管理科学09-多因子决策模型.ppt

Chapter 9 Multicriteria Decision Making Introduction to Management Science 8th Edition by Bernard W. Taylor III 1Chapter 9 - Multicriteria Decision Making Goal Programming Graphical Interpretation of Goal Programming Computer Solution of Goal Programming Problems with QM for Windows and Excel The Analytical Hierarchy Process Chapter Topics 2Chapter 9 - Multicriteria Decision Making Study of problems with several criteria, multiple criteria, instead of a single objective when making a decision. Two techniques discussed: goal programming, and the analytical hierarchy process. 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. Overview 3Chapter 9 - Multicriteria Decision Making Beaver Creek Pottery Company Example: Maximize Z = $40x1 + 50x2 subject to: 1x1 + 2x2 40 hours of labor 4x2 + 3x2 120 pounds of clay x1, x2 0 Where: x1 = number of bowls produced x2 = number of mugs produced Goal Programming Model Formulation (1 of 2) 4Chapter 9 - Multicriteria Decision Making 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. Goal Programming Model Formulation (2 of 2) 5Chapter 9 - Multicriteria Decision Making 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 in a goal programming model seeks to minimize the deviation from goals in the order of the goal priorities. Goal Programming Goal Constraint Requirements 6Chapter 9 - Multicriteria Decision Making Labor goals constraint (1, less than 40 hours labor; 4, minimum overtime): Minimize P1d1-, P4d1+ Add profit goal constraint (2, achieve profit of $1,600): Minimize P1d1-, P2d2-, P4d1+ Add material goal constraint (3, avoid keeping more than 120 pounds of clay on hand): Minimize P1d1-, P2d2-, P3d3+, P4d1+ Goal Programming Goal Constraints and Objective Function (1 of 2) 7Chapter 9 - Multicriteria Decision Making 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 x1, x2, d1 -, d1 +, d2 -, d2 +, d3 -, d3 + 0 Goal Programming Goal Constraints and Objective Function (2 of 2) 8Chapter 9 - Multicriteria Decision Making 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 - Goal Programming Alternative Forms of Goal Constraints (1 of 2) 9Chapter 9 - Multicriteria Decision Making Goal Programming Alternative Forms of Goal Constraints (2 of 2) Complete Model with New Goals: Minimize P1d1-, P2d2-, P3d3-, P4d4-, 4P5d5-, 5P5d6- subject to: x1 + 2x2 + d1- - d1+ = 40 40x1 + 50x2 + d2- - d2+ = 1,600 4x1 + 3x2 + d3- - d3+ = 120 d1+ + d4- - d4+ = 10 x1 + d5- = 30 x2 + d6- = 20 x1, x2, d1-, d1+, d2-, d2+, d3-, d3+, d4-, d4+, d5-, d6- 0 10Chapter 9 - Multicriteria Decision Making Minimize P1d1-, P2d2-, P3d3+, P4d1+ subject to: x1 + 2x2 + d1- - d1+ = 40 40x1 + 50 x2 + d2 - - d2 + = 1,600 4x1 + 3x2 + d3 - - d3 + = 120 x1, x2, d1 -, d1 +, d2 -, d2 +, d3 -, d3 + 0 Figure 9.1 Goal Constraints Goal Programming Graphical Interpretation (1 of 6) 11Chapter 9 - Multicriteria Decision Making Figure 9.2 The First-Priority Goal: Minimize Minimize P1d1-, P2d2-, P3d3+, P4d1+ subject to: x1 + 2x2 + d1- - d1+ = 40 40x1 + 50 x2 + d2 - - d2 + = 1,600 4x1 + 3x2 + d3 - - d3 + = 120 x1, x2, d1 -, d1 +, d2 -, d2 +, d3 -, d3 + 0 Goal Programming Graphical Interpretation (2 of 6) 12Chapter 9 - Multicriteria Decision Making Figure 9.3 The Second-Priority Goal: Minimize Minimize P1d1-, P2d2-, P3d3+, P4d1+ subject to: x1 + 2x2 + d1- - d1+ = 40 40x1 + 50 x2 + d2 - - d2 + = 1,600 4x1 + 3x2 + d3 - - d3 + = 120 x1, x2, d1 -, d1 +, d2 -, d2 +, d3 -, d3 + 0 Goal Programming Graphical Interpretation (3 of 6) 