灵敏度分析学习.pptx
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1、Session TopicsqSimultaneous Change in OFC(coefficient)同时改变目标函数系数q Shadow Price Analysis for RHS 右端项的影子价格分析q Range-of-Feasibility What-If Analysis 可行域的敏感性分析q Simultaneous Change in RHS 同时改变右端项第1页/共121页4.1 The Importance of What-If Analysis to ManagersWhat-If 分析对管理者的重要性第2页/共121页What is Sensitivity Ana
2、lysis 什么是敏感性分析qA particular mathematical model provides only a rough representation of the real problem.数学模型只是实际问题的一个粗略的抽象。qAn optimal solution is only optimal with respect to a particular mathematical model.最优解一般只是针对某一特定的数学模型。第3页/共121页What is Sensitivity Analysis 什么是敏感性分析qThe purpose of a linear pr
3、ogramming study is to help guide managements final decision by providing insights into the likely consequences of pursuing various managerial options under a variety of assumptions about future conditions.管理者要对未来做各种假设,在这些假设下,测试可能产生的结果,通过对各种结果深入分析来指导决策。第4页/共121页What is Sensitivity Analysis 什么是敏感性分析qM
4、ost of the important insights are gained while conducting analysis after finding an optional solution for the original version of the basic model.通常,在取得最初版本模型的最优解之后,进行分析才能取得对问题深入的认识。第5页/共121页What is Sensitivity Analysis 什么是敏感性分析qThis analysis is commonly referred to as what-if analysis because it in
5、volves addressing some questions about what would happen to the optimal solution if different assumptions are made about future conditions.这种分析称为what-if分析或敏感性分析(Sensitivity Analysis),因为其中所涉及的问题主要是:如果未来情况的假设变动的话,最优解将会有怎样的变化?第6页/共121页Parameters of the model模型的参数(1)Parameters of the model:the problems
6、provide the data needed to determine precisely that should go into the data cells to determine the LP optimal solution.The parameters of the model are rough estimates.Substantial time and efforts are needed to track down the needed data.For example,in the Wyndor case:the unit profits$300 for doors a
7、nd$500 for the windows.第7页/共121页Parameters of the model模型的参数(2)Some factors cannot be estimated with real accuracy until long after the linear programming study has been completed and the new products have been on the market for some time.For example,the profits depend on many factors:the costs of r
8、aw materials,production,shipping,advertising,and so on,as well as such things as the market reception to the new products and the amount of competition encountered.第8页/共121页Parameters of the model模型的参数(3)Wyndors managers want to know what the effect would be if the unit profits turn out to differ si
9、gnificantly from the estimates.管理者想要知道如果这些单位利润的估计值与实际情况相差很多,会有怎样的结果?For example,would the optimal solution change if the profit of doors:$300$200?第9页/共121页Parameters of the model模型的参数(4)How inaccurate can the estimate be in either direction before the optimal solution would change?估计值可以在什么范围内变动,而不会改
10、变最优解?第10页/共121页Parameters of the model模型的参数(5)If the optimal solution will remain the same over a wide range of values for a particular coefficient in the objective function,then management will be content with a fairly rough estimate for this coefficient.目标函数中某一系数在一定的范围内变动不会改变最优解,那么,管理者是能够接受该系数的估计值
11、。第11页/共121页Parameters of the model模型的参数(6)On the other hand,if even a small error in the estimate would change the optimal solution,then management will want to take special care to refine(精确)this estimate.第12页/共121页First benefit of what-if analysis1.Typically,many of the parameters of a LP model ar
12、e only estimates of quantities(e.g.,unit profits)that cannot be determined precisely at this time.线性规划模型的许多参数在建模时是很难精确确定的,只能是对一些数据的估计(如;单位利润)。第13页/共121页First benefit of what-if analysis What-if analysis reveals how close each of these estimates needs to be to avoid obtaining an erroneous optimal sol
