274 

AdvancesinProductionEngineering&Management ISSN1854‐6250

Volume12|Number3|September2017|pp274–284 Journalhome:apem‐journal.org

https://doi.org/10.14743/apem2017.3.258 Originalscientificpaper

 

An integer programming approach for process planning for mixed‐model parts manufacturing on a CNC machining center  

Kongchuenjai, J.a,*, Prombanpong, S.a  

aKing Mongkut’s University of Technology Thonburi (KMUTT), Department of Production Engineering, Bangkok, Thailand   

A B S T R A C T   A R T I C L E   I N F O

Themanufacturing system formixed parts is prevalent inmany industriesdue to the continuous demand of product variety. Thus, the mathematicalmodeltodesignaprocessplanisdevelopedbyusingtheinteger linearpro‐gramming.Themainaimistominimizethetotalproductiontime.Themaintime factors included in the model composed of the machining time, tooltraveling time, tool changing time and tombstone face changing time. Thesignificant design constraints are the precedence operations, fixture design,andavailablecuttingtoolconstraints.Furthermore,avariationofpartstylesisalsoaccountedforinthisstudyasthedifferenttypesofapartcanbecon‐currentlymountedandprocessedwhichmakes thisproblemunique.There‐fore, thisproblemismuchmorecomplexthanthenormalsinglemodelpro‐cess planning. Themodel developed using integer programmingwill deter‐mineasequenceofrequiredmachiningoperations.Italsodecidesthefaceofthemachiningparttobefastenedonthetombstoneface.Inaddition,asuita‐blecuttingtoolwillbeselectedbasedonminimumtotalproductiontime.Theresultofthispaper,aidsinsolvingprocessplanningdifficultyinthededicatedflexiblemanufacturingsystemintheeraofIndustry4.0.

©2017PEI,UniversityofMaribor.Allrightsreserved.

  Keywords:FlexiblemanufacturingsystemProcessplanning(CAPP)Mixed‐modelIntegerprogramming

*Correspondingauthor:janjiraie@yahoo.com(Kongchuenjai,J.)

Articlehistory:Received11April2017Revised10July2017Accepted16July2017 

  

1. Introduction 

Aprocessplanningtaskisapartofproductdesignandmanufacturingsystemthatconsidersthemanufacturingresourcesandengineeringtechniquesfordecisionmaking.Theefficientprocessplancanbeachievedbywell‐designed logicaloperationsteps, technologicalmachinecapabili‐ties, cutting toolselection,andmachiningconditions.Moreover, theprocessplannerhas tobeconcerned about the jigs and fixtures, route sheet generation, setup requirements and otherimportantprocessesduringthedesignprocess[1].Thus,theprocessplanrevealsthesequenceofmachiningoperationstogetherwithaselectionofcuttingtoolsaswellascuttingconditions.Aprocessplannermustmakeacrucialdecisionwhethertocontinueusingthesamecuttingtoolortochangetoanewcuttingtoolforthenextsetofremainingoperations.Thisdecisiondictatesaresultedmachiningsequenceandchallenges researchers to innovateefficientalgorithms forageneration of the process plan which is considered a classic problem for automated processplanning.Itisobviousthattheprocessplanningtaskiscrucialandaffectsbothoftheeconomicandefficiencyofthemanufacturingsystem.

Indecades,theCNCmachinetechnologyhasbeendevelopedbyequipmenttomakeitmorehighlyautomated,flexible,andrunatafasterspeed.TheATC(AutomatedToolChange)andAPC

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(AutomatedPalletChange),asanexample,augmentthecapabilityoftheCNCmachineandbe‐come thestandardequipmentequipped in theavailableCNCmachine in themarket.TheATCenablesthequicktoolchangefromthetoolmagazineatnotimeloss.Inaddition,amodularfix‐turefortheCNCmachineisdevelopedtoallowaquickchangeoffixturedesigntocopewiththeFMS(FlexibleManufacturingSystem)demand.TheautomatedprocessplanplaysacrucialroleinFMSsinceitenablesthesystemtoworkeffectivelyandmeetitsdesignobjective.TheFMSisdeemedanintelligentmanufacturingsystem(IMS)whichcorporatescomputernetworks,auto‐mation,andintelligentsoftware.

