Analytics as a Source of Business Innovation

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Business Intelligence, Analytics, and Data Science: A Managerial Perspective

Fourth Edition

Chapter 6

Prescriptive Analytics: Optimization and Simulation

Learning Objectives (1 of 2)

6.1 Understand the applications of prescriptive analytics techniques in combination with reporting and predictive analytics

6.2 Understand the basic concepts of analytical decision modeling

6.3 Understand the concepts of analytical models for selected decision problems, including linear programming and simulation models for decision support

6.4 Describe how spreadsheets can be used for analytical modeling and solutions

Slide 6-2

Slide 2 is a list of textbook LO numbers and statements.

Learning Objectives (2 of 2)

6.5 Explain the basic concepts of optimization and when to use them

6.6 Describe how to structure a linear programming model

6.7 Explain what is meant by sensitivity analysis, what-if analysis, and goal seeking

6.8 Understand the concepts and applications of different types of simulation

6.9 Understand potential applications of discrete event simulation

Slide 6-3

Slide 3 is a list of textbook LO numbers and statements.

OPENING VIGNETTE School District of Philadelphia Uses Prescriptive Analytics to Find Optimal Solution for Awarding Bus Route Contracts

Discussion Questions

What decision was being made in this vignette?

What data (descriptive and or predictive) might one need to make the best allocations in this scenario?

What other costs or constraints might you have to consider in awarding contracts for such routes?

Which other situations might be appropriate for applications of such models?

Slide 6-4

Model-Based Decision Making

Prescriptive analytics – making decision using some kind of analytical model

Descriptive and predictive analytics creates the foundation (i.e., choice alternatives) for prescriptive analytics (i.e., making best possible decision)

Descriptive and Predictive leads to Prescriptive

Descriptive, Predictive  Prescriptive

Example

Profit maximization based on optimal spending on promotions and product/service pricing

Slide 6-5

Prescriptive Analytics Model Examples

INFORMS publications such as Interfaces, ORMS Today, and Analytics Magazine, include real-world cases illustrating successful analytics applications.

Modeling is a key element to prescriptive analytics

Mathematical modeling

TurboRouter - DSS for ship routing

In just a few weeks, company saved $1-2M

Example: which customers should receive certain promotional offers to maximize overall response (while staying within a pre-specified budget).

Slide 6-6

Application Case 6.1 Optimal Transport for ExxonMobil Downstream through a Decision Support System (DSS)

Questions for Discussion

List three ways in which manual scheduling of ships could result in more operational costs as compared to the tool developed.

In what other ways can ExxonMobil leverage the decision support tool developed to expand and optimize their other business operations?

What are some strategic decisions that could be made by decision makers using the tool developed?

Slide 6-7

Major Modeling Issues

Problem identification and environmental analysis (information collection)

Variable identification

Influence diagrams, cognitive maps

Forecasting (predictive analytics)

More information leads to better forecast/prediction

Multiple models: A decision system can include several models, each of which representing a different part of the decision-making problem

Static versus dynamic models

See categories of models in the next slide

Slide 6-8

Major Modeling Issues

Model Management

Models (like data) must be managed to maintain their integrity and applicability

Model-based management systems (MBMS)

Knowledge-Based Modeling (KBM)

DSS usually uses quantitative models

Expert systems use qualitative, KB models

Current trends in modeling

Cloud-based modeling tools (efficient and cost effective)

Transparent models (multidimensional/visual models)

Model of models

e.g., Influence Diagrams (to build and solve models)

…

Slide 6-9

Categories of Models

Slide 6-10

Application Case 6.2 Ingram Micro Uses Business Intelligence Applications to Make Pricing Decisions

Questions for Discussion

What were the main challenges faced by Ingram Micro in developing a BIC?

List all the business intelligence solutions developed by Ingram to optimize the prices of their products and to profile their customers.

What benefits did Ingram receive after using the newly developed BI applications?

Slide 6-11

Non-Quantitative Models (Qualitative)

Quantitative Models: Mathematically links decision variables, uncontrollable variables, and result variables

Structure of Mathematical Models for Decision Support

Independent Variables

Dependent Variable

Slide 6-12

Examples - Components of Models

Slide 6-13

The Structure of a Mathematical Model

The components of a quantitative model are linked together by mathematical (algebraic) expressions—equations or inequalities.

