Stevenson and Ozgur First Edition Introduction to Management Science with Spreadsheets...

Stevenson and OzgurFirst Edition

Introduction to Management Science with Spreadsheets

reserved.

Chapter 10Chapter 10

Multicriteria Decision-Multicriteria Decision-Making ModelsMaking Models

Part 2 Deterministic Decision ModelsPart 2 Deterministic Decision Models

Learning ObjectivesLearning Objectives

1. Describe the type of problems that goal programming is designed to handle.

2. Describe the similarities and differences between goal programming and linear programming models.

3. Formulate goal programming models.

4. Solve goal programming models that have two decision variables using a graphical approach.

5. Solve goal programming models using Excel and interpret solutions of goal programming models.

After completing this chapter, you should be able to:

Learning Objectives Learning Objectives (cont’d)(cont’d)

6. Describe the type of problems that the analytical hierarchy process is designed to handle.

7. Describe how to determine pairwise comparisons.

8. Describe what a consistency check is and calculate a consistency ratio, priority percentage, and priority score for each alternative using AHP.

9. Use Excel to solve analytical hierarchy process problems.

10.Describe and solve scoring model multicriteria decision-making problems.

After completing this chapter, you should be able to:

Goal Programming Versus Linear ProgrammingGoal Programming Versus Linear ProgrammingGoal Programming Versus Linear ProgrammingGoal Programming Versus Linear Programming

• Goal Programming (GP)

– A variation of linear programming that allows multiple objectives (goals)—soft (goal) constraints or a combination of soft and hard (nongoal) constraints—that can deviate, allowing for tradeoffs in achieving satisficing rather than only optimal solutions.

–GP models are similar to LP models in that both are formulated under the same requirements and assumptions (e.g., linearity, nonnegativity, certainty).

–GP uses, like LP, graphical methods to illustrate linear programming concepts.

Figure 10–1Figure 10–1 A Plot of a Goal ConstraintA Plot of a Goal ConstraintFigure 10–1Figure 10–1 A Plot of a Goal ConstraintA Plot of a Goal Constraint

Figure 10–2Figure 10–2 Designating Priority and DirectionDesignating Priority and DirectionFigure 10–2Figure 10–2 Designating Priority and DirectionDesignating Priority and Direction

Figure 10–3Figure 10–3 Plot of the Hard Constraint and the Feasible Solution SpacePlot of the Hard Constraint and the Feasible Solution SpaceFigure 10–3Figure 10–3 Plot of the Hard Constraint and the Feasible Solution SpacePlot of the Hard Constraint and the Feasible Solution Space

Figure 10–4Figure 10–4 The Acceptable Region after Adding the First Goal ConstraintThe Acceptable Region after Adding the First Goal ConstraintFigure 10–4Figure 10–4 The Acceptable Region after Adding the First Goal ConstraintThe Acceptable Region after Adding the First Goal Constraint

Figure 10–5Figure 10–5 The Second Goal Is Added to the GraphThe Second Goal Is Added to the GraphFigure 10–5Figure 10–5 The Second Goal Is Added to the GraphThe Second Goal Is Added to the Graph

Figure 10–6Figure 10–6 The Third Goal Is Added, but It Doesn’t Change the SolutionThe Third Goal Is Added, but It Doesn’t Change the SolutionFigure 10–6Figure 10–6 The Third Goal Is Added, but It Doesn’t Change the SolutionThe Third Goal Is Added, but It Doesn’t Change the Solution

Figure 10–7Figure 10–7 Plotting the Acceptable RegionPlotting the Acceptable RegionFigure 10–7Figure 10–7 Plotting the Acceptable RegionPlotting the Acceptable Region

Exhibit 10-1Exhibit 10-1 Excel Worksheet for Robinson Chemical Company Goal Excel Worksheet for Robinson Chemical Company Goal Programming Problem, Considering Only Priority 1 Programming Problem, Considering Only Priority 1 (Minimizing Labor Underutilization) Goal(Minimizing Labor Underutilization) Goal

Exhibit 10-2Exhibit 10-2 Excel Solver Parameters Screen for Robinson Chemical Excel Solver Parameters Screen for Robinson Chemical Company Goal Programming Problem Considering Only Company Goal Programming Problem Considering Only Priority 1 (Minimizing Labor Underutilization) GoalPriority 1 (Minimizing Labor Underutilization) Goal

Exhibit 10–3Exhibit 10–3 Excel Worksheet for Robinson Chemical Company Goal Excel Worksheet for Robinson Chemical Company Goal Programming Problem, Considering Priority 1 (Minimizing Labor Programming Problem, Considering Priority 1 (Minimizing Labor Underutilization) and Priority 2 (Minimizing Machine Hour Underutilization) and Priority 2 (Minimizing Machine Hour Underutilization) GoalsUnderutilization) Goals

