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ORIGINALRESEARCHOpenAccessBuildingamaintenancepolicythroughamulti-criteriondecision-makingmodelElaheFaghihinia1*andNaserMollaverdi2AbstractAmajorcompetitiveadvantageofproductionandservicesystemsisestablishingapropermaintenancepolicy.
Therefore,maintenancemanagersshouldmakemaintenancedecisionsthatbestfittheirsystems.
Multi-criteriondecision-makingmethodscantakeintoaccountanumberofaspectsassociatedwiththecompetitivenessfactorsofasystem.
Thispaperpresentsamulti-criteriondecision-aidedmaintenancemodelwiththreecriteriathathavemoreinfluenceondecisionmaking:reliability,maintenancecost,andmaintenancedowntime.
TheBayesianapproachhasbeenappliedtoconfrontmaintenancefailuredatashortage.
Therefore,themodelseekstomakethebestcompromisebetweenthesethreecriteriaandestablishreplacementintervalsusingPreferenceRankingOrganizationMethodforEnrichmentEvaluation(PROMETHEEII),integratingtheBayesianapproachwithregardtothepreferenceofthedecisionmakertotheproblem.
Finally,usinganumericalapplication,themodelhasbeenillustrated,andforavisualrealizationandanillustrativesensitivityanalysis,PROMETHEEGAIA(thevisualinteractivemodule)hasbeenused.
UseofPROMETHEEIIandPROMETHEEGAIAhasbeenmadewithDecisionLabsoftware.
Asensitivityanalysishasbeenmadetoverifytherobustnessofcertainparametersofthemodel.
Keywords:Preventivemaintenance,Age-dependentPMpolicy,PROMETHEEII,Bayesianapproach,PROMETHEEGAIABackgroundGlobaltrade,higherlevelsofautomation,andthedesiretoapplyleanproductionaresomefactorsthatincreasethedemandforeffectivemaintenance(SalonenandDeleryd2011).
Inrecentdecades,industrialandservicesystemshaverealizedthatestablishingapropermainte-nancepolicyplaysanessentialroleinachievingtheirobjec-tives(Cholasukeetal.
2004;vanderMeulenetal.
2008).
Itcanalsoleadtomaximizingtheirprofits(Alsyouf2009).
Oneofthemostimportantreasonsofconsideringmainte-nanceasacrucialconceptcanbeitslargecontributionofoperatingbudgetinorganizationswithheavyinvestmentsinmachineryandequipment(Tsangetal.
1999).
Moreover,becauseofthedevelopmentoftechnology,competitivein-dustrialandservicesystemsshouldmakeuseofmoreadvancedmachinerywhichneedhigherlevelsofmainte-nancebecausetheyaremorecomplexandmoredifficulttocontrol(Alsyouf2009).
Theroleofmaintenanceinmodernmanufacturingsystemsisbecomingevenmoreimpor-tantwithcompaniesadoptingmaintenanceasaprofit-generatingbusinesselement(SharmaandYadava2011).
Inordertoavoidfailuresatrandomtimesandtheeffectofsuchfailuresontheperformanceofsystemsthatappearasareducingproductionrateandlossofqualityoftheproducts,maintenancemanagementisrequiredtoreducethelossofsystemoperatingtimeandthenumberofde-fectivepartsproduced(Tsarouhas2011).
Maintenanceisbecomingacriticalfunctionalareainmosttypesoforganizationsandsystemsincludingcon-struction,manufacturing,transportation,etc.
Thisincrea-singroleofmaintenanceisreflectedinitshighcost,whichisestimatedtobearound30%ofthetotalrunningcostofmodernmanufacturingandconstructionbusi-nesses.
Assuch,planningformaintenanceisbecominganessentialpartofplanningforthewholeorganization(Al-Turky2011).
Therefore,commonpracticeslikerepairingasystemwhenthereisaproblemhavetobesubstitutedbymonitoringthesystemconditionandplanningthemain-tenanceintervals(CavalcanteandDeAlmedia2007).
Also,effectivemaintenancecanextendtheequipmentlife,*Correspondence:elahe_faghihinia60@yahoo.
com1DepartmentofIndustrialEngineering,IslamicAzadUniversityofNajafabad,Isfahan8514143131,IranFulllistofauthorinformationisavailableattheendofthearticle2012FaghihiniaandMollaverdi;licenseeSpringer.
ThisisanOpenAccessarticledistributedunderthetermsoftheCreativeCommonsAttributionLicense(http://creativecommons.
org/licenses/by/2.
0),whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperlycited.
FaghihiniaandMollaverdiJournalofIndustrialEngineeringInternational2012,8:14http://www.
jiei-tsb.
com/content/8/1/14improveequipmentavailability,andrestoretheequipmenttoagoodcondition(Swanson2001).
Well-definedmain-tenancesystemwillensureoptimalperformanceofthemachineries(Oberschmidtetal.
2010).
Therefore,itcannotonlyimprovethequalityofgoodsandservicesbutalsosatisfyandratherexceedcustomers'demandsespe-ciallyinservicesectors(OkeandCharles-Owaba2006).
Theimportanceofrunningpropermaintenancepoliciesinorganizationshasledresearcherstodefinemaintenanceinseveralways.
Forexample,Tsarouhas(2011)definesmaintenanceasatoolwhoseobjectivesaretoincreasethetimetofailureandreducetherepairtimeofequipment.
Al-Turky(2011)definesitastheactivitiesrelatedtomain-tainingacertainlevelofavailabilityandreliabilityofthesystemanditscomponentsandthesystemabilitytoper-formwithastandardlevelofquality.
Still,maintenancecanbedefinedasthecombinationofalltechnicaleffortswhichcanretainanitemorequipment,orre-storeittoanacceptableoperatingcondition(Dhillon2002;BritishStandardsInstituteStaff1993).
Withre-gardtothecriticalroleofmaintenanceinimprovingreliability,preventingunexpectedsystemfailuresandreducingmaintenancecosts,maintenanceandreplace-mentproblemshavebeenwidelystudiedfromdifferentperspectivesintheliterature,andseveralmodelshavebeenproposed(Wang2002).
Allofthemseektoelabo-rateondifferentmaintenanceproblemsandproposemorerationalsolutions.
Thispaperproposesamulti-criteriondecision-aidedmaintenancemodelwithregardtothreecriteriaimportanttoselectingthebestmaintenancepo-licy.
Theyaremaintenancecosts,reliability,andmainte-nancedowntimecriteria.
