第5章 敏感性分析 改

第5章线性规划的what-if分析继续研究伟恩德公司案例5.2只有一个目标函数系数变动5.3–5.9目标函数系数同时变动的影响5.10–5.17单个约束条件变化的影响5.18–5.23约束右端值同时变动的情形5.24–5.26伟恩德公司案例（what-if分析之前）3456789101112BCDEFGDoorsWindowsUnitProfit$300$500HoursHoursUsedAvailablePlant1102=4Plant20212=12Plant33218=18DoorsWindowsTotalProfitUnitsProduced26$3,600HoursUsedPerUnitProduced用电子表格进行敏感性分析门的利润从300美元降到200美元，而最优解不变3456789101112BCDEFGDoorsWindowsUnitProfit$200$500HoursHoursUsedAvailablePlant1102=4Plant20212=12Plant33218=18DoorsWindowsTotalProfitUnitsProduced26$3,400HoursUsedPerUnitProduced应用电子表格进行敏感性分析门的利润从300美元增加到500美元，而最优解不变3456789101112BCDEFGDoorsWindowsUnitProfit$500$500HoursHoursUsedAvailablePlant1102=4Plant20212=12Plant33218=18DoorsWindowsTotalProfitUnitsProduced26$4,000HoursUsedPerUnitProduced应用电子表格进行敏感性分析门的利润从300美元增加到1000美元，而最优解变了3456789101112BCDEFGDoorsWindowsUnitProfit$1,000$500HoursHoursUsedAvailablePlant1104=4Plant2026=12Plant33218=18DoorsWindowsTotalProfitUnitsProduced43$5,500HoursUsedPerUnitProduced运用SolverTable进行敏感性分析345678910111213141516171819202122232425262728BCDEFGDoorsWindowsUnitProfit$300$500HoursHoursUsedAvailablePlant1102=4Plant20212=12Plant33218=18DoorsWindowsTotalProfitUnitsProduced26$3,600UnitProfitTotalforDoorsDoorsWindowsProfit26$3,600$100$200$300$400$500$600$700$800$900$1,000HoursUsedPerUnitProducedOptimalUnitsProducedSelectthesecells(B18:E28),beforechoosingtheSolverTable.161718CDETotalDoorsWindowsProfit=DoorsProduced=WindowsProduced=TotalProfitOptimalUnitsProduced运用SolverTable进行敏感性分析16171819202122232425262728BCDEUnitProfitTotalforDoorsDoorsWindowsProfit26$3,600$10026$3,200$20026$3,400$30026$3,600$40026$3,800$50026$4,000$60026$4,200$70026$4,400$80043$4,700$90043$5,100$1,00043$5,500OptimalUnitsProduced运用敏感度报告来寻找允许变化范围AdjustableCellsFinalReducedObjectiveAllowableAllowableCellNameValueCostCoefficientIncreaseDecrease$C$12UnitsProducedDoors20300450300$D$12UnitsProducedWindows605001E+30300运用图形来洞察可变范围通过约束边界的两条虚线分别表示PD在允许取值范围的上下限处的目标函数，0≤PD≤750.WD(2,6)isoptimalfor0PD750PD=0(Profit=0D+500W)PD=300(Profit=300D+500W)PD=750(Profit=750D+500W)LineALineCLineB02462468ProductionratefordoorsProductionrateforwindowsFeasibleregion应用电子表格进行敏感性分析门、窗的单位利润分别被改为450美元、400美元，但是最优解不变3456789101112BCDEFGDoorsWindowsUnitProfit$450$400HoursHoursUsedAvailablePlant1102=4Plant20212=12Plant33218=18DoorsWindowsTotalProfitUnitsProduced26$3,300HoursUsedPerUnitProduced应用电子表格进行敏感性分析门、窗的单位利润分别被改为600美元、300美元，从而最优解改变3456789101112BCDEFGDoorsWindowsUnitProfit$600$300HoursHoursUsedAvailablePlant1104=4Plant2026=12Plant33218