管理科学线性规划 精选PPT.ppt

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1、管理科学线性规划 Chapter 3-Linear Programming:Computer Solution and Sensitivity Analysis1第1页，此课件共38页哦Chapter 3-Linear Programming:Computer Solution and Sensitivity Analysis 2Chapter TopicsComputer SolutionSensitivity Analysis第2页，此课件共38页哦Chapter 3-Linear Programming:Computer Solution and Sensitivity Analysis

2、 3Early linear programming used lengthy manual mathematical solution procedure called the Simplex Method(See CD-ROM Module A).Steps of the Simplex Method have been programmed in software packages designed for linear programming problems.Many such packages available currently.Used extensively in busi

3、ness and government.Text focuses on Excel Spreadsheets and QM for Windows.Computer Solution第3页，此课件共38页哦Chapter 3-Linear Programming:Computer Solution and Sensitivity Analysis 4Beaver Creek Pottery ExampleExcel Spreadsheet Data Screen(1 of 5)Exhibit 3.1第4页，此课件共38页哦Chapter 3-Linear Programming:Compute

4、r Solution and Sensitivity Analysis 5Beaver Creek Pottery Example“Solver”Parameter Screen(2 of 5)Exhibit 3.2第5页，此课件共38页哦Chapter 3-Linear Programming:Computer Solution and Sensitivity Analysis 6Exhibit 3.3Beaver Creek Pottery ExampleAdding Model Constraints(3 of 5)第6页，此课件共38页哦Chapter 3-Linear Program

5、ming:Computer Solution and Sensitivity Analysis 7Exhibit 3.4Beaver Creek Pottery ExampleSolution Screen(4 of 5)第7页，此课件共38页哦Chapter 3-Linear Programming:Computer Solution and Sensitivity Analysis 8Beaver Creek Pottery ExampleAnswer Report(5 of 5)Exhibit 3.5第8页，此课件共38页哦Chapter 3-Linear Programming:Com

6、puter Solution and Sensitivity Analysis 9Linear Programming Problem Standard FormStandard form requires all variables in the constraint equations to appear on the left of the inequality(or equality)and all numeric values to be on the right-hand side.Examples:x3 x1+x2 must be converted to x3-x1-x2 0

7、x1/(x2+x3)2 becomes x1 2(x2+x3)and then x1-2x2-2x3 0 第9页，此课件共38页哦Chapter 3-Linear Programming:Computer Solution and Sensitivity Analysis 10Beaver Creek Pottery ExampleQM for Windows Data Screen(1 of 3)Exhibit 3.6第10页，此课件共38页哦Chapter 3-Linear Programming:Computer Solution and Sensitivity Analysis 11B

8、eaver Creek Pottery ExampleModel Solution Screen(2 of 3)Exhibit 3.7第11页，此课件共38页哦Chapter 3-Linear Programming:Computer Solution and Sensitivity Analysis 12Beaver Creek Pottery ExampleGraphical Solution Screen(3 of 3)Exhibit 3.8第12页，此课件共38页哦Chapter 3-Linear Programming:Computer Solution and Sensitivit

9、y Analysis 13Beaver Creek Pottery ExampleSensitivity Analysis(1 of 4)Sensitivity analysis determines the effect on optimal solutions of changes in parameter values of the objective function and constraint equations.Changes may be reactions to anticipated uncertainties in the parameters or to new or

10、changed information concerning the model.第13页，此课件共38页哦Chapter 3-Linear Programming:Computer Solution and Sensitivity Analysis 14Maximize Z=$40 x1+$50 x2subject to:1x1+2x2 40 4x2+3x2 120 x1,x2 0Figure 3.1Optimal Solution PointBeaver Creek Pottery ExampleSensitivity Analysis(2 of 4)第14页，此课件共38页哦Chapte

11、r 3-Linear Programming:Computer Solution and Sensitivity Analysis 15Maximize Z=$100 x1+$50 x2subject to:1x1+2x2 40 4x2+3x2 120 x1,x2 0Figure 3.2Changing the x1 Objective Function CoefficientBeaver Creek Pottery ExampleChange x1 Objective Function Coefficient(3 of 4)第15页，此课件共38页哦Chapter 3-Linear Prog

