供应链管理英文 Chapter 13 Exercise answers

Chapter13:DeterminingOptimalLevelofProductAvailabilityExerciseSolutions「ST*=———=———=0.2941「+「 50+120K-xuK-xoOptimallot-size=Q=NORMINV((JSL =NORMINV(0.2941,100,40)=78.34Giventhatp=$200,s=$30,c=$150:Expectedprofits=(p-s)/zNORMDIST((。- 0,1,1)-(p-s)aNORMDIST((O-刈o,0f/,0)-0(c-s)NORMDIST(Of“3”+O(p-c)[1-NORMDIST(O9从51)]=$2,657Expectedoverstock=(O—jli)NORMDIST((O-*/cr,0,1,1)+aNORMDIST((O-*/j0,1,0)=7.41Expectedunderstock=("一O)[l-NORMDIST((O-川/⑦0,1,1)]+oNORMDISTQO-4/50,1,0)=29.07EXCELworksheet13-1illustratesthesecomputationsWithrevisedforecasting:「S丁*=_—=———=0.29413L「5o+i2oOptimallot-size=Q=NORMINV((JSL "NORMINV(0.2941,100,15)=91.88Giventhatp=$200,s=$30,c=$150:Expectedprofits=(p-s)//NORMDIST((。- 0,1,1)-(p-s)aNORMDIST((O-刈o,0,1,0)—O(c-s)NORMDIST(Of51)+。(p—c)[1-NORMDIST(Of431)]=$4,121Expectedoverstock=(O—jli)NORMDIST((O-*/b,0,1,1)+aNORMDIST((O-*/q0,1,0)Withpostponement:Anticipateddemand=20,000+20,000+20,000+20,000=80,000Standarddeviation二V80002+80002+80002+80002=16000*=_Q_= =0.6154c+C8+5uo**Optimallot-size=。=NORMINV{(JSL，%6=NORMINV(0.6154,80000,16000)=84,694Giventhatp=$20,s=$7,c=$12:Expectedprofits=(p-NORMDIST((O-4)/50,1,1)-(p-s)aNORMDIST((O-刈o,0,/,O)-O(c-s)NORMDIST(Of4,3”+O(p-c)[l-NORMDIST(O,d51)]=$560,515Expectedoverstock=(O-ju)NORMDIST((O-*/g0,1,1)+aNORMDIST((O-刈o,0,1,0)=9,003Indifferent:Ataunitcostof$10.7thetwooptions,i.e.,postponementandnopostponementwouldbeindifferent.ThisunitcostisobtainedbyusingthesolveroptioninEXCELbyconsideringcell21asthechangingcellwhilecell35isutilizedasthetargetcellwithavalueof$673,446.EXCELworksheet13-12illustratesthesecomputations13.Thewithandwithoutpostponementcalculationsaresimilartoproblem12(EXCELworksheet13-13illustratesthesecomputations),butwhatisnewinthisproblemisthetailoredpostponementwhichisdiscussedbelow:Tailoredpostponement:Popularstylewithoutpostponement:「SI*= C_=15=0.68183Lc15+7Optimallot-size=Q=NORMINV(CSL=NORMINV(0.6818,30000,5000)=32,364Giventhatp=$35,s=$13,c=$20:Expectedprofits=(p-s)〃NORMDIST((O-4)/。,0,1,1)—(p—s)aN0RMDIST((0-*Optimallot-size=Q= =NORMINV(0.6842,20000,8000)/a0,7,0)-0[c-s)N0RMDIST(0f*Optimallot-size=Q= =NORMINV(0.6842,20000,8000)+O(p-c)[1-NORMDIST(Of//,o;1)J=$410,757Expectedoverstock=(O—jli)NORMDIST((O-*/b,0,1,1)+crN0RMDIST((0-川K0,1,0)=3,396Otherthreestyleswithpostponement:Aggregatedexpecteddemand=8,000+8,000+8,000=24,000Standarddeviation=740002+40002+40002:6928「ST*= G—=14=0.6182J"c+r14+8Il