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1、Chapter 9-Multicriteria Decision Making,1,Chapter 9Multicriteria Decision Making,Introduction to Management Science8th EditionbyBernard W.Taylor III,Chapter 9-Multicriteria Decision Making,2,Goal ProgrammingGraphical Interpretation of Goal ProgrammingComputer Solution of Goal Programming Problems wi
2、th QM for Windows and ExcelThe Analytical Hierarchy Process,Chapter Topics,Chapter 9-Multicriteria Decision Making,3,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 p
3、rocess.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 prefer
4、ences.,Overview,Chapter 9-Multicriteria Decision Making,4,Beaver Creek Pottery Company Example:Maximize Z=$40 x1+50 x2subject to:1x1+2x2 40 hours of labor4x2+3x2 120 pounds of clayx1,x2 0Where:x1=number of bowls produced x2=number of mugs produced,Goal ProgrammingModel Formulation(1 of 2),Chapter 9-
5、Multicriteria Decision Making,5,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 mini
6、mize the amount of overtime.,Goal ProgrammingModel Formulation(2 of 2),Chapter 9-Multicriteria Decision Making,6,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 var
7、iable(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 ProgrammingGoal Constr
8、aint Requirements,Chapter 9-Multicriteria Decision Making,7,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 c
9、lay on hand):Minimize P1d1-,P2d2-,P3d3+,P4d1+,Goal ProgrammingGoal Constraints and Objective Function(1 of 2),Chapter 9-Multicriteria Decision Making,8,Complete Goal Programming Model:Minimize P1d1-,P2d2-,P3d3+,P4d1+subject to:x1+2x2+d1-d1+=4040 x1+50 x2+d2-d2+=1,600 4x1+3x2+d3-d3+=120 x1,x2,d1-,d1+
10、,d2-,d2+,d3-,d3+0,Goal ProgrammingGoal Constraints and Objective Function(2 of 2),Chapter 9-Multicriteria Decision Making,9,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-“import
11、ant to achieve the goal for mugs”:x1+d5-=30 bowls x2+d6-=20 mugs minimize P1d1-,P2d2-,P3d3-,P4d4-,4P5d5-,5P5d6-,Goal ProgrammingAlternative Forms of Goal Constraints(1 of 2),Chapter 9-Multicriteria Decision Making,10,Goal ProgrammingAlternative Forms of Goal Constraints(2 of 2),Complete Model with N
12、ew Goals:Minimize P1d1-,P2d2-,P3d3-,P4d4-,4P5d5-,5P5d6-subject to:x1+2x2+d1-d1+=4040 x1+50 x2+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,Chapter 9-Multicriteria Decision Making,11,Minimize P1d1-,P2d2-,P3d3+,P4d1+subject to:x1+2x2+d
13、1-d1+=40 40 x1+50 x2+d2-d2+=1,600 4x1+3x2+d3-d3+=120 x1,x2,d1-,d1+,d2-,d2+,d3-,d3+0,Figure 9.1Goal Constraints,Goal ProgrammingGraphical Interpretation(1 of 6),Chapter 9-Multicriteria Decision Making,12,Figure 9.2The First-Priority Goal:Minimize,Minimize P1d1-,P2d2-,P3d3+,P4d1+subject to:x1+2x2+d1-d
14、1+=40 40 x1+50 x2+d2-d2+=1,600 4x1+3x2+d3-d3+=120 x1,x2,d1-,d1+,d2-,d2+,d3-,d3+0,Goal ProgrammingGraphical Interpretation(2 of 6),Chapter 9-Multicriteria Decision Making,13,Figure 9.3The Second-Priority Goal:Minimize,Minimize P1d1-,P2d2-,P3d3+,P4d1+subject to:x1+2x2+d1-d1+=40 40 x1+50 x2+d2-d2+=1,60
15、0 4x1+3x2+d3-d3+=120 x1,x2,d1-,d1+,d2-,d2+,d3-,d3+0,Goal ProgrammingGraphical Interpretation(3 of 6),Chapter 9-Multicriteria Decision Making,14,Figure 9.4The Third-Priority Goal:Minimize,Minimize P1d1-,P2d2-,P3d3+,P4d1+subject to:x1+2x2+d1-d1+=40 40 x1+50 x2+d2-d2+=1,600 4x1+3x2+d3-d3+=120 x1,x2,d1-
