Solution Manual for Matching Supply with Demand 5th Edition – Cachon & Terwiesch – Operations Management Answers

SOLUTION MANUAL FORj j

MatchingjSupplyjwithjDemandjAnjIntroductionjtojOperationsjManagement,j5thjEditionjCachonjC
hapterj2-19

Chapterj2
ThejProcessjViewjofjthejOrganization

Q2.1jDell
ThejfollowingjstepsjreferjdirectlyjtojExhibitj2.1.
#1:jForj2001,jwejfindjinjDell’sj10-k:j Inventoryj=j$400j(injmillion)
#2:jForj2001,jwejfindjinjDell’sj10-k:j COGSj=j$26,442j(injmillion)
26,j442$/jyearj
#3:jInventoryjturnsj=j =j66.105jturnsjperjyearj400$
40%j perj year
#4:jPerjunitjInventoryj costj = =j0.605%jperj year
66.105j perj year

Q2.2.jAirline
WejusejLittle’sjlawjtojcomputejthejflowjtime,jsincejwejknowjbothjthejflowjratejasjwelljasjth
ejinventoryjlevel:
FlowjTimej=jInventory/jFlowjRatej=j35jpassengers/j255jpassengersjperjhourj=j0.137jhours
=j8.24jminutes

Q2.3jInventoryjCost
(a) Salesj=j$60,000,000jperjyearj/j$2000jperjunitj=j30,000junitsjsoldjperjyearjIn
ventoryj=j$20,000,000j/j$1000jperjunitj=j20,000junitsjinjinventory

Flowj Timej=jInventory/jFlowj Ratej=j20,000j/j30,000j perj yearj =j2j/j3jyearj =j8jmonthsjTurnsj=j
1/jFlowjTimej=j1/(2j/j3jyear)j=j1.5jturnsj perj year

Note:jwejcanjalsojgetjthisjnumberjdirectlyjbyjwriting:j Inventoryjturnsj=jCOGSj/jInventory

(b) CostjofjInventory:j 25%jperjyearj/1.5jturnsj=j16.66%.jForjaj $1000j product,jthisjwouldjma
kejanjabsolutejinventoryjcostjofj $166.66j.

Q2.4.jAppareljRetailing

(a) Revenuejofj $100MjimpliesjCOGSjofj $50Mj (becausejofjthej100%jmarkup).
Turnsj =j COGS/jInventoryj =j $50M/j$5Mj =j10j.
(b) Thejinventoryjcost,jgivenj10jturns,jisj 40%/10j=j4%j.jForjaj 30$j item,jthejinventoryjcost
jisj 0.4j$30j=j$1.20jperjunitj.


Q2.5.jLajVilla
(a) Flowj Ratej =j Inventoryj/jFlowj Timej =j1200jskiersj/10jdaysj =j120j skiersj perj day
(b) Lastjyear:jonjanyjgivenjday,j10%j(1jofj10)jofjskiersjarejonjtheirjfirstjdayjofjskiing


©jMcGrawjHilljLLC.jAlljrightsjreserved.jNojreproductionjorjdistributionjwithoutjthejpriorjwrittenjconsentjofjM
cGrawjHilljLLC.

, Thisjyear:jonjanyjgivenjday,j20%j(1jofj5)jofjskiersjarejonjtheirjfirstjdayjofjskiing

Averagejamountjspentjinjlocaljrestaurantsj(perjskier)
Lastjyearj=j0.1$50j+j0.9$30j=j$32jThis
jyearj =j0.2$50j+j0.8$30j=j$34

%jchangej=j($34j−$32)j/j$32j=j6.25%jincrease


Q2.6.jHighway
Wejlookjatj1jmilejofjhighwayjasjourjprocess.jSincejthejspeedjisj60jmilesjperjhour,jitjtakesjaj
carj1jminutejtojtraveljthroughjthejprocessj(flowjtime).
Therejarej24jcarsjonj¼jofjajmile,ji.e.jtherejarej96jcarsjonjthej1jmilejstretchj(inventory).jInven
toryj=jFlowjRatej*jFlowjTime:j96jcarsj=jFlowjRatej*j1jminute
Thus,jthejFlowjRatejisj96jcarsjperjminute,jcorrespondingjtoj96*60j=j5760jcarsjperjhour.


Q2.7.jStrohrmannjBaking
Thejbreadjneedsjtojbejinjthejovenjforj12jminutesj(flowjtime).jWejwantjtojproducejatjajflowjr
atejofj4000jbreadsjperjhour,jorj 4000/60j=j66.66j breadsjperjminute.

Inventoryj=jFlowjRatej*jFlowjTime:jInventoryj=j66.66jbreadsjperjminute*j12jminutesjThus
,jInventoryj=j800jbreads,jwhichjisjthejrequiredjsizejofjthejoven.