oOptimallot-size=Q=NORMINV((J^£,<r)=NORMINV(0.6182,24000,6928)=26,083Giventhatp=$35,s=$13,c=$21.4:Expectedprofits=(p-NORMDIST((O-4)/50,1,1)-(p-s)aN0RMDIST((0-*/q0,7,O)-O(c-s)N0RMDIST(0f43”+O(p-c)[1-NORMDIST(Of//,o;1)J=$268,281Expectedoverstock=(O—jli)NORMDIST((O-*/b,0,1,1)+crNORMDIST((O-*/j0,1,0)=18,083Totalexpectedprofit=$410,757+$268,281二$679,038Totalexpectedoverstock=3,396+18,083=21,479EXCELworksheet13-13illustratesthesecomputations14.Withoutdiscount:£—=———=0.6842CQL「+r65+30=23,836Giventhatp=$95,s=$0,c=$30:Expectedprofits-{p-s)/liNORMDIST((O-4)/50,1,1)-(p-s)aN0RMDIST((0-刈o,0,7,O)-O(c-s)N0RMDIST(0f从a1)+0(p-c)[l-N0RMDIST(0,“o;/〃=$1,029,731Expectedoverstock=(O—^N0RMDIST((0-*/b,0,1,1)+aN0RMDIST((0-*/②0,1,0)二5,470Withdiscount:Optimallot-size-0=25,000Giventhatp=$95,s=$0,c=$28:Expectedprofits-(p-NORMDIST((。-4)/50,1,1)-(p-s)aN0RMDIST((0-4)/30,7,O)-O(c-s)N0RMDIST(0f51)+。(p—c)[l-N0RMDIST(0,乩51)]=$1,076,941Expectedoverstock=(O—^)N0RMDIST((0-刈50,1,1)+aN0RMDIST((0-刈o,0,1,0)=6,295Expectedprofitsincreasewithdiscount.EXCELworksheet13-14illustratesthesecomputations15.Withoutdiscount:*r7rsi=—j—=——=o.7c7+3v-zu oOptimallot-size=(J=NORMINV(CSL，NQ)=NORMINV(0.7,70000,25000)=83,110Giventhatp=$10,s=$0,c=$3:Expectedprofits=(p-s)"NORMDIST((。-4)/50,1,1)+。(p—c)[l-NORMDIST(Of以,o,1)]=$403,077Expectedoverstock=(O—jli)NORMDIST((O-"At,0,1,1)+oN0RMDIST((0-川/50,1,0)二17,869Withdiscount:Optimallot-size=0=100,000Giventhatp=$10,s=$0,c=$2.75:Expectedprofits=(p-s)4NORMDIST((。-4)/50,1,1)一(p-s)aNORMDIST((O-jLi)/af0,7,O)-O(c-s)NORMDIST(Of//,a1)+O(p-c)fl-N0RMDIST(0,乩o,1)]=$410,974Expectedoverstock=(O—^NORMDIST((O-*/50,1,1)+oN0RMDIST((0-"S,0,1,0)=31,403Expectedprofitsincreasewithdiscount.EXCELworksheet13-15illustratesthesecomputations16.themanufacturershouldorder:40-Gb 20-Gb 6-Gb26,772I47,419 | 84,054 |Theexpectedprofitsfortheunitsare:40-Gb 20-Gb 6-Gb$1,664,888 $2,048,931 $2,080,846Iftheavailablecapacityislimitedto140,000unitsthemanufacturershouldorder:40-Gb 20-Gb 6-Gb26,772 41,300 72,028expectedprofitswouldbe:40-Gb 20-Gb 6-Gb$1,790,125 $2,072,482 $2,002,170EXCELworksheet13-16illustratesthesecomputations.=2.78=2.78Expectedunderstock=(//-O)[l-NORMDIST((O-*/50,1,1)]+oNORMDISTQO-川/50,1,0)=10.9EXCELworksheet13-2illustratesthesecomputations3.Meandemandduringleadtime=DL=(2000)(2)=4000Standarddeviationofdemandduringleadtime=gl=a£)VZ=500a/2=707Safetyinventory=ROP—DL=6000-4000=2000CSL二NORMDIST(6000,4000,707,1)=0.9977Costofoverstocking=(0.25)(40)=$10Justifyingcostofunderstocking:Cu~Justifyingcostofunderstocking:Cu~HQQ-csl)d^10x10000(1-0.9977)x2000x52=$411OptimalCSL=—Q—=———=0.8889c+「 