final15 solutions

7/25/2019 Final15 Solutions

1/6

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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4

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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5

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.

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