高三数学数学归纳法3教学讲义ppt.ppt

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1、高三数学数学归纳法3请问：用数学归纳法证明的一般步骤是什么？一、用数学归纳法证明整除问题注意：当n只出现在底数中时，采用把k+1的幂展开后，分段组合，往归纳假设的n=k的式子上“凑”的方法。当n同时出现在指数和底数中时，先按出现在指数中思考，用加一“项”，再减这“项”的方法，让这一“项”含有因为指数k变成k+1而使幂增加的那个因子，又要含有有n=k时的式子中，底数含有k的某项可作为另一因子。二、证明图形中与自然数n有关的命题。说明：用数学归纳法证明图形问题，关键是：要结合图形进行思考，特别是对于从n=k到n=k+1的图形变化的情景

2、要细致地弄清楚。TheNewsvendorModel报童模型“Toomuch”and“toolittle”costsCo=overagecostThecostoforderingonemoreunitthanwhatyouwouldhaveorderedhadyouknowndemand.Inotherwords,supposeyouhadleftoverinventory(i.e.,youoverordered).Coistheincreaseinprofityouwouldhaveenjoyedhadyouorderedone

3、fewerunit.Cu=underagecostThecostoforderingonefewerunitthanwhatyouwouldhaveorderedhadyouknowndemand.Inotherwords,supposeyouhadlostsales(i.e.,youunderordered).Cuistheincreaseinprofityouwouldhaveenjoyedhadyouorderedonemoreunit.BalancingtheriskandbenefitoforderingaunitOrd

4、eringonemoreunitincreasesthechanceofoverage…ExpectedlossontheQthunit=CoxF(Q)F(Q)=Distributionfunctionofdemand=Prob{Demand<=Q)…butthebenefit/gainoforderingonemoreunitisthereductioninthechanceofunderage:ExpectedgainontheQthunit=Cux(1-F(Q))Asmoreunitsareordered,theexpect

5、edbenefitfromorderingoneunitdecreaseswhiletheexpectedlossoforderingonemoreunitincreases.NewsvendorexpectedprofitmaximizingorderquantityTomaximizeexpectedprofitorderQunitssothattheexpectedlossontheQthunitequalstheexpectedgainontheQthunit:Rearrangetermsintheaboveequatio

6、n->TheratioCu/(Co+Cu)iscalledthecriticalratio.（临界比或关键比例）Hence,tomaximizeprofit,chooseQsuchthatwedon’thavelostsales(i.e.,demandisQorlower)withaprobabilitythatequalsthecriticalratioTheNewsvendorModel:Performancemeasures绩效指标NewsvendormodelperformancemeasuresForanyorder

7、quantitywewouldliketoevaluatethefollowingperformancemeasures:Expectedlostsales（期望销售损失）TheaveragenumberofunitsdemandexceedstheorderquantityExpectedsales（期望销售）(comparedtoexpecteddemand)Theaveragenumberofunitssold.Expectedleftoverinventory（期望售后剩余库存）Theaveragenumberofunit

8、sleftoverattheendoftheseason.ExpectedprofitExpectedfillrate（期望订单完成率）ThefractionofdemandthatissatisfiedimmediatelyIn-stockpro