Mechanical Engineering - Design and Management of Production Systems

Completed notes of the course - Part 2

Complete course

Assembly: Classification: basedon--> layoutconfiguration -> Fixedposition: · allresourcescometoaprintwheretheyareassembled. · Bigorfragileproducts(lowvolume,highvariability)shop · Departmentsdevoted to specificassemblyactivities -> Assemblycell · Cellsdevoted to each/fewproducts.(highdemandprodel -> Assemblyline · Workstationin sequence · Onlyforproductsin highdemand&lowvariability -> ProductionMin -> singlemodel I· Assemblyofonly 1varietyofproduct(AAAAA) - minedmodel · Assemblyofmultiplevarietiesinsmallbatches(ABCCAABCABB) · Cinventoryd,#setup -so usedforproductswithunitarysetup&· IsetupmuchhigherthanmultimodelsoCatupoveralla-> MultiModel · Assemblyofmultiplevarietiesinlargebatches(AAAABBBCCC) · Usedforproductswithuniterysetup -so largerbatches - setups& · Cinventory -> Ta s kOrganization -> usedtoknowhowmanyoperatorstobehired. -> Ta s kparcelization · Iperson 1 (orfewltasks(Assemblyline) -> Ta s krecomposition · Iperson,fewtasks(Fixedposition or Assemblycell)team · team - allactivities · workforcecost -> Reciprocalmovement -> Operator - Assembly · Operatormovestoassembly · Fixedposition -> Assembly - Operator · Partmovestodiff.Stations · Assemblyline,cells,shopsData>Assemblytime(averagevalues:Mis -> standarddeviation,8K -> sinceworkforceinvolved>Wo r ksampling⑧ -> standardtimesIslidepage19-26)(MTM) - mostcommonlyusedMr:2miSx = VEssiz itk Learningeffectshouldbeincorporated. LayoutConfiguration: highvariabilitylowvolumed↑highvolumlowvarietyhighrepetiveness Fixedposition: · For big,heavy or fragileobjects · For simpleobjectsinmediumproductionvolume · Highquality -> Advantages: 1.Highflexibility - mainly intermsofproductionwin2.Lowinvestment - noconveyers,etc3.Jobenlargement&enrichment -> Disadvantages: 1.Potentialintertwiningofmaterialflows(notproducts) 2.HighWIP - high 1.73. Largespacerequired 4)Clabour-asmere skilled RoughDesign: -> designchoise:Astationseproductioncapacity 2 requestedPC - throughputrateN = PCXTL-> assembly timeno.ofstationsExampleExample&PC:2p/hPC = 2 p/hT = 30minT = ahsN = PCXT = 2x0.5:1statnN = PCXT=8stations:Istateassures2peseverybyhispiecefromIwketh.So,4whatwillgive meIpieceeverybr Assemblyshop · seriesofstations&eachstationassigned aphaseoftheassemblyprocess · Productswithverydifftechnologicalprocessesorprodvolumes · Bufferspresent(before&aftereachworkstations- Tr a n s p o r t a t i o nsystem: -> Tr a d i t i o n a l :cartguidedbyoperatorslessinvestment -> Automated:(AGV): moreinvestment · Ta x i :AGUpicksupassembly&morefrom1operator(orbuffer) to theother. · Pass-throughflow:Assemblycarried on theAGU-> Advantages: 1.CTnotconstraint ->as bufferbothatbegging&end2.Highflexibilityofmice,product&expansion-> Disadvantages: 1.Difficult tomanageflowofproducts&components2. Ifautomation->investment4(depends)&idletimesduetocomplexityofproductionplanning&control. AssemblyCell · suitableformediumvolumeproducts · Generallyoperatorfollowsproductbeingassembled · Operatornotforcestofollowspecificorder AssemblyLine: · Forhighvolume,highrepetitiveness · Eachlineconsistsof a seriesofstationhavingaspecificsequence · Productflowsthroughsysteminsameorder · Mostreleventparameter:CT-> Advantages: 1.LowWIP - lowidletime2.Limitedspacerequirement - buffernotrequired(orsmall 3.RationalizationofmaterialFlow4.Lowercostofworkforce(lessskilled)3.Labourtrainingmight beeasier("")- Disadvantages. 