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Stevenson and Ozgur First Edition Introduction to Management Science with Spreadsheets McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies,

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Presentation on theme: "Stevenson and Ozgur First Edition Introduction to Management Science with Spreadsheets McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies,"— Presentation transcript:

1 Stevenson and Ozgur First Edition Introduction to Management Science with Spreadsheets McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 10 Multicriteria Decision- Making Models Part 2 Deterministic Decision Models

2 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–2 Learning 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:

3 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–3 Learning Objectives (contd) 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:

4 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–4 Goal 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.

5 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–5 Figure 10–1A Plot of a Goal Constraint

6 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–6 Figure 10–2Designating Priority and Direction

7 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–7 Figure 10–3Plot of the Hard Constraint and the Feasible Solution Space

8 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–8 Figure 10–4The Acceptable Region after Adding the First Goal Constraint

9 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–9 Figure 10–5The Second Goal Is Added to the Graph

10 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–10 Figure 10–6The Third Goal Is Added, but It Doesnt Change the Solution

11 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–11 Figure 10–7Plotting the Acceptable Region

12 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–12 Exhibit 10-1Excel Worksheet for Robinson Chemical Company Goal Programming Problem, Considering Only Priority 1 (Minimizing Labor Underutilization) Goal

13 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–13 Exhibit 10-2Excel Solver Parameters Screen for Robinson Chemical Company Goal Programming Problem Considering Only Priority 1 (Minimizing Labor Underutilization) Goal

14 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–14 Exhibit 10–3Excel Worksheet for Robinson Chemical Company Goal Programming Problem, Considering Priority 1 (Minimizing Labor Underutilization) and Priority 2 (Minimizing Machine Hour Underutilization) Goals

15 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–15 Exhibit 10–4Excel Solver Parameters Screen for Robinson Chemical Company Goal Programming Problem, Considering Priority 2 (Minimizing Machine Hours Underutilization) Goal While Ensuring That Priority 1 Goal Is Satisfied

16 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–16 Exhibit 10–5Excel Solver Parameters Screen for Robinson Chemical Company Goal Programming Problem Considering Priority 3 (Minimizing the Unsatisfied Demand for Compound 200) Goal While Ensuring That the Priority 1 and Priority 2 Goals Are Still Satisfied

17 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–17 Exhibit 10–6 Excel Worksheet for Robinson Chemical Company Goal Programming Problem, Considering Priority 4 Goal (Minimizing Unsatisfied Demand for Compound 200) While Ensuring That Priority 1 (Minimizing Labor Underutilization), Priority 2 (Minimizing Machine Hour Underutilization), and Priority 3 (Unsatisfied Demand for Compound 200) Goals Are Satisfied

18 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–18 Exhibit 10–7Excel Solver Parameters Screen for Robinson Chemical Company Goal Programming Problem Considering Priority 4 (Minimizing the Unsatisfied Demand for Compound 100) Goal While Ensuring that Priority 1, priority 2, and Priority 3 Goals Are Still Satisfied

19 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–19 Exhibit 10–8Excel Worksheet for Robinson Chemical Company Weighted Goal Programming Problem

20 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–20 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.

21 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–21 Figure 10–8Graphical Representation of the Hierarchies for the stereo system-selection problem

22 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–22 Table 10–1Preference Scale for the Pairwise Comparisons

23 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–23 Table 10–2 Pairwise Comparison Table for the Stereo System Selection Problem

24 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–24 Table 10–3 Normalized Pairwise Comparison Table for the Stereo System Selection Problem

25 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–25 Table 10–4Calculation of the Weighted Priorities for the Criteria Table 10–5Random Index Values for the Comparison of n items

26 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–26 Table 10–6Pairwise Comparison Matrix Price Table 10–7Proportion Matrix for Price

27 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–27 Table 10–8Priority Percentage for Price

28 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–28 Table 10–9Determination of the Overall Priority

29 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–29 Table 10–9Determination of the Overall Priority (contd)

30 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–30 Exhibit 10–9Analytical Hierarchy Process for the Stereo System Selection Example

31 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–31 Table 10–10Excel Formulas for the AHP Worksheet in Exhibit 10-9

32 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–32 Table 10–10Excel Formulas for the AHP Worksheet in Exhibit 10-9 (contd)

33 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–33 Scoring 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

34 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–34 Figures A & B

35 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–35 Figures C & D

36 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–36 Exhibit 10–10Excel Worksheet for Solved Problem 1, Goal Programming Problem, Considering Only Priority 1 (Minimizing Labor Underutilization) Goal

37 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–37 Exhibit 10–11Excel Solver Parameters Screen for Solved Problem 1, Goal Programming Problem Considering Only Priority 1 (Minimizing Labor Underutilization) Goal

38 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–38 Exhibit 10–12Excel Solver Parameters Screen for Solved Problem 1, Goal Programming Problem Considering Priority 2 Goal Given That Priority 1 Goal Is Met

39 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–39 Exhibit 10–13Excel Solver Parameters Screen for Solved Problem 1, Goal Programming Problem Considering Priority 3 Goal Given That Priority 1 and Priority 2 Goals Have Been Met

40 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–40 Exhibit 10–14Excel Worksheet for Solved Problem 1, Goal Programming Problem, Considering Priority 4 (Minimizing Labor Overutilization) Goal Given That Priority 1, 2, and 3 Goals Have Been Met

41 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–41 Exhibit 10–15Excel Solver Parameters Screen for Solved Problem 1, Goal Programming Problem Considering Priority 4 Goal, Given That Priority 1, Priority 2, and Priority 3 Goals Have Been Met

42 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–42 Exhibit 10–16Excel Worksheet for Solved Problem 2, Goal Programming Problem, Considering Only Priority 1 (Minimizing u1) Goal

43 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–43 Exhibit 10–17Excel Solver Parameters Screen for Solved Problem 1, Goal Programming Problem Considering Only Priority 1 (Minimizing u1) Goal

44 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–44 Exhibit 10–18Excel Worksheet for Solved Problem 2, Goal Programming Problem, Considering Priority 2 (Minimizing u2) Goal Given That Priority 1 Goal Has Not Been Met: u1 = 6

45 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–45 Exhibit 10–19Excel Solver Parameters Screen for Solved Problem 2, Goal Programming Problem Considering Priority 2 (Minimizing u2) Goal Given That Priority 1 (Minimizing u1) Goal Has Not Been Met: u1 = 6

46 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 10–46 Exhibit 10–20Analytical Hierarchy Process for Solved Problem 3 (Selection of the Head Coaching Job)


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