Q2.8.jMtjKinleyjConsulting

Wejhavejthejfollowingjinformationjavailablejfromjthejquestion:

Level Inventoryj(numberjofjconsultantsjat FlowjTimej(timejspentjatjthat
thatjlevel) level)
Associate 200 4jyears
Manager 60 6jyears
Partner 20 10jyears

(a) WejcanjusejLittle’sjlawjtojfindjthejflowjratejforjassociatejconsultants:jInventoryj=jFlowj
Ratej*jFlowjTime;j200jconsultantsj=jFlowjRatej*j4jyears;jthus,jthejflowjratejisj50jconsul
tantsjperjyear,jwhichjneedjtojbejrecruitedjtojkeepjthejfirmjinjitsjcurrentjsizej(note:jwhilejt
herejarejalsoj50jconsultantsjleavingjthejassociatejlevel,jthisjsaysjnothingjaboutjhowjman
yjofjthemjarejdismissedjvsjhowjmanyjofjthemjarejpromotedjtojManagerjlevel).

(b) Wejcanjperformjajsimilarjanalysisjatjthejmanagerjlevel,jwhichjindicatesjthatjthejflowjrat
ejtherejisj10jconsultants.jInjorderjtojhavej10jconsultantsjasjajflowjratejatjthejmanagerjlev
el,jwejneedjtojpromotej10jassociatesjtojmanagerjlevelj(remember,jthejfirmjisjnotjrecruiti
ngjtojthejhigherjranksjfromjthejoutside).jHence,jeveryjyear,jwejdismissj40jassociatesjan
djpromotej10jassociatesjtojthejmanagerjlevelj(thejoddsjatjthatjleveljarej20%)




©jMcGrawjHilljLLC.jAlljrightsjreserved.jNojreproductionjorjdistributionjwithoutjthejpriorjwrittenjconsentjofjM
cGrawjHilljLLC.

, Now,jconsiderjthejpartnerjlevel.jThejflowjratejtherejisj2jconsultantsjperjyearj(obtainedjviajth
ejsamejcalculationsjasjbefore).jThus,jfromjthej10jmanagerjcasesjwejevaluatejeveryjyear,j8jar
ejdismissedjandj2jarejpromotedjtojpartnerj(thejoddsjatjthatjleveljarejtherebyjalsoj20%).

Injorderjtojfindjthejoddsjofjajnewjhirejtojbecomejpartner,jwejneedjtojmultiplyjthejpromotionj
probabilities:j0.2*0.2j=j0.04.jThus,jajnewjhirejhasjaj4%jchancejofjmakingjitjtojpartner.


Q2.9.jMajorjUSjRetailers
a. Productjstaysjonjaveragejforj31.9jdaysjinjCostco’sjinventory
b. Costcojhasjforjaj$5jproductjanjinventoryjcostjofj$0.1311jwhichjcomparesjtoja
$0.2049j atjWal-Mart

Q2.10.jMcDonald’s
a. InventoryjturnsjforjMcDonald’sjwerej92.3.jTheyjwerej30.05jforjWendy’s.
b. McDonald’sjhasjperjunitjinventoryjcostsjofj0.32%,jwhichjforjaj3$jmealjabout
$0.00975.jThatjcomparesjtoj0.998%jatjWendy’sjwherejthejcostjperjmealjisj $0.0299j.

Q2.11.jBCH
Ij=j400jassociates,jTj=j2jyears.jRj=jIj/jTj=j400jassociatesj/j2jyrsj=j200jassociatesj/jyrj.

Q2.12.jKroger
Turnsj=jRj/jIj=j76858j/j6244j=12.3




MatchingjSupplyjwithjDemand:jAnjIntroductionjtojOperationsjManagementj5e
SolutionsjtojChapterjProblemsjChap

terj3
UnderstandingjthejSupplyjProcess:jEvaluatingjProcessjCapacity


Q3.1jProcessjAnalysisjwithjOnejFlowjUnit
(a) Capacityjofjthejthreejresourcesjinjunitsjperjhourjarej 602j/10j=12j,j 601/j6j=10;j603j/
16j=11.25j.jThejbottleneckjisjthejresourcejwithjthejlowestjcapacity,jwhichjisjresourcej
2.
(b) Thejprocessjcapacityjisjthejcapacityjofjthejbottleneck,jwhichjisj 10junits/hrj.
(c) Ifj j demandj=j8junitsj/jhrj,jthenjthejprocessjisjdemandjconstrainedjandjthejflowjratejis
8junits/hr
(d) Utilizationj=jFlowjRatej/jCapacityj.jForjthejthreejresourcesjtheyjarej 8j/j12j,j 8j/j10j,jand
8j/11.25j.




©jMcGrawjHilljLLC.jAlljrightsjreserved.jNojreproductionjorjdistributionjwithoutjthejpriorjwrittenjconsentjofjM
cGrawjHilljLLC.