Thismodelnotonlyconsidersthevariousaspectsofamaintenanceproblembutalsoattendstothepreferenceofadecisionmaker.
Further-more,Bayesianapproachhasbeenappliedtoovercomefailuredatashortage.
Finally,asensitivityanalysishasbeenmadetoverifytherobustnessofcertainparametersofthemodel.
PreventivemaintenanceComplexequipmentandmachinerysystemsusedintheproductionofgoodsanddeliveryofservicescon-stitutethevastmajorityofcapitalinvestedinindustry(Savsar2011).
Astimepasses,themachinesageandunplannedfailuresoccur,causingthesystemperformancetodriftawayfromitsinitialstate.
Infact,nopieceofequip-mentorsystemcancontinuetofunctionwithoutfailureforever;however,carefullyitmighthavebeendesignedandmanufactured(SamarAliandKannan2011).
Systemdete-riorationisoftenreflectedinhigherproductioncostsandlowerproductquality.
Therefore,thefunctionofthesystemmustbeperiodicallyrestoredtothedesiredlevel;thisispracticallyachievedbymaintenanceoperations.
Propermaintenancecanincreasethereliabilityofapieceofequipmentorasystematregularintervals(SamarAliandKannan2011).
Suchmaintenanceisknownaspreventivemaintenance(PM);itisdoneperiodicallybeforethefailureofthesystem;hence,itisdifferentfromcorrect-iveorrepairmaintenance,whichiscarriedoutonlyafterthefailureoftheitemorthesystem(Savsar2011).
Tokeepproductioncostsdownwhilemaintaininggoodproductquality,PMisoftenperformedonsystemssubjecttodete-rioration(Savsar2011).
Theprobabilityoffailurewouldincreaseasamachineisaged,anditwouldsharplydecreaseafteraplannedPMisimplemented(Savsar2011).
Itshouldbepointedoutquicklythatthemaintenanceactionswhicharenormallyclassifiedascorrectivemain-tenance(CM)includeallactionsperformedasaresultofafailuretorestoreanitemtoaspecifiedworkingcondition,whilePMincludesallactionsperformedonanoperatingequipmenttorestoreittoabettercondi-tion(Oberschmidtetal.
2010).
Moreover,makinguseofCMcouldbecostlyfororganizationsbecausemostofthetime,CMtakesalongtimetohaveanacceptableef-fectonafailedsystemorcomponent(Nakagawa2005).
Thus,itcanbedisastrousforsomesystemswherefailuresandinterruptionscouldbedangerous.
Forexample,wecanconsidermilitarysystems,aircraft,andhealthsystemswhereasmallmistakecanleadtoahorribledisaster(CavalcanteandDeAlmedia2008).
Also,thecostsofapplyingCMinorganizationsareusuallythreeorfourtimesbiggerthanapplyingPM(Chitra2003).
So,itwouldbemorerationaltostudyPMmodelsasabasicconceptforthepurposeofpro-posinganoptimummaintenancemodel.
Inaddition,PMpoliciesareusedforcontextswherethecomponentfailurerateincreasesbyageandusage(CavalcanteandDeAlmedia2008).
PMmodelsAlthoughalotofmaintenancemodelshavebeencre-atedduringthepastdecades,therearefewmaintenancepoliciesonwhichalltheothermaintenancemodelscanbebased(Wang2002).
Thereisacategorizationpro-posedbyWang(2002).
Accordingtohim,therearesevencategoriesofmaintenancepolicies,ofwhichfivearepreventive.
Theyareage-dependentPM,periodicPM,failurelimit,sequentialPM,andrepairlimit.
Accordingtoage-dependentPMpolicy,aunitisreplacedatthepredeterminedtimeTorinthecaseoffailure,whicheveroccursfirst,whereTisaconstant(BarlowandHunter1960).
ThegiventimeTismeasuredfromthetimeofthelastreplacement(Wang2002).
AccordingtoperiodicPMpolicy,aunitispreventivelymaintainedatfixedtimeintervalsindependentofthefai-lurehistoryoftheunitandrepairedatinterveningfailureswhereTisaconstant.
FaghihiniaandMollaverdiJournalofIndustrialEngineeringInternational2012,8:14Page2of15http://www.
jiei-tsb.
com/content/8/1/14Accordingtofailurelimitpolicy,PMisperformedonlywhenthefailurerateorotherreliabilityindicesofaunitreachapredeterminedlevel,andinterveningfailuresarecorrectedbyrepairs.
AccordingtosequentialPMpolicy,aunitispreventivelymaintainedatunequaltimeinter-valsunderthesequentialPMpolicy.
Usually,thetimeintervalsbecomeshorterandshorterastimepasses,consideringthatmostunitsneedmorefrequentmain-tenancewithincreasedages.
AccordingtorepairlimitPMpolicy,whenaunitfails,therepaircostisestimatedandrepairisundertakeniftheestimatedcostislessthanapredeterminedlimit;otherwise,theunitisreplaced.
Healsoindicatesthattheage-dependentpolicycanbethemostcommonandpopularPM.
Inseveralrecentworks,age-replacementpolicywasextensivelystudied.
Theage-replacementpolicyanditsextensionsbelongtotheage-dependantpolicy(Wang2002).
Therefore,bytakingalookatPMmodels,wecanrealizethattherearealargevarietyofpreventivemain-tenancemodelsandtheirextensions,soitwouldbene-cessarytospecifyagivenproblemtoresolveinthiscontext.
Therefore,theage-replacementpolicyhasbeenchosenasthebasisforthisresearch.
Alsointhispaper,itisassumedthatthereplacementofapieceofequipmentorpartgivesthesystemagood-as-newperformance.
Inaddition,therearetworequisitesforPMimplemen-tationineachsystemwhere(CavalcanteandDeAlmedia2008):1.
Thereplacementcostofacomponent(cp)beforefailuresshouldbelessthanthecostofreplacementduetofailures(cf).
2.
Thecomponentfailurerateshouldincreasebyageandusage.
Thispaperproposesamulti-criteriondecision-aidedmodelwiththreecriteriawhichdealswiththeproblemofthereplacementtimes.
Itdeterminesthebesttimingandfrequencyforreplacingcomponentsbytakingintoaccountthreecriteria,whicharethetotalcostofmain-tenanceperunitoftime,thereliability,andthetotalmaintenancedowntimeperunitoftime.
Thus,afterchoosingthepolicyfollowedbythisresearch,itisim-portanttodescribetheimportanceofthesethreecriteriainmaintenancedecisionmaking.
