Matching Supply with Demand 5th Edition Solution Manual | Cachon & Terwiesch – 2025 Step-by-Step Operations Management Solutions

SOLUTION MANUAL FOR
g g

MatchinggSupplygwithgDemandgAngIntroductiongtogOperationsgManagement,g5thgEditiongCacho
ngChapterg2-19

Chapterg2
ThegProcessgViewgofgthegOrganization

Q2.1gDell
ThegfollowinggstepsgrefergdirectlygtogExhibitg2.1.
#1:gForg2001,gwegfindgingDell’sg10-k:g Inventoryg=g$400g(ingmillion)
#2:gForg2001,gwegfindgingDell’sg10-k:g COGSg=g$26,442g(ingmillion)
26,g442$/gyearg
#3:gInventoryg turnsg=g =g66.105gturnsgpergyearg40
0$
40%g perg year
#4:gPergunitgInventoryg costg =g0.605%gpergyear
= 66.105 g per g yea
r

Q2.2.gAirline
WegusegLittle’sglawgtogcomputegthegflowgtime,gsincegwegknowgbothgthegflowgrategasgwel
lgasgtheginventoryglevel:
FlowgTimeg=gInventory/gFlowgRateg=g35gpassengers/g255gpassengersgperghourg=g0.137ghours
=g8.24gminutes

Q2.3gInventorygCost
(a) Salesg=g$60,000,000gpergyearg/g$2000gpergunitg=g30,000gunitsgsoldgpergye
argInventoryg=g$20,000,000g/g$1000gpergunitg=g20,000gunitsginginventory

Flowg Timeg=gInventory/gFlowg Rateg=g20,000g/g30,000g perg yearg =g2g/g3gyearg =g8gmonthsgT
urnsg=g1/gFlowgTimeg=g1/(2g/g3gyear)g=g1.5gturnsg perg year

Note:gwegcangalsoggetgthisgnumbergdirectlygbygwriting:g Inventorygturnsg=gCOGSg/gInventory

(b) CostgofgInventory:g 25%gpergyearg/1.5gturnsg=g16.66%.gForgag $1000g product,gthisgwoul
dgmakegangabsoluteginventorygcostgofg $166.66g.

Q2.4.gApparelgRetailing

(a) Revenuegofg $100MgimpliesgCOGSgofg $50Mg (becausegofgtheg100%gmarkup).
Turnsg =g COGS/gInventoryg =g $50M/g$5Mg =g10g.
(b) Theginventorygcost,ggiveng10gturns,gisg 40%/10g=g4%g.gForgag 30$g item,gtheginventor
ygcostgisg 0.4g$30g=g$1.20gpergunitg.

Q2.5.gLagVilla
(a) Flowg Rateg =g Inventoryg/gFlowg Timeg =g1200gskiersg/10gdaysg =g120g skiersg perg day
(b) Lastg year:gonganyggivengday,g10%g(1gofg10)gofgskiersgaregongtheirgfirstgdaygofgskiing
©gMcGrawgHillgLLC.gAllgrightsgreserved.gNogreproductiongorgdistributiongwithoutgthegpriorgwrittengconsen
tgofgMcGrawgHillgLLC.

, Thisgyear:gonganyggivengday,g20%g(1gofg5)gofgskiersgaregongtheirgfirstgdaygofgskiing

Averagegamountgspentginglocalgrestaurantsg(pergskier)
Lastgyearg=g0.1$50g+g0.9$30g=g$32gT
hisgyearg=g0.2$50g+g0.8$30g=g$34
%gchangeg=g($34g−$32)g/g$32g=g6.25%gincrease


Q2.6.gHighway
Weglookgatg1gmilegofghighwaygasgourgprocess.gSincegthegspeedgisg60gmilesgperghour,gitgt
akesgagcarg1gminutegtogtravelgthroughgthegprocessg(flowgtime).
Theregareg24gcarsgong¼gofgagmile,gi.e.gtheregareg96gcarsgongtheg1gmilegstretchg(inventory).
gInventoryg=gFlowgRateg*gFlowgTime:g96gcarsg=gFlowgRateg*g1gminute
Thus,gthegFlowgRategisg96gcarsgpergminute,gcorrespondinggtog96*60g=g5760gcarsgperghour.


Q2.7.gStrohrmanngBaking
Thegbreadgneedsgtogbegingthegovengforg12gminutesg(flowgtime).gWegwantgtogproducegatgag
flowgrategofg4000gbreadsgperghour,gorg 4000/60g=g66.66g breadsgpergminute.

Inventoryg=gFlowgRateg*gFlowgTime:gInventoryg=g66.66gbreadsgpergminute*g12gminutesg
Thus,gInventoryg=g800gbreads,gwhichgisgthegrequiredgsizegofgthegoven.