1.Law flexibility (almostnon-existentinpacedlines)timereg.tostartnewproducts.3.Linn balancingmight bedifficult.4.Repetitiveworkkessjobenrichments-> Classification. I Paced:WelldefinedCycletimewhichrestrictsprocesstimesinallwokstations. · Alwayssynchronous(Productsfromallwokstnmove symultaneously > Intermittent:movementnotcontinuous.Handlingsystemscompletelystopmovingwhenoperationtakesplace · Hasriskofincompletion - canbesolvedbyCTP or stationsm] · Nobuffersbetweenworkstations.-> Continuous:handlingsystemkeepsmoving even whenoperationtakesplace.(En:conveyorbelt). -> Case1:Operator'scan'tstoptheline · CT&productioncapacity areperfectlycontrolled · Riskofincompletion -> Case2:Operatorscanstoptheline · Noriskofincompletion · CTCPCnotperfectlycontrolled.-> unpaced: NostrictpaceorCT.Productmovesonlywhendifferentoperationshavebeencompleted.Inon-constrained)ofincompletion-> synchronous:productsalongdifferentstationsmoresimultaneouslyoncetheoperationinthesloweststationiscomplete. · CTvariable · Impossibletokeepproductionrateundercontrol. -> Asynchronous:eachworkstationmovesitsproductindependently oncetheoperationsaredone.Bufferisneededin asynchronousunpacedlines. · Bufferpresentbefore&aftereveryworkstation · CT&PCnotperfectlycontrolled. · CT can beexceededoccassionally. stepsto DesignAssembly line: (Single ModelLine)Step8:Productmix Identificationmajorsteps · Ty p e sofproducts · QuantitiesStep1: DefinitionofBalancing Constraints -> precedenceconstraint(majori Ta s kTa s kPrecedence/1234 · 1 - w 9) /1I2I2>IH3,4 = 1Assemblygraph3I3/I↓42,34/op3preceedsoperate4.PrecedenceTa b l eHoffmanMatrix -> respecttheCT ·noworkstationcanexceedtheCT -> negativezoning · operationsthatcan'tbeputtogether duetosafety or logisticissues -> positivezoning · operationswhich,ifputtogether,leadtobenefits.Example:2operationsrequiring samemachinewhichisveryexpensive. -> spaceconstraint ·manstationsthatcanbedesigned(sinceeachstationneedsspace) -> wakeconstraint · basedon operatorskills.Ex:somesafetycertificatemightbeneededbytheworkerforaoperations&so,theseoperationsshouldbeputtogether orinclosestations. -> materialflowmanagement ·basedon materialflowsystem.If we haveoverheadconveyers, we putthatsetofworkstationsclose. -> opportunitytousemoreoperatorsforsingleworkstation · Ty p i c a l l y :1wksth-1operator,butsomestationsmightneedmultipleoperators&theyshouldbeplacedclose to eachotherStep2:EvaluationoftimeofeachAssemblyOperation · Howlongeachoperationstake · #waystocollectthem · notdeterministic Step3:CalculationofCycle Time(Forbothpaced&unpaced)CT = eciu (n)[thisisrequiredCT] -> allows me toknowhowmuchIshouldIn/u]aggregatemyworks in 1station.setofoperationsneeded "¥ productioncapacity(required)aggregation -> CTP.toassembletheprod.Nmin:rang timetoperformi - ActionDurationminnotofstations2toavoidriskofincompletion22 I CT.SRsaturationrateI2 lettercitiesare34minStep4: Assembly Line Balancing#stations - notalwayssameasNminOutputs besNmindoesn'tconsiderprecedences->operationsassignedtoeachstation.Step3: Sizing thelabour · #operates ->generallyIoperator/station + Iquality control,missingI works,etc.butmightbemore. GenericModel+AdditionalSteps[depending on typeofline] -> Unpaced:Buffer size -> continuous:lengthofstationsspeedofconveyers Balancingobjectives: ->A Te c h n o l o g i c a lObjectives -> iminimizestations,givenCT(ginenPC) - mostused>i.minimizeCT,given#stations(manPC) · example:highdemand,spaceconstraint,dismissing a product&tryingtodevelop anewone(usingsamewkstaths&workers)totalidletime(timeavailableat differentrkstathbutnotused)IT - Ava i l a b l etime - Usedtime=n27-2yearattivities #stationsits->ivminimizeprobabilityofincompletion · mimenizingnotbeingabletoassemble(whenhavinghighincompletel . notusedin unpacedlines ->B.EconomicalObjectives: -> i.minimizetotalexpectedcost(TEC) - (i)IoperatorXlineii)ifthereareunfinishedproducts,theymovealongtheline&operatorsonlyperformoperationsnotaffectedbyincompletion.(policyforunfinishedproducts)TEC = LC+ E.CUYExpectedcostofUnfinishedtackLa(linecost)cost - OperatorCost -> probabilityofoccurance E.CUT(costofIncompletion)Tk)ofincompletion I%Elminmin#operati->Timetocompleteactivities"¥castofincompsoftask1. higher no. ofactivitiesin1wokstath-higherriskofincompletionSo,thisismorerelevantwhen we have more steps/operatusperstate.#stations&LCPE.CUSAPat&riceversa. unfinishedproductpolicy: -> Hospitalstation(end)stoppedveryimmediate heartas operatormorestatea-ii.Maximizationofprofit · mainlyformulti-modelline · generallyforproductshavingdifferentvalues. BalancingModels/Methods: -> Optimizationmethods · Linearprogramming ->Heuristics ->Manincompletionprobability - Relatedtotechnologicalobjectives -> Kottas&Lan - Relatedtoeconomicalobjectives(minTEC) · Heuristicsmoreusedbecauseduetoallthedeviations(manualprocess), even theoptimizationmethodsaren'tperfect.. ProbabilityofNo-completion:whichtaskshouldIassigntoastation?>Px#station4 hypothesis times toperformtheoperationareindependent->timesaredistributedfollowinganermaldistribution[wN(ti,Ii) - Createastation - Voperationsthatcanbeassigned " · -compute PKvalues - if4KP*-assign - ifP. P * -opennewstationsteps:1.Calculateremaining timerelatedtotaskKRTK = CT - Esti CT = 1min I RTK = (60-50):10s⑧PA=40s e 2. Computingthe"z"variableassociatedwithRikzx = s 3. Identifythe probabilityofcompletionof $(fromthedistributiontable) I(zk) 4. Probabilityofincompletionof K1 - 0(zk) Actualvaluespentbythe ~operatortoperformthe operationP(completionK) = P(Esti- CT)valuestandardizeS~mean(ul7-actualvalue int (seeitl = P(z = se = P(zzk)Kottas&Lau: -> solutecloseto optimalobjective: minimizing costhypothesis:CT-> constraints--precedence -> timetocompleteatask-N(t,xxl ->timeto...is independentfrompreviousones~> in minimizingthepeckofincompletion-> unfinishedproducts go to hospitalstation we want to put a cap ontheincompletion. Wedon'tcareaboutthecost,sowedon't mentinethe-> eachworkerispaidindependentlyfromworkimbalance -> costtocomplete an operationisfreefromitsprogress We s tDWKsa,bnew (empty) & 48 where dowe placek? - WherevercastLowestAvailableOperations:Operationswithpredecessersallocatedtoawhite.