7/25/2019 Solutions Review Questions Session 4

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SolutionstoReviewQuestionsSession4

Specialty

Coffeehouse

(a)EOQ=229.13pounds

(b)Timebetweenorders=0.82years

(c)Averageannualsetupandholdingcost=$109.98(d)Reorderlevel=16.15pounds

Davids

Delicatessen

(a)Optimalorder=1297salamis,Cycletime=0.62years

(b)Reorderpoint=122salamis

(c)Annualrevenueis$4515,Annualsalamipurchasecostis$3885andAnnualsetupandholding

costis$647.75andthereforetheannuallossis$17.75.

UncleBob

(A)Answerb).Theprocessisnotat6sigma(foraprocesstobeat6sigmaCpkshouldbe2).

(B)Answer:c).FortheprocesstobeatsixsigmaCpkmustbe=2.Toachievethisobjectiveoneshould:

Centertheprocessmeanwithinthetolerancelimits(i.e.setprocessmeanat=43.5),and

Reducestandarddeviationsothat, 2)3

5.430.45,

3

0.425.43min(

Iftheprocessmeaniscentered,itisindifferentwhetheroneconsidersthelowerortheupper

tolerancelimittocomputethenewprocessstandarddeviation.ForinstanceifoneusestheLTL,the

newstandarddeviationcanbecomputedasfollows

25.023

0.425.43hence,2

3

0.425.43Cpk

new

new

Notethatstrictlyspeakingitisnotnecessarytocentertheprocessmeanatthemidpointofthe

toleranceintervaltoachieve6sigma.Doingsoisconvenientbecauseitallowsthedesiredsixsigmaobjectivetobereachedwiththeminimalreductioninthevariance.Forinstance,toreachthe6

sigmacapabilitylevelwithoutcenteringtheprocessmeanonewouldhavetoreducetheprocess

standarddeviationat: 20.023

0.422.43

Forevon

A)

No. Theinformationprovidedbythecontrolchartsonlysuggeststhattheprocessisin

control(i.e.itsunderlyingdistributionisnotshifting).Howeveritdoesntsayanythingabout

itscapability.Inotherwordstheprocesscouldstillgenerateanunacceptablenumberof

defectiveitems(althoughitwoulddosoquiteconsistently...).Toconcludethatno

immediateimprovementactionisneeded,themanagershouldalsocomputeacapabilityindexandconductacapabilityanalysistocheckwhethertheprocessdeliversoutputsin

accordancetocustomerrequirements.

B)

LineA.TheproblemsoccurredinlineBaremoredifficulttoidentifybecausetheyseemto

beduetorandomornaturalvariation.Inotherwordstherearenoclearsignalsthatcan

helpthemanageridentifythesourceoftheproblem.Mostlikelythedeteriorationofquality

iscausedbythesimultaneousdegradationofanumberoffactors.Conversely,theproblems

occurredtolineAareclearlyduetoanassignablecausewhichdeterminesasystematic

biasintheprocess.Assignablecausesaremucheasiertoidentifyandshouldimmediately

triggertheimplementationofaPDCAcycle.

7/25/2019 Solutions Review Questions Session 4

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Inventory

Management

Costs

Yes.Inapushproductionsystem,theproductionscheduleofeachstationissetaheadoftimeand

dependsontheestimateddemand.Apushsystemadjuststodemandfluctuationsbyeither

consumingorbuildingupinventory.Conversely,apullproductionprocessisaselfregulatedsystem

inwhichproductionisauthorizedwhenthelevelofinventorybeforeeachstation(i.e.WorkIn

Progress)fallsbelowapredeterminedthreshold.Apullenvironmentreactstofluctuationsin

demandbyautomaticallyslowingdownorspeedingupoperationswhilemaintainingaconstant

levelofWIPinthesystem. Therefore,apushsysteminmorelikelythanapullsystemto incur

higherinventorycostswhendemandforecastsareinaccurate.

Solarex

LineA:Donotinvestigate.Theprocessappearstobeincontrol.Nosamplefalloutsidethecontrol

region.Furthermorethesamplesfollowacompletelyrandompattern,withnocleartrendorerratic

behavior.

LineB:Investigate.Theprocesswentoutofcontrolonday20.Althoughnosamplefallsoutsidethe

controlregion,for10consecutivedaystheaveragethicknessofthecellsmanufacturedwasbelow

thenaturalmeanoftheprocess,therebyindicatingthatanassignablecauseofvariationmusthave

occurred.Giventhatinthisparticularcaseproducingthincellsisdesirable,Petershouldanalyzethe

reasonsthatledtotheparticularlygoodperformanceinthelasttendaysoftheanalysisandtryto

replicatetheminasystematicfashion.

LineC:Investigate.Theprocesswasneverincontrol.Althoughnosamplefelloutsidethecontrol

regionduringthetimeoftheanalysis,thepatternisclearlynotrandombuterratic(odddaysabove

themeanandevendaysbelowthemean).Thiscouldbedueforinstancetothefactthattwo

operatorswithdifferentskillsworkalternativelyontheprocess.Again,giventhatinthisparticular

caseproducingthincellsisdesirable,Petershouldanalyzethebehavioroftheskilledoperator,codifyitandrenderitavailabletootherworkersintheorganization.