Example: Profit - 𝑃 = 𝑅 − 𝐶

where P = profit, R = revenue, and C = cost

Example: Simple Present-Value formulation

where P = present value, F = future cash-flow, i = interest rate, and n = number of period/years

Slide 6-14

Modeling and Decision Making - Under Certainty, Uncertainty, and Risk

Certainty

Assume complete knowledge

All potential outcomes are known

May yield optimal solution

Uncertainty

Several outcomes for each decision

Probability of each outcome is unknown

Knowledge would lead to less uncertainty

Risk analysis (probabilistic decision making)

Probability of each of several outcomes occurring

Level of uncertainty  Risk (expected value)

Slide 6-15

Modeling and Decision Making - Under Certainty, Uncertainty, and Risk

The zones of decision making

Slide 6-16

Application Case 6.3 American Airlines Uses Should-Cost Modeling to Assess the Uncertainty of Bids for Shipment Routes

Questions for Discussion

Besides reducing the risk of overpaying or underpaying suppliers, what are some other benefits AA would derive from its “should-be” model?

Can you think of other domains besides air transportation where such a model could be used?

Discuss other possible methods with which AA could have solved its bid overpayment and underpayment problem.

Slide 6-17

Decision Modeling with Spreadsheets

Spreadsheet

Most popular end-user modeling tool

Flexible and easy to use

Powerful functions (add-in functions)

Programmability (via macros)

What-if analysis and goal seeking

Simple database management

Seamless integration of model and data

Incorporates both static and dynamic models

Examples: Microsoft Excel, Lotus 1-2-3

Slide 6-18

Application Case 6.4 Pennsylvania Adoption Exchange Uses Spreadsheet Model to Better Match Children with Families

Questions for Discussion

What were the challenges faced by PAE while making adoption matching decisions?

What features of the new spreadsheet tool helped PAE solve their issues of matching a family with a child?

Slide 6-19

Application Case 6.5 Metro Meals on Wheels Treasure Valley Uses Excel to Find Optimal Delivery Routes

Questions for Discussion

What were the challenges faced by Metro Meals on Wheels Treasure Valley related to meal delivery before adoption of the spreadsheet-based tool?

Explain the design of the spreadsheet-based model.

What are the intangible benefits of using the Excel-based model to Metro Meals on Wheels?

Slide 6-20

Excel spreadsheet - Static Model Example: (Simple loan calculation of monthly payments)

Slide 6-21

Excel spreadsheet - Dynamic Model Example: (Simple loan calculation of monthly payments & effects of prepayment)

Slide 6-22

Optimization via Mathematical Programming

Mathematical Programming

A family of tools designed to help solve managerial problems in which the decision maker must allocate scarce resources among competing activities to optimize a measurable goal

Optimal solution: The best possible solution to a modeled problem

Linear programming (LP): A mathematical model for the optimal solution of resource allocation problems. All the relationships are linear.

Slide 6-23

Application Case 6.6 Mixed-Integer Programming Model Helps the University of Tennessee Medical Center with Scheduling Physicians

Questions for Discussion

What was the issue faced by the Regional Neonatal Associates group?

How did the HPSM model solve all of the physician’s requirements?

Slide 6-24

LP Problem Characteristics

Limited quantity of economic resources

Resources are used in the production of products or services

Two or more ways (solutions, programs) to use the resources

Each activity (product or service) yields a return in terms of the goal

Allocation is usually restricted by constraints

Slide 6-25

Linear Programming Steps

Identify the …

Decision variables

Objective function

Objective function coefficients

Constraints

Capacities / Demands / …

Represent the model

LINDO: Write mathematical formulation

EXCEL: Input data into specific cells in Excel

Run the model and observe the results

Slide 6-26

Modeling in LP - An Example

The Product-Mix Linear Programming Model (for MBI Corporation)

Decision variable: How many computers to build?

