Multicriteria Decision-Making Models

Chapter 10Multicriteria Decision-Making ModelsPart 2 Deterministic Decision ModelsLearning ObjectivesDescribe 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.After completing this chapter, you should be able to:2Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Learning Objectives (cont’d)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.After completing this chapter, you should be able to:3Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Goal Programming Versus Linear ProgrammingGoal 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.4Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 10–1 A Plot of a Goal Constraint5Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 10–2 Designating Priority and Direction6Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 10–3 Plot of the Hard Constraint and the Feasible Solution Space7Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 10–4 The Acceptable Region after Adding the First Goal Constraint8Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 10–5 The Second Goal Is Added to the Graph9Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 10–6 The Third Goal Is Added, but It Doesn’t Change the Solution10Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 10–7 Plotting the Acceptable Region11Copyright © 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) Goal12Copyright © 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) Goal13Copyright © 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) Goals14Copyright © 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 Satisfied15Copyright © 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 Satisfied16Copyright © 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 Satisfied17Copyright © 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 Satisfied18Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 10–8 Excel Worksheet for Robinson Chemical Company Weighted Goal Programming Problem19Copyright © 2007 The McGraw-Hill Companies. All rights reserved. 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.20Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 10–8 Graphical Representation of the Hierarchies for the stereo system-selection problem21Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 10–1 Preference Scale for the Pairwise Comparisons22Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 10–2 Pairwise Comparison Table for the Stereo System Selection Problem23Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 10–3 Normalized Pairwise Comparison Table for the Stereo System Selection Problem24Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 10–4 Calculation of the Weighted Priorities for the CriteriaTable 10–5 Random Index Values for the Comparison of n items25Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 10–6 Pairwise Comparison Matrix PriceTable 10–7 Proportion Matrix for Price26Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 10–8 Priority Percentage for Price27Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 10–9 Determination of the Overall Priority28Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 10–9 Determination of the Overall Priority (cont’d)29Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 10–9 Analytical Hierarchy Process for the Stereo System SelectionExample30Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 10–10 Excel Formulas for the AHP Worksheet in Exhibit 10-931Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 10–10 Excel Formulas for the AHP Worksheet in Exhibit 10-9 (cont’d)32Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Scoring ModelsScoring ModelA 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 applicationFacility locationProduct selection33Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figures A & B34Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figures C & D 35Copyright © 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) Goal36Copyright © 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) Goal37Copyright © 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 Met38Copyright © 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 Met39Copyright © 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 Met40Copyright © 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 Met41Copyright © 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) Goal42Copyright © 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) Goal43Copyright © 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 = 644Copyright © 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 = 645Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 10–20 Analytical Hierarchy Process for Solved Problem 3 (Selectionof the Head Coaching Job)46Copyright © 2007 The McGraw-Hill Companies. All rights reserved.