-> Desirableoperations:Ava i l a b l eoperationsforwhichLK7PK. 1k castofincompleteofcostofperformingactivity14↓K&itsfollowers(all) asthe1stoperation ina stationP(incompletion)Ik = Ik + 2Is, 2: setoffollowersofKLk = (r.tkI'k:incompletioncostoftaskonly "¥ unitcostIt: ... no n· Sureoperation:d ~- followerofK.DesirableoperationwithPKwo(P Generation&managementofproductionplan. ProblemsinProduction Planning: - Manyvariables · Hems · Productionresources · Differentwaysofproducing an item->Datavolumes · volume&qualityofdata to bemanaged -> uncertainty · Externalmain imput - demand · Internalforecastingnoteasy -> constraints · Internal · External-> conflictingobjectives · Minimizathofcost · Maximizationofquality/servicelevelCompanyobjectives: ->commercial:Productavailability-stockoutnotwantedsoproduction->Production:Regular Utilizationofmachinery ->HR:Regularityoflaborutilization.(eg: noovertimel-> Management:Minionizationofstock-> Purchasing:Long termview(toobtaindiscounts) Planning: Hierarchicalapproach HorizonTimebucketItemdecisionstrategic 2bys1yearproducti ~ PC -"¥ longterm asa wholeStyproducedourfoursMedium1yearmonthitemwhenstartprodsmidterm&Te r m16-18months)corweek)machinesoperativelOperative1week1day/shiftpiecesegofprod "¥ mostprecise(orday) on dailybasisbasisofdecis -> Demandforecasting - outsideproductionplanningforall3 - smanprofit ->Productionbudgeting ->notnecessaryforthiscoursemincost --> AggregatePlanning - butM7&Strategic(moreMT) · MasterProductionSchedule(MPS) ->howmuchtoproduceeverymonth -> MaterialPlanning · MaterialRequirementsPlan(MRP) ->howmuch raw mattoorderto fulfillproducttarget, -> scheduling A↓L12MPs -inJanproduce150AXYMRP ->inDecorder150x&300Y MPS: · hewmanyunitsoffinishedproducttobeproducedinthemediumlongterm,ineachtimebucket · onlyfinishedproductsconsidered,notmaterials · onlybottlenecks(mostcriticalproductionresources)considered.MRP: · quantityofitemtobemanufactured/producedinshort-mediumterm · formaterials · MPSisan inputProductionSchedule: · decision on productionordertobestartedassoonasmachinefinishesworkingoncurrentorder. · bothMPS&MRP are inputs-slide - RollingHorizonProductTy p e : · RawmaterialPartsorcomponents · subassemblies·FinishedproductsBillofMaterial(BUM)ofhowproductismadeup · Containsinfo on type&no ofrawmat,parts,componentsasub-assembliesrequiredfor a finishedproduct · Ty p e s -> simple:singlelevel -> complex:Multilevel -> Engineering(orDesign)BOM -> MaintenanceBOM Relevantcosts: -> Facility/Plancost-> Productioncost -> variable:Dependan productvolume -> Fixed:Doesn't ---> Direct:canbeassigned to specificprod -> Indirect:Can't" -· onlyrelevantcosts(costsdifferentbetweenalternativeplans)considered Example:Plan1100A100B200A200BRelevantcost:InventorycostRelevant [ 2150A150B150A150B I -> setupcostirrelevantherebecausecost:3300A300Bbothhave4setups,Set-upcost2InventorycostConsideringDemand:Plan1)soallcostsdonotneedtobeconsidered.MainCosts:(Relevant) -> Labourcost -> Personnel(Overtime) - standardtimepersonnelcostnotrelevant - sub-contracting · Coub.cant"(purchasing + CtransptEquality -contros+ CsupplierrelationCrawmat&Conergyexcluded).-> stock-outcost: ->Real > Figurative - Depends oncustomer'sreaction.