Two types of mainframe computers: CC-7 and CC-8

Constraints: Labor, Materials, and Marketing limits CC-7 CC-8 Rel Limit Labor (days) 300 500 <= 200,000 /mo Materials ($) 10,000 15,000 <= 8,000,000 /mo Units 1 >= 100 Units 1 >= 200 Profit ($) 8,000 12,000 (Max) Objective: Maximize Total Profit / Month

Slide 6-27

LP Solution – Algebraic Formulations

Slide 6-28

LP Solution with Excel

Decision Variables:

X1: unit of CC-7

X2: unit of CC-8

Objective Function:

Maximize Z (profit)

Z=8000X1+12000X2

Subject To

300X1 + 500X2  200K

10000X1 + 15000X2  8000K

X1  100

X2  200

Slide 6-29

Illustrating the Power of Spreadsheet Modeling

Election Resource Allocation Problem (Data)

Slide 6-30

Illustrating the Power of Spreadsheet Modeling

Election Resource Allocation Problem (Formulation)

Slide 6-31

Illustrating the Power of Spreadsheet Modeling

Election Resource Allocation Problem (Compact Formulation)

Slide 6-32

Common Optimization Models

Assignment (best matching of objects)

Dynamic programming

Goal programming

Investment (maximizing rate of return)

Linear and integer programming

Network models for planning and scheduling

Nonlinear programming

Replacement (capital budgeting)

Simple inventory models (e.g., economic order quantity)

Transportation (minimize cost of shipments)

Slide 6-33

Multiple Goals, Sensitivity Analysis, What-If Analysis, and Goal Seeking

Multiple Goals

Simple-goal vs. multiple goals

Vast majority of managerial problems has multiple goals (objectives) to achieve

Attaining all goals simultaneously

Methods of handling multiple goals

Utility theory

Goal programming

Expression of goals as constraints, using LP

A points system

Slide 6-34

Multiple Goals, Sensitivity Analysis, What-If Analysis, and Goal Seeking

Certain difficulties may arise when analyzing multiple goals:

Difficult to obtain a single organizational goal

The importance of goals change over time

Goals and sub-goals are viewed differently

Goals change in response to other changes

Dynamics of groups of decision makers

Assessing the importance (priorities)

Slide 6-35

Multiple Goals, Sensitivity Analysis, What-If Analysis, and Goal Seeking

Sensitivity analysis

It is the process of assessing the impact of change in inputs on outputs

Helps to …

eliminate (or reduce) variables

revise models to eliminate too-large sensitivities

adding details about sensitive variables or scenarios

obtain better estimates of sensitive variables

alter a real-world system to reduce sensitivities

…

Can be automatic or trial and error

Slide 6-36

Multiple Goals, Sensitivity Analysis, What-If Analysis, and Goal Seeking

What-if analysis

Assesses solutions based on changes in variables or assumptions (scenario analysis)

What if we change our capacity at the milling station by 40% [what would be the impact on output?]

Goal seeking

Backwards approach, starts with the goal and determines values of inputs needed

Example is break-even point determination

In order to break even (profit = 0), how many products do we have to sell each month?

Slide 6-37

What-If Analysis Example in Excel

Slide 6-38

Goal Seeking Example in Excel

Slide 6-39

Decision Analysis with Decision Tables and Decision Trees

Decision Tables – a tabular representation of the decision situation (alternatives)

Investment example:

Goal: maximize the yield after one year

Yield depends on the status of the economy (the state of nature)

Solid growth

Stagnation

Inflation

Slide 6-40

Decision Table - Investment Example: Possible Situations

1. If solid growth in the economy, bonds yield 12%; stocks 15%; time deposits 6.5%

2. If stagnation, bonds yield 6%; stocks 3%; time deposits 6.5%

3. If inflation, bonds yield 3%; stocks lose 2%; time deposits yield 6.5%

Slide 6-41

Payoff decision variables (alternatives)

Uncontrollable variables (states of economy)

Result variables (projected yield)

Tabular representation:

Decision Table Investment Example: Decision Table

Slide 6-42

Decision Table Investment Example: Treating Uncertainty

Optimistic approach vs. pessimistic approach

Treating Risk/Uncertainty:

Use known probabilities (expected values)

Multiple goals: yield, safety, and liquidity

Slide 6-43

Decision Trees

Graphical representation of relationships

Can be induced (driven) from data [data mining]

Can be driven from experts [knowledge-driven]

Multiple criteria approach

Demonstrates complex relationships

Cumbersome, if many alternatives exist

Many tools exist:

