7/25/2019 Solutions Review Questions Session 2

1/1

Solutions

to

Review

Questions

Session

2

A

four

stage

process

(a)Alwayschoosingthefastermachines:minTT=9+6+5+8=28minutes

(b)CapacityatStage1:60[min/hour]/9[min/unit]+60[min/hour]/9[min/unit]=13.33[units/hr]

Stage2:60/6=10[units/hr]

Stage3:

60

/5=12

[units/hr]

Stage4:60/8 +60/12 =12.5[units/hr]

(c)Sincethestagewiththeleastcapacityisthebottleneck,itisStage2. Theprocesscapacityisthus

10[units/hr].

(d)Weshouldincreasethecapacityofstage2from10to12[units/hr].Beyondthis,thebottleneck

shifts to Stage3,andoutputwillnot increase.Thus, this additionalmachineneeds toproduce2

[units/hr]oritshouldhavethedesignCT=1/TR=30[min/unit].

Luis

Poisson

1) Theprocesscapacityisdeterminedbythebottleneck. Toidentifythebottleneck orslowest

stage youneedtocalculatetheCTorCapacityofthedifferentstations.

Amongstations2,3,and4,station2istheslowestone,withacapacityperhourof60min/hr / 6

min

/

unit

=

10

units

per

hour.

You

also

need

the

capacity

of

the

other

two

stations.

Here

you

have

parallelservers,whosecapacityadds.SoforStation1:60/40+60/20=45unitsperhour,andfor

Station5:60/12+60/6+60/4=30unitsperhour.Sincebothstationshavealargercapacitythan

station2,station2isthebottleneckandtheoverallcapacity(orTR)is10unitsperhour.(Allother

stationscanprocessunitsfaster,buteithertheywouldnothaveanyinput(iftheyfollowstation2)

orincaseofstation1,producingfasterwouldjustproduceunnecessaryworkinprocessinventory.

2)TheminimumTTisthefastesttimeyoucanproducesomethingwhenthesystemisempty,i.e.,if

theprocessstartsup. ThefastestpartAAcanenterthebufferis2min.ThefastestpartBBcanenter

thebufferis6+5=11min.After11minyouhavebothparts,onlythentheassemblyinStep4can

start,whichtakes5min,so16minsofar.Finallyinstep5youchooseagainthefastestmachine

(sincetheseareagainparallelstations,alldoingthesamething,sousedalternatively).So16+4=20

ministhefastestyoucouldproduceaproduct.

3)

Station

2

is

the

process

bottleneck

(see

1)

Eric

&

Old

Itwillworsenthesituation.Clearly,thesystemisconstrainedbytheupstreamworkstation,whichis

therealbottleneck,notbythedownstreammachine.Changingthescheduleontheupstream

machinewillnothaveanimpactontheutilizationofthedownstreammachine,becauseonaverage

thelatterwillalwaysseethearrivalofthesamenumberofjobs(determinedbythethroughputof

thebottleneckworkstation).

Therefore,theonlywaytoincreasetheutilizationrateofthedownstreammachineistoincreasethe

throughputatthebottleneck.However,thelargernumberofsetupsrequiredbythenewpolicyis

likelytohavetooppositeeffect:itwillwastevalueaddedtimeatthebottleneckandfurther

constraintheproductivityofthewholefactory.

Asaresult,atbestthepolicywillhavenoeffect.Mostlikelyitwillevenmakethesituationworse.

Asageneralremark,youshouldsuggesttoyourclientthatmaximizingutilizationatanon

bottleneckmachineisawrongobjective.YoushouldadviseRoditomanagethesystemtoachieve

maximalthroughput,notmaximalutilizationofmachines.