80+10Optimalsafetystock=(NORMSINV(0.8889))(707)=863unitsEXCELworksheet13-3illustratesthesecomputations4.Usingthecurrentpolicy:「ST'= £—=—=0.75J"「30+10Optimallot-size二Q=NORMINV(CSL小，6=NORMINV(0.75,20000,10000)=26,745Giventhatp=$60,s=$20,c=$30:Expectedprofits=(p-s)/nNORMDIST((6>-4)/0;0,1,1)(p-s)aNORMDIST((O-go,0,1,0)-0(c-s)NORMDIST(O,o,1)

+。(p—c)[l-NORMDIST(O,r,。1)]=$472,889Expectedoverstock=(O—jli)NORMDIST((O-)Ar,0,1,1)+oNORMDISTQO-刈o,0,1,0)=8,236UsingSouthAmericaoption:——=3()=0.857J“C+C30+5Optimallot-size=Q=NORMINV((J^]^\^cr)=NORMINV(0.857,20000,10000)=30,676Giventhatp=$60,s二$25,c=$30:Expectedprofits=(p-s)jliNORMDIST((。-川/②0,1,1)-(p-s)aN0RMDIST((0-6S,0,7,O)-O(c-s)N0RMDIST(0f〃，51)+O(p-c)[l-N0RMDIST(0f4,5/〃=$521,024Expectedoverstock=(O-jli)NORMDIST((O-*0,1,1)+aNORMDIST((O-*/j0,1,0)=11,407So,itisevidentthatusingSouthAmericaoptionresultsinincreasedexpectedprofits,butalsoincreasestheproductioncapacityrequirementsneededatChampion.EXCELworksheet13-4illustratesthesecomputations5.Currentsourcing(oneline):Reguplo:CSL=V-ZuCSL=V-ZuK-X<100100+20=0.8333Optimallot-size=Q=NORMINV(CS匚，NORMINV(0.8333,10000,1000)二=10,967Giventhatp=$200,s=$80,c=$100:Expectedprofits=(p-s)"NORMDIST((<9一4)/50,1,1)

-(p-s)oN0RMDIST((0-刈o,0,7,O)-O(c-s)NORMDIST(Of禺o,1)^O(p-c)[l-NORMDIST(Of//,o;1)]=$970,018Eachoftheothermodels:「ST= C—=—110=0.7857DU'c+0 110+30Optimallot-size-0=NORMINV(CSl=NORMINV(0.7857,1000,700)==1,554Giventhatp=$220,s=$80,c=$110:Expectedprofits=(p—s)//NORMDIST((。-4)/50,1,1)-(p-s)aN0RMDIST((0-刈o,0,1,0)—O(c-s)NORMDIST(Ot51)+O(p-c)[l-N0RMDIST(0f乩o,1)]=$81,421Totalexpectedprofits=$970,018+3($81,421)=$1,214,280Tailoredsourcingpolicy:ThecomputationsareexactlythesamewithreviseddataforReguplo(c=$90)andforeachoftheotherthreemodels(c=$120)Totalexpectedprofits=$1,281,670Thus,itisbeneficaltoutilizethetailoredsourcingoptionduetoincreasedexpectedprofits.ThisoptionincreasestheoptimalproductionlotsizeforReguploanddecreasesthelotsizesforeachoftheotherthreeoptions.EXCELworksheet13-5illustratesthesecomputationsIBM:CSL=WCSL=W=0.744735+12Optimallot-size=Q=NORMINV(CSL,〃，b)=NORMINV(0.7447,5000,2000)=6,316Giventhatp=$50,s=$3,c=$15:Expectedprofits=(p—s)rNORMDIST((。-4)/50,1,1)-(p-s)aN0RMDIST((0-*/q0,7,0)-0(c-s)N0RMDIST(0f4,a"+。