, Q3.2jProcessjAnalysisjwithjMultiplejFlowjUnits
a) Bottleneckjisjresourcej3jbecausejitjhasjthejhighestjimpliedjutilizationjofj125%.jThejdeman
dsjperjhourjofjthejthreejproductsjarej 40j/j8j=j5 , j 50j/j8j=j6.25jandj 60j/j8j=j7.5.j j The
totaljminutesjofjworkjdemandedjperjhourjatjresourcej1jisj5j×j5j+j6.25j*j5j+j7.5j*j5j=
93.75.jTwojworkersjatjresourcej1jproducej2j*j60j=j120jminjofjworkjperjhour.jSojres
ourcej1’sjutilizationjisj 93.75j/120j=j0.78.jUtilizationjatjthejotherjresourcesjarejsimila
rlyjevaluated.
b) Thejcapacityjofjresourcej3jisj 60j/15j=j4junitsj perjhour.jGivenjthejratiojofjunitsjproducedjmus
tjbej4jtoj5jtoj6,jthejprocessjcanjproducej 4junits/jhrj ofjA,j 5junitsj/jhrjofjBjand
6junitsj/jhrjofjC.


Q3.3.jCranberry
Cranberriesjarrivejatjajratejofj150jbarrelsjperjhour.jTheyjgetjprocessedjatjajratejofj100jbarrelsjperjho
ur.jThus,jinventoryjaccumulatesjatjajratejofj150-
100j=j50jbarrelsjperjhour.jThisjhappensjwhilejtrucksjarrive,ji.e.jfromj6amjtoj2pm.jThejhighestjinve
ntoryjleveljtherebyjisj8h*50jbarrelsjperjhourj=j400jbarrels.jFromjthesej400jbarrels,j200jbarrelsjareji
njthejbins,jthejotherj200jbarrelsjarejinjtrucks.
(a) 200jbarrels
(b) Fromj2pmjonwards,jnojadditionaljcranberriesjarejreceived.jInventoryjgetsjdepletedjatjajratejofj
100jbarrelsjperjhour.jThus,jitjwilljtakej2hjuntiljthejinventoryjleveljhasjdroppedjtoj200jbarrels,ja
tjwhichjtimejalljwaitingjcranberriesjcanjbejstoredjinjthejbinsj(nojmorejtruckjwaiting)
(c) Itjwilljtakejanotherj2jhoursjuntiljalljthejbinsjarejempty
(d) Sincejthejseasonaljworkersjonlyjstartjatj10:00am,jthejfirstj4jhoursjofjthejdayjwejaccumulatej4ho
ursj*j50barrelsjperjhourj=j200jbarrels.jForjthejremainingjtimejthatjwejreceivejincomingjcranberr
ies,jourjprocessingjratejisjhigherj(125jbarrelsjperjhour).jThus,jinventoryjonlyjaccumulatesjatjajra
tejofj25j(150-
125jbarrelsjperjhour).jGivenjthatjthisjhappensjoverj4jhours,jwejgetjanotherj100jbarrelsjinjinvent
ory.jAtj2pm,jwejtherebyjhavej300jbarrelsjinjinventory.jAfterj2pm,jwejreceivejnojfurtherjcranber
ries,jyetjwejinitiallyjprocessjcranberriesjatjajratejofj125jbarrelsjperjhour.jThus,jitjonlyjtakesj 100j
barrelsj/125jbarrels/hourj=j0.8jhoursj=j48jminutes
untiljalljbinsjarejempty.jFromjthen,jwejneedjanotherj2hjuntiljthejbinsjarejempty.


Q3.4.jWesternjPennsylvaniajMilk
Wejstartjthejdayjwithj25,000jgallonsjofjmilkjinjinventory.jFromj8amjonwards,jwejproducej5,000jgal
lons,jyetjwejshipj10,000jgallons.jThusjinventoryjisjdepletedjatjajratejofj5000jgallonsjperjhour,jwhichj
leavesjusjwithoutjmilkjafterj5jhoursj(atj1pm).jFromjthenjonwards,jclientsjwilljhavejtojwait.jThisjsitu
ationjgetsjworsejandjworsejandjbyj6pmj(lastjclientjarrives),jwejarejshortj25,000jgallons.
(a) 1pm
(b) Clientsjwilljstopjwaitingjwhenjwejhavejworkedjoffjourj25,000jgallonjbacklogjthatjwejarejfac
ingjatj6pm.jSincejwejarejdoingjthisjatjajratejofj5,000jgallonjperjhour,jclientsjwilljstopjwaitin
gjatj11pmj(afterj5jmorejhours).
(c) Atj6pm,jwejhavejajbacklogjofj25,000jgallons,jwhichjisjequivalentjtoj20jtrucks
(d) Thejwaitingjtimejisjthejareajinjthejtriangle



©jMcGrawjHilljLLC.jAlljrightsjreserved.jNojreproductionjorjdistributionjwithoutjthejpriorjwrittenjconsentjofjM
cGrawjHilljLLC.