Introduction to management science 10e by bernard taylor chapter 09

Multicriteria Decision Making Chapter Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 9-1 Chapter Topics ■ Goal Programming ■ Graphical Interpretation of Goal Programming ■ Computer Solution of Goal Programming Problems with QM for Windows and Excel ■ The Analytical Hierarchy Process ■ Scoring Models Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 9-2 Overview ■ Study of problems with several criteria, multiple criteria, instead of a single objective when making a decision ■ Three techniques discussed: goal programming, the analytical hierarchy process and scoring models ■ Goal programming is a variation of linear programming considering more than one objective (goals) in the objective function ■ The analytical hierarchy process develops a score for each decision alternative based on comparisons of each under different criteria reflecting the decision makers preferences ■ Scoring models are based on a relatively simple Copyright © 2010 Pearson Education, Inc Publishing as scoring technique Prenticeweighted Hall 9-3 Goal Programming Example Problem Data (1 of 2) Beaver Creek Pottery Company Example: Maximize Z = $40x1 + 50x2 subject to: 1x1 + 2x2  40 hours of labor 4x1 + 3x2  120 pounds of clay x1 , x  Where: x1 = number of bowls produced x2 = number of mugs produced Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 9-4 Goal Programming Example Problem Data (2 of 2) ■ Adding objectives (goals) in order of importance, the company: Does not want to use fewer than 40 hours of labor per day Would like to achieve a satisfactory profit level of $1,600 per day Prefers not to keep more than 120 pounds of clay on hand each day Would like to minimize the amount of overtime Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 9-5 Goal Programming Goal Constraint Requirements ■ All goal constraints are equalities that include deviational variables d- and d+ ■ A positive deviational variable (d+) is the amount by which a goal level is exceeded ■ A negative deviation variable (d-) is the amount by which a goal level is underachieved ■ At least one or both deviational variables in a goal constraint must equal zero ■ The objective function seeks to minimize the deviation from the respective goals in the order of the goal priorities Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 9-6 al Programming Model Formulation al Constraints (1 of 3) Labor goal: x1 + 2x2 + d1- - d1+ = 40 (hours/day) Profit goal: 40x1 + 50 x2 + d2 - - d2 + = 1,600 ($/day) Material goal: 4x1 + 3x2 + d3 - - d3 clay/day) Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall + = 120 (lbs of 9-7 Goal Programming Model Formulation Objective Function (2 of 3) Labor goals constraint (priority - less than 40 hours labor; priority minimum overtime):  Minimize P1d1-, P4d1+ Add profit goal constraint (priority - achieve profit of $1,600):  Minimize P1d1-, P2d2-, P4d1+ Add material goal constraint (priority - avoid keeping more than 120 pounds of clay on hand): Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 9-8 Goal Programming Model Formulation Complete Model (3 of 3) Complete Goal Programming Model: Minimize P1d1-, P2d2-, P3d3+, P4d1+ subject to: x1 + 2x2 + d1- - d1+ = 40 40x1 + 50 x2 + d2 - - d2 + = 1,600 4x1 + 3x2 + d3 - - d3 + = 120 (labor) (profit) (clay) x1, x2, d1 -, d1 +, d2 -, d2 +, d3 -, d3 +  Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 9-9 Goal Programming Alternative Forms of Goal Constraints (1 of 2) ■ Changing fourth-priority goal “limits overtime to 10 hours” instead of minimizing overtime:  d1- + d4 - - d4+ = 10  minimize P1d1 -, P2d2 -, P3d3 +, P4d4 + ■ Addition of a fifth-priority goal- “important to achieve the goal for mugs”:  x1 + d5 - = 30 bowls  x2 + d6 - = 20 mugs  minimize P1d1 -, P2d2 -, P3d3 +, P4d4 +, 4P5d5 - + 5P5d6 - Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 9-10 Analytical Hierarchy Process Excel Spreadsheets (2 of 4) Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall Exhibit 9-48 Analytical Hierarchy Process Excel Spreadsheets (3 of 4) Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall Exhibit 9.14 9-49 Analytical Hierarchy Process