Multicriteria Decision-Making Models Part 2 Deterministic Decision Models Chapter 10 Multicriteria Decision-Making Models

Learning Objectives After completing this chapter, you should be able to: Describe the type of problems that goal programming is designed to handle. Describe the similarities and differences between goal programming and linear programming models. Formulate goal programming models. Solve goal programming models that have two decision variables using a graphical approach. Solve goal programming models using Excel and interpret solutions of goal programming models. Copyright © 2007 The McGraw-Hill Companies. All rights reserved.

Learning Objectives (cont’d) After completing this chapter, you should be able to: Describe the type of problems that the analytical hierarchy process is designed to handle. Describe how to determine pairwise comparisons. Describe what a consistency check is and calculate a consistency ratio, priority percentage, and priority score for each alternative using AHP. Use Excel to solve analytical hierarchy process problems. Describe and solve scoring model multicriteria decision-making problems. Copyright © 2007 The McGraw-Hill Companies. All rights reserved.

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. Copyright © 2007 The McGraw-Hill Companies. All rights reserved.

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

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

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

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

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

Figure 10–6 The Third Goal Is Added, but It Doesn’t Change the Solution Copyright © 2007 The McGraw-Hill Companies. All rights reserved.

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

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

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

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

Exhibit 10–4 Excel 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 Copyright © 2007 The McGraw-Hill Companies. All rights reserved.

Exhibit 10–5 Excel 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 Copyright © 2007 The McGraw-Hill Companies. All rights reserved.

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 Copyright © 2007 The McGraw-Hill Companies. All rights reserved.

Exhibit 10–7 Excel 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 Copyright © 2007 The McGraw-Hill Companies. All rights reserved.

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

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. Copyright © 2007 The McGraw-Hill Companies. All rights reserved.

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

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

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

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

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

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

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

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

Table 10–9 Determination of the Overall Priority (cont’d) Copyright © 2007 The McGraw-Hill Companies. All rights reserved.

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

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

Table 10–10 Excel Formulas for the AHP Worksheet in Exhibit 10-9 (cont’d) Copyright © 2007 The McGraw-Hill Companies. All rights reserved.

Scoring Models Scoring Model Areas of application 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 Copyright © 2007 The McGraw-Hill Companies. All rights reserved.

Figures A & B Copyright © 2007 The McGraw-Hill Companies. All rights reserved.

Figures C & D Copyright © 2007 The McGraw-Hill Companies. All rights reserved.

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

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

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

Exhibit 10–13 Excel 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 Copyright © 2007 The McGraw-Hill Companies. All rights reserved.

Exhibit 10–14 Excel 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 Copyright © 2007 The McGraw-Hill Companies. All rights reserved.

Exhibit 10–15 Excel 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 Copyright © 2007 The McGraw-Hill Companies. All rights reserved.

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

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

Exhibit 10–18 Excel 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 Copyright © 2007 The McGraw-Hill Companies. All rights reserved.

Exhibit 10–19 Excel 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 Copyright © 2007 The McGraw-Hill Companies. All rights reserved.

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