It canbeenhancedbywireless communication, sensornetworks, Internetof thing (IoT) tobecomeahigh‐resolutionmanufacturingsystem(HMS)[2,3].Therefore,theFMSisconsideredan indispensable physical platform for the fourth industrial revolution so‐called Industry 4.0.TheFMSenablesmixed‐modelpartstobeconcurrentlyperformedinthesameenvironment.Itrequires an automatedpart identification and a quick changeof bothphysical setup andpartprogramming.Toenablethequickphysicalsetupchange,atower‐typepalletortombstonetype,togetherwithAPC,areinventedtofastenmulti‐partfacesandtochangeapalletintheCNCma‐chine.Thetower‐typetombstoneallowsupto fourdifferentpart facestobemachinedinonlyonesetup.Thepartfastenedateachtombstonefaceisnotnecessarilyfromthesamework‐part.Itcanbe froma totallydifferentpartwhichshares thesamesetofavailable tools.Logically,aprocessplannermustmakeanadditionalefforttodecidewhichpartfacehastobefastenedateachtombstonefacewhichcertainlyrelatesandaffectsatoolselection.Meaningthataplannercancontinueusingthesametoolformoreoperationsatdifferentlocationsbyrotatingthetomb‐stone.TheAPCallowsaquickpalletchangeinordertoeliminatesetuptimeduetopartchange.Inotherwords,themachiningoperationscanbeperformedatonetombstonewhereasunload‐ing/loadingofthenewpartscanbeconcurrentlyoperatedattheothertombstone.Asaresult,theprocessplanner'staskisenlargedbytheadventofthenewmentionedtechnology.Thiswillincreasethecomplexityofaprocessplanningtasksincemoremachiningoperationsandmorepart‐facesoptionsneededtobeconsidered.Therefore,asoundprocessplanmustintegratethemachiningoperationrequirementandthework‐partsequenceandorientationintheconsidera‐tion,inordertosuittoday'sCNCmachine.Inotherwords,theintelligentprocessplanmustbeable to reveala sequenceofmachiningoperationswith theselected tool andalso identify thetombstone rotation sequencewith the selectedwork‐part face.Obviously, this task cannot beaccomplishedwithouttheintelligentmathematicalprogram.

Thisresearchdealswiththeflexiblejobshopschedulingproblem,whichistheNP‐hardprob‐lem[2]. Thisresearch alsoproposedtheComputer‐AidedProcessPlanning(CAPP)byusingtheintegerlinearprogramming.

2. Literature review 

Theresearchinanautomatedprocessplanningareahasbeenlongconductedforafewdecades.Amyriad of algorithms andmethods both in heuristic and optimization are presented in theprevious literature [2].However, one of themost classicmethods used to generate a processplanisanoptimizationthroughalinearprogrammingmethodandcanbeappliedinallmanufac‐turingsystems.Asreferredtoin[3],themixedintegerprogrammingwasamathematicaltech‐nique used for flow shop scheduling and job shop scheduling, including the fuzzy processingtime under precedence constraints andmachine capacity constraints. Themixed integer pro‐grammingalsowasusedintheworkof[4]forintegratedprocessplanningandschedulingmod‐el(IPPS)inajobshopproblem.Thelinearintegerprogrammingmodelwasalsousedtoselectthemachine‐toolandallocatetheoperationsforFMS,inwhicheachpartandtoolcanbedynam‐icallychangedduringtheproduction[5]. Inaddition, themixedinteger linearprogrammingisusedtominimizethemaximumcompletiontimeoffinalproductsinaflexibleassemblyjobshopwith the sequential‐dependent setup time [6]. Themathematical programming in the formoflinearprogrammingisalwaysutilizedintheflexiblejobshopschedulingproblem(FJSP)[7‐9],flowshopscheduling[3,10,11]andintegratedprocessplanningandscheduling(IPPS)systems[4,6,12].Differentconditionswerefoundintheobjectivefunctions,forexample,minimization

