Final15 Solutions
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Transcript of Final15 Solutions
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7/25/2019 Final15 Solutions
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1
HEC
Paris
Operations
Management
Prof.
Svenja
Sommer
Final
Exam
NAME,
First
Name
(in
BLOCK
letters):______________________________________
Signature:
_________________________________
Instructions:
(i)
This
is
a
closed
book
exam;
only
the
distributed
formula
sheet
is
allowed.
(ii)
Computers
and
cell
phones
are
not
allowed,
calculators
are
allowed.
(iii) ExamDuration=2hrs
(iv)
There
are
5
questions
for
100
points
in
total.
(v)
Points
for
each
question
are
in
parentheses
(
)
next
to
the
question.
(vi)
Answer
all
questions
in
the
space
provided,
using
the
back
of
pages
if
necessary.
(vii)
For
full
credit
show
your
calculations.
Question Points
1 _________outof40
2
_________outof25
3
_________outof10
4 _________outof10
5 _________outof15
TOTAL _________outof100
Question
1
(40
points):
Shortanswerquestions(10pointseach).
(a) WhycanShouldice(aCanadianclinicperformingonlyherniaoperations)beconsideredafocused
factoryandwhatadvantagesmightitobtainfrombeingafocusedfactoryascomparedtoa
generalhospital? Doyouseeanydrawbacksorrisksassociatedwithit?
Keypoints:
Explainfocusedfactory:standardizedprocess,oneorfewproductswithsameprocessing
requirements;hereonetypeofoperationscomparedtomanydifferentailmentstreatedata
generalhospital
Processhasanumberofadvantages:lowercoste.g.duetoeconomiesofscale,higherquality
duetostandardizedprocessandexperienceofdoctors, higherspeedofdeliveryduetolower
variabilityinprocessingtimesandherewithwaitinglistsalsoinarrivaltimes
Key
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drawbacks/risks:riskofoverlookingnewtechnologies,limitedmarketsizeandgrowth(and
sometimesriskofmarketsdisappearing,thoughnotinthiscase),motivationandretentionof
personnel
(b) IncreaseddemandvolatilityintheUShascausedmanymanufacturerstoconsidermoving
productionbacktotheUS. Whymightincreaseddemandvolatilitymakedomesticproduction
moreattractive?
WhenUSmanufacturersoffshore,theydosoforlowertotalcosts.Ifdemandvolatilityincreases,
thismeansthedemandbecomeshardertopredict. Theresultsarehigherexpectedlostsales
(remember:stockouts=L(z)*sigma*Sqrt(LT))andhigherrequiredsafetystockandhencehigher
inventorycosts(remember:safetystock=z*sigma*Sqrt(LT)). Bymovingtheproductionbackto
theUS,manufacturerslowertheleadtime,andhencelowertheseexcessandshortagecosts.
Thehigherthevariability,themorethedifferenceinexcessandshortagecosts.Thus,increasing
demandvariabilityhaschangedthetradeoffbetweenlowerproductioncostsoffshoreandlower
excessandshortagecostsintheUSinfavoroflocalproduction.
(c)
Aproduction
plant
for
industrially
produced
bread
faces
huge
swings
in
demand.
Some
weeks
thetotaldemandfromitscustomers,thelocalsupermarkets,is5timestheorderquantity
receivedinotherweeks.Tomeetthesedemandpeaks,theplantmanagerisfacingpressure
fromhiscustomerstoexpandhiscapacity;however,capacityexpansionsareverycostly,sinceit
isahighlyautomatedproductionline.Theplantmanagerisprettysurethattheendcustomer
demandisstableovertime,andheseeksyourhelpinimprovingthesituation. What
phenomenonishefacingandwhatrecommendationswouldyoumaketohim?
Thephenomenonheisfacingiscalledthebullwhipeffect: Thedemandvariabilityincreasesasone
movesupthesupplychain.
Tomakegoodrecommendations,youmightwanttoaskhimfirstsomequestions: Doyouoffer
discountsforlargeorderquantities?Doyouofferpromotionsduringtheyear? How isthe
transportationorganizeddoesthesupplierpickupeachbatch?