13Chapter 9 - Multicriteria Decision Making Figure 9.4 The Third-Priority Goal: Minimize Minimize P1d1-, P2d2-, P3d3+, P4d1+ subject to: x1 + 2x2 + d1- - d1+ = 40 40x1 + 50 x2 + d2 - - d2 + = 1,600 4x1 + 3x2 + d3 - - d3 + = 120 x1, x2, d1 -, d1 +, d2 -, d2 +, d3 -, d3 + 0 Goal Programming Graphical Interpretation (4 of 6) 14Chapter 9 - Multicriteria Decision Making Figure 9.5 The Fourth-Priority Goal: Minimize Minimize P1d1-, P2d2-, P3d3+, P4d1+ subject to: x1 + 2x2 + d1- - d1+ = 40 40x1 + 50 x2 + d2 - - d2 + = 1,600 4x1 + 3x2 + d3 - - d3 + = 120 x1, x2, d1 -, d1 +, d2 -, d2 +, d3 -, d3 + 0 Goal Programming Graphical Interpretation (5 of 6) 15Chapter 9 - Multicriteria Decision Making Goal programming solutions do not always achieve all goals and they are not optimal, they achieve the best or most satisfactory solution possible. Minimize P1d1-, P2d2-, P3d3+, P4d1+ subject to: x1 + 2x2 + d1- - d1+ = 40 40x1 + 50 x2 + d2 - - d2 + = 1,600 4x1 + 3x2 + d3 - - d3 + = 120 x1, x2, d1 -, d1 +, d2 -, d2 +, d3 -, d3 + 0 x1 = 15 bowls x2 = 20 mugs d1- = 15 hours Goal Programming Graphical Interpretation (6 of 6) 16Chapter 9 - Multicriteria Decision Making Exhibit 9.1 Minimize P1d1-, P2d2-, P3d3+, P4d1+ subject to: x1 + 2x2 + d1- - d1+ = 40 40x1 + 50 x2 + d2 - - d2 + = 1,600 4x1 + 3x2 + d3 - - d3 + = 120 x1, x2, d1 -, d1 +, d2 -, d2 +, d3 -, d3 + 0 Goal Programming Computer Solution Using QM for Windows (1 of 3) 17Chapter 9 - Multicriteria Decision Making Exhibit 9.2 Goal Programming Computer Solution Using QM for Windows (2 of 3) 18Chapter 9 - Multicriteria Decision Making Exhibit 9.3 Goal Programming Computer Solution Using QM for Windows (3 of 3) 19Chapter 9 - Multicriteria Decision Making Exhibit 9.4 Goal Programming Computer Solution Using Excel (1 of 3) 20Chapter 9 - Multicriteria Decision Making Exhibit 9.5 Goal Programming Computer Solution Using Excel (2 of 3) 21Chapter 9 - Multicriteria Decision Making Exhibit 9.6 Goal Programming Computer Solution Using Excel (3 of 3) 22Chapter 9 - Multicriteria Decision Making Minimize P1d1-, P2d2-, P3d3-, P4d4-, 4P5d5-, 5P5d6- subject to: x1 + 2x2 + d1- - d1+ = 40 40x1 + 50x2 + d2- - d2+ = 1,600 4x1 + 3x2 + d3- - d3+ = 120 d1+ + d4- - d4+ = 10 x1 + d5- = 30 x2 + d6- = 20 x1, x2, d1-, d1+, d2-, d2+, d3-, d3+, d4-, d4+, d5-, d6- 0 Goal Programming Solution for Altered Problem Using Excel (1 of 6) 23Chapter 9 - Multicriteria Decision Making Exhibit 9.7 Goal Programming Solution for Altered Problem Using Excel (2 of 6) 24Chapter 9 - Multicriteria Decision Making Exhibit 9.8 Goal Programming Solution for Altered Problem Using Excel (3 of 6) 25Chapter 9 - Multicriteria Decision Making Exhibit 9.9 Goal Programming Solution for Altered Problem Using Excel (4 of 6) 26Chapter 9 - Multicriteria Decision Making Exhibit 9.10 Goal Programming Solution for Altered Problem Using Excel (5 of 6) 27Chapter 9 - Multicriteria Decision Making Exhibit 9.11 Goal Programming Solution for Altered Problem Using Excel (6 of 6) 28Chapter 9 - Multicriteria Decision Making Exhibit 9.12 Goal Programming Excel Spreadsheets (1 of 4) 29Chapter 9 - Multicriteria Decision Making Exhibit 9.13 Goal Programming Excel Spreadsheets (2 of 4) 30Chapter 9 - Multicriteria Decision Making Exhibit 9.14 Goal Programming Excel Spreadsheets (3 of 4) 31Chapter 9 - Multicriteria Decision Making Exhibit 9.15 Goal Programming Excel Spreadsheets (4 of 4) 32Chapter 9 - Multicriteria Decision Making 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