13、ution,and therefore pinpoints the sensitive parameters where extra care is needed to refine their estimates.通过What-if 分析可以表明,系数估计值必须精确到怎样的程度,才能避免得出错误的最优解,而且,可以找出哪些系数是需要重新精确定义的灵敏度参数。第14页/共121页Second benefit of what-if analysis2.If conditions change after the study has been completed(a common occurren
14、ce),what-if analysis leaves signposts that indicate(without solving the model again)whether a resulting change in a parameter of the model changes the optimal solution.如果在研究结束后,问题的条件发生了变化,通过what-if分析,即使不求解,也可以表明模型参数的变化是否会改变最优解。第15页/共121页Sensitivity Analysis灵敏度分析To study how changes in the parameters
15、 of a LP model affect the optimal solution.研究线性规划模型的参数如何变化会影响最优解。It involves checking how sensitive the optimal solution is to the value of each parameters.最优解对每一参数变化的灵敏度。第16页/共121页Third benefit of what-if analysis3.When certain parameters of the model represent managerial policy decisions,what-if a
16、nalysis provides valuable guidance to management about what the impact would be of altering these policy decision.当模型特定的参数反映管理政策决策时,what-if分析可以表明改变这些决策对结果的影响,从而有效指导管理者作出最终的决策。第17页/共121页4.2 Continuing the Wyndor Case Study继续研究伟恩德公司案例第18页/共121页Wyndor Case1.Two new products:An 8-foot glass door with al
17、uminum framing 一种8英尺的铝框玻璃门A 4-foot6-foot double-hung wood-framed window 一种4X6英尺的双把木框窗2.Three plants:vPlant 1 produces aluminum frames and hardware 工厂1:生产铝框和硬制件vPlant 2 produces wood frames 工厂2:生产木框vPlant 3 produces the glass and assembles the windows and doors 工厂3:生产玻璃、组装窗和门第19页/共121页Fig 4.1 Spreads
18、heet for Wyndor Case第20页/共121页Optimal solution for Wyndor CaseOptimal solution:D=2(produce 2 doors per week)W=6(produce 6 windows per week)Profit=3,600(The estimate total weekly profit is$3,600)第21页/共121页Managements Discussion of the Recommended Product Mix(1)1.the unit profit?What happens if the es
19、timate of the unit profit of one of Wyndors new products is inaccurate?How far off can one of these estimates be without changing the optimal product mix?Range-of-optimality sensitivity analysis第22页/共121页Managements Discussion of the Recommended Product Mix(2)2.What happens if the estimates of the u
20、nit profits of both of Wyndors new products are inaccurate?第23页/共121页Managements Discussion of the Recommended Product Mix(3)3.available production timeWhat happens if a change is made in the number of hours of production time per week being made available to Wyndors new products in one of the plant
21、s?How much more profit could we get from the new products for each additional hour of production time?We would compare this additional profit with the profit we could lose by cutting back on the production of current products.第24页/共121页Managements Discussion of the Recommended Product Mix(4)4.What h
22、appens if simultaneous changes are made in the number of hours of production time per week being made available to Wyndors new products in all the plants?第25页/共121页4.3 Range-of-Optimality Sensitivity Analysis最优域灵敏度分析第26页/共121页Question 1What happens if the estimate of the unit profit of one of Wyndor
23、s new products is inaccurate?如果伟恩德公司一种新产品单位利润的估计值是不精确的,结果会怎么样?第27页/共121页Example(1)For example,(PD,PW)=($300,$500),how much larger or how smaller PD can be and still have(D,W)=(2,6)as the optimal solution?在保持最优解(D,W)=(2,6)不变的条件下,PD可能的最大值与最小值。第28页/共121页Example(2)In other words,how much can the estimat
24、e of$300 for the unit profit for these doors be off before the model will give an erroneous optimal solution?门的单位利润$300 的这一估计可以在多大程度上偏离实际值,而不会产生错误的最优解。第29页/共121页Wyndor Case Study 伟恩德公司案例研究ThespreadsheetmodelanditsoptimalsolutionfortheoriginalWyndorproblembeforebeginningwhat-ifanalysis.第30页/共121页Fig
25、4.2PD=$300$200No change at all in the optimal solution.第31页/共121页WyndorCase Study 伟恩德公司案例研究TherevisedWyndorproblemwheretheestimateoftheunitprofitfordoorshasbeendecreasedfromPD=$300toPD=$200,butnochangeoccursintheoptimalsolution.第32页/共121页Fig 4.3PD=$300$500No change at all in the optimal solution.PD
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