Iftheanswerisyestoanyofthesequestions,thesemightbethemainreasonsforthedemand
variability, andyoucouldsuggesttohimdiscountstobebasedonitemssoldduringtheyear
(ratherthanorderquantityperbatch),toskippromotions(andexplaintoretailersbenefitof
everydaylowprices),andoffertodeliverthebreadwithonedeliverytrucktoallsupermarketsin
thesamearea(forthesamecostascurrentdelivery,butwithalotmorefrequentdeliveries)
Iftheanswerisnototheabovequestions,thevariabilityisseeminglyjustrandom.Leadtimeand
intermediariesdonotseemtobetheproblem(localsupermarketsaredirectcustomersbut
worthwhiletocheckifleadtimecouldbereduced). Iftheendcustomerdemandisindeedstable,
themanagercouldtrytoimplementVMI(JITdistribution),i.e.,asysteminwhichthe
manufacturerreplenishesthestockbasedonpointofsalesandinventorydata. Thisincreasesthe
visibilityoftheendcustomerdemand,butmoreimportantlythemanufacturercanmatchhis
productiontotheactualcustomerneeds. (Notethatjustsharingthepointofsalesandinventory
data,withthesupermarketsstillinsistingontheirbulkdeliveries,wouldnotreallyhelp,unless
therearemultiplelayersthatcoulddistorttheinformation,whichdoesnotseemtobethecase.)
ImplementingVMImightfacesomeresistance,sotheplantmanagermightneedtoproposesome
trialperiodtoitscustomers(andifinplace,changehissalespeopleincentives)tomakethiswork.
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(d)
Anewtechnologyallowsbookstobeprintedintenminutes. BOOKYhasdecidedtopurchase
machinesforeachofitsstores. Assumethatthecostofprintingabookinthestoreissomewhat
higherthanthatofbuyingitreadyfromthepublisher. WhichbooksshouldBOOKYcarryinstock
andwhichbooksshouldBOOKYprintondemand?Doyourecommendthistechnologyforbest
sellersorforslowsellingbooks(assumingthecostofeachbookisthesame)?Explain.
Thisnewtechnologyallowsfordelayedthedifferentiation(rememberBenettonorZara). Thisis
particularlyvaluableiftheproducthashighriskofshortagesand/orleftovers. Hereyoudonon
perishablegoods,sotheleftovercostsarelargelytheholdingcosts.
Ifyouhavetomakeachoice,itisbettertouseitforslowsellinggoods.Onetheonehand,the
demandisveryhardtoforecast.(Oneweekyousellthem,thenseveralweeksnot,thatmakes
forecastingdifficult.)Inaddition,youtendtoholdtheminstockforalongtimebeforesellinga
bookyouhaveinstock,soyouhavehighholdingcosts.(Bestsellers,ontheotherhand,are
easiertoforecastandyoucanbefairlycertaintosellthebooksyouorderedforthismonth,the
nextmonthifnecessary. Soyoucankeepahighsafetystocktoavoidrunningout,andstillbe
reasonablysurenottoholdthisinventorytoolong. (Ofcourse,oncethebestsellerisslowing
down,and
becomes
aslow
selling
book,
the
same
argument
as
for
slow
selling
books
applies.)
Finally,ifyouhavetomakethischoice,youwouldhavetoprintalotofbestsellers,incurring
highadditionalcostsandalsorunningmostlikelyintoacapacityproblemofyourmachine.
Ifyoucancombinesellingprintedandpurchasedbooks,youcouldalsolowerthesafetystockfor
bestsellers(stillnottoomuch;youdonotwanttoincurthehigherproductioncoststoooften),
andprintthebestseller,wheneveryouriskrunningout.(Dualsourcing)
Question
2:
Chair
production
(25
points)
Thefollowingrepresentsaprocessusedtoassembleachairwithanupholsteredseat. StationsA,B,
andCmaketheseat;stationsJandKassemblethechairframe;stationXiswherethetwo
subassembliesarebroughttogether;andsomefinaltasksarecompletedinstationsYandZ. One
worker
is
assigned
to
each
of
the
stations,
except
in
station
X
where
two
workers
(X
1
and
X
2)
performthesametaskinparallel. Generally,thereisnoinventorykeptanywhereinthesystem,
althoughthereisroomforsomeunitsbetweeneachofthestations(notdrawnexceptbefore
stationX)thatmightbeusedforinventorystorage,wheneverneeded.(Thatis,thereisnoplanned
inventorybuffer,butitcanhappenthatthereisinventoryinthesystem.)
Thefollowingamountofworkinsecondsisrequiredateachstation. (Youmaynoticethedifference
for
the
two
workers
in
station
X.
This
difference
is
due
to
a
difference
in
experience
and
is
expected
tostaylikethisforthenearfuture.)
A 42 C 35 J 32 X1 60 Y 45
B 33 K 30 X2 75 Z 20
a.
Whatisthepossibledailyoutputofthisprocessifoneshiftwith7hoursofprocessingtimeis
availableeachday? (10points)
A B C
J K
X-1
Y Z
X-2
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Weneedtofindthebottleneckoftheprocess. LetsfirstcalculatethecapacityofstationXper
minute: 60/60+60/75=1.8unitsperminute.
Outoftheotherstations,stationYistheslowestandhencethepotentialbottleneck.Itscapacityis
60/45=1.33unitsperminute,andhencelowerthanthatofstationX. ThusYisthebottleneckand
determinesthedailyoutput.
