統(tǒng)計(jì)應(yīng)用案例-報(bào)童模型課件

《統(tǒng)計(jì)應(yīng)用案例-報(bào)童模型》

在你面前有三個(gè)門，其中兩個(gè)門里面是山羊，另外一個(gè)是汽車。你當(dāng)然想得到那輛汽車，而不是臭氣轟轟的山羊。主持人要求你選中一個(gè)，但是不能打開。此時(shí)主持人打開另外一個(gè)，是山羊?，F(xiàn)在主持人問你，你要不要改成第三個(gè)門？3

誰是更好的采購經(jīng)理?如果產(chǎn)品是賀卡:利潤=$3.00成本=$0.20？設(shè)想有倆個(gè)經(jīng)理管理同樣的一產(chǎn)品（超10個(gè)品種）的采購。假定條件相同。在季節(jié)結(jié)束，張經(jīng)理基本沒有剩余；王經(jīng)理多個(gè)品種有剩余。報(bào)亭老板如何決策？銷售份數(shù)天數(shù)110220340420510南大北門的報(bào)亭在過去100天里，某報(bào)紙的銷售記錄如左表。報(bào)紙銷售價(jià)1元，進(jìn)價(jià)0.3元。問：報(bào)亭老板每天訂幾份報(bào)紙合適？A.2B.3C.45什么是分析能力？

一位物理學(xué)家，工程師和數(shù)學(xué)家在東馬徒步旅行，看到一頭黑山羊在山坡上吃草。物理學(xué)家首先發(fā)表高見:“所有馬國的山羊都是黑色的?！?“不對(duì)，西蒙。有些馬國的山羊是黑色,”工程師糾正到。 數(shù)學(xué)家最后發(fā)言：“從所看到的，我們只能說，在東馬，至少有一只山羊至少身體的一面是黑色的?！睕Q策思路邊際成本=邊際收入7單周期最優(yōu)訂貨量-1定義：

－期末庫存余量為正時(shí)的單位成本（滯銷成本）

－需求未滿足導(dǎo)致的成本（機(jī)會(huì)成本） －周期一開始購買的商品數(shù)量

－需求量D的概率密度函數(shù)

－需求量D的概率分布函數(shù)案例：報(bào)童模型Pandora皮衣：單位利潤14.50$，因滯銷降價(jià)而帶來損失5.00$/件.成員CorolnLauraTomKenyWallyWendy平均標(biāo)準(zhǔn)差預(yù)測12001150125013001100120012001309單周期最優(yōu)訂貨量-2

從A-1看出，對(duì)于面積=0.74，z=0.65。因此面積=0.74需求量，Xf(x)O’Neill’sHammer3/2wetsuitHammer3/2timelineandeconomicsEconomics:Eachsuitsellsforp=$180TECchargesc=$110persuitDiscountedsuitssellforv=$90The“toomuch/toolittleproblem”:OrdertoomuchandinventoryisleftoverattheendoftheseasonOrdertoolittleandsalesarelost.Marketing’sforecastforsalesis3200unitsNewsvendormodelimplementationstepsGathereconomicinputs:Sellingprice,production/procurementcost,salvagevalueofinventoryGenerateademandmodel:Useempiricaldemanddistributionorchooseastandarddistributionfunctiontorepresentdemand,e.g.thenormaldistribution,thePoissondistribution.Chooseanobjective:e.g.maximizeexpectedprofitorsatisfyafillrateconstraint.Chooseaquantitytoorder.TheNewsvendorModel:

DevelopaForecastHistoricalforecastperformanceatO’NeillForecastsandactualdemandforsurfwet-suitsfromthepreviousseasonEmpiricaldistributionofforecastaccuracyNormaldistributiontutorialAllnormaldistributionsarecharacterizedbytwoparameters,mean=mandstandarddeviation=s

Allnormaldistributionsarerelatedtothestandardnormalthathasmean=0andstandarddeviation=1.Forexample:LetQbetheorderquantity,and(m,s)theparametersofthenormaldemandforecast.Prob{demandisQorlower}=Prob{theoutcomeofastandardnormaliszorlower},where(Theabovearetwowaystowritethesameequation,thefirstallowsyoutocalculatezfromQandthesecondletsyoucalculateQfromz.)LookupProb{theoutcomeofastandardnormaliszorlower}intheStandardNormalDistributionFunctionTable.ConvertingbetweenNormaldistributionsStartwith=100,=25,Q=125Centerthedistributionover0bysubtractingthemeanRescalethexandyaxesbydividingbythestandarddeviationStartwithaninitialforecastgeneratedfromhunches,guesses,etc.O’Neill’sinitialforecastfortheHammer3/2=3200units.EvaluatetheA/Fratiosofthehistoricaldata:SetthemeanofthenormaldistributiontoSetthestandarddeviationofthenormaldistributiontoUsinghistoricalA/FratiostochooseaNormaldistributionforthedemandforecastO’Neill’sHammer3/2normaldistributionforecastO’Neillshouldchooseanormaldistributionwithmean3192andstandarddeviation1181torepresentdemandfortheHammer3/2duringtheSpringseason.EmpiricalvsnormaldemanddistributionEmpiricaldistributionfunction(diamonds)andnormaldistributionfunctionwithmean3192andstandarddeviation1181(solidline)“Toomuch”and“toolittle”costsCu

=underagecostCo=overagecostThecostoforderingonemoreunitthanwhatyouwouldhaveorderedhadyouknowndemand.Inotherwords,supposeyouhadleftoverinventory(i.e.,youoverordered).Coistheincreaseinprofityouwouldhaveenjoyedhadyouorderedonefewerunit.FortheHammer3/2Co=Cost–Salvagevalue=c–v=110–90=20Thecostoforderingonefewerunitthanwhatyouwouldhaveorderedhadyouknowndemand.Inotherwords,supposeyouhadlostsales(i.e.,youunderordered).Cuistheincreaseinprofityouwouldhaveenjoyedhadyouorderedonemoreunit.FortheHammer3/2Cu=Price–Cost=p–c=180–110=70BalancingtheriskandbenefitoforderingaunitOrderingonemoreunitincreasesthechanceofoverage…ExpectedlossontheQthunit=CoxF(Q)F(Q)=Distributionfunctionofdemand=Prob{Demand<=Q)…butthebenefit/gainoforderingonemoreunitisthereductioninthechanceofunderage:ExpectedgainontheQthunit=Cux(1-F(Q))Asmoreunitsareordered,theexpectedbenefitfromorderingoneunitdecreaseswhiletheexpectedlossoforderingonemoreunitincreases.NewsvendorexpectedprofitmaximizingorderquantityTomaximizeexpectedprofitorderQunitssothattheexpectedlossontheQthunitequalstheexpectedgainontheQthunit:Rearrangetermsintheaboveequation->TheratioCu/(Co+Cu)iscalledthecriticalratio.

Hence,tomaximizeprofit,chooseQsuchthatwedon’thavelostsales(i.e.,demandisQorlower)withaprobabilitythatequalsthecriticalratioFindingtheHammer3/2’sexpectedprofitmaximizingorderquantitywiththeempiricaldistributionfunctionInputs:Empiricaldistributionfunctiontable;p=180;c=110;v=90;Cu=180-110=70;Co=110-90=20Evaluatethecriticalratio:Lookup0.7778intheempiricaldistributionfunctiontableIfthecriticalratiofallsbetweentwovaluesinthetable,choosetheonethatleadstothegreaterorderquantity(choose0.788which