-> Set-upcost: -> Expenses(Real)setupdirectcost(labor,mat,consumables),timewasteopportunityloss -> Opportunitycost(Figurative - lassofprofit)costincurred. - ->no.ofhoursforset-up x cost/ hour->Overtimehours(OH) xOvertimeCost/hour(02) -> Quantityofproduct to buy(39)x[sub-contractingcost(s)Variablecost(1C)] ->SOXunitgrossmargin "¥material, energy... = s9X(unitprice -unitvariablecost) (stock)Holdingcost - Expenses:storage,depreciation,handlingitems -> opportunitycost(figurative): costofcapitalmoneytiedupininventory)SHC:AILXhe(perunit) ↓ AvgInvent. -> storagelevel -> Depreciation/obsolence -> costofcapital DemandForecasting: I· Thisstepisoutsideproductionplanningbutisitsprerequisite.ForecastingofIndependentDemand "¥ Demandthatdoesnotdepend on anyotherproduct.lEx:Customerdemand,demandforfinalfinishedgood).Forecasting - tryingtoestimatefuturevalueofdemandPlanning/Managingdemand - takingactiontochangedemandormeetcertaindemand -> example:Promotions -Input:Receivedorders,pastdemanddata,marketexperience,causalfactors(en:weather-> Output: a plan/forecastfor a specifictimehorizon.Anestodefineforecastingprob:(volumesofsales,salesintermsofmoney)offorecasting-productpiece her, orderline i -> product:type-product,version,item,sky(stockkeepingunit · higherthedetaillevel,lowertheaccuracy(SKUmustaccurate,productmest) S t =0->time->1.Horizon:6monthsI>Gmonths · Periodoftimeforwhichweare makingtheforecastt =0-> 2.TimeBucket:1monthI IIIII7t =0· Unitofanalysis2monthsIII7t =0->3.Frequency:IIIIII7Inew forecast1month IIIII- 3monthsIIIIII7· frequencywithwhichweperformforecast. · everyfewweeks/months we makeforecastsbased on theactualdemand. · if timebuckettheverypunctualintakingdecisionbutdegreeoferrors · horizonabetterbuthasprecise · freq-veryresponsive. -> geographicalaggregation-> influencingvariables:en:weather,seasons,emotions,etc. -> requiredaccuracy:depends on to aggretionlevel,anticipation S ForecastingMethodologies: ->TimeSeriesApproaches -> Analysis - Entrapolation: -> Tr e n d :Regressionanalysis -> seasonality:AutocorrelationCoefficient · Analysespastdata&accountsfortrends&seasonalities · WintessModel- Extrapolation: · applyingmathematicalformulasthatgiveforecastbasedonpreviousvalues. · Noregardsfortrendor seasonality · MovingAve r a g eModel · Brown'sModelFt + 1 = f(De,Dt-1,Dt-2, ... DE-N):D:actualdemand-> Causal/Relationalapproaches: · Someindependentvariables areusedtoestimatedemand · Regressionmodel · econometrics/input-outputmodelFt+1 = f(X1t + 1,x2+- N...)X2:independentvariables-> Qualitativeapproaches: -. based on expertopinion · SalesForce: · ExpertPand: · DelphiMethod:Paneanonymous · MarketSurvey:notsuperefficientFt+ 1 = f(expertopinion)Tr a d e - o f f overestimatinginventedtheI bothunwanted. AccuracyofForecasting: ->Error,Et : Dt-Ft -> Et +ve:DDF - underestimating -> Et-ve:DCF - overestimating ->MeanError,ME: II - Theargerror for a specifictimeperiod.Limitationsof ME: ~ peotsrelatedto sign Sit4JanFellD100SOE9090ME= 110) = 0, MAD to · mighthaveautocompensationof evors.->MeanAbsoluteDeviation,MAD: t -> peobrelatedtomagnitudesite JanFelsME = 0 = 10,MAD: 0 = 10 E 20201010bothsituation&&&give sameMAD = 10.Butactuallytheimpaloftheerroroftheargvalueofdemandis different. ->MeanAbsolutePercentage Error,MAPE t0 .eSituation0 ->MAPE=2Situation& -> MAPE: Nett = 50%2 · Weuse diffwaysbasedonhowaccuratewewanttobe -> biggererrorsweighmuchmore.