Mind Tools Ltd., mindtools.com

TreeAge Software Inc., treeage.com

Palisade Corp., palisade.com

Slide 6-44

Simulation

Simulation is the “appearance” of reality

It is often used to conduct what-if analysis on the model of the actual system

It is a popular DSS technique for conducting experiments with a computer on a comprehensive model of the system to assess its dynamic behavior

Often used when the system is too complex for other DSS techniques

Slide 6-45

Imitates reality and captures its richness both in shape and behavior

“Represent” versus “Imitate”

Technique for conducting experiments

Descriptive, not normative tool

Often to “solve” [i.e., analyze] very complex systems/problems

Simulation should be used only when a numerical optimization is not possible

Major Characteristics of Simulation

Slide 6-46

Application Case 6.7 Simulating Effects of Hepatitis B Interventions

Questions for Discussion

Explain the advantage of OR methods such as simulation over clinical trial methods in determining the best control measure for Hepatitis B.

In what ways do the decision and Markov models provide cost-effective ways of combating the disease?

Discuss how multidisciplinary background is an asset in finding a solution for the problem described in the case.

Slide 6-47

Advantages of Simulation

The theory is fairly straightforward

Great deal of time compression

Experiment with different alternatives

The model reflects manager’s perspective

Can handle wide variety of problem types

Can include the real complexities of problems

Produces important performance measures

Often it is the only DSS modeling tool for non-structured problems

Slide 6-48

Disadvantages of Simulation

Cannot guarantee an optimal solution

It is a descriptive model that can help develop prescriptive outcomes

Time-demanding and costly construction process

Cannot transfer solutions and inferences to solve other problems (models are problem specific)

So easy to explain/sell to managers, may lead to overlooking analytical/optimal solutions

Software may require special skills/experience

Slide 6-49

Simulation Methodology

Model Development Steps:

1. Define problem 5. Conduct experiments

2. Construct the model 6. Evaluate results

3. Test and validate model 7. Implement solution

4. Design experiments

Slide 6-50

Simulation Types

Stochastic vs. Deterministic Simulation

Uses probability distributions

Time-dependent vs. Time-independent Simulation

Monte Carlo Simulation (X = A + B) [A, B, and X are all probability distributions]

Discrete Event vs. Continuous Simulation vs. Agent-Based Simulation

Simulation Implementation

Visual Simulation and/or Object-Oriented Simulation

Slide 6-51

Application Case 6.8 Cosan Improves Its Renewable Energy Supply Chain Using Simulation

Questions for Discussion

What type of supply chain disruptions might occur in moving the sugar cane from the field to the production plants to develop sugar and ethanol?

What types of advanced planning and prediction might be useful in mitigating such disruptions?

Slide 6-52

Visual interactive modeling (VIM), also called Visual Interactive Simulation or Visual Interactive Problem Solving

Goal is to address conventional simulation modeling inadequacies

Uses computer graphics and animation

Often integrated with RFID and GIS

Allows for interactive/immersive sensitivity analysis

Virtual reality

Immersive presence

Visual Interactive Simulation (VIS)

Slide 6-53

Application Case 6.9 (1 of 4) Improving Job-Shop Scheduling Decisions through RFID: A Simulation-Based Assessment

Questions for Discussion

In situations such as what this case depicts, what other approaches can one take to analyze investment decisions?

How would one save time if an RFID chip can tell the exact location of a product in process?

Research to learn about the applications of RFID sensors in other settings. Which one do you find most interesting?

Slide 6-54

Application Case 6.9 (2 of 4) Improving Job-Shop Scheduling Decisions through RFID: A Simulation-Based Assessment (Simio - Modeling Interface)

Slide 6-55

Application Case 6.9 (3 of 4) Improving Job-Shop Scheduling Decisions through RFID: A Simulation-Based Assessment (Simio - Process Definition)

Slide 6-56

Application Case 6.9 (4 of 4) Improving Job-Shop Scheduling Decisions through RFID: A Simulation-Based Assessment (Simio – Result Reporting)

Slide 6-57

Simulation Software

A comprehensive list can be found at

orms-today.org/surveys/Simulation/Simulation.html

Simio LLC, simio.com

SAS Simulation [SAS OR], sas.com

Lumina Decision Systems, lumina.com

Oracle Crystal Ball, oracle.com

Palisade Corp., palisade.com

Rockwell Software, arenasimulation.com …

Slide 6-58

End of Chapter 6

Questions / Comments

Slide 6-59

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