Maintenancehasbecomeoneofthemostimport-antissuesinthemanufacturingindustryduetohighcostsinvolved(Savsar2011).
Inproductionsystems,main-tenancemanagersconcentrateonreducingmaintenancecosts(CavalcanteandDeAlmedia2008).
Inmanufacturingorganizations,maintenance-relatedcostsareestimatedtobe25%oftheoveralloperatingcost(Cross1988).
AccordingtoMaggardandRhyne(1992),themain-tenancecanrepresentbetween10%and40%oftheproductioncostinacompany.
Coetzee(2004)meansthatthenumbersshouldbe15%to50%.
BevilacquaandBraglia(2000)statethatmaintenancecostscanrepresentasmuchas15%to70%ofthetotalproduc-tioncost.
So,itseemsplausiblethatthemaintenancecostsmayverywellrepresentover15%ofthetotalpro-ductioncostinindustry(SalonenandDeleryd2011).
Thesefindingsshowthatmaintenancecostcannotbeignoredbymaintenancemanagers.
Butthereareseveralsituationsinsomeorganizationswhereothercriterialikereliability,availability,down-time,etc.
,playcriticalrolesinsystems.
Earlier,research-erswereusingtheoptimizationcriteriaasminimizingsystemmaintenancecostrate,ignoringthereliabilityperformance.
Infact,minimizingsystemmaintenancecostratemaynotimplymaximizingthesystemreliabi-litymeasures.
Sometimes,whenthemaintenancecostrateisminimized,thesystemreliabilitymeasuresarealsosolowthattheyarenotacceptableinpractice(SharmaandYadava2011).
AccordingtoCavalcanteandDeAlmedia(2008),intheservicessector,thedecisionmakercanshowapre-ferenceforminimizingundesirableconsequenceswhicharedifficulttomeasureinfinancialunits.
Becauseinthiscontext,thecustomerisindirectcontactwiththepro-duction,andfrequentinterruptionintheservicecannegativelyaffectthedesireofthecustomertoenterintoanewcontractwiththatsupplierorcanleadthecus-tomertocancelthecurrentcontract,whichisunaccept-ableincompetitivemarketstoday.
Generally,managerswouldliketoseetheirsystemrunasplanned,andanunscheduledeventsuchasamachinefailurewilldisruptthesmoothrunningoftheplant.
Some-times,themarketingdepartmentbringsemergencypro-ductordersforimportantcustomers,andasystemfailuremayresultinseverelosses(Chareonsuketal.
1997).
Therefore,lookingatthecostcriterionasthemostimportantfactortoestablishanoptimummaintenancemodelisaverydangerousperspectiveforindustrialandservicesystems,especiallyforsystemswherefai-luresandinterruptionscouldbedisastrous.
Itismore-overimpossibletocaptureallofasystem'seffectsinacostfunction.
Insomesystems,thereliabilitycriterionplaysanes-sentialroleandwhichmustbetakenintoaccountwhenanoptimummaintenancemodelistobeestablished.
Therefore,inanumberofsituations,maintenancema-nagersmeantoconsiderreliabilityasaseparatecriterion(Chareonsuketal.
1997).
Reliability,R(t),istheprobabilitythatacomponentorsystemwillperformitsdesignfunctionforaspe-cifiedmissiontime,giventheoperatingconditions.
FaghihiniaandMollaverdiJournalofIndustrialEngineeringInternational2012,8:14Page3of15http://www.
jiei-tsb.
com/content/8/1/14Table1Preferencefunctions(adaptedfromBransandMareschal2005)GeneralizedcriterionDefinitionParameterstofixPd0d≤01d>0&-Pd0d≤q1d>q&QPd0d≤0dp0≤d≤p1d>p8>:PPd1d≤q12qp8>:p,qPd0d≤qdqpqqp8>:p,qPd0d≤01ed22e2d>080;t>01Table2Model'sparametersca($)cb($)Tf(days)Tp(days)β1η1β2η21,00025030.
53.
404.
152.
802200Figure1GAIAplane.
Figure2Decisionmodelflowchart.
FaghihiniaandMollaverdiJournalofIndustrialEngineeringInternational2012,8:14Page5of15http://www.
jiei-tsb.
com/content/8/1/14whereηiscalledthescaleparameter;β,theshapepara-meter.
Inordertoestablishoptimummaintenanceinter-vals,weneedtorecognizethefailurebehaviorofsystemorcomponent.
Thus,theparametersofthefailuredistributionofsystemorcomponentshouldbeestimated.
Inordertoestimatethedistributionfunctionparameters,historicaldataareoftenused;therefore,alargequantityofdataisneededtoobtainreliableestimates.
Butbecauseoftherapidgrowthofindustry,oftensufficienthistoricalinformationaboutthecomponentsorsystemfailuresisnotavailable(ChenandPopova2002).
Often,onlyafewfailuredataareavailable,andinsomecaseswherethereareenoughdata,theyarenotreliable(Scarf1997).
Therefore,estimationparametersfromfailuredataisanotherdifficultyinmain-tenanceprogram(CavalcanteandDeAlmedia2008).
However,duringtheprocessofthesystemproductionanditsoperatingtime,reliabilityengineersandspecialistsfindoutbyintuitionaboutitsfailurebehavior(ChenandPopova2002).
Combinedwithactualobservations,thisin-formationcanprovidebetterassessmentofthefailurerateparameters.
Bayesiananalysisisonewaytoenterthisin-formationintothedecision-makingprocessinordertomakeamoreobjectivedecision.
Therefore,amajoradvantageofBayesiananalysisiswhenonlyafewdataareavailable.
Bayesianstatisticsprovidesawaytoincor-poratespecialistadviceaboutasystemintothemainte-nancemodel.
TheBayesianmaintenancemodelshavebeenusedfrequentlytoestablishmaintenancepoliciesinrecentdecades(CavalcanteandDeAlmedia2008).
SomeauthorssuchasJorgensonetal.
(1967),McCall(1965),DayanlkandGurler(2002),WilsonandBenmerzouga(1995),Sheuetal.
(2001),JuangandAnderson(2004),KallenandVanNoortwijk(2005),MakisandJardine(1992),McNaughtandChan(2011),andmanyothershaveusedthisapproachindifferentmaintenancemodels(Oberschmidtetal.
2010).
Finally,usingaWeibulldistributiontomodelfailureincasesofincompletedata,specialistknowledgecanbeused.
Therefore,theWeibulldistributionparametersareconsideredrandomvariableswithaprioridistributionsrepresentingspecialistknowledge:μ(η)andμ(β).
