Solution Manual for Matching Supply with Demand An Introduction to Operations Management, 5th Edition Cachon

SOLUTION MANUAL FOR g g


MatchingSupplywithDemandAnIntroductiontoOperationsManagement,5thEditionCachon j




Chapter2-19
g




Chapter2
TheProcessViewoftheOrganization
g j j j




Q2.1Dell
Thefollowingsteps referdirectlytoExhibit2.1. g


#1:For2001,wefindinDell’s10-k: Inventory=$400(inmillion)
g g


#2:For2001,wefindinDell’s10-k:
g j j




COGS=$26,442(inmillion)
g


26, 442$/year
=66.105turnsperyear400$
g
#3:Inventory turns=
b


g


40% per year
#4:PerunitInventory cost=
g g


=0.605%per year g
g

66.105 per year g g




Q2.2.Airline
WeuseLittle’slawtocomputetheflowtime,sinceweknowboththeflowrateaswellas the
j j g j



inventorylevel:
g


FlowTime=Inventory/FlowRate=35passengers/255passengersperhour =0.137hours g



=8.24minutes

Q2.3InventoryCost
(a) Sales =$60,000,000peryear/$2000perunit=30,000unitssoldperyear
b




Inventory =$20,000,000/$1000 per unit = 20,000 unitsin inventory
g g g g g g g g




Flow Time= Inventory/Flow Rate= 20,000/30,000 per year = 2/3year =8monthsTurns=
g j g j g g g j g


1/FlowTime= 1/(2/3year)= 1.5turns per year
g b g g g




Note:wecanalsogetthisnumberdirectlybywriting: j j g g Inventoryturns= COGS /Inventory j b




(b) CostofInventory: 25%peryear/1.5turns=16.66%.Fora $1000
j g g



product,thiswould makeanabsoluteinventorycostof $166.66.
g g g




Q2.4.ApparelRetailing
j




(a) Revenueof $100MimpliesCOGSof $50M (becauseofthe100%markup).
j g j g g g


Turns = COGS/Inventory =$50M/$5M =10.
g g g g g



(b) Theinventorycost,given10turns,is 40%/10= 4%.Fora 30$ item,theinventorycost is j j g b g j g g g


0.4$30=$1.20perunit.

Q2.5.LaVilla
(a) FlowRate=Inventory/Flow Time=1200skiers /10days= 120 skiers per day g g b j g g g g



(b) Lastyear:onanygivenday,10%(1of10)ofskiersareontheirfirstdayofskiing j j j j j j




©McGrawHill LLC. g g g g Allrightsreserved.Noreproductionordistributionwithouttheprior g

gwrittenconsentof
McGrawHillLLC.

, Thisyear:onanygivenday,20%(1of5)ofskiersareontheirfirstdayofskiing j j j j




Averageamountspentinlocalrestaurants(perskier)
j



Last year=0.1$50+0.9$30=$32 This year
g g g


=0.2$50+0.8$30=$34
%change=($34−$32)/$32=6.25% increase b




Q2.6.Highway
Welookat1mileofhighwayasourprocess.Sincethespeedis60milesperhour,ittakesacar 1
j j g


minutetotravelthroughtheprocess(flowtime).
g


Thereare24carson¼ofamile,i.e.thereare96carsonthe1milestretch(inventory).
Inventory=FlowRate*FlowTime:96cars=FlowRate*1minute
g j



Thus,theFlowRateis96carsperminute,correspondingto96*60=5760carsperhour.
g j j




Q2.7.StrohrmannBaking
j



Thebread needs tobein theoven for12minutes(flowtime).Wewanttoproduceat aflowrate of
g g b g j g g


