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Chapter 9:

Model-Based Decision Making: Optimization and Multi-Criteria Systems

Business Intelligence and Analytics: Systems for Decision Support

(10th Edition)

Business Intelligence and Analytics: Systems for Decision Support

(10th Edition)

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Learning Objectives

Understand the basic concepts of analytical decision modeling

Describe how prescriptive models interact with data and the user

Understand some different, well-known model classes

Understand how to structure decision making with a few alternatives

Describe how spreadsheets can be used for analytical modeling and solution

(Continued…)

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Learning Objectives

Explain the basic concepts of optimization and when to use them

Describe how to structure a linear programming model

Describe how to handle multiple goals

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

Describe the key issues of multi-criteria decision making

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Opening Vignette…

Midwest ISO Saves Billions by Better Planning of Power Plant Operations and Capacity Planning

Company background

Problem description

Proposed solution

Results

Answer & discuss the case questions...

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Questions for the Opening Vignette

In what ways were the individual companies in Midwest ISO better off being part of MISO as opposed to operating independently?

The dispatch problem was solved with a linear programming method. Explain the need of such method in light of the problem discussed in the case.

What were the two main optimization algorithms used? Briefly explain the use of each algorithm.

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Decision Support Systems Modeling

DSS modeling (optimization & simulation) contribute to organizational success. Examples include:

Pillowtex (see ProModel, 2013),

Fiat (see ProModel, 2006),

Procter & Gamble (see Camm et al., 1997),

and others.

INFORMS publications such as Interfaces, ORMS Today, and Analytics magazine have plenty of such example cases

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Application Case 9.1

Optimal Transport for ExxonMobil Downstream Through a DSS

Questions for Discussion

List three ways in which manual scheduling of ships could result in more operational cost 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?

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Major Modeling Issues

Problem identification and environmental analysis (information collection)

Variable identification

Influence diagrams, cognitive maps

Forecasting/predicting

More information leads to better prediction

Multiple models: An MSS can include several models, each of which represents a different part of the decision-making problem

Categories of models >>>

Model management – DBMS vs. MBDM

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Categories of Models

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Model Categories Static and Dynamic Models

Static Analysis

Single snapshot of the situation

Single interval

Steady state

Dynamic Analysis

Dynamic models

Evaluate scenarios that change over time

Time dependent

Represents trends and patterns over time

More realistic: Extends static models

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Application Case 9.2

Optimal Transport for ExxonMobil Downstream Through a DSS

Company

Problem description

Proposed solution

Results

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Model Categories Current Trends in Modeling

Development of Model/Solution Libraries

NEOS Server for Optimization

neos.mcs.anl.gov/neos/index.html

Resources link at informs.org

lionhrtpub.com/ORMS.shtml

Web-based modeling (optimization/simulation/…)

Multidimensional analysis (modeling)

Influence Diagrams

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Structure of Mathematical Models for Decision Support

Decision

Variables

Mathematical

Relationships

Uncontrollable

Variables

Result

Variables

Non-Quantitative Models (Qualitative)

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

Independent Variables

Dependent Variable

Intermediate

Variables

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Examples - Components of Models

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The Structure of a Mathematical Model

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

Example – Profit -

whereP= profit, R= revenue, and C= cost

Example - Simple Present-Value -

whereP= present value, F= future cash-flow, i= interest-rate, and n = number of period (years)

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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)

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

The Zones of Decision Making

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Application Case 9.3

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.

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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

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Application Case 9.4

Showcase Scheduling at Fred Astaire East Side Dance Studio

Company

Problem description

Proposed solution

Results

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Excel spreadsheet - static model example: (Simple loan calculation of monthly payments)

Static model example:

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Excel spreadsheet - Dynamic model example: Simple loan calculation of monthly payments and effects of prepayment

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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.

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Application Case 9.5

Spreadsheet Model Helps Assign Medical Residents

Company

Problem description

Proposed solution

Results

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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

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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

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Modeling in LP - An Example

The Product-Mix Linear Programming Model

MBI Corporation

Decision variable: How many computers to build next month?