Figure3Criteriarelationships.
Table3Performancesofalternatives(gi(t))T(days)R(t)C(t)D(t)2000.
99041.
28740.
00303000.
97970.
88900.
00184000.
96430.
69960.
00145000.
94410.
59440.
00136000.
91920.
53150.
00127000.
88990.
49280.
00118000.
85660.
46900.
00119000.
81980.
45510.
00111,0000.
78020.
44780.
00111,1000.
73830.
44520.
00121,2000.
69470.
44580.
00121,3000.
65020.
44890.
00121,4000.
60510.
45340.
00121,5000.
56040.
45910.
00131,6000.
51620.
46540.
00131,7000.
47300.
47220.
00131,8000.
43140.
47920.
00141,9000.
39160.
48610.
00142,0000.
35380.
49300.
00142,1000.
31820.
49960.
00142,2000.
28490.
50600.
00152,3000.
25410.
51200.
00152,4000.
22580.
51790.
00152,5000.
19980.
52300.
00152,6000.
17620.
52740.
00162,7000.
15490.
53180.
00162,8000.
13580.
53570.
00162,9000.
11870.
53930.
00163,0000.
10340.
54250.
0016Table4CriteriathresholdsCriteriaThresholdspQReliability0.
03000.
1000Cost0.
01500.
2000Downtime0.
00110.
0001FaghihiniaandMollaverdiJournalofIndustrialEngineeringInternational2012,8:14Page6of15http://www.
jiei-tsb.
com/content/8/1/14AfterestimatingtheWeibullparameters,evaluationofthecost,reliability,andmaintenancedowntimecriteriacanbeobtainedusingthemodel,andthenamulti-criterionde-cisionwithPROMETHEEmethodscanbemade.
PROMETHEE:oneofthemulti-criteriondecision-makingmethodsBytakingalookatdecision-makingproblemsintherealworld,itcanbeseenthatmostofthemaremulti-criterion.
Decisionmakinginmanycontextsdependsonseveralcriterianotjustononecriterion.
Thiscanbeseeninmanyfieldssuchasindustries,economics,finance,orpolitics.
Makingdecisionsinmaintenanceprogramscanbeamulti-criteriondecisionproblem.
AccordingtoShyjithetal.
(2008),selectingamainte-nancepolicybasedonafewfactorsmakesitunrealistic.
Thereisaneedtoconsidermaintenanceproblemsasmulti-criterion.
Thisoutlookcangiveacomprehensiveviewtomaintenancemanagement.
So,itcanbecriticaltoconsidermaintenanceproblemsasmulti-criterionespe-ciallyinsystemsthattakeintoaccountonlythecostcri-terionformakingamaintenancedecisionbecauseinsomesystemswithspecialconditions,itcouldresultindisasters.
Ifthemaintenancedepartmentonlywantstolookatthecostcriterion,itcouldleadittoignoringothercriterialikereliabilityormaintenancedowntime.
Amulti-criterionproblemismathematicallydefinedas(BransandMareschal1994a,b;Bransetal.
1984):Maxg1a;g1agiagkaaAjg;8whereAisafinitesetofnpossiblealternatives{a1,a2,an},and{g1(.
),g2(gk(.
)}isasetofevaluation-1-0.
8-0.
6-0.
4-0.
200.
20.
40.
620030040050060070080090010001100Scenario1Scenario2Scenario3Scenario4Scenario5Scenario6Scenario7Scenario8Scenario9Scenario10Figure5Netflowvalues.
Table5CriteriaweightsCriteriaWeights(%)Reliability35Cost40Downtime25Figure4PROMETHEEIIranking1.
FaghihiniaandMollaverdiJournalofIndustrialEngineeringInternational2012,8:14Page7of15http://www.
jiei-tsb.
com/content/8/1/14criteria.
Theyarecalledthebasicdataofamulti-criterionproblem(BransandMareschal1994a,b;Bransetal.
1984).
Inrecentyears,manydecision-aidmethodshavebeenproposed.
ThePROMETHEEmethodsareonegroupofthesemethodsconsistingofseven.
PROMETHEEme-thodsdevelopedbyBransareoneofthebestknownandmostwidelyusedoutrankingapproachesinmanyapplica-tions(MakisandJardine1992).
AcomprehensiveoverviewofapplicationscanbefoundinBehzadianetal.
(2010).
Ingeneral,outrankingapproachesarebasedoncomparisonsofpairsofalternatives(Oberschmidtetal.
2010).
ThePRO-METHEEmethodshavebeenfrequentlyusedinmanyfields,andtheirsuccessisduetotheirmathematicalpro-cessesandthefactthattheyareeasytousebydecisionmakers(BransandMareschal1994a,b;Bransetal.
1984).
Theinputrequiredconcernstheevaluationofthecriteriaforallofthealternativesconsideredaswellastheweight-ingsneededtoreflecttheirrelativeimportance.
InordertoapplyPROMETHEE,first,theperformanceofthealterna-tivesregardingallcriterianeedstobedetermined.
Then,alternativesarecomparedinpairsforeachcriterionbasedongeneralizedpreferencefunctions.
Basedontheweightedsumofsinglecriterionpreferences,positiveandnegativeoutrankingflowsarecalculatedasameasureofdominanceofalternatives.
Criteriaweightsreflectthesubjectiverelativeimportanceofthecriteria.
Basedonpositiveandnegativeoutrankingflows,apartialpreorderofalternativescanbedefinedaccordingtoPROMETHEEI.
ThenetoutrankingflowcanalsobecalculatedtoavoidincomparabilitiesanddefineacompletepreorderonthesetofalternativesaccordingtoPROMETHEEII(Oberschmidtetal.
2010).
Afterthat,PROMETHEEIIIthatranksalternativesbasedonintervalsandPROMETHEEIV,thecontinuouscase,weredevelopedbyBransandMareschal.
TheyalsoproposedthevisualinteractivemoduleGAIAin1988,whichprovidesaninterestinggra-phicalviewtosupportthePROMETHEEmethodology.
In1992and1994,BransandMareschalextendedthesetwotypes:PROMETHEEV,anextensionofPROMETHEEIandIIwhereasubsetofalternativeshastobeselectedbyconsideringasetofconstraints,andPROMETHEEVI,anextensionoftheresultsfromPROMETHEEIandIIthatprovidesthedecisionmakerwiththefreedomtothinkoftheweightintermsofintervals,ratherthanofexactvalues(BransandMareschal1994a,b;Bransetal.