Q2.8.gMtgKinleygConsulting

Weghavegthegfollowingginformationgavailablegfromgthegquestion:

Level Inventoryg(numbergofgconsultantsgat FlowgTimeg(timegspentgatgthat
thatglevel) level)
Associate 200 4gyears
Manager 60 6gyears
Partner 20 10gyears

(a) WegcangusegLittle’sglawgtogfindgthegflowgrategforgassociategconsultants:gInventoryg=gF
lowgRateg*gFlowgTime;g200gconsultantsg=gFlowgRateg*g4gyears;gthus,gthegflowgrategis
g50gconsultantsgpergyear,gwhichgneedgtogbegrecruitedgtogkeepgthegfirmgingitsgcurrentgsi
zeg(note:gwhilegtheregaregalsog50gconsultantsgleavinggthegassociateglevel,gthisgsaysgnot
hinggaboutghowgmanygofgthemgaregdismissedgvsghowgmanygofgthemgaregpromotedgtog
Managerglevel).

(b) Wegcangperformgagsimilarganalysisgatgthegmanagerglevel,gwhichgindicatesgthatgthegflo
wgrategtheregisg10gconsultants.gIngordergtoghaveg10gconsultantsgasgagflowgrategatgtheg
managerglevel,gwegneedgtogpromoteg10gassociatesgtogmanagerglevelg(remember,gthegfi
rmgisgnotgrecruitinggtogtheghighergranksgfromgthegoutside).gHence,geverygyear,gwegdis
missg40gassociatesgandgpromoteg10gassociatesgtogthegmanagerglevelg(thegoddsgatgthatgl
evelgareg20%)



©gMcGrawgHillgLLC.gAllgrightsgreserved.gNogreproductiongorgdistributiongwithoutgthegpriorgwrittengconsen
tgofgMcGrawgHillgLLC.

, Now,gconsidergthegpartnerglevel.gThegflowgrategtheregisg2gconsultantsgpergyearg(obtainedg
viagthegsamegcalculationsgasgbefore).gThus,gfromgtheg10gmanagergcasesgwegevaluategever
ygyear,g8garegdismissedgandg2garegpromotedgtogpartnerg(thegoddsgatgthatglevelgaregtherebyg
alsog20%).

Ingordergtogfindgthegoddsgofgagnewghiregtogbecomegpartner,gwegneedgtogmultiplygthegprom
otiongprobabilities:g0.2*0.2g=g0.04.gThus,gagnewghireghasgag4%gchancegofgmakinggitgtogpar
tner.


Q2.9.gMajorgUSgRetailers
a. Productgstaysgongaveragegforg31.9gdaysgingCostco’sginventory
b. Costcoghasgforgag$5gproductganginventorygcostgofg$0.1311gwhichgcomparesgtoga
$0.2049gatgWal-Mart

Q2.10.gMcDonald’s
a. InventorygturnsgforgMcDonald’sgwereg92.3.gTheygwereg30.05gforgWendy’s.
b. McDonald’sghasgpergunitginventorygcostsgofg0.32%,gwhichgforgag3$gmealgabout
$0.00975.gThatgcomparesgtog0.998%gatgWendy’sgwheregthegcostgpergmealgisg $0.0299g.

Q2.11.gBCH
Ig=g400gassociates,gTg=g2gyears.gRg=gIg/gTg=g400gassociatesg/g2gyrsg=g200gassociatesg/gyrg.

Q2.12.gKroger
Turnsg=gRg/gIg=g76858g/g6244g=12.3




MatchinggSupplygwithgDemand:gAngIntroductiongtogOperationsgManagementg5
e
SolutionsgtogChaptergProblemsgCha

pterg3
UnderstandinggthegSupplygProcess:gEvaluatinggProcessgCapacity


Q3.1gProcessgAnalysisgwithgOnegFlowgUnit
(a) Capacitygofgthegthreegresourcesgingunitsgperghourgareg 602g/10g=12g,g 601/g6g=10;g
603g/16g=11.25g.gThegbottleneckgisgthegresourcegwithgtheglowestgcapacity,gwhichgi
sgresourceg2.
(b) Thegprocessgcapacitygisgthegcapacitygofgthegbottleneck,gwhichgisg 10gunits/hrg.
(c) Ifg g demandg=g8gunitsg/ghrg,gthengthegprocessgisgdemandgconstrainedgandgthegflowgrategis
8gunits/hr
(d) Utilizationg=gFlowgRateg/gCapacityg.gForgthegthreegresourcesgtheygareg 8g/g12g,g 8g/g10g,gand
8g/11.25g.


©gMcGrawgHillgLLC.gAllgrightsgreserved.gNogreproductiongorgdistributiongwithoutgthegpriorgwrittengconsen
tgofgMcGrawgHillgLLC.

