing rate over time as
positive customer feedback spreads. Eventually, the
market begins to become saturated and the rate of
sales begins to decrease.
Copyright © 2021 Pearson Education Ltd. Slide - 22
Example 1.2 Continued
2. Visual model: A sketch of sales as an S-shaped curve
over time
Copyright © 2021 Pearson Education Ltd. Slide - 23
Example 1.2 Continued
3. Mathematical model:
where S is sales, t is time, e is the base of natural
logarithms, and a, b and c are constants
Copyright © 2021 Pearson Education Ltd. Slide - 24
Decision Models
• Decision Model - a logical or mathematical
representation of a problem or business situation that
can be used to understand, analyze, or facilitate making
a decision
• Inputs:
– Data – assumed to be constant
– Uncontrollable inputs – quantities that can change
but cannot be controlled
– Decision options – controllable and selected at the
discretion of the decision maker
Copyright © 2021 Pearson Education Ltd. Slide - 25
Nature of Decision Models
Copyright © 2021 Pearson Education Ltd. Slide - 26
Descriptive Models
• Descriptive models explain behavior and allow
users to evaluate potential decisions by asking
“what-if?” questions.
Copyright © 2021 Pearson Education Ltd. Slide - 27
Example 1.3: Gasoline Usage Model
• G = gallons of fuel consumed per month
• m = miles driven per day to and from work or
school
• d = number of driving days per month
• f = fuel economy in miles per gallon (mpg)
• a = additional miles for leisure and household
activities per month
Copyright © 2021 Pearson Education Ltd. Slide - 28
Example 1.3 Continued
• Use dimensions for logical consistency:
(m miles/day) x (d days/month) = m x d miles/month
• Total miles driven per month = m x d + a
• Gallons consumed per month
= (m x d + a miles/month)/(f miles/gallon)
= (m x d + a)/f gallons/month
Copyright © 2021 Pearson Education Ltd. Slide - 29
Example 1.4: An Outsourcing
Decision Model
• Production cost: $125/unit plus fixed cost of $50,000
• Outsourcing cost: $175/unit
• Q = production volume
• TC (manufacturing) = $50,000 + $125 x Q
• TC (outsourcing) = $175 x Q
• Breakeven Point: TC (manufacturing) = TC (outsourcing)
$50,000 + $125 x Q = $175 x Q
$50,000 = 50 x Q
Q = 1,000
• If Q < 1,000, outsourcing is cheaper.
Copyright © 2021 Pearson Education Ltd. Slide - 30
Example 1.4 Continued
Copyright © 2021 Pearson Education Ltd. Slide - 31
Predictive Models
• Predictive models focus on what will happen in
the future.
• Many predictive models are developed by
analyzing historical data and assuming that the
past is representative of the future.
Copyright © 2021 Pearson Education Ltd. Slide - 32
Example 1.5: A Sales-Promotion
Decision Model
In the grocery industry, managers typically need to know
how best to use pricing, coupons, and advertising
strategies to influence sales. Grocers often study the
relationship of sales volume to these strategies by
conducting controlled experiments to identify the
relationship between them and sales volumes. That is, they
implement different combinations of pricing, coupons, and
advertising, observe the sales that result, and use analytics
to develop a predictive model of sales as a function of
these decision strategies.
Copyright © 2021 Pearson Education Ltd. Slide - 33
Example 1.5 Model
If the price is $6.99, no coupons are offered, and no advertising is done
(the experiment corresponding to week 1), the model estimates sales as
Model:
Total Sales = 1105.55 +
56.18 x Price + 123.88 x
Coupon + 5.25 x Advertising
Total Sales = 1105.55 + 56.18 x 6.99 + 123.88 x 0 + 5.25 x 0 = 1,498.25 units
Copyright © 2021 Pearson Education Ltd. Slide - 34
Prescriptive Models
• Prescriptive models help decision makers identify
the best solution to a decision problem.