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

Constraints: Labor limits, Materials limit, Marketing lower 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

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LP Solution – Algebraic Formulations

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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

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Illustrating the Power of Spreadsheet Modeling

Election Resource Allocation Problem

Analysis of “swing states” for the 2012 election…

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Common Optimization Models

Product-mix problems (how many of each product to produce for max profit)

Transportation (minimize cost of shipments)

Assignment (best matching of objects)

Investment (maximizing rate of return)

Network optimization models for planning and scheduling

Replacement (capital budgeting), …

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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 simultaneous goals

Methods of handling multiple goals

Utility theory

Goal programming

Expression of goals as constraints, using LP

A points system

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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)

…

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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

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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]

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

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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

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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%

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Payoff decision variables (alternatives)

Uncontrollable variables (states of economy)

Result variables (projected yield)

Tabular representation:

Decision Table Investment Example: Decision Table

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Decision Table Investment Example: Treating Uncertainty

Optimistic approach

Pessimistic approach

Treating Risk/Uncertainty:

Use known probabilities

Expected values

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Decision Table Investment Example: Multiple Goals

Multiple goals

Yield, safety, and liquidity

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Decision Trees

Graphical representation of relationships

Multiple criteria approach

Demonstrates complex relationships

Cumbersome, if many alternatives exists

Tools include

Mind Tools Ltd., mindtools.com

TreeAge Software Inc., treeage.com

Palisade Corp., palisade.com

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Decision Trees – An Example

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Multi-Criteria Decision Making with Pairwise Comparisons

Having more than one criterion makes decision-making process complicated

Usually some type of weighing algorithm is used to analyze such problems

The Analytic Hierarchy Process

Developed by Thomas Saaty (1995, 1996)

A very popular technique for MCDM

Popular Tools - ExpertChoice.com

Web-based Tools - Web-HIPRE (hipre.aalto.fi)

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Application Case 9.6

U.S. HUD Saves the House by Using AHP for Selecting IT Projects

Company

Problem description

Proposed solution

Results

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Tutorial - Applying AHP Using Web-HIPRE

Goal: select the most appropriate movie

Identify some criteria for making this decision

The main and sub-criteria for movie selection are

a. Genre: Action, Comedy, Sci-Fi, Romance

b. Language: English, Hindi

c. Day of Release: weekday, weekend

d. User/Critics Rating: High, Average, Low

Alternatives are the following current movies:

SkyFall, The Dark Knight Rises, The Dictator, Dabaang, Alien, and DDL

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Tutorial - Applying AHP Using Web-HIPRE

Step 1: define the goal, criteria, and alternatives

Web-HIBRE allows defining all of these and relationships within an easy-to-use Web-based interface.

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Tutorial - Applying AHP Using Web-HIPRE

Step 2: the main criteria are then ranked as they relate to the goal

A comparative ranking scale from 1 to 9 (with ascending order of importance) is used

The ranking is done using a Pairwise comparison procedure (i.e., divide-and-concur) between any two criteria for all combinations of twos

The tool readily normalizes the rankings of each of the main criteria over one another to a scale ranging from 0 to 1 and then calculates the row averages to arrive at an overall importance rating ranging from 0 to 1

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Tutorial - Applying AHP Using Web-HIPRE

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Tutorial - Applying AHP Using Web-HIPRE

Step 3: All of the subcriteria related to each of the main criteria are then ranked with their relative importance over one another

Step 4: Each alternative is ranked with respect to all of the subcriteria that are linked with the alternatives in a similar fashion using the relative scale of 0–9; then the overall importance of each alternative is calculated

Step 5: The final result are obtained from the composite priority analysis involving all the subcriteria and main criteria

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Tutorial - Applying AHP Using Web-HIPRE

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Tutorial - Applying AHP Using Web-HIPRE

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Tutorial - Applying AHP Using Web-HIPRE

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End of the Chapter

Questions, comments

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All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America.

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