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of themake‐span(thecompletion timeof the lastoperationofall jobs), the lateness, the totalprocessingcostandtheweightednumberoftardyjobs.In[8‐9],theintegratedconstraintpro‐gramming(CP)modelwasdevelopedfortheFMS,includingthetoolallocation,machineloading,part routing, and scheduling. The branch‐and‐bound algorithmwas also used by the processplanning and sequencing of CAPP and flexible manufacturing systems was studied [8]. Toolchangingandtoolsequencingproblemswereproposedwherethebranch‐and‐boundwasusedtominimizethetotalflowtime[11,12].Variousalgorithmsareproposedinthepreviouslitera‐ture.Forexample, thegametheorywasproposed in [12] to investigate the interactionamongdecision alternatives, whereas the game theory was developed for multi‐objective integratedprocessplanningandscheduling(IPPS).Theobjectivefunctioniscomposedoftheminimizationofthemaximalcompletiontimeofmachines(makespan),theminimizationofthemaximalma‐chineworkloadandtheminimizationofthetotalworkloadofmachines.Theintegratedprocessplanningwaspresented as amathematicalmodel to consider optimummachining conditions,operations sequences and toolmagazine arrangement by CNCmachine. The objectivewas tominimizetheproductioncosts[13].Asmentionedin[14], theprocess‐planningmodelforma‐chining cylinder heads in a typical engine manufacturing plant was designed in the form ofmathematicalprogrammingmodelsthatincludethepartgrouping,machineloading,toolalloca‐tion, and scheduling. Theminimization of the non‐productive toolmovement and orientationtimewasproposed in this research. Theproblemof production scheduling,which consists ofloadingandsequencing,istackledinthisstudy[15].Themajorfindingsofthisstudyaregener‐atinganoptimumsequencingordertocompleteallthejobswhichhavebeenassignedalreadyoneachmachine.The solution formaximizingmachineand laborutilizationand reducing theidletimeoneachmachineispresented.ThetwoNP‐hardoptimizationproblemsarecomposedoftheflexiblejob‐shopschedulingproblems(FJSPs)andtheFJSPswithprocessplanflexibility(FJSP‐PPFs)[16].TheFJSPsistheroutingandsequencingsub‐problems,whereastheFJSP‐PPFs,withprocessplanflexibility,istheprocessplanselectionsub‐problem.Therearetwostepsforprobesolving,whichare1)amixed‐integer linearprogrammingmodel(MILP‐1) isdevelopedfor FJSPs and 2) amodification ofmixed‐integer linear programmingmodel is developed forFJSP‐PPFs.

Table1Summaryofmathematicalmodelingapproachforprocessplanningofmachiningprocesses

Author/Year

Mathematicalmodelingapproach

Processplanningactivities

Mathematical

programming

Constraint

programming

Branchand

bound

Gam

etheory

Sequencingof

operation

Set‐upplan‐

ning

Selectionof

plan

Selectionof

part

Selectionof

machine

Selectionof

cuttingtool

Cal.process

times

Cal.cost

Lietal.,2010 * *DemirandIsleyen,2013 * * * * MilosSeda,2007 * * * Lietal.,2010 * * * *JahromiandMoghaddam,2012 * * * * *Nouralietal.,2012 * * * * * Dejaetal.,2013 * * * Zeballosetal.,2010 * * * * Zeballos,2010 * * * * * KarakayalandAzizoglu,2006 * * * Chandraetal.,2007 * * * Lietal.,2012 * * * AkturkandAvci,1996 * * * *Dasetal.,2009 * * * Ahmadetal.,2009 * * * * Ozguvenetal.,2010 * * * *Prombanpongetal.,1992 * * KongchuenjaiandPrombanpong,2015 * * *