=18DoorsWindowsTotalProfitUnitsProduced43$3,300HoursUsedPerUnitProduced运用SolverTable进行敏感性分析3456789101112131415161718192021BCDEFGHIDoorsWindowsUnitProfit$300$500HoursHoursUsedAvailablePlant1102=4Plant20212=12Plant33218=18DoorsWindowsTotalProfitUnitsProduced26$3,600TotalProfitUnitProfitforWindows$3,600$100$200$300$400$500$300UnitProfit$400forDoors$500$600HoursUsedPerUnitSelectthesecells(C17:H21),beforechoosingtheSolverTable.17C=TotalProfit运用SolverTable进行敏感性分析161718192021BCDEFGHTotalProfitUnitProfitforWindows$3,600$100$200$300$400$500$300$1,500$1,800$2,400$3,000$3,600UnitProfit$400$1,900$2,200$2,600$3,200$3,800forDoors$500$2,300$2,600$2,900$3,400$4,000$600$2,700$3,000$3,300$3,600$4,200运用SolverTable进行敏感性分析242526272829BCDEFGHUnitsProduced(Doors,Windows)UnitProfitforWindows(2,6)$100$200$300$400$500$300(4,3)(4,3)(2,6)(2,6)(2,6)UnitProfit$400(4,3)(4,3)(2,6)(2,6)(2,6)forDoors$500(4,3)(4,3)(4,3)(2,6)(2,6)$600(4,3)(4,3)(4,3)(4,3)(2,6)25C=(&DoorsProduced&,&WindowsProduced&)百分之百法则如果目标函数的系数同时变动，计算出每一系数变动量占该系数允许变化范围允许变动量的百分比，而后，将各个系数的变动百分比相加，如果所得的和不超过100％，最优解不会改变，如果超过100％，则不能确定最优解是否改变。用图形来看百分比法则当门和窗的单位利润的估计值分别改为525美元和350美元，刚好处在百分百法则所允许的临界点上，(D,W)=(2,6)还是最优解。WD02462468ProductionratefordoorsProductionrateforwindowsFeasibleregion10ObjectivefunctionlinenowisProfit=$3150=525D+350WsincePD=$525,PW=$350.Entirelinesegmentisoptimal(4,3)(2,6)8用图形来看百分比法则当门和窗的单位利润的估计值分别改为150美元、250美元（最初解的一半时），用作图法可知(D,W)=(2,6)还是最优解，尽管百分百法则表示最优解有可能变动。02462468(2,6)FeasibleregionOptimalsolutionProductionratefordoorsProductionrateforwindowsProfit=$1800=150D+250W8WD应用电子表格进行敏感性分析将工厂２的可变时从12小时增加到１３小时，总利润增长150美元3456789101112BCDEFGDoorsWindowsUnitProfit$300$500HoursHoursUsedAvailablePlant1101.667=4Plant20213=13Plant33218=18DoorsWindowsTotalProfitUnitsProduced1.6676.5$3,750HoursUsedPerUnitProduced应用电子表格进行敏感性分析将工厂２的可用工时从13增加到18小时，总利润将增加750美元（也就是每小时增加150美元）3456789101112BCDEFGDoorsWindowsUnitProfit$300$500HoursHoursUsedAvailablePlant1100=4Plant20218=18Plant33218=18DoorsWindowsTotalProfitUnitsProduced09$4,500HoursUsedPerUnitProduced应用电子表格进行敏感性分析再增加２个工时，从18小时增长为20小时，总利润没有变化，因为最优解没有用到这些多余工时。3456789101112BCDEFGDoorsWindowsUnitProfit$300$500HoursHoursUsedAvailablePlant1100=4Plant20218=20Plant33218=18DoorsWindowsTotalProfitUnitsProduced09$4,500HoursUsedPerUnitProduced运用SolverTable进行敏感性分析34567891011121314151617181920212223242526272829303132333435BCDEFGDoorsWindowsUnitProfit$300$500HoursHoursUsedAvailablePlant1102=4Plant20212=12Plant33218=18DoorsWindowsTotalProfitUnitsProduced26$3,600TimeAvailableTotalIncreme