• Optimization - finding values of decision variables
that minimize (or maximize) something such as
cost (or profit)
– Objective function - the equation that minimizes (or
maximizes) the quantity of interest
– Optimal solution - values of the decision variables at
the minimum (or maximum) point
Copyright © 2021 Pearson Education Ltd. Slide - 35
Example 1.6: A Prescriptive Pricing
Model
• A firm wishes to determine the best pricing for one
of its products in order to maximize revenue.
• Analysts determined the following model:
Sales = -2.9485 x Price + 3,240.9
Total Revenue = Price x Sales
= Price x (-2.9485 x Price + 3,240.9)
= -2.9485 x Price2 + 3,240.9 x Price
• Identify the price that maximizes total revenue.
Copyright © 2021 Pearson Education Ltd. Slide - 36
Model Assumptions
• Assumptions are made to
– simplify a model and make it more tractable; that is,
able to be easily analyzed or solved.
– better characterize historical data or past
observations.
• The task of the modeler is to select or build an
appropriate model that best represents the
behavior of the real situation.
Copyright © 2021 Pearson Education Ltd. Slide - 37
Model Assumptions - Example
• Economic theory tells us that demand for a
product is negatively related to its price. Thus, as
prices increase, demand falls, and vice versa
(modeled by price elasticity — the ratio of the
percentage change in demand to the percentage
change in price).
• A key assumption in developing a model is the
type of relationship between demand and price.
Copyright © 2021 Pearson Education Ltd. Slide - 38
Example 1.7: A Linear Demand
Prediction Model
As price increases,
demand falls. A simple
model is:
D = a – bP
where D is the demand,
P is the unit price, a is a
constant that estimates
the demand when the
price is zero, and b is
the slope of the demand
function.
Copyright © 2021 Pearson Education Ltd. Slide - 39
Example 1.8: A Nonlinear Demand
Prediction Model
Assumes price elasticity is
constant (constant ratio of %
change in demand to %
change in price):
D = cP-d
where c is the demand when
the price is 0 and d > 0 is
the price elasticity.
Copyright © 2021 Pearson Education Ltd. Slide - 40
Uncertainty and Risk
• Uncertainty is imperfect knowledge of what will happen
in the future.
• Risk is associated with the consequences of what
actually happens.
• “To try to eliminate risk in business enterprise is futile. Risk is
inherent in the commitment of present resources to future
expectations. Indeed, economic progress can be defined as the
ability to take greater risks. The attempt to eliminate risks, even the
attempt to minimize them, can only make them irrational and
unbearable. It can only result in the greatest risk of all: rigidity.”
– Peter Drucker
Copyright © 2021 Pearson Education Ltd. Slide - 41
Problem Solving with Analytics
1. Recognizing a problem
2. Defining the problem
3. Structuring the problem
4. Analyzing the problem
5. Interpreting results and making a decision
6. Implementing the solution
Copyright © 2021 Pearson Education Ltd. Slide - 42
Recognizing a Problem
Problems exist when there is a gap between what is
happening and what we think should be happening.
• For example, costs are too high compared with
competitors.
Copyright © 2021 Pearson Education Ltd. Slide - 43
Defining the Problem
• Clearly defining the problem is not a trivial task.
• Complexity increases when the following occur:
– large number of courses of action
– the problem belongs to a group and not an
individual
– competing objectives
– external groups are affected
– problem owner and problem solver are not the
same person
– time limitations exist
Copyright © 2021 Pearson Education Ltd. Slide - 44
Structuring the Problem
• Stating goals and objectives
• Characterizing the possible decisions
• Identifying any constraints or restrictions
Copyright © 2021 Pearson Education Ltd. Slide - 45
Analyzing the Problem
• Analytics plays a major role.
• Analysis involves some sort of experimentation or
solution process, such as evaluating different
scenarios, analyzing risks associated with various
decision alternatives, finding a solution that meets
certain goals, or determining an optimal solution.