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Computerized fixturedesignsystemandprocessplansgeneratedbycomputer,aided thepro‐cess planning. Amathematical model was developed to integrate process planning in fixturedesign considerations [17]. The objective of this research was to review the CAPP researchworksincludingthecriticalanalysisofjournalsthatpublishCAPPresearchworksandalsothedirection of future researchwork. The general information, past reviews, anddiscussions aresummarizedinvariousaspects[18].Intheworkof[19],themathematicalprogrammingtode‐terminetheoptimalsequenceofsinglepartmanufacturedonaCNCmachiningcenterequippedwith the single tombstone‐type fixture was developed. The minimization of total productiontimerequiredformachining,tooltravelingandtoolchangingwerethendeterminedunderrele‐vant constraints.Table1 concludes the relevant literature reviewsofprocessplanningofma‐chiningprocesses.

3. Materials and methods 

3.1 Pallet configuration 

Asmentionedearlierthemixed‐modelpartsintheFMSaretobemachinedbytheCNCmachin‐ingcenterwithanautomatictoolchangeandapalletchangefunction.Withapalletchangefunc‐tion,itallowsuptotwopalletstobeinstalled.Thus,thetwotower‐typepalletsareequippedinthemachinewhichallowsuptoeight‐partfacestobereadyformachiningasshowninFig.1.

Fig.1Tower‐typepallet

3.2 Mathematical model 

Letassumetwodifferentpartsareinthesystemandeachfour‐partfacesarerequiredforma‐chining operations. Thus, a process plannermust integrate twoplanning tasks i.e.whichpartface tobe fastenedoneachtombstone faceandwhat is thesequenceofmachiningoperationsandtoolstocompletealltherequiredmachiningoperations.Itisobviousthattheplanningtaskismuchmorecomplicated; consequently, themathematicalmodelusing0‐1 Integerprogram‐mingisproposedandcanbedescribedasfollows:

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Indices:i Indexoftombstonefixturefaces(i=1,2,···,I).j Indexofpartfacesofthework‐piece(j=1,2,···,J). k,k' Indexofmachiningoperationnumber(k,k'=1,2,···,N).l Indexoftoolnumber(l=1,2,···,L).m,m' Indexofconsecutivenumber(m,m'=1,2,···,N).

Parameters:I MaximumnumberoftombstonefixturefacesJ Maximumnumberofpartfaceskj SetofoperationstobeperformedinpartfacejL Numberofallavailablecuttingtoolsinthetoolmagazinelk Setoftoolsthatcanperformforoperationk;lk LN MaximumnumberofoperationsorsequencesMTkl Machiningtimeforoperationkbytooll TC Toolchangetime whichisconstantTTkk' Tooltraveltimefromoperations ktooperationk'TFCii' Tombstonefacechangetimefromthetombstoneface itoi'

Decisionvariables:E Totalproductiontime.Xijklm =1whenoperationk isperformedon the tombstone face i onpart face jwith

toollinsequencem. =0,otherwiseZkk’lm =1whentoollisusedforbothoperationkandk'insequencemandm+1,re‐

spectively. =0,otherwiseWii’m =1whensequencemissetupthetombstonefaceiandsequencem+1issetup

thetombstonefacei'. =0,otherwiseYij =1whenpartfacejoccupiesintombstonefacei. =0,otherwise

Theobjectivefunctionistominimizethetotalproductiontimeofthepartswhichisasumma‐tionofthefourentities,namely,themachiningtimes,thetoolchangetime,thetooltraveltimesandthepalletchangetimeandcanbeformulatedas(1).

Minimize∈

1∈

∈

,

(1)

Thesetofconstrainsinthemathematicalmodelareasfollows:

1.Operation completion constraint. All the requiredmachining operationsmust be completedandmustnotbe repeated.Each requiredmachiningoperationmustbe completedat theonlyonetombstonepalletfaceandtheonlyonecuttingtool.

∈

1 for all

(2)

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2.Singularsequenceconstraint.Thisconstrainensuresthattheoperationkmustbescheduledinonlyonesequenceslotinthesequenceplan.

