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1、Chapter13:DeterminingOptimalLevelofProductAvailabilityExerciseSolutions1.0.2941Optimallot-size==NORMINV(0.2941,100,40)=78.34Giventhatp=$200,s=$30,c=$150:Expectedprofits=(p–s)mNORMDIST((O–m)/s,0,1,1)–(p–s)sNORMDIST((O–m)/s,0,1,0)–O(c–s)NORMDIST(O,m,s,1)+O(p–
2、c)[1–NORMDIST(O,m,s,1)]=$2,657Expectedoverstock=(O–m)NORMDIST((O–m)/s,0,1,1)+sNORMDIST((O–m)/s,0,1,0)=7.41Expectedunderstock=(m–O)[1–NORMDIST((O–m)/s,0,1,1)]+sNORMDIST((O–m)/s,0,1,0)=29.07EXCELworksheet13-1illustratesthesecomputations2.Withrevisedforecastin
3、g:0.2941Optimallot-size==NORMINV(0.2941,100,15)=91.88Giventhatp=$200,s=$30,c=$150:Expectedprofits=(p–s)mNORMDIST((O–m)/s,0,1,1)–(p–s)sNORMDIST((O–m)/s,0,1,0)–O(c–s)NORMDIST(O,m,s,1)+O(p–c)[1–NORMDIST(O,m,s,1)]=$4,121Expectedoverstock=(O–m)NORMDIST((O–m)/s,0
4、,1,1)+sNORMDIST((O–m)/s,0,1,0)14=2.78Expectedunderstock=(m–O)[1–NORMDIST((O–m)/s,0,1,1)]+sNORMDIST((O–m)/s,0,1,0)=10.9EXCELworksheet13-2illustratesthesecomputations3.Meandemandduringleadtime=DL=(2000)(2)=4000Standarddeviationofdemandduringleadtime=sL==500=7
5、07Safetyinventory=ROP–DL=6000–4000=2000CSL=NORMDIST(6000,4000,707,1)=0.9977Costofoverstocking=(0.25)(40)=$10Justifyingcostofunderstocking:=OptimalCSL=Optimalsafetystock=(NORMSINV(0.8889))(707)=863unitsEXCELworksheet13-3illustratesthesecomputations4.Usingthe
6、currentpolicy:0.75Optimallot-size==NORMINV(0.75,20000,10000)=26,745Giventhatp=$60,s=$20,c=$30:Expectedprofits=(p–s)mNORMDIST((O–m)/s,0,1,1)–(p–s)sNORMDIST((O–m)/s,0,1,0)–O(c–s)NORMDIST(O,m,s,1)14+O(p–c)[1–NORMDIST(O,m,s,1)]=$472,889Expectedoverstock=(O–m)NO
7、RMDIST((O–m)/s,0,1,1)+sNORMDIST((O–m)/s,0,1,0)=8,236UsingSouthAmericaoption:0.857Optimallot-size==NORMINV(0.857,20000,10000)=30,676Giventhatp=$60,s=$25,c=$30:Expectedprofits=(p–s)mNORMDIST((O–m)/s,0,1,1)–(p–s)sNORMDIST((O–m)/s,0,1,0)–O(c–s)NORMDIST(O,m,s,1)
8、+O(p–c)[1–NORMDIST(O,m,s,1)]=$521,024Expectedoverstock=(O–m)NORMDIST((O–m)/s,0,1,1)+sNORMDIST((O–m)/s,0,1,0)=11,407So,itisevidentthatusingSouthAmericaoptionresultsinincreasedexpectedprofits,butalsoincr