12、ramming:Computer Solution and Sensitivity Analysis 16Maximize Z=$40 x1+$100 x2subject to:1x1+2x2 40 4x2+3x2 120 x1,x2 0Figure 3.3Changing the x2 Objective Function CoefficientBeaver Creek Pottery ExampleChange x2 Objective Function Coefficient(4 of 4)第16页，此课件共38页哦Chapter 3-Linear Programming:Compute

13、r Solution and Sensitivity Analysis 17The sensitivity range for an objective function coefficient is the range of values over which the current optimal solution point will remain optimal.The sensitivity range for the xi coefficient is designated as ci.Objective Function CoefficientSensitivity Range(

14、1 of 3)第17页，此课件共38页哦Chapter 3-Linear Programming:Computer Solution and Sensitivity Analysis 18objective function Z=$40 x1+$50 x2 sensitivity range for:x1:25 c1 66.67 x2:30 c2 80Figure 3.4Determining the Sensitivity Range for c1Objective Function CoefficientSensitivity Range for c1 and c2(2 of 3)第18页

15、，此课件共38页哦Chapter 3-Linear Programming:Computer Solution and Sensitivity Analysis 19Minimize Z=$6x1+$3x2subject to:2x1+4x2 164x1+3x2 24 x1,x2 0sensitivity ranges:4 c1 0 c2 4.5Objective Function CoefficientFertilizer Cost Minimization Example(3 of 3)Figure 3.5Fertilizer Cost Minimization Example第19页，此

16、课件共38页哦Chapter 3-Linear Programming:Computer Solution and Sensitivity Analysis 20Exhibit 3.9Objective Function Coefficient RangesExcel“Solver”Results Screen(1 of 3)第20页，此课件共38页哦Chapter 3-Linear Programming:Computer Solution and Sensitivity Analysis 21Exhibit 3.10Objective Function Coefficient Ranges

17、Beaver Creek Example Sensitivity Report(2 of 3)第21页，此课件共38页哦Chapter 3-Linear Programming:Computer Solution and Sensitivity Analysis 22Exhibit 3.11Objective Function Coefficient RangesQM for Windows Sensitivity Range Screen(3 of 3)第22页，此课件共38页哦Chapter 3-Linear Programming:Computer Solution and Sensit

18、ivity Analysis 23Changes in Constraint Quantity ValuesSensitivity Range(1 of 4)The sensitivity range for a right-hand-side value is the range of values over which the quantity values can change without changing the solution variable mix,including slack variables.第23页，此课件共38页哦Chapter 3-Linear Program

19、ming:Computer Solution and Sensitivity Analysis 24Changes in Constraint Quantity ValuesIncreasing the Labor Constraint(2 of 4)Maximize Z=$40 x1+$50 x2subject to:1x1+2x2 40 4x2+3x2 120 x1,x2 0Figure 3.6Increasing the Labor Constraint Quantity第24页，此课件共38页哦Chapter 3-Linear Programming:Computer Solution

20、 and Sensitivity Analysis 25Changes in Constraint Quantity ValuesSensitivity Range for Labor Constraint(3 of 4)Sensitivity range for:30 q1 80 hrFigure 3.7Determining the Sensitivity Range for Labor Quantity第25页，此课件共38页哦Chapter 3-Linear Programming:Computer Solution and Sensitivity Analysis 26Changes

21、 in Constraint Quantity ValuesSensitivity Range for Clay Constraint(4 of 4)Sensitivity range for:60 q2 160 lbFigure 3.8Determining the Sensitivity Range for Clay Quantity第26页，此课件共38页哦Chapter 3-Linear Programming:Computer Solution and Sensitivity Analysis 27Exhibit 3.12Constraint Quantity Value Range