Exhibit 10–4Exhibit 10–4 Excel Solver Parameters Screen for Robinson Chemical Excel Solver Parameters Screen for Robinson Chemical Company Goal Programming Problem, Considering Priority 2 Company Goal Programming Problem, Considering Priority 2 (Minimizing Machine Hours Underutilization) Goal While (Minimizing Machine Hours Underutilization) Goal While Ensuring That Priority 1 Goal Is SatisfiedEnsuring That Priority 1 Goal Is Satisfied

Exhibit 10–5Exhibit 10–5 Excel Solver Parameters Screen for Robinson Chemical Excel Solver Parameters Screen for Robinson Chemical Company Goal Programming Problem Considering Priority 3 Company Goal Programming Problem Considering Priority 3 (Minimizing the Unsatisfied Demand for Compound 200) Goal (Minimizing the Unsatisfied Demand for Compound 200) Goal While Ensuring That the Priority 1 and Priority 2 Goals Are While Ensuring That the Priority 1 and Priority 2 Goals Are Still SatisfiedStill Satisfied

Exhibit 10–6Exhibit 10–6 Excel Worksheet for Robinson Chemical Company Goal Programming Excel Worksheet for Robinson Chemical Company Goal Programming Problem, Considering Priority 4 Goal (Minimizing Unsatisfied Demand for Problem, Considering Priority 4 Goal (Minimizing Unsatisfied Demand for Compound 200) While Ensuring That Priority 1 (Minimizing Labor Compound 200) While Ensuring That Priority 1 (Minimizing Labor Underutilization), Priority 2 (Minimizing Machine Hour Underutilization), and Underutilization), Priority 2 (Minimizing Machine Hour Underutilization), and Priority 3 (Unsatisfied Demand for Compound 200) Goals Are SatisfiedPriority 3 (Unsatisfied Demand for Compound 200) Goals Are Satisfied

Exhibit 10–7Exhibit 10–7 Excel Solver Parameters Screen for Robinson Chemical Excel Solver Parameters Screen for Robinson Chemical Company Goal Programming Problem Considering Priority 4 Company Goal Programming Problem Considering Priority 4 (Minimizing the Unsatisfied Demand for Compound 100) Goal (Minimizing the Unsatisfied Demand for Compound 100) Goal While Ensuring that Priority 1, priority 2, and Priority 3 Goals While Ensuring that Priority 1, priority 2, and Priority 3 Goals Are Still SatisfiedAre Still Satisfied

Exhibit 10–8Exhibit 10–8 Excel Worksheet for Robinson Chemical Company Weighted Excel Worksheet for Robinson Chemical Company Weighted Goal Programming ProblemGoal Programming Problem

Analytical Hierarchy Process (AHP)Analytical Hierarchy Process (AHP)Analytical Hierarchy Process (AHP)Analytical Hierarchy Process (AHP)

• Analytical Hierarchy Process (AHP)

– An approach to complex multicriteria decision making based on pairwise comparisons.

• Consistency

– A concept that compares the quality of pairwise comparisons made by the decision maker. It measures how consistent the decision maker is regarding the values he or she assigns to the pairwise comparisons.

• Consistency Ratio (Index)

– A numerical measure (the ratio of the consistency index (CI) to the random index (RI) of pairwise comparisons made by the decision maker. A ratio of less than .10 is considered acceptable.

Figure 10–8Figure 10–8 Graphical Representation of the Hierarchies for the stereo Graphical Representation of the Hierarchies for the stereo system-selection problemsystem-selection problem

Table 10–1Table 10–1 Preference Scale for the Pairwise ComparisonsPreference Scale for the Pairwise ComparisonsTable 10–1Table 10–1 Preference Scale for the Pairwise ComparisonsPreference Scale for the Pairwise Comparisons

Table 10–2 Table 10–2 Pairwise Comparison Table for the Stereo System Selection Pairwise Comparison Table for the Stereo System Selection ProblemProblem

Table 10–3 Table 10–3 Normalized Pairwise Comparison Table for the Stereo System Normalized Pairwise Comparison Table for the Stereo System Selection ProblemSelection Problem

Table 10–4Table 10–4 Calculation of the Weighted Priorities for the CriteriaCalculation of the Weighted Priorities for the CriteriaTable 10–4Table 10–4 Calculation of the Weighted Priorities for the CriteriaCalculation of the Weighted Priorities for the Criteria