(p—c)[l-NORMDIST(O,以，5D]=$144,796Expectedoverstock=(O—jli)NORMDIST((O-)/o,0,1,1)+oNORMDISTQO-刈o,0,1,0)=1,622Similarly,theotherthreeareevaluatedandtheresultsaresummarizedbelow:Optimalcycleservicelevel0.74470.74470.7447Optimalproductionsize5,447Expectedprofits$207,245$109,796$106,776Expectedoverstock2,0281,6221,785OutputsAT&T HP CiscoTotalproductionlotsize=6316+8,645+5,316+5,447=25,723Totalexpectedprofits=$144,796+$207,245+$109,796+$106,776二$568,612Totalexpectedoverstock=1,622+2,028+1,622+1,785=7,057(=amountdonatedtocharityonaverage)EXCELworksheet13-6illustratesthesecomputationsWithaggregation:Anticipateddemand=5,000+7,000+4,000+4,000=20,000Standarddeviation=720002+25002+20002+22002=4369=———=32=0.88893L0+「 32+4Optimallot-size二Q=NORMINV(CS匚，"")=NORMINV(0.8889,20000,4369)=25,333Giventhatp=$50,s=$14,c=$18:Expectedprofits=(p-s)rNORMDIST(((9-4)/50,1,1)-(p-s)aNORMDIST((O-6/o,0,7,O)-O(c-s)NORMDIST(Ofda1)+O(p-c)[l-NORMDIST(Of45/〃=$610,210Expectedoverstock=(O—pi)N0RMDIST{(0-*/b,0,1,1)+crNORMDIST((O-*/a0,1,0)=5,568Ascanbeseenfromtheresultsabove,postponementincreasestheexpectedprofitanddecreasestheamountofoverstock.EXCELworksheet13-7illustratesthesecomputations(a)Costofoverstocking,Co=$0.50Costofunderstocking,Cu=$1.00Meandemand50,000Standarddeviationofdemand15,000OptimalCSL==_C_=_!_=0.67c+C1+0.5Optimalorderquantity=(NORMSINV(0.67))(15,000)+50,000=56,461(b)Costofoverstocking,Co=$0.50Costofunderstocking,Cu=$5.00Meandemand50,000Standarddeviationofdemand15,000OptimalCSL==—Q—=—5—=0.91C+C5+0.5Optimalorderquantity=(NORMSINV(0.91))(15,000)+50,000=70,028EXCELworksheet13-8illustratesthesecomputations9.Meandemand=5,000Standarddeviationofdemand=2,000Costofoverstocking,Co$40.00Ordersize=6,000CSL(impliedbytheordersize)=NORMDIST(6000-5000/2000)=0.691Impliedcostofunderstocking,Cu=(CO)(CSL)/(1-CSL)=(40)(0.691)/(1-0.691)=$89.64(b)Meandemand=5,000Standarddeviationofdemand=2,000Costofoverstocking,Co$40.00Ordersize=8,000CSL(impliedbytheordersize)=NORMDIST(8000-5000/2000)=0.933Impliedcostofunderstocking,Cu=(CO)(CSL)/(1-CSL)=(40)(0.933)/(1-0.933)=$558.74EXCELworksheet13-9illustratesthesecomputations10.Currentpolicy:「SI"= ——=———=0.69233乙0+「45+20Optimallot-size=。=NORMINV(CSl=NORMINV(0.6923,4000,1750)=4879Giventhatp=$125,s=$60,c=$80:Expectedprofits=(p-s)jliNORMDIST((O-4)/0;0,1,1)

+。(p—c)[l-NORMDIST(O,以，o,1)]=$140,001Expectedoverstock=(O—ju)NORMDIST((O-"At,0,1,1)+oN0RMDIST((0-刈o,0,1,0)二1,224SouthernHemisphereoption:C—=45=o.9oJ"C45+5Optimallot-size=。=NORMINV(CSC，〃，。)=NORMINV(0.9,4000,1750)=6243Giventhatp=$125,s=$75,c=$80:Expectedprofits=(p-s)从NORMDIST((。-4)/50,1,1)-(p-s)aN0RMDIST((0-*/q0,h0)-O(c-s)NORMDIST(Ot4,3”+O(p-c)[1-NORMDIST(O,3/〃=$164,644Expectedoverstock=(O-jli)NORMDIST((O-刈o,0,1,1)+aNORMDIST((O