1984;CavalcanteandDeAlmedia2008).
ThePROMETHEEIImethodhasbeenchosenforout-rankingresultsinthisresearch,andthePROMETHEEGAIAhasbeenchosenforavisualrealizationandsensi-tivityanalysisoftheresultsinthisresearch.
Thereasonsforselectingthesemethodsarefastuse,easy-to-analyzeresults,andaflexiblecomparisonprocess(CavalcanteandDeAlmedia2008).
Moreover,theinformationwhichneededtousePROMETHEEandGAIAiseasyandcleartodefinefordecisionmakers(Bransetal.
1984;BransandMareschal1994b).
TomakeuseofPROMETHEEmethods,first,thetwofollowingphasesshouldbepassed(BransandMareschal1994a,b;Bransetal.
1984;CavalcanteandDeAlmedia2008):1.
Calculatingtheevaluationofeachalternativeforeachcriterion:gi(a);and2.
Calculatingthedifferencesbetweentheevaluationsofthealternativeswithineachcriterion:dia;bgia–gib9WealsoneedtwotypesofadditionalinformationtorunPROMETHEE(BransandMareschal1994a):1.
Theinformationbetweenthecriteriathatconsistsoftherelativeimportanceofthedifferentcriteriaandwhichdependsonthepreferencesofadecisionmaker.
Theyareshownbywj,j=1,2,k.
Theyareconsideredasnormweights.
2.
Theinformationwithinthecriteriaisreferredtoassignapreferencefunctiontoeachcriterion.
Aftercalculatingthedifferencesbetweeneachtwoalternativesforacriterion,di(a,b),thedecisionmaker'spreferencesareneededtoidentifytheindifferencethreshold(q)thatisthelargestdeviationtoignoreandthepreferencethreshold(p),i.
e.
,thesmallestdeviationconsideredtobeaTable6ScenariosScenariosReliabilityweight(%)Costweight(%)Downtimeweight(%)12025552255520355202541045455454510645104571080108801010910108010333334Table7Scenario1t(days)2003004005006007008009001,0001,100(.
)0.
65230.
27510.
04420.
12670.
1980.
20290.
17120.
13050.
09370.
0486FaghihiniaandMollaverdiJournalofIndustrialEngineeringInternational2012,8:14Page8of15http://www.
jiei-tsb.
com/content/8/1/14preferencerelationbetweentwoalternatives.
Sointhisphase,decisionmakerselectsageneralizedcriterion,Fi(di(a,b)),tomodelhispreferencesforeverycriterion.
Afterspecifyingthefunctionparametersbythedecisionmaker,thepreferencefunctioncanbeobtained.
Pia;bFidia;bdia;b>010Pia;b0dia;b<011Therearesixpreferencefunctionssuggestedforde-cisionmakers.
Thesefunctionshavesatisfiedthecon-ditionsofmanyreal-worldproblems.
TheyareshowninTable1.
ThePROMETHEEIImethodhasbeenchosentorankthealternatives.
Thisrankingisbasedonnetflow(a)(BransandMareschal1994a;CavalcanteandDeAlmedia2008):a1n1XxAXkiPia;xPix;awi:12Therefore,eachalternativecangetthehighestscoreonthenetflowwhichisthebestcompromisesolution.
Becauseofconsideringthedifferencesditorankthealter-nativesinPROMETHEEII,moreinformationgetlost(BransandMareschal1994a,b;Bransetal.
1984).
Inordertoovercomeandhaveabetterrealizationofthesituationsofalternativesandcriteria,thispaperhasmadeuseofPROMETHEEGAIA.
TheGAIAplanewillbeshownandinterpretedinFigure1.
TheGAIAplanecanalsoprovideapowerfulgraphicalvisualizationtoolforadecisionmaker(Bransetal.
1984;BransandMareschal1994b).
Thespecificpowerofeachcriterion,theconflictingaspects,andtheattributesofeachalternativeonthediffer-entcriteriaareGAIAplane'sspecificqualities(Bransetal.
1984).
Finally,asensitivityanalysisusuallyservestode-monstratetheinfluenceofdifferentweightingsontheresultsoftheassessment(Oberschmidtetal.
2010).
ResultsanddiscussionsMathematicalconfigurationsofthecriteriaThegoalofthispaperistoevaluatethedifferenttimealter-nativesandrankthemaccordingtothedecisionmaker'spreferencesandtothevaluesofthethreecriteriaineachal-ternative.
Therefore,themathematicalconfigurationsofthesecriteriaareneeded.
Toachievethisgoal,themathema-ticalequationsofthesethreecriteriahavebeenillustrated.
Thefirstequationisthereliabilityformulawhichisbasedonreliabilitydefinition.
Itistheprobabilityoflackofacomponentorsystemfailurebeforetimet.
Thus,itismathematicallydefinedasfollows,wheref(t)isthedensityfunctionofthecomponentfailurebehavior:RtZ1tftdt2Thesecondandthirdequationsarethemaintenancecostandmaintenancedowntimeformulas,respectively.
TheywerecreatedbyJardine(1973).
Thedetailsoftheseformulasaredefinedasfollows:cp:Replacementcostbeforefailurecf:ReplacementcostduetofailureTp:ThetimetakentomakeapreventivereplacementTf:ThetimetakentomakeareplacementduetofailureCtCpRtCf1RttTpRtZt1xfxdx,1RtTf0B@1CA1Rt3DtTpRtTf1RttTpRtZt1xfxdx,1RtTf0B@1CA1Rt4Becauseoftheabsenceofthemaintenancedataanduncertaintyinbothparametersofthecomponentfailuredistributionfunction,specialistinformationcanbeusedtoestimatethem.
Hence,bymakinguseofBayesianapproach,theparametersofWeibulldistributionareTable9Scenario3t(days)2003004005006007008009001,0001,100(.
)0.
08590.
08240.
18550.
24520.
21850.
11020.
01670.
14520.
25450.
3396Table8Scenario2t(days)2003004005006007008009001,0001,100(.
)0.
58160.
34830.
14350.
07380.
19790.
22680.
20650.
16370.
12170.
0831FaghihiniaandMollaverdiJournalofIndustrialEngineeringInternational2012,8:14Page9of15http://www.
jiei-tsb.
com/content/8/1/14consideredrandomvariables,andtheirdistributionsshouldbeassessedfromthespecialistinformationonthesevariablesπ(η)andπ(β).