Thusthepossibledailyoutputis60/45units/perminute*(7*60)minutes/shift=560unitsperday.
(Alternatively,youcancalculatethecycletimeofstationx.)
b.
Whatistheminimumthroughputtimeoftheprocessinseconds?Explain.(5points)
Theseatreachesthebufferafter42+33+35=110seconds;thechairframereachesthebufferafter
32+30=62seconds.StationXcanstartassemblyonlyafter110seconds,whenbothsubassemblies
areavailable.Usingthefasterworker(forminimumTT)atstationXandaddingtheremaining
processingtimes,weget:minimumTT=110+60+45+20=235seconds.
c.
Thecompanyconsidershiringanadditionalworkertoincreasethecapacityoftheprocess. You
havetohirethisworkerforthefullshift.Atwhichstationwouldyouaddtheworker,ifyou
decidedto
do
so?
(Why?)
Is
it
worth
it,
ifthis
worker
costs
200
per
day,
has
the
same
processingtimeastheotherworkeratthechosenstationandtheprofitmarginforthechairis
currently8perunit?(Assumealladditionallyproducedunitscanbesold.) Showallcalculations
tojustifyyouranswer.(10points)
Toincreasetheprocesscapacity,youneedtoaddtheworkeratthebottleneck,i.e.,instationY.
Therewouldbenowtwoworkersperformingthesametaskinparallel(likeinstationXbefore).Given
thesameprocessingtimes,thecapacityatstationYwoulddoubleto2.66unitsperminute.
However,theprocesscapacitywillNOTdouble,sincethebottleneckshifts. Wealreadyknowthat
stationXhasacapacityof1.8unitsperminute. TheotherpotentialbottleneckisnowstationA(the
sloweststationotherwise). ThecapacityofstationAperminuteis60/421.43unitsperminute,and
itisindeedthebottleneckanddeterminesthenewprocesscapacity.
Thenewdailyprocessoutputisnow60/42units/perminute*(7*60)minutes/shift=600units/
shift,hencehiringthenewworkerresultsinapossibleincreaseinoutputof600560=40units. Ifall
unitsaresold,thisincreasestherevenuesperdayby40units*8=320comparedtoanincreasein
thecostsof200. Hence,itisworthittohiretheadditionalworker.
Question
3
(10
points)
PharmaDevdevelopsandmarketsnewtechnologicalproductstobeusedinhealthcare.The
developmentofanewproductoperatesasfollows.
Whenanewtechnologymeetstherequisitemarketpotential,anewpatentisfiled.Patentsare
grantedforaperiodof12years,startingfromthedateofissue.Oncethepatentisissued,thenew
technologyisdevelopedatitsdevelopmentcenter,andisthenlaunchedtothemarket.
Onaverage,PharmaDevwinsanewpatentevery5monthswithacoefficientofvariationforarrivals
of1.
The
average
development
process
lasts
4months
with
acoefficient
of
variation
for
the
developmentprocessof2.
(a) Howmanymonthsofpatentlifeareleftforanaverageproductlaunchedtothemarket? [7
points]?
TotalPatentLife=12years=144months
PatentLifeleft=1444monthsintheprocesswaitingtime
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Utilization=4/5=0.8
Waitingtimeinthequeue=4*0.8/(10.8)*(1^2+2^2)/2=40months
PatentLifeleft=144440=100months
(b) Onaveragehowmanypatentedproductsareundergoingdevelopmentorwaitingtobe
developed?
[3
points]
LittlesLaw:FlowRate=1/5patentspermonth,Timeinsystem=FT=44months;
WIP=FR*FT=8.8products.
Question4(10points)
TomRichandJoeMiserhaveanechecking/savingsaccountattheeJouyBank.BothTomandJoe
had5000intheiraccountatthestartofthecalendaryear2012.Bothhaveprojectedcashusageof
50perweekataconstantrate.eJouyBankchargesa0.75ATMwithdrawalfeeforeveryATM
transaction,whichisbilledtotheaccountattheendofthecalendaryear.Inreturn,theaccount
offersagreatannualinterestrateof6%,whichisbasedontheaverageannualbalance,and
depositedintheaccountattheendoftheyear.Forthepurposeofsimplifyingyourcalculations,
assume
50
weeks
per
year.
(a)Tomhasafatwalletandhencewithdraws$500wheneverherunsoutofcash,whileJoe
withdrawscasheveryMondayonhiswaytolunch.Whowillhaveahigheraccountbalanceatthe
endofcalendaryear? (5points)
ThisisanEOQproblem;toknowwhowillhavethehigherbalance,wejustneedtocomparewho
willhavethelowercosts.Sincebothstartwiththesamebalanceandbothhavethesame
projectedcashusage,weonlyneedtocomparetheannualholdingandorderingcosts(AHO):
Tom: AHO=0.06*500/2+0.75*2500/500=18.75
Joe: Withdraws2500/50=50perweek.