->MeanSquareEsser,MSE: E pob:unitofmeasurement->StandardDeviationesser, SDE= · Anyofthisonesdon'tsayif weare overestinating or underestimatingassignsareremoved.Solution-> - - 1 ->trackingsignal,is: mp:2/s).n -> giveswhether we under or overestimateD.:nSales - stockout.Demandcomponents:Elements affectingtimeseries -↑ It: Tr e n dattimet a ~>Ct:Cilicityattime--similartoseasonalitybuthaslongertimehorizonRelated to macro-economicNproblems(ex:Inflation)MV > St:Seasonalityattimet Inlew, St:noiseattimetTr e n d : · canbegrowing or decreasing · Mostlylinearbutcanalsobenon-linear · canbeduetochange inmarketshare,servedmarketoroverallmarketvolumecyclicity: · cyclicpatternarisingfromdatarising&falling · Duration - atleasteyes · Inmacro-economiccycles, ea:inflation,realestate,etc. Seasonality · Duration - generallyyearly a6months · causes - climaticecstumesCyclicpromotionsActivityrate(mainlyB2B)Holidays · Identifyingseasonality:autocorrelationJan22 autocorrelationcoefficient, rk= ED-EL.(Deaner consideringinmenthe↓timehorizonforwhichd (D+ - i - *) we expectseasonality.dex: Jan2023Demand&Ave r a g edemandE = E De-i ifu>0.5-seasonality. · seasonalitycoefficient:Ratioofdemandina period&anyvalueofdemandinthatperiod8i= I ex: Si:DemandinJan23Angdemandinlast6Jan Extrapolation: shortterm MovingAverage I objectives was (FatiEntrapolation-Brown'sapplicationHoft-wintersIAnalysis+Extrapolationlongterms "¥ > morecomplex "¥ Sothisalsoconsiderstrendsorseasonalities->Moving Average orMMFt+1= MACKItconsidering:Remandvariesina regularway/slowly. "¥ex:I'minDec.trying to finddemandinJan.anaverageof atimeperiodbeforeistakenasthedemandExample:20212022I11IIIIWI11IIIIWx = 4(quarterly) 120110150115150120160ditobechosencorrectly.F1,2023 = MA(4),1,22 = 160 + 120 + 150+115 = 151,25ferE2,2023weneedtohavethenewvaluesofdemand.ReactiveModelif we adaptfastertochanges ->modelmorereactivewhenIobservation:1)K:Reactivityofthemodel An # is wouldgiveithave. It theproblemisthatitReactivemodelvReactivemodelXweincreasestheforecast. -> lowsvaluehelpsherehighvaluebetterhereascontributeof a singledemandvaluedwewillhavemoredata&just"largechangewillimpactlegs.observation)notsuitableforlongtermor fortrendor seasonality "¥ Itwouldsmoothenthetrendor seasonalityabecausethat's #1,8az= MAKv0+128 + 150+115=s1,25the onlydatae ↑"¥ but we don'tknowthisyet.So, -> Brown/Exponential Smoothing Model:SF1+) = a.D+ + (1 - x) FxForecastrelated topeer.Dereen forecastofthe "¥ ActualDemandofPrevperioddemandtobefoundt = april23Fray = x Dapeil + (1-x)FapeiltH = may23232323tactualwayitbehaved. "¥ forecastmadebeforechoiseofadecideswhetherweightofactualdemandhigheror forecasteddemand.observ1)Howtoinitializethemodel?Ft + 1 = 2.D+ + (1 - x)FtI&>Ft = xD+ -1+(1 - x)Ft -1"¥ Ft -1= 2D+-z+(1 - x)Ft -2= xD+ + (1 - x)xD + -1+ (1 - x)Ft -1 I (l-d)"Dt- valuesofpastdemandsavalable Generalformula is Ex+1= all-a "Dei - onlyfor initializing Example:20212022I11IIIIWI11IIIIWx = 0.4D100120110150115150120160F1,23 = 2.D,v,z + (1 - 2)F,v, 2 2 - 2D,v,x + x(1 - x)D.x,z2 + G(1 - x)D,1,22+....1.2 -60% 0.4(1-0.4)+0.4x0.6x 115+....S = 136.Ol↓contributionofmostrecentvalue - highest.contributeSupposeD, 2 3 =153gettingmuchsmalleraswegobackintime.F11,23 = 0.4x153+(1-0.4)136.01 = observation2)notsuitableforlongtermor fortrendor seasonality -> flattensthemReactiveModel-> high 2.IfI weightofArtSowe adapttoforecastslower. ·Howto finx? - looking