22、s by ComputerExcel Sensitivity Range for Constraints(1 of 2)第27页，此课件共38页哦Chapter 3-Linear Programming:Computer Solution and Sensitivity Analysis 28Exhibit 3.13Constraint Quantity Value Ranges by ComputerQM for Windows Sensitivity Range(2 of 2)第28页，此课件共38页哦Chapter 3-Linear Programming:Computer Soluti

23、on and Sensitivity Analysis 29Changing individual constraint parametersAdding new constraintsAdding new variablesOther Forms of Sensitivity AnalysisTopics(1 of 4)第29页，此课件共38页哦Chapter 3-Linear Programming:Computer Solution and Sensitivity Analysis 30Other Forms of Sensitivity AnalysisChanging a Const

24、raint Parameter(2 of 4)Maximize Z=$40 x1+$50 x2subject to:1x1+2x2 40 4x2+3x2 120 x1,x2 0Figure 3.9Changing the x1 Coefficient in the Labor Constraint第30页，此课件共38页哦Chapter 3-Linear Programming:Computer Solution and Sensitivity Analysis 31Adding a new constraint to Beaver Creek Model:0.20 x1+0.10 x2 5

25、hours for packaging Original solution:24 bowls,8 mugs,$1,360 profitExhibit 3.13Other Forms of Sensitivity AnalysisAdding a New Constraint(3 of 4)第31页，此课件共38页哦Chapter 3-Linear Programming:Computer Solution and Sensitivity Analysis 32Adding a new variable to the Beaver Creek model,x3,a third product,c

26、upsMaximize Z=$40 x1+50 x2+30 x3subject to:x1+2x2+1.2x3 40 hr of labor 4x1+3x2+2x3 120 lb of clay x1,x2,x3 0Solving model shows that change has no effect on the original solution(i.e.,the model is not sensitive to this change).Other Forms of Sensitivity AnalysisAdding a New Variable(4 of 4)第32页，此课件共

27、38页哦Chapter 3-Linear Programming:Computer Solution and Sensitivity Analysis 33Defined as the marginal value of one additional unit of resource.The sensitivity range for a constraint quantity value is also the range over which the shadow price is valid.Shadow Prices(Dual Values)第33页，此课件共38页哦Chapter 3

28、-Linear Programming:Computer Solution and Sensitivity Analysis 34Maximize Z=$40 x1+$50 x2 subject to:x1+2x2 40 hr of labor4x1+3x2 120 lb of clay x1,x2 0Exhibit 3.14Excel Sensitivity Report for Beaver Creek PotteryShadow Prices Example(1 of 2)第34页，此课件共38页哦Chapter 3-Linear Programming:Computer Solutio

29、n and Sensitivity Analysis 35Excel Sensitivity Report for Beaver Creek PotterySolution Screen(2 of 2)Exhibit 3.15第35页，此课件共38页哦Chapter 3-Linear Programming:Computer Solution and Sensitivity Analysis 36Two airplane parts:no.1 and no.2.Three manufacturing stages:stamping,drilling,milling.Decision varia

30、bles:x1(number of part no.1 to produce)x2(number of part no.2 to produce)Model:Maximize Z=$650 x1+910 x2 subject to:4x1+7.5x2 105(stamping,hr)6.2x1+4.9x2 90(drilling,hr)9.1x1+4.1x2 110(finishing,hr)x1,x2 0 Example ProblemProblem Statement(1 of 3)第36页，此课件共38页哦Chapter 3-Linear Programming:Computer Sol

31、ution and Sensitivity Analysis 37Maximize Z=$650 x1+$910 x2subject to:4x1+7.5x2 105 6.2x1+4.9x2 90 9.1x1+4.1x2 110 x1,x2 0s1=0,s2=0,s3=11.35 hr485.33 c1 1,151.43137.76 q1 89.10Figure 3.10Graphical SolutionExample ProblemGraphical Solution(2 of 3)第37页，此课件共38页哦Chapter 3-Linear Programming:Computer Solution and Sensitivity Analysis 38Example ProblemExcel Solution(3 of 3)Exhibit 3.16第38页，此课件共38页哦