, Q3.2gProcessgAnalysisgwithgMultiplegFlowgUnits
a) Bottleneckgisgresourceg3gbecausegitghasgtheghighestgimpliedgutilizationgofg125%.gThegde
mandsgperghourgofgthegthreegproductsgareg 40g/g8g=g5 , g 50g/g8g=g6.25gandg 60g/g8g=g7.5.g g The
totalgminutesgofgworkgdemandedgperghourgatgresourceg1gisg5g×g5g+g6.25g*g5g+g7.5g*g5g=
93.75.gTwogworkersgatgresourceg1gproduceg2g*g60g=g120gmingofgworkgperghour.g
Sogresourceg1’sgutilizationgisg 93.75g/120g=g0.78.gUtilizationgatgthegothergresources
garegsimilarlygevaluated.

b) Thegcapacitygofgresourceg3gisg 60g/15g=g4gunitsg perghour.gGivengthegratiogofgunitsgproduce
dgmustgbeg4gtog5gtog6,gthegprocessgcangproduceg 4gunits/ghrg ofgA,g 5gunitsg/ghrgofgBgand
6gunitsg/ghrgofgC.


Q3.3.gCranberry
Cranberriesgarrivegatgagrategofg150gbarrelsgperghour.gTheyggetgprocessedgatgagrategofg100gbarrelsg
perghour.gThus,ginventorygaccumulatesgatgagrategofg150-
100g=g50gbarrelsgperghour.gThisghappensgwhilegtrucksgarrive,gi.e.gfromg6amgtog2pm.gTheghighest
ginventoryglevelgtherebygisg8h*50gbarrelsgperghourg=g400gbarrels.gFromgtheseg400gbarrels,g200gb
arrelsgaregingthegbins,gthegotherg200gbarrelsgaregingtrucks.
(a) 200gbarrels
(b) Fromg2pmgonwards,gnogadditionalgcranberriesgaregreceived.gInventoryggetsgdepletedgatgagrat
egofg100gbarrelsgperghour.gThus,gitgwillgtakeg2hguntilgtheginventoryglevelghasgdroppedgtog20
0gbarrels,gatgwhichgtimegallgwaitinggcranberriesgcangbegstoredgingthegbinsg(nogmoregtruckgw
aiting)
(c) Itgwillgtakeganotherg2ghoursguntilgallgthegbinsgaregempty
(d) Sincegthegseasonalgworkersgonlygstartgatg10:00am,gthegfirstg4ghoursgofgthegdaygwegaccumulat
eg4hoursg*g50barrelsgperghourg=g200gbarrels.gForgthegremaininggtimegthatgwegreceivegincomi
nggcranberries,gourgprocessinggrategisghigherg(125gbarrelsgperghour).gThus,ginventorygonlygac
cumulatesgatgagrategofg25g(150-
125gbarrelsgperghour).gGivengthatgthisghappensgoverg4ghours,gweggetganotherg100gbarrelsgingi
nventory.gAtg2pm,gwegtherebyghaveg300gbarrelsginginventory.gAfterg2pm,gwegreceivegnogfurt
hergcranberries,gyetgweginitiallygprocessgcranberriesgatgagrategofg125gbarrelsgperghour.gThus,gi
tgonlygtakesg 100gbarrelsg/125gbarrels/hourg=g0.8ghoursg=g48gminutes
untilgallgbinsgaregempty.gFromgthen,gwegneedganotherg2hguntilgthegbinsgaregempty.


Q3.4.gWesterngPennsylvaniagMilk
Wegstartgthegdaygwithg25,000ggallonsgofgmilkginginventory.gFromg8amgonwards,gwegproduceg5,00
0ggallons,gyetgwegshipg10,000ggallons.gThusginventorygisgdepletedgatgagrategofg5000ggallonsgpergh
our,gwhichgleavesgusgwithoutgmilkgafterg5ghoursg(atg1pm).gFromgthengonwards,gclientsgwillghaveg
togwait.gThisgsituationggetsgworsegandgworsegandgbyg6pmg(lastgclientgarrives),gwegaregshortg25,00
0ggallons.
(a) 1pm
(b) Clientsgwillgstopgwaitinggwhengweghavegworkedgoffgourg25,000ggallongbackloggthatgwega
regfacinggatg6pm.gSincegwegaregdoinggthisgatgagrategofg5,000ggallongperghour,gclientsgwillg
stopgwaitinggatg11pmg(afterg5gmoreghours).
(c) Atg6pm,gweghavegagbackloggofg25,000ggallons,gwhichgisgequivalentgtog20gtrucks
(d) Thegwaitinggtimegisgthegareagingthegtriangle
©gMcGrawgHillgLLC.gAllgrightsgreserved.gNogreproductiongorgdistributiongwithoutgthegpriorgwrittengconsen
tgofgMcGrawgHillgLLC.