∈∈

1 for all (3)

3.Precedenceconstraint.Anoperationk'mustfollowtheprecedenceconstraintrule.Thatisifkmustprecedek'andkissequencedinsequencem,k'mustbeabletoperformonlyatsequencem'wherem'≥m+1.Thisconstrainensuresalogicalprocesssequence.

∈∈ ∈∈

0 (4)

4.Toolchange timeequation.Whenever there is any tool change, itwill increaseaproductiontime in the objective function. Thus, this tool change timemust be taken into account. In themathematicalexpression, isusedasaflagtoindicatethetoolchangeaction.Thatis,ifthesametoollisusedinoperationkandk',then issettobe1;otherwise0.

∈ ∈

2 0

forall , 1, … , 1, ∈

(5)

∈ ∈

2 1

forall , 1, … , 1, ∈

(6)

5.Tombstone faceoccupiedconstraint. This constrain ensures that therewill beonly onepartfacejoccupiedateachtombstonefacei.

1 for all (7)

1 for all (8)

∈

0 for all , (9)

6.Tombstone rotationor change time equation.Whenever there is any tombstone rotation byitselforcompletelyalternatetotheotherone,thelosttimeofthisactionmustbetakenintoac‐count intheproductiontime.Thelogic isthattimerequiredtorotate itself is lessthanthatofchanging to theotherwhereTFCii', tombstone facechange time isvarieddependingupon faceindex relationship. In the mathematical expression, is utilized as a flag to indicate thechangeaction.Iftombstonefaceiisscheduledinsequencemandthetombstonefacei'issched‐uledinsequencem+1,then isassignedto1;otherwise0.

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∈ ∈

2 0

forall , 1,2, … , , , 1, … , 1, ∈

(10)

∈ ∈

2 1

forall , 1,2, … , , , 1, … , 1, ∈

(11)

7.Integralityconstraints.Alldecisionvariablesare0‐1integer.

0,1 for all , , , and (12)

0,1 for all , ′ and (13)

0,1 for all , ′ and (14)

4. Case study: Automotive parts (manifold inlet and console) 

4.1 Preparatory steps 

Thedevelopedmathematicalmodel isappliedwithactual twoautomotiveparts. It isassumedthatthemanifoldinletandtheconsoleasshowninFig.2andFig.3,respectively,arethemixed‐modelpartsneededtobemachinedbythemachiningcenterinFMS.

Alistofavailablecuttingtools,equippedwiththetoolmagazine,isshowninTable2.Itisas‐sumedthatthereareninecuttingtoolsavailablethatcanbeusedtocompletealltheoperationsintheabove‐mentionedparts.

Themanifoldrequirestenmachiningoperationswhicharearbitrarilyassignedasoperationnumbers1to10.Theconsole,ontheotherhand,alsoneedstenmachiningoperationswhichwillbeassignedasoperationnumbers11to20.Thus, therewillbeatotalof twentyrequiredma‐chiningoperationstocompleteasshowninTable3.Notethatmachiningoperationnumbers1to10belongtothemanifoldandtheremainingoperationsbelongtotheconsole.Foreachoper‐ation,thereisalistoffeasibletoolsaswellasthecalculatedmachiningtimeassociatedwiththetool.Inaddition,therequiredprecedenceoperationisalsoprovided.Asanexample,operationnumber6mustprecedeoperationnumber7.Likewise,operationnumber13mustprecedeop‐erationnumber14andsoon.

Fig.2Manifold Fig.3Console

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Table2AlistofcuttingtoolsinthetoolmagazineToolnumber Toolspecification

1 Facecutter32mm2 Facecutter80mm3 Spotfacecutter24mm4 Drillbit6.8mm5 Drillbit10mm6 TapcutterM87 Endmill3mm8 Endmill6mm9 Ballmill6mm

Table3Thenecessarymachiningdata

Work‐piece

PartfaceOperationno.anddescription

Toolno.anddescription

Machiningtime(min)