Copyright © 2021 Pearson Education Ltd. Slide - 46
Interpreting Results and Making a
Decision
• Models cannot capture every detail of the real
problem.
• Managers must understand the limitations of
models and their underlying assumptions and often
incorporate judgment into making a decision.
Copyright © 2021 Pearson Education Ltd. Slide - 47
Implementing the Solution
• Translate the results of the model back to the real
world.
• Requires providing adequate resources, motivating
employees, eliminating resistance to change,
modifying organizational policies, and developing
trust.

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Business PPT on Business Analytics For Beginners

  • 1. Slide - 1 Business Analytics: Methods, Models, and Decisions Third Edition, Global Edition Chapter 1 Introduction to Business Analytics Copyright © 2021 Pearson Education Ltd.
  • 2. Copyright © 2021 Pearson Education Ltd. Slide - 2 Business Analytics (Business) Analytics is the use of: • data, • information technology, • statistical analysis, • quantitative methods, and • mathematical or computer-based models to help managers gain improved insight about their business operations and make better, fact-based decisions.
  • 3. Copyright © 2021 Pearson Education Ltd. Slide - 3 Examples of Applications • Pricing – setting prices for consumer and industrial goods, government contracts, and maintenance contracts • Customer segmentation – identifying and targeting key customer groups in retail, insurance, and credit card industries • Merchandising – determining brands to buy, quantities, and allocations • Location – finding the best location for bank branches and ATMs, or where to service industrial equipment
  • 4. Copyright © 2021 Pearson Education Ltd. Slide - 4 Examples of Applications (continued) • Supply Chain Design – determining the best sourcing and transportation options and finding the best delivery routes • Staffing – ensuring appropriate staffing levels and capabilities, and hiring the right people • Health care – scheduling operating rooms to improve utilization, improving patient flow and waiting times, purchasing supplies, and predicting health risk factors
  • 5. Copyright © 2021 Pearson Education Ltd. Slide - 5 Impacts of Analytics • Benefits – …reduced costs, better risk management, faster decisions, better productivity and enhanced bottom-line performance such as profitability and customer satisfaction. • Challenges – …lack of understanding of how to use analytics, competing business priorities, insufficient analytical skills, difficulty in getting good data and sharing information, and not understanding the benefits versus perceived costs of analytics studies.
  • 6. Copyright © 2021 Pearson Education Ltd. Slide - 6 Evolution of Business Analytics • Analytic Foundations – Business Intelligence (BI) – Information Systems (IS) – Statistics – Operations Research/Management Science (OR/MS)
  • 7. Copyright © 2021 Pearson Education Ltd. Slide - 7 Evolution of Business Analytics • Modern Business Analytic – Data mining – Simulation and risk analysis – Decision Support Systems (DSS) – Visualization
  • 8. Copyright © 2021 Pearson Education Ltd. Slide - 8 A Visual Perspective of Business Analytics
  • 9. Copyright © 2021 Pearson Education Ltd. Slide - 9 Software Support and Spreadsheet Technology • Commercial software – IBM Cognos Express – SAS Analytics – Tableau • Spreadsheets – Widely used – Effective for manipulating data and developing and solving models – Support powerful commercial add-ons – Facilitate communication of results
  • 10. Copyright © 2021 Pearson Education Ltd. Slide - 10 Software Used in This Book • Primary Spreadsheet Software – Excel 2016 for Windows – Excel 2016 for Mac • Optional Software – StatCrunch (Technology Help sections) – Analytic Solver (online supplements)
  • 11. Copyright © 2021 Pearson Education Ltd. Slide - 11 Descriptive, Predictive, and Prescriptive Analytics • Descriptive analytics: the use of data to understand past and current business performance and make informed decisions • Predictive analytics: predict the future by examining historical data, detecting patterns or relationships in these data, and then extrapolating these relationships forward in time. • Prescriptive analytics: identify the best alternatives to minimize or maximize some objective