attheforecasting everex:MAPEforlast3,6&9monthsMAPEfor 9&6monthsbutforlast3monthsMAPE↑So,we trykeepingsamea fornext3months&recomputeMAPE. IfMAPEgetsd ->xokifMAPE gets 4 - &needstobeadaptedNo analysis madehere. · Brown'smodeor moving averageappliedonlywhenweare-> Holt-Winter'sModel. -canalsomakelongtermforecasts~seasonalitycoefficientFt+1= (+ no.ofperiodsofseasonalitydLAve r a g eTr e n d ex: Ye a r l yseasonality,1:12months en: Fran = (Ab + TD) =12]23Fora subsequentperiod,(sincecanbeusedforlongterm).Fttm = (Ax+mT t )characterisedbytrend&seasonalitychangeofbendin1period.....Da be "¥ ifdecreasing, wewillonlyhaveI-vel. " I -> 3periods -> 3.It - -ForecastIt(Deparated) - - At Amal seman water re I: F= (A + T)S] ~ BrownActualtrendne E -> Tt = Y(A t - A+ - 1) + (1 - 2).It-1-Forecastedvalueoftend·allthesevaluesare = coffweightedaverages.# Actual "¥ - S = B+ (l-)e -Forecasted -> Ao=Ayear1 + 1 To = In-> periods -> to : Azearn-Ave e "), year * - Some site Example:20212022I11IIIIWI11IIIIWD100120110150115150120160F1,23 = (A,v,22 + Tiv,22).S1,22argof2022Iangof2021 (110 + 130)TIvice:To = 10 = 2.8units/quarter -> expectedincreaseperquarter(anarg)AN,22 = Ar=Aal+To = 131.25 + 1 x2.8:136.85units31,22 = 50,1 = S1,21, + 51,22 = -0.876: 0.855->S1,21 = D1,21 = 100 => 0.833Az120->S1,22 = 2 = 25= 0.876: F1,23 = (136.85 + 2.8)122.33 ->Thiswastheinitialization.F11,23=(AIV,22+2TIV,22)SII,22 = (136.85 + 2x2.8) "¥ S1,2 "¥ 81,227Arg.If we gettheactualdemandweusethe"A p p l i c a t i o n"formulas. InventoryManagement:MaterialPlanningApproaches: -> Pull/InventoryManagement · newmuchtoorder&when,basedon consumption -> Push/On-DemandManagementgues:Whyholdinventories?Effectiveness(to beabletoneedcustomer Idemand-Reducestockoutrisk)Demand->evenwhen wehave uncertaintyof I LeadTime Efficiency - Reduce purchasingcost. -> Reducelogisticscost(ex:transportation) m -> PLANTWA S-> Reduceproductioncost(lessensno. ofsetups) · INVENTORY:inventories-Finishedproducts->Rawmaterialswithdemandusedin differentprods. objectivesforInventoryManagement: · Minimizerelatedcosts(atotalcest) -> SHC -> Executioncosts(order/setup)ofcontrol ->costof LowSL(stockoutcosts TIMEINTERVALFixedvariableEOG:EconomicOrderSty Ee EOG-ROPROP:Reorderpointmodel Fixed-time~ periodmodelLswitchmodelEOG-ROPmodel - everytime we reachROPwereorder&the quantity toreaderisEOG.Fixedtime-periodmodel -wereaderafterfinedtimeinvervals. -> Styis defined inordertoreacha target availabSwitchmodel.Acombinationoftheothera EOG-ROP Model:Characteristics: · variableintervaloforderissuing(afterreachingROP) quantity ordered(EOG)central(toknowwhenwe reachROP) · IndependentEntriesreorderleveryproductmighthave a different ROP&soreordermighthavetobemanagedindependently) objectives: · Whentoreorder - reachingROP · Howmuchtoorder -> EOS InventoriesR up: no uncertaintyROGen "¥WewouldliketogettheorderassoonasE0G are theproductsfinish. - availability:inventories+ordersROPen nee Man _inv= EOS 1. Min-inv =0>IOrderReceiveMan-avail:ROP+EOG*1 Min-avail = ROPROP:Dit >DemandduringleadtimeaTo t a lcost-EOG?->min2107incaseweproduce~Classical " EOg -> RelevantcostI · Purchasingcast/Productioncost((p)annual · InventoryHoldingcost(Cstock)·Orderissuing/Setup - cost(20)Cp = DAXP - purchasing/variableproductioncost(unitary(estock = 2m(%)xPXAverageInventories I equal.S "¥ valueofinventoriescaustownership rate : (stock = cm(Y)xPx 8 quantityperorder.