Table 10Table 10–5–5 Random Index Values for the Comparison of n itemsRandom Index Values for the Comparison of n itemsTable 10Table 10–5–5 Random Index Values for the Comparison of n itemsRandom Index Values for the Comparison of n items

Table 10–6Table 10–6 Pairwise Comparison Matrix PricePairwise Comparison Matrix PriceTable 10–6Table 10–6 Pairwise Comparison Matrix PricePairwise Comparison Matrix Price

Table 10Table 10–7–7 Proportion Matrix for PriceProportion Matrix for PriceTable 10Table 10–7–7 Proportion Matrix for PriceProportion Matrix for Price

Table 10–8Table 10–8 Priority Percentage for PricePriority Percentage for PriceTable 10–8Table 10–8 Priority Percentage for PricePriority Percentage for Price

Table 10–9Table 10–9 Determination of the Overall PriorityDetermination of the Overall PriorityTable 10–9Table 10–9 Determination of the Overall PriorityDetermination of the Overall Priority

Table 10–9Table 10–9 Determination of the Overall Priority Determination of the Overall Priority (cont’d)(cont’d)Table 10–9Table 10–9 Determination of the Overall Priority Determination of the Overall Priority (cont’d)(cont’d)

Exhibit 10–9Exhibit 10–9 Analytical Hierarchy Process for the Stereo System SelectionAnalytical Hierarchy Process for the Stereo System SelectionExampleExample

Table 10–10Table 10–10 Excel Formulas for the AHP Worksheet in Exhibit 10-9Excel Formulas for the AHP Worksheet in Exhibit 10-9Table 10–10Table 10–10 Excel Formulas for the AHP Worksheet in Exhibit 10-9Excel Formulas for the AHP Worksheet in Exhibit 10-9

Table 10–10Table 10–10 Excel Formulas for the AHP Worksheet in Exhibit 10-9 Excel Formulas for the AHP Worksheet in Exhibit 10-9 (cont’d)(cont’d)Table 10–10Table 10–10 Excel Formulas for the AHP Worksheet in Exhibit 10-9 Excel Formulas for the AHP Worksheet in Exhibit 10-9 (cont’d)(cont’d)

Scoring ModelsScoring ModelsScoring ModelsScoring Models

• Scoring Model–A subjective multicriteria method in which the decision

maker assigns weights to each criterion based on the importance of the criterion and then assigns a rating for each decision alternative on each criterion.

–Model outcomes are the sum of the products of the criteria weight with the respective ratings of criteria for that decision alternative.

• Areas of application–Facility location–Product selection

Figures A & BFigures A & BFigures A & BFigures A & B

Figures C & DFigures C & DFigures C & DFigures C & D

Exhibit 10–10Exhibit 10–10 Excel Worksheet for Solved Problem 1, Goal Programming Problem, Excel Worksheet for Solved Problem 1, Goal Programming Problem, Considering Only Priority 1 (Minimizing Labor Underutilization) GoalConsidering Only Priority 1 (Minimizing Labor Underutilization) Goal

Exhibit 10–11Exhibit 10–11 Excel Solver Parameters Screen for Solved Problem 1, Goal Excel Solver Parameters Screen for Solved Problem 1, Goal Programming Problem Considering Only Priority 1 (Minimizing Programming Problem Considering Only Priority 1 (Minimizing Labor Underutilization) GoalLabor Underutilization) Goal

Exhibit 10–12Exhibit 10–12 Excel Solver Parameters Screen for Solved Problem 1, Goal Excel Solver Parameters Screen for Solved Problem 1, Goal Programming Problem Considering Priority 2 Goal Given That Programming Problem Considering Priority 2 Goal Given That Priority 1 Goal Is MetPriority 1 Goal Is Met

Exhibit 10–13Exhibit 10–13 Excel Solver Parameters Screen for Solved Problem 1, Goal Excel Solver Parameters Screen for Solved Problem 1, Goal Programming Problem Considering Priority 3 Goal Given That Programming Problem Considering Priority 3 Goal Given That Priority 1 and Priority 2 Goals Have Been MetPriority 1 and Priority 2 Goals Have Been Met

Exhibit 10–14Exhibit 10–14 Excel Worksheet for Solved Problem 1, Goal Programming Problem, Excel Worksheet for Solved Problem 1, Goal Programming Problem, Considering Priority 4 (Minimizing Labor Overutilization) Goal Given Considering Priority 4 (Minimizing Labor Overutilization) Goal Given That Priority 1, 2, and 3 Goals Have Been MetThat Priority 1, 2, and 3 Goals Have Been Met