Precedence

Manifold

1

1 Facemilling 1 Facecutter32mm 30 ‐ 2 Facecutter80mm 15 ‐

2 Drilling 5 Drillbit10mm 1 ‐3 Drilling 5 Drillbit10mm 1 ‐

24 Facemilling 3 SpotFacecutter24mm 3 ‐5 Facemilling 3 SpotFacecutter24mm 3 ‐

36 Drilling 4 Drillbit6.8mm 1 ‐7 TappingM8 6 TapM8 2 Operation6

4

8 Boring 7 Endmill3mm 8 ‐ 8 Endmill6mm 5

9 Grooving 7 Endmill3mm 7 ‐10 Grooving 7 Endmill3mm 7 ‐

Console

5

11 Boring 7 Endmill3mm 6 ‐ 8 Endmill6mm 3

12 Boring 7 Endmill3mm 6 ‐ 8 Endmill6mm 3

13 Roughmilling 7 Endmill3mm 360 ‐ 8 Endmill6mm 240

14 Finishmilling 9 Ballmill6mm 480Operation

13

6

15 Drilling 4 Drillbit6.8mm 1 ‐

16 TappingM8 6 TapM8 2Operation

1517 Drilling 5 Drillbit10mm 1 ‐18 Drilling 5 Drillbit10mm 1

7 19 Grooving 7 Endmill3mm 7 ‐8 20 Grooving 7 Endmill3mm 7 ‐

Otheressentialdataare tool travel timebetween theoperationsand tombstone rotation timeandtombstonechangetimeasshowninTable4and5,respectively.Thetooltraveltimeisthetimerequiredtoreachthenextoperation.Itassumedthatthetravelspeedusedtocalculatetooltraveltimeisthemaximumspeedthatthemachinecanprovide.Inthisstudycase,themaximumtravelspeed(rapidtraverse)is1.969in/min.InTable5thetombstonerotationtimeisaround0.6minwhereasthetombstonechangetimeisaround2minsincethisoperationrequirestheothertombstonetoswingintoplace.

AllthenecessarydatainTables2to5willbeusedtoformulatethemathematicalmodelandexecutedusingGurobiOptimizer.Atotalnumberofgeneratedvariables is2.252andthecom‐puterprocessingtimeis31.18min.TheobtainedresultissummarizedinTable6and7.

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Table4Tooltraveltimebetweentheoperations

Tooltraveltime(min)

FromoperationkTooperationnumberk'

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

1 ‐ 0.2 0.1 0.1 0.1 0.1 0.1 0.2 0.1 0.1 0.4 0.4 0.2 0.2 0.2 0.1 0.3 0.3 0.4 0.4

2 0.2 ‐ 0.2 0.2 0.3 0.2 0.2 0.1 0.3 0.3 0.3 0.4 0.3 0.3 0.3 0.3 0.1 0.4 0.2 0.4

3 0.1 0.2 ‐ 0.1 0.2 0.1 0.1 0.2 0.2 0.2 0.3 0.4 0.2 0.2 0.2 0.2 0.4 0.4 0.4 0.4

4 0.1 0.2 0.1 ‐ 0.2 0.1 0.1 0.2 0.2 0.2 0.3 0.4 0.2 0.2 0.2 0.2 0.2 0.3 0.3 0.3

5 0.1 0.3 0.2 0.2 ‐ 0.2 0.2 0.3 0.1 0.1 0.3 0.3 0.2 0.2 0.2 0.2 0.3 0.3 0.3 0.3

6 0.1 0.2 0.1 0.1 0.2 ‐ ‐ 0.1 0.1 0.1 0.3 0.3 0.2 0.2 0.1 0.2 0.3 0.3 0.3 0.3

7 0.1 0.2 0.1 0.1 0.2 ‐ ‐ 0.1 0.1 0.1 0.3 0.3 0.2 0.2 0.2 0.1 0.3 0.3 0.3 0.3

8 0.2 0.1 0.2 0.2 0.3 0.1 0.1 ‐ 0.3 0.3 0.2 0.4 0.1 0.1 0.2 0.2 0.1 0.3 0.1 0.4

9 0.1 0.3 0.2 0.2 0.1 0.1 0.1 0.3 ‐ 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.4