  • 12. Copyright © 2021 Pearson Education Ltd. Slide - 12 Example 1.1: Retail Markdown Decisions • Most department stores clear seasonal inventory by reducing prices. • Key question: When to reduce the price and by how much to maximize revenue? • Potential applications of analytics in retail: – Descriptive analytics: examine historical data for similar – Predictive analytics: predict sales based on price – Prescriptive analytics: find the best sets of pricing and advertising to maximize sales revenue products (prices, units sold, advertising …)
  • 13. Copyright © 2021 Pearson Education Ltd. Slide - 13 Data for Business Analytics • Data: numbers or textual data that are collected through some type of measurement process • Information: result of analyzing data; that is, extracting meaning from data to support evaluation and decision making
  • 14. Copyright © 2021 Pearson Education Ltd. Slide - 14 Examples of Data Sources and Uses • Annual reports • Accounting audits • Financial profitability analysis • Economic trends • Marketing research • Operations management performance • Human resource measurements • Web behavior – page views, visitor’s country, time of view, length of time, origin and destination paths, products they searched for and viewed, products purchased, what reviews they read, and many others
  • 15. Copyright © 2021 Pearson Education Ltd. Slide - 15 Big Data • Big data refers to massive amounts of business data (volume) from a wide variety of sources (variety), much of which is available in real time (velocity), and much of which is uncertain or unpredictable (veracity). • “The effective use of big data has the potential to transform economies, delivering a new wave of productivity growth and consumer surplus. Using big data will become a key basis of competition for existing companies, and will create new competitors who are able to attract employees that have the critical skills for a big data world.” - McKinsey Global Institute, 2011
  • 16. Copyright © 2021 Pearson Education Ltd. Slide - 16 Data Reliability and Validity • Reliability - data are accurate and consistent. • Validity - data correctly measures what it is supposed to measure.
  • 17. Copyright © 2021 Pearson Education Ltd. Slide - 17 Data Reliability and Validity Examples A tire pressure gage that consistently reads several pounds of pressure below the true value is not reliable, although it is valid because it does measure tire pressure.
  • 18. Copyright © 2021 Pearson Education Ltd. Slide - 18 Data Reliability and Validity Examples The number of calls to a customer service desk might be counted correctly each day (and thus is a reliable measure) but not valid if it is used to assess customer dissatisfaction, as many calls may be simple queries.
  • 19. Copyright © 2021 Pearson Education Ltd. Slide - 19 Data Reliability and Validity Examples A survey question that asks a customer to rate the quality of the food in a restaurant may be neither reliable (because different customers may have conflicting perceptions) nor valid (if the intent is to measure customer satisfaction, as satisfaction generally includes other elements of service besides food).
  • 20. Copyright © 2021 Pearson Education Ltd. Slide - 20 Models in Business Analytics • Model - an abstraction or representation of a real system, idea, or object. – Captures the most important features – Can be a written or verbal description, a visual representation, a mathematical formula, or a spreadsheet.
  • 21. Copyright © 2021 Pearson Education Ltd. Slide - 21 Example 1.2: Three Forms of a Model The sales of a new product, such as a first-generation iPad or 3D television, often follow a common pattern. 1. Verbal description: The rate of sales starts small as early adopters begin to evaluate a new product and then begins to grow at an increasing rate over time as positive customer feedback spreads. Eventually, the market begins to become saturated and the rate of sales begins to decrease.