Becauseofuncertaintyonparametersηandβ,thecomputationsofreliability,cost,anddowntimecriteriashouldincorporatethedistributionsπ(η)andπ(β)thatfollowtheWeibulldistribution.
Hence,accordingtoCavalcanteandDeAlmedia(2008),reliabilityandcostcriteriaformulasfollowtheseequations:ERt;η;βZ1tZ11Z11πηπβfx;η;βdηdβdx5CtCpRtCf1RttTpRtZt1Z11Z11xπηπβfx;η;βdηdβdxTf1Rt6Attheendthethirdequation,whichcalculatesthemaintenancedowntime,thisequationfollows:DtTpRtTf1RttTpRtZt1Z11Z11xπηπβfx;η;βdηdβdxTf1Rt7ThedecisionmodelprocessUptothispoint,allthedetailsofthemodelhavebeendescribed.
Inordertodescribetheprocessofthemodel,thefollowing14stepsneedtobecompleted.
Theflow-chartofthemodelhasbeenbroughtinFigure2.
1.
DeterminethetimealternativesTibydecisionmakers,thosewhichareapplicablefordoingPM;2.
DetermineBayesianparametersβ1,η1,β2,η2;3.
Determinecp,cf,Tp,Tf;4.
Calculategi(a)whereg1=R(t),g2=C(t),g3=D(t)forallofthetimealternativesT;5.
Analyzethevaluesofthethreecriteriaanddeterminetheacceptablealternatives;6.
Calculatedi(a,b)=gi(a)–gi(b)foreachtwotimealternatives;7.
Determinewj,j=1.
.
3;8.
DetermineFj(di(a,b)),j=1.
.
3andtheirthresholds;9.
Calculateφ(ai)foreachtimealternatives;10.
Rankthetimealternativesbythevaluesofφ(ai);11.
DrawtheGAIAplane;12.
Analyzethesensitivityoftheresultsintovariationofwj,j=1.
.
3;13.
Choosethebesttimealternative;14.
StopNumericalapplicationInordertoevaluatethepracticalaspectsofthemodelandtoseethemodel'svalueinpractice,anumericalap-plicationwillbeneeded.
Infact,byanumericalexample,theeffectivenessofthemodelcanbeobserved,anddeci-sionmakerscangetabetterideaofit.
Therefore,thissectionpresentsahypotheticalexamplewhichisclosertotherealsituationofacomponent.
Thedataconsistofinformationaboutthepriordistri-butionsofηandβ.
Therefore,thereareβ1andη1whicharetheparametersoftheWeibulldistributionthatbelongstoβandβ2andη2,theparametersoftheWeibulldistributionthatbelongstoη.
Theyhavebeenobtainedfromspecialistinformation.
Also,thereplace-mentcostsbefore(cp)andafterfailure(cf),thetimetakentomakeareplacementbefore(Tp)andafterfailure(Tf)areneeded.
ThesevaluesareshowninTable2.
Also,thetimealternativesincorporatetheintervalbe-tween200and3,000dayswithanintervalof100daysbetweenthealternatives.
Theperformancesofthealter-nativesarecalculatedforthethreecriteriaandareshowninTable3.
ThecalculationsinrelationtoTable3havebeendonebymakinguseofMaple13software.
Inordertoseetherelationshipsbetweenthesethreecri-teriainthetimealternativeswhosevalueshavebeenpluggedinTable3,theyhavebeendrawnasthreecurvesinFigure3.
Thehorizontalaxesshowthetimealternativesfrom200to3,000daysandtheverticalaxesshowthevaluesofthreecriteriaineachthetimealternative.
Itisobviousthatthecostcriterionshouldbemini-mized.
AsseeninTable3andFigure3,thiscriterionTable11Scenario5t(days)2003004005006007008009001,0001,100(.
)0.
25560.
11510.
01840.
15780.
21040.
16520.
08470.
01070.
09540.
1597Table10Scenario4t(days)2003004005006007008009001,0001,100(.
)0.
82030.
45240.
18970.
05060.
19030.
25180.
26240.
25310.
24030.
2139FaghihiniaandMollaverdiJournalofIndustrialEngineeringInternational2012,8:14Page10of15http://www.
jiei-tsb.
com/content/8/1/14getsitsbestvalueinthetimealternative1,100days.
Also,thereliabilitycriterionshouldbemaximized.
AsseeninTable3andFigure3,itisdescendingduringthetimealternatives.
Infact,ithasitsbestvalueatpointzero.
Thedowntimecriterionalsoneedstobeminimized,andascanbeseeninTable3andFigure3,itgetsitsmini-mumvaluein1,200days.
Therefore,forthetimealterna-tivesgreaterthan1,100days,thecostcriterionincreasesduringthetimeandsimultaneouslythereliabilitycriterionisdescendingandthedowntimecriterionisincreasingduringthetime.
Therefore,evaluatingthealternativesgreaterthan1,100daysisnotuseful.
Theycannotresultinthebestcompromiseresponsebetweenthesethreecri-teria.
Hence,theycanbeneglected.
Finally,therearetenalternativeswhichneedtoberanked.
Therearethetimealternativesfrom200to1,100days.
InordertomakeuseofthePROMETHEEIIranking,thepreferencefunctionisdeterminedasthelinearfunc-tion,thefifthamongtheDecisionLabfunctions(accordingtoTable1),andithasbeenusedforallofthethreecri-teria.
Theirthresholdshavebeendeterminedaccordingtothepreferenceofthedecisionmaker,andtheyareshowninTable4.
Moreover,thePROMETHEEmethodsneedcriteriaweightswhicharechosenbythedecisionmaker.
TheweightswhichareassumedforthethreecriteriainthispaperareshowninTable5.
AfterdeterminingthewholedataneededinordertousetheDecisionLabsoftwareandrankthealternatives,theycanbeputinthesoftware.
DecisionLab2000isamulti-criterionanalysisanddecision-makingsoftware.
DecisionLab2000wasdesignedtobeappliedtovariousmulti-criteriondecisionproblemsanddesignedforallWindowsplatforms.
Afterputtingtherequireddatainthesoftware,itranksthetimealternativesimmediately.
ThePROMETHEEIIrankingisusedfortheten-timealternativeschosenasshowninFigure4.
Assaidbefore,thePROMETHEEIImethodranksthealternativesbycalculatingthe(.
)values.
Therefore,eachalternativecapableofgettingthehighestscorein(.
)isthebestcompromisesolution.
Figure5showsthatthebestcompromisesolutionisAction5whichpresentsthetimealternative600days.