(2017)20 = 0xNorders "¥ AlL coefficientofvariation, or= ->unitorder/setupcost...c = 0 x :210r = DAXP+2m(y) + Oxb wecan findoTofindminvalue,cost:for =0 + xx-)= 0RCTOTCstock ⑳ DAXP win a ne 207⑤ - - OXDA: EOG:y2XOXDA = 1 Cm()xPCstock,unsunitstockholdingcost-> Forno uncertainty. For uncertainty: -> Idoesnotchange wewantaplayswhereit higher ordemand-> ROPchangesbecauseIT changes. -init higherbeforeROP ->nostockouts -can happenduringLT.So,uncertintheLT. - > LTo r,But canbehighercausing:foruncertainty -> safetystock -leadtimestockout 1 toconsidervariabilityofDemand · IfdemandbeforeROPit'snot a problembecauseitonlyindicatesthatwewillreachROPfaster.ProblemisifDemandafterreachingROPbecausewehaveaminimumleadtimebeforegettingournextorders.So,beforeROPwecan'thavestockout·Howmuchtoreorder? -> EOR:N2x0XDACmY.xP· when? -> ROP=DLT +SS = DLT+K.*,=DLT+KULTO+aD2SL: Ta r g e t Servicelevel->SL=PSC: ProbabilityofstockcoverageDL-N(Di,04, tr->standarddeviationProbabilitynottoSS:KX CD, LT during 2havestockout "¥ constdepending onthesh=>don'thavestockoutsinLT ifDLTCROP.PSC:Prob(DL+AnydemandduringLT&=Drob(DLT AlL= *- 35 = PxDA + cmy.xP + 9(1 - ) + ox -) iss2707 = 0Neweconomicorderquantity.EOG*:N 2xOXDAcy.xPx(1 - 2)Va r i a b l eCostofPurchasing/Production: purchasing/productcostnotalways -....?8constinreallife.Generallyhigherorder -> priced HowtofindbestEOS?⑧We findEOSatdifferent&valuesandchoosethebest(849,,9(92,0 = B,,9 = G2,etc.) costpriceNd100&1000e-EOGI-&1000u..... a bit in theP298971000n↓wewant1000y EOG2 - not feasible -as still aspricelowerthere.↓lessthan10,00& : 1000u 2707 everyt · How much? -> D: sothatAvailabilityreaches an objectivelevel(02)Availability: Inventories - Ordersinprogress - ReservedstocksLT = 0.5week. t"¥T 12345↑↑orderreorder &i = 0L-Availability,i=indexofthemomentsinwhichweissueorders .. - Availability - Inventory OL---------------OL-B,---------------max-Ava i l = OL: D, + ++S5 I min-Avait = 0L-D,OLD---------------a I = Di ++ + SS - D-after7 --------- whenalread) = B,x+ sLTLTAA-I13I vener ↑T↑T↑min-in=min-avail-DL=ss I!+LT considering noreservedstockmax-inv =+ 3S = 5T+ss↓averageordersize,G:Ds &max-avil-D wehavemax-inv - IXTafterLT. · herewedon'tmonitorinventoriesconstantly&weorderonlyaftertime7.See,herewehaveuncertainty(wiskofstock-out)faceuncertaintyduring T+LT(becausethat'swhenweforEOG-ROPthiswas justLTsee a reaction). S 39 = kx8D,T+ 2T-k->servicelevel:PSC (Probabilityof StockCoverage)anormaldistributionD++L+ - N(D+ +2;G,T+ xe) = P(D ++2> 8T+2 = GTas:0 fifidedtenodev.T => minGOT, T+LT = V(T + (T)4 + 4 + 242(Purchasing/production + in-holding+ setup/order) EOG-ROPmodel:Numberoforders - is Average timebetweenorders,I = E (yearsFixed - Tmodellotimaltimefor reader, 4 = to as" in TE vchea --ordercost = No.ofordersx0 = 2 x0Averagecyclestock: =5 = ⑤xTAnydem= berthe 2 AverageInventorylevel = + ss.(B) TimeIntervalFinedvariable Find////, *pS Obals Fred Switchen -> eg:Fixed - butoptionalordersvar↓onlyifavailabilitycertainlevel.(similartoROP)inventoriesdon'tneedtobecheckedcontinuously,onlypriortoreordertime. -> More interestingformultipleproducts. becausethegeneralImightnotbe optimalforallproducts.