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1、NewsvendorProblemHeXuSchoolofmanagement,HuazhongUniversityofScienceandTechnologyCONTENTTheNewsvendorproblemDecisionsundercontinuousanddiscretedemandsApplicationtopostponementApplicationtooperationsproblemsinteractingwithmarketingissuesApplicationtomultipleproductswithdemand
2、substitution2NEWSVENDORPROBLEMNewsvendorproblemconsiderstheorderingdecisionofoneproduct(e.g.,newspapers,magazines,fish,meat,produce,bread,milk,highfashion…)inOne-periodwithOneorderingopportunityandwithAuncertaindemandD3NEWSVENDORPROBLEMSequenceofevents:Maketheorderingdecisi
3、onQ;Receivetheproducts;DemandsarerealizedObjectiveofthenewsvendor:Minimizeherexpectedcost;Ormaximizeherexpectedprofit4THETRADEOFFLetCubeunderagecost(i.e.,Cu=p-c),andCobeoveragecost(i.e.,Co=c-s).Thenewsvendorneedstoconsiderthetradeoffbetweenthetotalunderagecostandthetotalove
4、ragecost:IfD>Q,therewillbestockoutsThecost(risk)=Cumax{D–Q,0}IfD≤Q,therewillbeoverstocksThecost(risk)=Comax{Q–D,0}5FORMULATIONCostminimization:Profitmaximization:or6COSTMINIMIZATIONUNDERCONTINUOUSDEMANDThecostfunction:Firstordercondition:7COSTMINIMIZATIONUNDERCONTINUOUSDEMA
5、NDSecondordercondition:TheoptimaldecisionisdeterminedbyacriticalratioCu/(Cu+Co):Undertheoptimaldecision,theType1servicelevelequalsthecriticalratio8PROFITMAXIMIZATIONUNDERCONTINUOUSDEMANDTheprofitfunction:Firstordercondition:9PROFITMAXIMIZATIONUNDERCONTINUOUSDEMANDSecondorde
6、rcondition:Again,theoptimaldecisionisdeterminedbythecriticalratioCu/(Cu+Co)Observation:Costminimizationisequivalenttoprofitmaximization10EXAMPLEFORDISCRETEDEMANDSupposeforthenewsvendor,Cu=51,Co=49,thecriticalratioequals0.51,andthedemandcanbe10,20,30,40withequalchance.Whatis
7、theoptimaldecision?20?21?or30?G(x)x0.250.500.751.00104030200.5111DISCRETEDEMANDDiscretedemand:demandcanonlybenonnegativeintegers,x0,x1,…,xn,…ForanynonnegativeintegerQ,weobserve:QQ+1012OPTIMALDECISIONUNDER DISCRETEDEMANDOptimaldecision:IfG(xn)8、Cu/(Cu+Co)