10 0.1 0.3 0.2 0.2 0.1 0.1 0.1 0.3 0.2 ‐ 0.4 0.1 0.2 0.2 0.2 0.2 0.3 0.1 0.4 0.2

11 0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.4 ‐ 0.4 0.4 0.4 0.2 0.2 0.2 0.3 0.1 0.4

12 0.4 0.4 0.4 0.4 0.3 0.3 0.3 0.4 0.2 0.1 0.4 ‐ 0.4 0.4 0.2 0.2 0.4 0.1 0.4 0.1

13 0.2 0.3 0.2 0.2 0.2 0.2 0.2 0.1 0.2 0.2 0.4 0.4 ‐ ‐ 0.1 0.1 0.2 0.2 0.2 0.3

14 0.2 0.3 0.2 0.2 0.2 0.2 0.2 0.1 0.2 0.2 0.4 0.4 ‐ ‐ 0.1 0.1 0.2 0.2 0.2 0.3

15 0.2 0.3 0.2 0.2 0.2 0.1 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.1 ‐ ‐ 0.2 0.2 0.2 0.2

16 0.1 0.3 0.2 0.2 0.2 0.2 0.1 0.2 0.2 0.2 0.2 0.2 0.1 0.1 ‐ ‐ 0.2 0.2 0.2 0.2

17 0.3 0.1 0.4 0.2 0.3 0.3 0.3 0.1 0.2 0.3 0.2 0.4 0.2 0.2 0.2 0.2 ‐ 0.4 0.1 0.4

18 0.3 0.4 0.4 0.3 0.3 0.3 0.3 0.3 0.2 0.1 0.3 0.1 0.2 0.2 0.2 0.2 0.4 ‐ 0.4 0.1

19 0.4 0.2 0.4 0.3 0.3 0.3 0.3 0.1 0.2 0.4 0.1 0.4 0.2 0.2 0.2 0.2 0.1 0.4 ‐ 0.4

20 0.4 0.4 0.4 0.3 0.3 0.3 0.3 0.4 0.4 0.2 0.4 0.1 0.3 0.3 0.2 0.2 0.4 0.1 0.4 ‐

Table5Tombstonerotationandchangetime

Tombstonerotationandchangetime(min)

Fromtombstoneface iTotombstonefacei'

1 2 3 4 5 6 7 81 ‐ 0.6 0.6 0.6 2 2 2 22 0.6 ‐ 0.6 0.6 2 2 2 23 0.6 0.6 ‐ 0.6 2 2 2 24 0.6 0.6 0.6 ‐ 2 2 2 25 2 2 2 2 ‐ 0.6 0.6 0.66 2 2 2 2 0.6 ‐ 0.6 0.67 2 2 2 2 0.6 0.6 ‐ 0.68 2 2 2 2 0.6 0.6 0.6 ‐

 

4.2 Results and discussion

TheobtainedresultsinTables6and7canbedelineatedasthefollowing.InTable6theoptimalsolutionindicateswhichpartfaceofthepartwillbefastenedonwhichfaceofthetombstone.ItcanbeseenfromTable4thatbothManifoldandConsolearefastenedatbothtombstonetowersandeachpartfaceisassignedtoaparticulartombstoneface.Withoutthesolutionobtainedfromthispaper,onewill randomly fasten thepartona tombstone tower. Inaddition, it iscommonthatonetombstonefixture foronetypeofwork‐part,notamixedpart.Therefore, theprocessplannerwillnotbeabletogeneratethemostoptimalprocessplanduetothework‐partsetupconstraint.Thispaperthereforeadvancesafurtherstepintheprocessplanningresearchfield.AccordingtoTable7,theresultedoptimaloperationsequenceis18‐17‐15‐6‐7‐16‐…..‐5.Inotherwords,thefirstoperationsequenceintheplanisoperationnumber18whichisadrillingopera‐tionwithtoolnumber5.Notethattheoperation18islocatedatpartface6whichisfastenedattombstoneface2.Thesecondsequence isoperationnumber17usingthesamecuttingtoolasthefirstsequence.Next, thecuttingtoolwillbechangedtotoolnumber4 inordertoperformanotherdrillingoperationnumber15.