  • 22. Copyright © 2021 Pearson Education Ltd. Slide - 22 Example 1.2 Continued 2. Visual model: A sketch of sales as an S-shaped curve over time
  • 23. Copyright © 2021 Pearson Education Ltd. Slide - 23 Example 1.2 Continued 3. Mathematical model: where S is sales, t is time, e is the base of natural logarithms, and a, b and c are constants
  • 24. Copyright © 2021 Pearson Education Ltd. Slide - 24 Decision Models • Decision Model - a logical or mathematical representation of a problem or business situation that can be used to understand, analyze, or facilitate making a decision • Inputs: – Data – assumed to be constant – Uncontrollable inputs – quantities that can change but cannot be controlled – Decision options – controllable and selected at the discretion of the decision maker
  • 25. Copyright © 2021 Pearson Education Ltd. Slide - 25 Nature of Decision Models
  • 26. Copyright © 2021 Pearson Education Ltd. Slide - 26 Descriptive Models • Descriptive models explain behavior and allow users to evaluate potential decisions by asking “what-if?” questions.
  • 27. Copyright © 2021 Pearson Education Ltd. Slide - 27 Example 1.3: Gasoline Usage Model • G = gallons of fuel consumed per month • m = miles driven per day to and from work or school • d = number of driving days per month • f = fuel economy in miles per gallon (mpg) • a = additional miles for leisure and household activities per month
  • 28. Copyright © 2021 Pearson Education Ltd. Slide - 28 Example 1.3 Continued • Use dimensions for logical consistency: (m miles/day) x (d days/month) = m x d miles/month • Total miles driven per month = m x d + a • Gallons consumed per month = (m x d + a miles/month)/(f miles/gallon) = (m x d + a)/f gallons/month
  • 29. Copyright © 2021 Pearson Education Ltd. Slide - 29 Example 1.4: An Outsourcing Decision Model • Production cost: $125/unit plus fixed cost of $50,000 • Outsourcing cost: $175/unit • Q = production volume • TC (manufacturing) = $50,000 + $125 x Q • TC (outsourcing) = $175 x Q • Breakeven Point: TC (manufacturing) = TC (outsourcing) $50,000 + $125 x Q = $175 x Q $50,000 = 50 x Q Q = 1,000 • If Q < 1,000, outsourcing is cheaper.
  • 30. Copyright © 2021 Pearson Education Ltd. Slide - 30 Example 1.4 Continued
  • 31. Copyright © 2021 Pearson Education Ltd. Slide - 31 Predictive Models • Predictive models focus on what will happen in the future. • Many predictive models are developed by analyzing historical data and assuming that the past is representative of the future.
  • 32. Copyright © 2021 Pearson Education Ltd. Slide - 32 Example 1.5: A Sales-Promotion Decision Model In the grocery industry, managers typically need to know how best to use pricing, coupons, and advertising strategies to influence sales. Grocers often study the relationship of sales volume to these strategies by conducting controlled experiments to identify the relationship between them and sales volumes. That is, they implement different combinations of pricing, coupons, and advertising, observe the sales that result, and use analytics to develop a predictive model of sales as a function of these decision strategies.
  • 33. Copyright © 2021 Pearson Education Ltd. Slide - 33 Example 1.5 Model If the price is $6.99, no coupons are offered, and no advertising is done (the experiment corresponding to week 1), the model estimates sales as Model: Total Sales = 1105.55 + 56.18 x Price + 123.88 x Coupon + 5.25 x Advertising Total Sales = 1105.55 + 56.18 x 6.99 + 123.88 x 0 + 5.25 x 0 = 1,498.25 units
  • 34. Copyright © 2021 Pearson Education Ltd. Slide - 34 Prescriptive Models • Prescriptive models help decision makers identify the best solution to a decision problem. • Optimization - finding values of decision variables that minimize (or maximize) something such as cost (or profit) – Objective function - the equation that minimizes (or maximizes) the quantity of interest – Optimal solution - values of the decision variables at the minimum (or maximum) point
  • 35. Copyright © 2021 Pearson Education Ltd. Slide - 35 Example 1.6: A Prescriptive Pricing Model • A firm wishes to determine the best pricing for one of its products in order to maximize revenue. • Analysts determined the following model: Sales = -2.9485 x Price + 3,240.9 Total Revenue = Price x Sales = Price x (-2.9485 x Price + 3,240.9) = -2.9485 x Price2 + 3,240.9 x Price • Identify the price that maximizes total revenue.