16、,d1+,d2-,d2+,d3-,d3+0,Goal ProgrammingGraphical Interpretation(4 of 6),Chapter 9-Multicriteria Decision Making,15,Figure 9.5The Fourth-Priority Goal:Minimize,Minimize P1d1-,P2d2-,P3d3+,P4d1+subject to:x1+2x2+d1-d1+=40 40 x1+50 x2+d2-d2+=1,600 4x1+3x2+d3-d3+=120 x1,x2,d1-,d1+,d2-,d2+,d3-,d3+0,Goal Pr
17、ogrammingGraphical Interpretation(5 of 6),Chapter 9-Multicriteria Decision Making,16,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+=4040 x1+50 x2
18、+d2-d2+=1,600 4x1+3x2+d3-d3+=120 x1,x2,d1-,d1+,d2-,d2+,d3-,d3+0 x1=15 bowlsx2=20 mugsd1-=15 hours,Goal ProgrammingGraphical Interpretation(6 of 6),Chapter 9-Multicriteria Decision Making,17,Exhibit 9.1,Minimize P1d1-,P2d2-,P3d3+,P4d1+subject to:x1+2x2+d1-d1+=40 40 x1+50 x2+d2-d2+=1,600 4x1+3x2+d3-d3
19、+=120 x1,x2,d1-,d1+,d2-,d2+,d3-,d3+0,Goal ProgrammingComputer Solution Using QM for Windows(1 of 3),Chapter 9-Multicriteria Decision Making,18,Exhibit 9.2,Goal ProgrammingComputer Solution Using QM for Windows(2 of 3),Chapter 9-Multicriteria Decision Making,19,Exhibit 9.3,Goal ProgrammingComputer So
20、lution Using QM for Windows(3 of 3),Chapter 9-Multicriteria Decision Making,20,Exhibit 9.4,Goal ProgrammingComputer Solution Using Excel(1 of 3),Chapter 9-Multicriteria Decision Making,21,Exhibit 9.5,Goal ProgrammingComputer Solution Using Excel(2 of 3),Chapter 9-Multicriteria Decision Making,22,Exh
21、ibit 9.6,Goal ProgrammingComputer Solution Using Excel(3 of 3),Chapter 9-Multicriteria Decision Making,23,Minimize P1d1-,P2d2-,P3d3-,P4d4-,4P5d5-,5P5d6-subject to:x1+2x2+d1-d1+=4040 x1+50 x2+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
22、-0,Goal ProgrammingSolution for Altered Problem Using Excel(1 of 6),Chapter 9-Multicriteria Decision Making,24,Exhibit 9.7,Goal ProgrammingSolution for Altered Problem Using Excel(2 of 6),Chapter 9-Multicriteria Decision Making,25,Exhibit 9.8,Goal ProgrammingSolution for Altered Problem Using Excel(
23、3 of 6),Chapter 9-Multicriteria Decision Making,26,Exhibit 9.9,Goal ProgrammingSolution for Altered Problem Using Excel(4 of 6),Chapter 9-Multicriteria Decision Making,27,Exhibit 9.10,Goal ProgrammingSolution for Altered Problem Using Excel(5 of 6),Chapter 9-Multicriteria Decision Making,28,Exhibit
24、9.11,Goal ProgrammingSolution for Altered Problem Using Excel(6 of 6),Chapter 9-Multicriteria Decision Making,29,Exhibit 9.12,Goal ProgrammingExcel Spreadsheets(1 of 4),Chapter 9-Multicriteria Decision Making,30,Exhibit 9.13,Goal ProgrammingExcel Spreadsheets(2 of 4),Chapter 9-Multicriteria Decision
25、 Making,31,Exhibit 9.14,Goal ProgrammingExcel Spreadsheets(3 of 4),Chapter 9-Multicriteria Decision Making,32,Exhibit 9.15,Goal ProgrammingExcel Spreadsheets(4 of 4),Chapter 9-Multicriteria Decision Making,33,Goal Programming Example ProblemProblem Statement,Public relations firm survey interviewer
26、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.Mainta
27、in daily budget of$2,500.At least 1,000 interviews should be by telephone.Formulate a goal programming model to determine number of interviewers to hire in order to satisfy the goals,and then solve the problem.,Chapter 9-Multicriteria Decision Making,34,Step 1:Model Formulation:Minimize P1d1-,P2d2-,
28、P3d3-subject to:80 x1+40 x2+d1-d1+=3,000 interviews50 x1+70 x2+d2-d2+=$2,500 budget80 x1+d3-d3+=1,000 telephone interviewswhere:x1=number of telephone interviews x2=number of personal interviews,Goal Programming Example ProblemSolution(1 of 2),Chapter 9-Multicriteria Decision Making,35,Goal Programming Example ProblemSolution(2 of 2),Step 2:QM for Windows Solution:,