Inordertoseethevaria-tionsbetweenthealternativesinthevalueofthenetflow,Figure5canbeillustrative.
Itshowsthatalternative600dayshasmadethehighestscoreinnetflow;therefore,itisthebestcompromisesolutionthatPROMETHEEIIhasdetermined.
GAIAplaneGAIAplaneisausefultooltoevaluateadecision-makingproblem.
Itcanshowtherelationshipbetweencriteriaandalternatives.
Inordertogetabetterunderstandingoftheproblem,theGAIAplaneoftheproblemhasbeenshowninFigure1.
Thealternativesareshownbytriangle-shapedpoints,andthecriteriaareshownbysquare-shapedpoints.
ThereisanaxisnamedPi.
ItiscalledthePROMETHEEdecisionaxis,namely,eachalterna-tivewhichisclosertothisaxisthantheothersisbet-tertochoose.
Criteria2and3showsimilarpreferencesbecausetheyareapproximatelyinthesamedirection.
Moreover,inGAIAplane,eachalternativewhichisclosertoacrite-rionshouldbegoodatthecriterion.
Itcanbeseenaboutalternative4atcriterion1,alternative5atcrite-rion3,andalternative6atcriterion2.
Itissoobviousthatalternatives1,2,3,and4arenotgoodatcriterion2oralternatives6,7,8,9and10arenotgoodatcriterion1.
Alternative6isbetweencriteria2and3;therefore,itisgoodatbothcriteria.
Alternative5isbetweencriteria1and3;therefore,itisgoodatbothcriteria.
ButseeninFigure1,alternative5isclosertoPithanothers.
Therefore,itshouldbethebestcompromisesolution.
AsseeninTable5,theseresultsareobtainedfromspe-cificweights.
Therefore,iftheweightschange,therankingwillchange.
ChangingtheweightswillonlychangethesituationofaxisPiandthesituationsofthecriteria,andthealternativeswillremainunchanged.
Therefore,itcanbeseenhowthisrankingissensitivetothevariationoftheweights.
Inordertoanswerthisquestion,asensitivityana-lysishasbeenmade.
SensitivityanalysisWithagoodsensitivityanalysis,itispossibletoobtainmoreinterpretativeresultswhichenhancethedecision-makerunderstandingofthemaintenanceproblemandtoevaluatewhethersolutionsproposedbythemodelaresensitivetoparameterchange.
Therefore,inthissection,Table13Scenario7t(days)2003004005006007008009001,0001,100(.
)0.
8320.
5940.
34030.
02890.
18690.
29410.
33320.
33580.
32890.
3163Table12Scenario6t(days)2003004005006007008009001,0001,100(.
)0.
24390.
02650.
16910.
23730.
21380.
12290.
01390.
09340.
1840.
2621FaghihiniaandMollaverdiJournalofIndustrialEngineeringInternational2012,8:14Page11of15http://www.
jiei-tsb.
com/content/8/1/14theresearchhastriedtotestdifferentweightstogetabetterideaabouttheproblem.
Forthepurposeofanalyzingthesensitivityoftheresultstothechangingweights,differentweightsneedtobechosenandtested.
Inordertochoosesomeweights,tenscenarioshavebeendefinedinTable6:Foreachscenario,thenetflowvaluesofthealternativehavebeencalculatedbyDecisionLabsoftwareandarebroughtinTables7,8,9,10,11,12,13,14,15,and16.
Itshouldbenoticedthatthevaluesinitalicsshowthattheyarethebestanswersofthosescenariosbasedonthemaximumvaluesof(.
)Moreover,toachieveavisualrealizationoftheresultsofnetflowsforthescenarios,theyareshowninFigure6.
Atfirst,itisobviousthatthevariationoftheweightschangestherankingofthealternatives.
Therefore,itisimportanttoproperlydeterminetheweights.
Thedeci-sionmakershouldstudytheconditionofthesystemcarefullyandthendefinetheweightsregardingtheirpreferences.
Withregardtothetables,itisobviousthatalternatives600daysand700daysaremorefrequentlyusedasthebestcompromisesolutions.
Forthepurposeofstudyingthebehaviorofeachcri-terion,theweightofthecriterioncanbechangedataconstantrate,andtheweightsoftheothertwocriterianeedtobechangesimultaneouslyequally.
Forthispur-pose,thefollowingeightscenarioshavebeendefinedforeachcriterion,andthemovementofthedecisionaxisPihasbeeninmind:Scenario1={20,25,55}Scenario2={25,55,20}Scenario3={55,20,25}Scenario4={10,45,45}Scenario5={45,45,10}Scenario6={45,10,45}Scenario7={10,10,80}Scenario8={80,10,10}Scenario9={10,10,80}Scenario10={33,33,34}So,theobservationofthebehaviorofthereliabilitycriterionshowsthatbymovingfromscenario1tosce-nario8,thedecisionaxismovesfromalternative800daystoalternative400days.
Theobservationofthebehaviorofthecostcriterionshowsthatbymovingfromscenario1toscenario8,thedecisionaxismovesfromalternative500daystoalternative900days.
Theobservationofthebehaviorofthedowntimecri-terionshowsthatbymovingfromscenario1toscenario8,thedecisionaxismovesfromalternative600daystoalternative700days.
Theseobservationsshowthatthetwocriteriaofreliabilityandcostareconflicting.
Also,thealternativedowntimedoesnotchangewidely.
Itonlymovesbetweentwoalternatives.
GapofresearchItisobviousthatresearchersinthefieldofmaintenancetrytomakethebestpolicythatismostcompatiblewiththeirsystems.
Thus,therearemanyresearchesinthisfieldwithdifferentfocuses.
Tsarouhas(2011)performsacomparativestudyofperformanceevaluationbetweenfourpizzaproductionlines.
Heestimatesthereliabilityandmaintainabilityofthelines,focusingonthemain-tenanceandrepairstrategiesnecessaryformaintenancestafftokeepequipmentoperatingattherequiredlevelofreliability,whichleadstothesituationwherelinesareoperatingmoreprofitablythroughreducedmain-tenancecostsandincreasedproductivityandefficiency(Tsangetal.
1999).
Savsar(2011)presentsapracticalapplicationofmodelingandanalysisproceduresformaintenanceoperationsinthecontextofanoilfillingplant.
Systemisanalyzedunderthecurrentandapro-posedPMpolicy,whichreducedtheequipmentdowntimeduetoCMs(SamarAliandKannan2011).
Mohideenetal.