4000breadsperhour,or 4000/60=66.66 breadsperminute.
g j g g




Inventory=FlowRate*FlowTime:Inventory=66.66breadsperminute*12minutesThus, j



Inventory=800breads,whichistherequiredsizeoftheoven.
g j




Q2.8.MtKinleyConsulting
j




Wehavethefollowinginformationavailablefromthequestion: j




Level Inventory(numberofconsultantsat FlowTime(timespentatthat level) j g


gthatlevel) j



Associate 200 4years
Manager 60 6years
Partner 20 10years

(a) WecanuseLittle’slawtofindtheflowrateforassociateconsultants:Inventory=Flow Rate* j g


FlowTime;200consultants=FlowRate*4years;thus,theflowrateis50 consultantsper
g j g


year,whichneedtoberecruitedtokeepthefirminitscurrentsize(note: whiletherearealso50
g j j j g j



consultantsleavingtheassociatelevel,thissaysnothingabouthow manyof
g g


themaredismissedvshowmanyofthemarepromotedto Managerlevel).
g g




(b) Wecanperformasimilaranalysisatthemanagerlevel,whichindicatesthattheflowrate
j j j



thereis10consultants.Inordertohave10consultantsasaflowrateatthemanagerlevel, we
g j j g


needtopromote10associatestomanagerlevel(remember,thefirmisnotrecruiting tothe
g j j j j j j j j g


higherranksfrom theoutside).Hence,everyyear,wedismiss40associatesand
g j j j j



promote10 associatestothemanagerlevel(theoddsatthatlevelare20%)
g g g




©McGrawHill gLLC. g g g Allrightsreserved.Noreproductionordistributionwithouttheprior g

gwrittenconsentof
McGrawHillLLC.

, Now,considerthepartnerlevel.Theflowratethereis2consultantsperyear(obtainedviathe same j j g


calculationsasbefore).Thus,fromthe10managercasesweevaluateeveryyear,8are
g j j



dismissedand2arepromotedtopartner(theoddsatthatlevelaretherebyalso20%).
g j j j




Inordertofindtheoddsofanewhiretobecomepartner,weneedtomultiplythepromotion
j j j j



gprobabilities:0.2*0.2=0.04.Thus,anewhirehasa4%chanceofmakingittopartner.


Q2.9.MajorUSRetailers
j



a. Productstaysonaveragefor31.9daysinCostco’sinventory
b. Costcohasfora$5productaninventorycostof$0.1311whichcomparestoa j j



$0.2049 atWal-Mart g




Q2.10.McDonald’s
a. InventoryturnsforMcDonald’swere92.3.Theywere30.05forWendy’s. j



b. McDonald’shasperunitinventorycostsof0.32%,whichfora3$mealabout j



$0.00975.Thatcomparesto0.998%atWendy’swherethecostpermealis $0.0299.
j j j g




Q2.11.BCH
I=400associates,T=2years. R =I/T=400associates /2yrs=200associates/yr. g b b




Q2.12.Kroger
Turns = R/I =76858/6244 =12.3
j j j j




MatchingSupplywithDemand:AnIntroductiontoOperationsManagement5e
SolutionstoChapterProblems

Chapter3 g


UnderstandingtheSupplyProcess:EvaluatingProcessCapacity


Q3.1ProcessAnalysiswithOneFlowUnit j



(a) Capacityofthethreeresourcesinunitsperhourare 602/10 =12 , 601/6=10;603 g j j g


/16=11.25.Thebottleneckisthe resourcewith thelowest capacity,whichisresource 2. j j j g


(b) Theprocesscapacityisthecapacityofthebottleneck,whichis 10units/hr. j j g



(c) If demand =8units/hr, then theprocessisdemandconstrained and theflowrateis
g j j j j j



8units/hr
g



(d) Utilization=FlowRate/Capacity.Forthethreeresourcestheyare 8/12, 8/10,and g g g



8/11.25.




©McGrawHill LLC.
g g g g Allrightsreserved.Noreproductionordistributionwithouttheprior g

gwrittenconsentof
McGrawHillLLC.