Exhibit 10–15Exhibit 10–15 Excel Solver Parameters Screen for Solved Problem 1, Goal Excel Solver Parameters Screen for Solved Problem 1, Goal Programming Problem Considering Priority 4 Goal, Given That Programming Problem Considering Priority 4 Goal, Given That Priority 1, Priority 2, and Priority 3 Goals Have Been MetPriority 1, Priority 2, and Priority 3 Goals Have Been Met

Exhibit 10–16Exhibit 10–16 Excel Worksheet for Solved Problem 2, Goal Programming Excel Worksheet for Solved Problem 2, Goal Programming Problem, Considering Only Priority 1 (Minimizing u1) GoalProblem, Considering Only Priority 1 (Minimizing u1) Goal

Exhibit 10–17Exhibit 10–17 Excel Solver Parameters Screen for Solved Problem 1, Excel Solver Parameters Screen for Solved Problem 1, Goal Programming Problem Considering Only Priority 1 Goal Programming Problem Considering Only Priority 1 (Minimizing u1) Goal(Minimizing u1) Goal

Exhibit 10–18Exhibit 10–18 Excel Worksheet for Solved Problem 2, Goal Programming Excel Worksheet for Solved Problem 2, Goal Programming Problem, Considering Priority 2 (Minimizing u2) Goal Given Problem, Considering Priority 2 (Minimizing u2) Goal Given That Priority 1 Goal Has Not Been Met: u1 = 6That Priority 1 Goal Has Not Been Met: u1 = 6

Exhibit 10–19Exhibit 10–19 Excel Solver Parameters Screen for Solved Problem 2, Goal Excel Solver Parameters Screen for Solved Problem 2, Goal Programming Problem Considering Priority 2 (Minimizing u2) Programming Problem Considering Priority 2 (Minimizing u2) Goal Given That Priority 1 (Minimizing u1) Goal Has Not Been Goal Given That Priority 1 (Minimizing u1) Goal Has Not Been Met: u1 = 6Met: u1 = 6

Exhibit 10–20Exhibit 10–20 Analytical Hierarchy Process for Solved Problem 3 (SelectionAnalytical Hierarchy Process for Solved Problem 3 (Selectionof the Head Coaching Job)of the Head Coaching Job)

Stevenson and Ozgur First Edition Introduction to Management Science with Spreadsheets...

Documents

McGraw-Hill/Irwin ©2005 The McGraw-Hill Companies, All rights reserved ©2005 The McGraw-Hill Companies, All rights reserved McGraw-Hill/Irwin

McGraw-Hill 6-1. 6 McGraw-Hill Communications, Networks, & Safeguards

McGraw-Hill/Irwin Copyright © 2008, The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies,

© McGraw-Hill Companies, Inc., McGraw-Hill/Irwin

© 2002 McGraw-Hill Companies, Inc., McGraw-Hill/Irwin

McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill

Local Marketing in Mature Markets Chapter Eight. Irwin/McGraw-Hill ©The McGraw-Hill Companies,, Inc., 2000 Irwin/McGraw-Hill ©The McGraw-Hill Companies,,

Stevenson and Ozgur First Edition Introduction to Management Science with Spreadsheets Part 1 Introduction to Management Science and Forecasting McGraw-Hill/Irwin

McGraw-Hill/Irwin McGraw-Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved

McGraw-Hill © 2005 The McGraw-Hill Companies, Inc. All rights reserved. 1 The Sociological Perspective CHANGING SOCIETY part McGraw-Hill © 2005 The McGraw-Hill

McGraw-Hill The McGraw-Hill Companies, Inc., 2004

McGraw-Hill © 2006 The McGraw-Hill Companies, Inc. All rights reserved. 3-1 McGraw-Hill © 2006 The McGraw-Hill Companies, Inc. All rights reserved. SOCIOLOGY:

McGraw-Hill/Irwin Copyright © 2008 The McGraw-Hill Companies

McGraw-Hill © 2005 The McGraw-Hill Companies, Inc. All rights reserved. 1 The Sociological Perspective McGraw-Hill © 2005 The McGraw-Hill Companies, Inc

McGraw-Hill Science Newsroom - Macmillan/McGraw-Hill€¦ · McGraw-Hill Science Newsroom Primary Edition complements the McGraw-Hill Science 2000textbook series by offering one interactive

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin

McGraw-Hill 10-1. 10 McGraw-Hill Systems Analysis & Programming

Mcgraw Hill

© McGraw-Hill Companies, Inc., McGraw-Hill/Irwin McGraw-Hill/Irwin Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved

Chapter 10 · Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 2001 $ Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc.,