Post on 01-Mar-2018
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.