, Q3.2ProcessAnalysiswithMultipleFlowUnits
a) Bottleneckis resource3because it hasthehighestimpliedutilization of125%. Thedemands per
g g g g g g g g g


hourofthethreeproductsare 40/8=5, 50/8= 6.25and 60/8=7.5. The
g j j g g b g


totalminutesofworkdemandedperhouratresource1is5×5+6.25*5+7.5*5=
g


93.75. Two workers at resource 1 produce 2 * 60 = 120 min of work per hour. So
g g g g g g g g g g g g g g g g g


resource 1’s utilization is 93.75 /120 = 0.78. Utilization at the other resources are
g g g g g g g g g g g g g g


similarlyevaluated.
g


b) Thecapacityof resource3is 60/15=4units perhour.Given theratioofunitsproducedmust be4to j j g j g



5to6,theprocesscanproduce 4 units/hr ofA, 5units/hrofBand
g j g j g g


6units/hrofC.


Q3.3.Cranberry
gCranberriesarriveatarateof150barrelsperhour.Theygetprocessedatarateof100barrelsper hour.
j j j j j j g


gThus,inventoryaccumulatesatarateof150-100=50barrelsperhour.Thishappenswhile trucksarrive, j j g


gi.e.from6amto2pm.Thehighestinventoryleveltherebyis8h*50barrelsperhour= 400barrels.
j j j j g


Fromthese400barrels,200barrelsareinthebins,theother200barrels areintrucks.
j g


(a) 200barrels
(b) From2pmonwards,noadditionalcranberriesarereceived.Inventorygets depletedatarateof 100 j j g


barrelsperhour.Thus,itwilltake2huntiltheinventorylevelhasdroppedto200barrels,at which
g j j j g


timeallwaitingcranberriescanbestoredinthebins(nomoretruckwaiting)
g j j j j j



(c) Itwilltakeanother2hoursuntilallthebinsareempty
(d) Sincetheseasonalworkersonlystartat10:00am,thefirst4hoursofthedayweaccumulate 4hours*
j j j j g j



50barrelsperhour=200barrels.Fortheremainingtimethatwereceiveincoming cranberries,our
g j j j j j g


processingrateishigher(125barrelsperhour).Thus,inventoryonly accumulatesatarateof25(150-
g j g


125barrelsperhour).Giventhatthishappensover4hours,wegetanother100barrelsininventory.At
g j j j g j j



2pm,wetherebyhave300barrelsininventory.After 2pm,wereceivenofurthercranberries,yetwe
g j g j j j



initiallyprocesscranberriesatarateof125barrels perhour.Thus,itonlytakes
g j j j g g


100barrels/125barrels/hour =0.8hours= 48minutes
g g b




untilallbinsareempty.Fromthen,weneedanother2huntilthebinsareempty. j g




Q3.4.WesternPennsylvaniaMilk
j



Westart thedaywith 25,000 gallonsofmilkininventory. From 8amonwards,weproduce5,000
g g g g g


ggallons, yetweship10,000gallons.Thusinventoryisdepletedat arateof5000gallonsperhour, which
g j b j j g


gleavesuswithoutmilkafter5hours(at1pm).Fromthenonwards,clientswillhavetowait. Thissituation
j j j j j j g


ggetsworseandworseandby6pm(lastclientarrives),weareshort25,000gallons. j j j j j



(a) 1pm
(b) Clientswillstopwaitingwhen wehave workedoffour25,000 gallon backlog that we are facing g g g b g g g


at 6pm. Since we aredoingthis at arate of 5,000 gallon perhour, clientswill stop waiting at
g g g g g g g g g g g g g g g


11pm(after5morehours).
g


(c) At6pm,wehaveabacklogof25,000gallons,whichisequivalentto20trucks j



(d) Thewaitingtimeistheareainthetriangle




©McGrawHill LLC. g g g g Allrightsreserved.Noreproductionordistributionwithouttheprior g

gwrittenconsentof
McGrawHillLLC.