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Table6SummaryofpartandfixturesetupresultTombstoneface Part Partface Operation

i j k1 Manifold 4 10,9,82 Console 6 18,17,15,163 Console 8 204 Manifold 3 6,75 Console 5 12,11,13,146 Manifold 1 3,2,17 Console 7 198 Manifold 2 4,5

Table7Summaryoftheresultobtainedfromtheoptimizationmodel

Sequence Operationno. Toolno.Machiningtime

(min)Toolchangetime(min)

Tooltraveltime(min)

Tombstonefacechangetime(min)

m k l MTkl TC TTkk' TFCii'1 18 5 1 ‐ 0.4 ‐2 17 5 1 0.5 ‐ ‐3 15 4 1 ‐ 0.1 0.64 6 4 1 0.5 ‐ ‐5 7 6 2 ‐ 0.1 0.66 16 6 2 0.5 ‐ 0.67 20 7 7 ‐ 0.2 0.68 10 7 7 ‐ 0.2 ‐9 9 7 7 0.5 ‐ ‐10 8 8 5 ‐ 0.4 211 12 8 3 ‐ 0.4 ‐12 11 8 3 ‐ 0.4 ‐13 13 8 240 0.5 ‐ ‐14 14 9 480 0.5 ‐ 0.615 19 7 7 0.5 ‐ 0.616 3 5 1 ‐ 0.2 ‐17 2 5 1 0.5 ‐ ‐18 1 2 15 0.5 ‐ 0.619 4 3 3 ‐ 0.2 ‐20 5 3 3 ‐ ‐ ‐ 790 4.5 2.6 6.2

Totalproductiontime(min) 803.3Afterthat,thetombstonepalletrotatesfromface2toface4inordertoperformthedrillingop‐erationnumber6.Next, thecutting toolwillbechanged to toolnumber6 inorder tooperateoperationnumber7andthenrotatethetombstonetoface2inordertoperformmachiningop‐erationnumber16bythesamecuttingtoolnumber6.

Inbrief,allthetwentyrequiredmachiningoperationsarecompletedusingatotalofninecut‐tingtools.Thereisatotalofninetoolchangeswithsixtimestombstonerotationandonetomb‐stonechange.Thetotalmachiningtime is790min,andtoolchangetime, tool travel time,andtombstonefacechangetimeare4.5min,2.6min,and6.2min,respectively.Therefore,thetotalproductiontimeis803.3min.

5. Conclusion 

Thisresearchproposedtheintegerlinearprogrammingapproachtodetermineanoptimalsolu‐tionforamixed‐modelpartmanufacturedonamachiningcenter.Thismodelisapartofauto‐matedprocessplanning,whichhas longbeenresearchedbyusingvariousmathematical tech‐niques.Themathematicalmodelhasbeenverifiedbyanumberofexamplesinrealcasesanditisdeemedpractical.Theuniquenessofthisdevelopedmodelistheabilitytogeneratetheopti‐mal process plan with a simultaneous consideration of tombstone change for mixed‐modelparts.The mathematicalmodel thatwasdeveloped in this researchdealswith the complexityanddecisionmakingofTombstoneproblems.Inaddition,basedontheliteraturereview,noneoftheresearchhasaddressedthistypeofproblem. Thisresearchappliedthereal‐worldcasestudy

Kongchuenjai, Prombanpong

of automotive parts manufacturing. The two types of automotive parts under consideration compose of manifold inlet and console. The results provide the process planning that can simul-taneously produce two different part types. This mixed-model part consumes the minimum total production time. For future research work, the heuristics methods and mathematical relaxation techniques should be applied to solve the problems that have more machining operations, whereas the large-scale problems cannot easily be solved by general linear programming.

Acknowledgement Authors would like to thank Thai – German Institute (TGI) and Yamaha Motor Parts Manufacturing (Thailand) for providing relevant data used in the research.

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