  • 36. Copyright © 2021 Pearson Education Ltd. Slide - 36 Model Assumptions • Assumptions are made to – simplify a model and make it more tractable; that is, able to be easily analyzed or solved. – better characterize historical data or past observations. • The task of the modeler is to select or build an appropriate model that best represents the behavior of the real situation.
  • 37. Copyright © 2021 Pearson Education Ltd. Slide - 37 Model Assumptions - Example • Economic theory tells us that demand for a product is negatively related to its price. Thus, as prices increase, demand falls, and vice versa (modeled by price elasticity — the ratio of the percentage change in demand to the percentage change in price). • A key assumption in developing a model is the type of relationship between demand and price.
  • 38. Copyright © 2021 Pearson Education Ltd. Slide - 38 Example 1.7: A Linear Demand Prediction Model As price increases, demand falls. A simple model is: D = a – bP where D is the demand, P is the unit price, a is a constant that estimates the demand when the price is zero, and b is the slope of the demand function.
  • 39. Copyright © 2021 Pearson Education Ltd. Slide - 39 Example 1.8: A Nonlinear Demand Prediction Model Assumes price elasticity is constant (constant ratio of % change in demand to % change in price): D = cP-d where c is the demand when the price is 0 and d > 0 is the price elasticity.
  • 40. Copyright © 2021 Pearson Education Ltd. Slide - 40 Uncertainty and Risk • Uncertainty is imperfect knowledge of what will happen in the future. • Risk is associated with the consequences of what actually happens. • “To try to eliminate risk in business enterprise is futile. Risk is inherent in the commitment of present resources to future expectations. Indeed, economic progress can be defined as the ability to take greater risks. The attempt to eliminate risks, even the attempt to minimize them, can only make them irrational and unbearable. It can only result in the greatest risk of all: rigidity.” – Peter Drucker
  • 41. Copyright © 2021 Pearson Education Ltd. Slide - 41 Problem Solving with Analytics 1. Recognizing a problem 2. Defining the problem 3. Structuring the problem 4. Analyzing the problem 5. Interpreting results and making a decision 6. Implementing the solution
  • 42. Copyright © 2021 Pearson Education Ltd. Slide - 42 Recognizing a Problem Problems exist when there is a gap between what is happening and what we think should be happening. • For example, costs are too high compared with competitors.
  • 43. Copyright © 2021 Pearson Education Ltd. Slide - 43 Defining the Problem • Clearly defining the problem is not a trivial task. • Complexity increases when the following occur: – large number of courses of action – the problem belongs to a group and not an individual – competing objectives – external groups are affected – problem owner and problem solver are not the same person – time limitations exist
  • 44. Copyright © 2021 Pearson Education Ltd. Slide - 44 Structuring the Problem • Stating goals and objectives • Characterizing the possible decisions • Identifying any constraints or restrictions
  • 45. Copyright © 2021 Pearson Education Ltd. Slide - 45 Analyzing the Problem • Analytics plays a major role. • Analysis involves some sort of experimentation or solution process, such as evaluating different scenarios, analyzing risks associated with various decision alternatives, finding a solution that meets certain goals, or determining an optimal solution.
  • 46. Copyright © 2021 Pearson Education Ltd. Slide - 46 Interpreting Results and Making a Decision • Models cannot capture every detail of the real problem. • Managers must understand the limitations of models and their underlying assumptions and often incorporate judgment into making a decision.
  • 47. Copyright © 2021 Pearson Education Ltd. Slide - 47 Implementing the Solution • Translate the results of the model back to the real world. • Requires providing adequate resources, motivating employees, eliminating resistance to change, modifying organizational policies, and developing trust.