AHO=0.06*50/2+0.75*2500/50=39
JoesAHO>TomsAHO
Hence,Tomwillhaveahigherendingbalance.
(b)TomandJoeobviouslyhavenotenrolledforOperationsManagement.Whatwillbeyouradvice
toTomandJoeontheirrespectiveCashwithdrawalstrategies?(Thatis,howmuchcashshouldTom
withdraw/howfrequentshouldJoegototheATM.)(5points)
EOQ=Sqrt(2*2500*0.75)/0.06)=250
Tomshouldwithdraw250;thiscorrespondsto10timesperyear;henceintermsofJoespolicy:
every5weeks.
Question
5
(15
points)
Yourcompanybuildsfullycustomizedoneofakindcruiseshipsforecotourismcruiseoperatorsthat
visitdestinationssuchastheGalapagos Islands,theAntarctic,etc.Everytimeacustomer(acruise
company)ordersaship,youhavetoquoteadeliverydate,butyoustrugglewiththeuncertainty
involved.Becauseeachindividualshipishighlycustomized,youcannotpredictinadvanceprecisely
howlongitwilltaketodesignandbuildeachship.Currently,acustomerfromAmazonRiverCruises
Inc.requestedyoutosubmitaquoteQ(thedecisionvariable)foraship.TheactualdeliverytimeDis
uncertainandwillfollowanormaldistribution,withameanof12monthsandastd.dev.of3months.
Thecustomerassumesthatyouwilldeliver theshippreciselyonthedeliverydateyouquote; for
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instance,ifyousayQ=12;i.e.,theshipwillbedeliveredin12months,thecustomerwillimmediately
beginsellingcruisesonthatshipstartingprecisely12monthsfromnow.Thecustomerhasnousefor
theshippriortotheagreeddeliverydate,soifyoucompletetheshipbeforethequoteddeliverydate,
youorthecustomerwillhavetoberthitsomewhereuntiltheoriginallyagreedupondeliverydate.
ThatwillcostEur12,000perday.Ifyoudelivertheshiptoolate,thecustomerhastopostponetaking
theshipintoservice,whichmeanscancelingcruisesthathavealreadybeensold.Youwillhavetopay
thecustomer
apenalty
of
EUR
24,000
for
each
day
by
which
you
exceed
the
originally
agreed
upon
deliverydate.
(a)Whatdeliverydate(inmonthsfromtoday)shouldyouofferAmazonRiverCruisesInc.?(7p)
Ifyouhavetoolittletimebuffer:Cu=24,000;ifyouhavetoomuch:Co=12,000.
TargetSL=Cu/(Cu+Co)=0.666;Z=0.426
Deliverydate=12+0.426*3= 13.278monthsfromtoday
(b)Assumethatthecostsassociatedwithearlyorlatedeliveryaresimilarforalltheshipsyoubuildin
thefollowingsense:thepenaltyforeachdayyouarelateisalwaystwiceashighasthecostsinvolved
witheachdayyoudeliveryearly.Forexample,inthecaseofyourcurrentorder,thelatepenaltyis
EUR
24,000
per
day,
which
is
double
the
costs
of
being
too
early
(i.e.,
EUR
12,000).
For
some
other
order,thosefigurescouldbeforinstanceEUR50,000andEUR25,000respectively.Inrecentyears,
youhavedeliveredapproximately70%ofordersontime(i.e.,notbeinglate).
YourCEOisnothappywiththe70%ontimedeliveryperformanceandwantstobringthatto90%.
Howshouldyoumodifyyouroffer(fromparta)forthecurrentrequestfromAmazonRiverCruises
Inc.?(4p)
NewTargetSL=90%;z=1.28
Deliverydate=12+1.28*3=15.84monthsfromtoday
Hencequoteadeliverydelay~2.5monthslaterthaninanswer(a)
(c)
Whatvalue(inEUR)isyourCEOimplicitlyattachingtotheintangiblecostsofbeinglatesoas
tojustify
an
on
time
delivery
target
of
90%?
(4p)
Intangiblecostsofdelaycancapturecostssuchasareducedchanceofwinninganorderinthefuture.
Tofindouthowmuchvalueheputsonit,weneedtoseewhatcouldincreasetheTargetSL=90%.
Cu/(Cu+Co)=(2+i)/(2+i+1)=0.9 =>i=7. Thatmeans,theratioofCutoCoisnot2:1but9:1.Incaseof
theAmazonRiverCruisescontract,thecostofbeinglateishencenot24,000perdaybut108,000.He
clearlyassumesthatbeingontimecanhelpyouwinalotofadditionalcontracts.