Excel Spreadsheets (4 of 4) Exhibit 9.15 Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 9-50 Scoring Model Overview Each decision alternative graded in terms of how well it satisfies the criterion according to following formula: Si = gijwj where: wj = a weight between and 1.00 assigned to criterion j; 1.00 important, unimportant; sum of total weights equals one gij = a grade between and 100 indicating how well alternative i satisfies criteria j; 100 indicates high satisfaction, low Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 9-51 Scoring Model Example Problem Mall selection with four alternatives and five criteria: S1 = (.30)(40) + (.25)(75) + (.25)(60) + (.10)(90) + (.10)(80) = 62.75 S2 = (.30)(60) + (.25)(80) + (.25)(90) + (.10)(100) + (.10)(30) = 73.50 S3 = (.30)(90) + (.25)(65) + (.25)(79) + (.10)(80) + (.10)(50) Copyright © 2010 Pearson Education, Inc Publishing as Prentice 9-52 = Hall 76.00 Scoring Model Excel Solution Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall Exhibit 9.16 9-53 Goal Programming Example Problem Problem Statement Public relations firm survey interviewer staffing requirements determination ■ One person can conduct 80 telephone interviews or 40 personal interviews per day ■ $50/ day for telephone interviewer; $70 for personal interviewer ■ Goals (in priority order): At least 3,000 total interviews Interviewer conducts only one type of interview each day; maintain daily budget of $2,500 At least 1,000 interviews should be by telephone Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall Formulate and solve a goal programming model to 9-54 Goal Programming Example Problem Solution (1 of 2) Step 1: Model Formulation: Minimize P1d1-, P2d2+, P3d3subject to: 80x1 + 40x2 + d1- - d1+ = 3,000 interviews 50x1 + 70x2 + d2- - d2 + = $2,500 budget 80x1 + d3- - d3 + = 1,000 telephone interviews where: x1 = number of telephone interviews x2 = number of personal interviews Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 9-55 Goal Programming Example Problem Solution (2 of 2) Step 2: QM for Windows Solution: Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 9-56 Analytical Hierarchy Process Example Problem Problem PurchasingStatement decision, three model alternatives, three decision criteria Pairwise comparison matrices: Prioritized decision criteria: Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 9-57 Analytical Hierarchy Process Example Problem Problem Solution (1 of 4) Step 1: Develop normalized matrices and preference vectors for all the pairwise comparison matrices for criteria Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 9-58 Analytical Hierarchy Process Example Problem Problem Solution (2 normalized of 4) matrices and Step continued: Develop preference vectors for all the pairwise comparison matrices for criteria Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 9-59 Analytical Hierarchy Process Example Problem Problem Solution (3 of 4) Step 2: Rank the criteria   Price 0.6479    0.2299   Gears     0.1222   Weight  Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 9-60 Analytical Hierarchy Process Example Problem Problem Solution (4 of 4) Step 3: Develop an overall ranking Bike X0.6667 0.0853 0.4429 0.6479         Bike Y0.2222 0.2132 0.1698  0.2299     Bike Z 0.1111 0.7014 0.3837 0.1222     Bike X score = 6667(.6479) + 0853(.2299) + 4429(.1222) = 5057 Bike Y score = 2222(.6479) + 2132(.2299) + 1698(.1222) = 2138 Bike Z score = 1111(.6479) + 7014(.2299) + 3873(.1222) = 2806 Overall ranking of bikes: X first followed by Z and Y (sum of scores equal 1.0000) Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 9-61 Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 9-62 ... want to use fewer than 40 hours of labor per day Would like to achieve a satisfactory profit level of $1,600 per day Prefers not to keep more than 120 pounds of clay on hand each day Would like to. . .Chapter Topics ■ Goal Programming ■ Graphical Interpretation of Goal Programming ■ Computer Solution... ■ A positive deviational variable (d+) is the amount by which a goal level is exceeded ■ A negative deviation variable (d-) is the amount by which a goal level is underachieved ■ At least one