(2011)presentsaproposaltominimizetherecoverytimeandthebreakdowncostinthesysteminacon-structionplant(McNaughtandChan2011).
SharmaandYadava(2011)reviewtheliteratureonmainte-nanceoptimizationmodelsandassociatedcasestudies(Scarf1997).
Theyconcludethatagoodresearchworkhasbeenreportedonoptimizationtobringdownmainte-nancecost.
Themaintenancecostoptimizationworkhasbeendoneonselectingmaintenancepolicies,equipmentavailability,sparepartsmanagement,workforceschedu-ling,andintervalofinspectionfrequencybasedondiffer-entsimulationmodel.
Thisfindingshowsthatinmostcasesothercriteria,likereliability,availability,downtime,havebeenignoredinthechoiceofamaintenancepolicy.
SharmaandYadava(2011)alsoshowthattheapplicationsTable15Scenario9t(days)2003004005006007008009001,0001,100(.
)0.
80860.
31080.
03910.
13010.
19370.
20950.
19170.
17050.
15160.
1114Table14Scenario8t(days)2003004005006007008009001,0001,100(.
)0.
32090.
36380.
37720.
34450.
23390.
03620.
16390.
35730.
51960.
6357FaghihiniaandMollaverdiJournalofIndustrialEngineeringInternational2012,8:14Page12of15http://www.
jiei-tsb.
com/content/8/1/14onDSSofoptimizationmodelsareverylimitedinindus-tryandnotmuchhasbeenfromliterature.
Asseenbefore,theapplicationofPROMETHEEinthisresearchisoneanswertothislack.
ApointofstrengthinthismodelisspecifyingperiodicfrequencyforPMoperationsbytheanalystsandthoseinvolvedinthesystem.
InthosemodelwhereoptimumtimeforPMoperationsiscalculatedbythemodelitself,ordinarily,theobtainedanswersandtheoutputofthemodelarenotimmediatelyapplicableandwouldneedadaptationsandmodifications,sincethemaintenanceoperationisnotperformedindependentlyandwouldre-quirecoordinationwiththeproductionandoperationssections,withproductionschedulingsection,andevenattimesotherengineeringsections.
Infact,theanswerproducedisnotapplicableandwouldgenerallyrequireconcurrencewiththeconditionsattheworkshop,andthisiswhilemodificationwoulddistanceouranswerfromoptimalconditions.
Inthepresentmodel,fre-quencyisdeterminedbeforehandbytheanalystandthoseinvolvedinthesystem,andtheiropinionsarethoroughlyincorporatedintothesystem;thus,theobtainedFigure6Sensitivityanalysis.
Table16Scenario10t(days)2003004005006007008009001,0001,100(.
)0.
44520.
18220.
00130.
14830.
20460.
18040.
12130.
05140.
01070.
0667FaghihiniaandMollaverdiJournalofIndustrialEngineeringInternational2012,8:14Page13of15http://www.
jiei-tsb.
com/content/8/1/14answersand,infact,theoutputofthemodelareim-mediatelyandwithoutanyalterationsapplicableandcanbeutilized.
ConclusionThispaperpresentsamulti-criteriondecision-makingmodelforpreventivemaintenanceplanningwhichdeter-minesthebestcompromisetimeforreplacementofacertainitembasedonmorethanonecriterion.
ThismodelalsoenvisionsthedifficultywiththeshortageofmaintenancefailuredatabymakinguseofBayesianap-proachandPROMETHEEIIfordecisionmaking.
Inmostcases,whenmaintenancemanagerstrytode-terminethebestpolicyfortheirsystems,theyonlycon-siderthecostcriterionasthemostimportantandtheonlycriteriontobetakenintoaccount.
Thisisaverydangerouspointofview.
Therefore,oneofthemostim-portantgoalsthatthispaperseekstoreachistogiveabroaderviewofthemaintenancemanagersbyconside-ringmorethanonecriterioninmakinganappropriatedecisionforreplacementofaniteminPMproblems.
Takingthesethreecriteriaintoconsideration,thispaperdoesnotimplythattheyarethemostimportantcriteriathatneedtobeconsideredforreplacementofaniteminPMplanning.
ItimpliesthatinordertomakeacompleteandtimelyPMplanningwhichconsidersmanyaspectsoftheproblem,decisionmakershavetostudytheproblemcompletelyandconsiderthefactorswhichaffectaPMplanningforreplacementofitembecauseignoringthein-fluentialfactorsindifferentsituationscanleadtodisas-trousresults.
Therefore,itisnottruetosaythattherearesomefactorswhichareimportantforallthesystems.
Moreover,changingtheweightsshowsthatfordifferentpreferencesofdecisionmakersanddifferentconditionsofthesystems,differentweightsareneeded.
Therefore,thestructureofthemodelcanbeappliedtodifferentsystemsandsituations.
MethodsInthissection,themethodsusedinthisresearchhavebeenreviewed.
Inthisresearch,multi-criteriondecisionmakingmethodshavebeenusedtomodelamainte-nanceplanning.
Threecriteriaasreliability,maintenancecost,andmaintenancedowntimehavebeenconsideredtomakethebestreplacementintervalsforpreventivemaintenance.
Inordertocompensatethelossofhisto-ricaldata,Bayesiananalysishasbeenused.
ThisresearchhaschosenPROMETHEEIImethodtooutranktheresultsbecauseoffastuse,easy-to-analyzeresults,andaflexiblecomparisonprocess.
Thismethodrequirescri-teriaweightsreflectingthesubjectiverelativeimportanceofthecriteriabydecisionmakers.
Inthisresearch,inordertoanalyzesensitivityandgraphicalvisualizationofresults,PROMETHEEGAIAhasbeenused.
CompetinginterestsTheauthorsdeclarethattheyhavenocompetinginterests.
Authors'contributionsBothauthorshaveparticipatedincompletingeverysectionofthepaperequally.
Allauthorsreadandapprovedthefinalmanuscript.
Authordetails1DepartmentofIndustrialEngineering,IslamicAzadUniversityofNajafabad,Isfahan8514143131,Iran.
2DepartmentofIndustrialEngineering,IsfahanUniversityofTechnology,Isfahan8415683111,Iran.
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JournalofIndustrialEngineeringInternational20128:14.
Submityourmanuscripttoajournalandbenetfrom:7Convenientonlinesubmission7Rigorouspeerreview7Immediatepublicationonacceptance7Openaccess:articlesfreelyavailableonline7Highvisibilitywithintheeld7RetainingthecopyrighttoyourarticleSubmityournextmanuscriptat7springeropen.
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