Decision evaluation process in end-of-life systems management

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To link to this article: DOI:10.1016/j.jmsy.2015.03.007

http://dx.doi.org/10.1016/j.jmsy.2015.03.007

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http://oatao.univ-toulouse.fr/

Eprints ID:

15534

To cite this version:

Bouzarour-Amokrane, Yasmina and Tchangani, Ayeley and Pérès,

François Decision evaluation process in end-of-life systems management.

(2015) Journal of Manufacturing Systems, vol. 37. pp. 715-728. ISSN

0278-6125

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Technical

Paper

Decision

evaluation

process

in

end-of-life

systems

management

q

Yasmina

Bouzarour-Amokrane

a

_,

_Ayeley

_Tchangani

b,∗

_,

_Franc¸

_ois

_Peres

a

a_Universite_De_{Toulouse/INPT/LGP,}_47,_Avenue_d’Azereix,_BP_1629,₆₅₀₁₆_Tarbes_Cedex,_France

b_Université_de_Toulouse/IUT_de_Tarbes/LGP,_1,_rue_Lauréamont,₆₅₀₁₆_Tarbes_Cedex,_France

Keywords:

End-of-lifeproductmanagement

Reverselogistics

Withdrawalplan

BOCRanalysis

Satisficinggame

a

b

s

t

r

a

c

t

Inmanufacturingsectors,firmsarepayinganincreasingattentiontosustainabilityconceptwithregardto theirend-of-lifeproductsinordertorespectenvironmentalnormsandsatisfytheconsumersensitivity. Thispractiseallowscreatingvaluebyreintroducingdismantlingandrecoveringpartsand/ormaterialsof end-of-lifeproductsintomanufacturingprocess,orintomaintenanceprocess.Thus,deconstruction pro-cessesaredevelopedinordertoexamineallactivitiesaddressingtheendoflife(EOL)systemstoensure itsdisposalaccordingtoenvironmentalconstraintswhenseekinganeconomicoptimum.Inthiscontext, oneofthefirsttaskstoperformistorepatriatetheEOLsystemsatlowestcostconsidering geographi-caloptimizationoftreatmentcenters.Consideringthispoint,thepresentpaperproposesanevaluation andoptimizationapproachforthewithdrawallocationprocessinthefieldofaircraftdismantling.Given themultitudeandheterogeneityofcharacteristicstobetakenintoaccount,weproposetoconsider dis-mantlingsitelocationproblemasmulti-criteria/multi-objectivesdecisionmakingproblemandsolveit usinganewAHP-BOCRapproachbasedonqualitativeandquantitativeevaluations.Abipolar structur-ingframeworkisconsideredtodistinguishpositiveandnegativeaspectsintheelicitation/evaluation processtoavoidcompensationandsatisficinggametheoryisusedassuitablemathematicaltoolfor recommendationprocess.Anexperimentalstudyiscarriedouttoshowtheusefulnessofthe

1. Introduction

Firmsareincreasinglyinterestedinrecoveringusedproducts dueinparticulartogrowingenvironmentalawarenessof popula-tionandincreasingcustomerexpectationsofenterprisestodispose ofmanufacturedproductssafely[1].Consideredasthebestwayfor recoveringsomecategoriesofend-of-lifeproducts[2,3],theEOL managementbecomingpervasiveinsocio-economiclife,inorder toconsiderquestionsdealingwiththetransport,reuse, refurbish-ment,recycling,disposal,securestorage,valorization,or,scrapped ofEOLproduct[4,5].Theseactivitiesareincludedinthe decon-structionprocess[6]whichincludesservicesofproductreturning, recycling,materialsubstitution,reuseofmaterials,wastedisposal, refurbishing,repair,andremanufacturing[7].

Thedeconstructionprocessisdevelopedaspartofthereverse logisticswhichdiscussesfirst,theplanningprocessestablishment toimplementandcontrolrawmaterialflows,currentinventory,

q_Preliminary_version_of_this_paper_was_presented_at_IFAC_MIM₂₀₁₃_as_a

commu-nication.

∗ Correspondingauthor.Tel.:+330562444253;fax:+330562444219.

E-mailaddresses:yasmina.bouzarour@enit.fr(Y.Bouzarour-Amokrane),

ayeley.tchangani@enit.fr(A.Tchangani),francois.peres@enit.fr(F.Peres).

finished goods from thepoint of useto thepoint of recovery. Reverselogisticsalsodiscussestheselectionofproperdisposalsite andtheoptimizationofthedismantlingsystemsinordertoreduce thenegativeimpactofEOLproductsontheenvironmentandto increasebenefitsofmanufacturersthankstorecyclingandrecovery operations.

Intheaerospacesector,increasingnumberofend-of-lifeplanes requirestopaymoreattentiontotheeliminationphasebecause EOLaircraftscontainvaluablecomponentsandpartsthatcanbe reused and reintroduced in the aftermarket [8]. Moreover, the olderfleetmanagementandaircraftscrappingmustfacelegislative pressureintermsofenvironmentalprotectionlawsandeconomic benefits[5]generatedbypolicyofsustainableenvironment.These aspectsareconsideredascriticalfactorsinmeasuringthe contri-butionofafirmtosustainabledevelopment.Thus,environmental, economicandsocialfactorscanbeconsideredinreverselogisticsto evaluatetheefficiencyofimprovementactions.Forexample, eco-nomicfactorscanprovideinformationonthebenefitsofadopting reverselogisticsbymanufacturers.Wherecostsavingand improv-ingthecorporateimageallowtogaincompetitiveadvantageand toincreasetheenvironmentalperformance[9–12].

Amongtheissuesaddressedbythereverselogistics,the selec-tionofproperdisposalsitesconsistsinaerospacesectortochoose a withdrawal plan for the dismantlingEOL aircraft. This issue

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requiresoptimizingsomepreference indicatorssuchas,logistic costs,environmentaleffects,jobcreations,oreconomic enhance-ment.Thewithdrawaldesignphaseallowstoensuregeographical deploymentreducing,longdistanceof EOLsystemsrepatriation tothedismantlingsitesandlimitingtheirstorageneedsortheir processing capacity. This phase may take into account various parametersas:thecomplexityofthetransport,thedepthof dis-assembly(whichproductswillberecycled?)andthesequencing ofoperationsaccordingtosustainabledevelopment(howtoget theproductswhileminimizingthetimeandcostof deconstruc-tion,andmaximizingtheincomegeneratedbytheproductsofthe deconstruction?)[13].Anevaluationphasemustthenberealized tochoose thebest alternative among different existing decon-structionplaces.In fact,severalsites canbecandidatesfor the deconstructionoperationswhichleadtomanysolutionsintermsof logistics.Inthiscontext,thescrappedaircraftwithdrawalplan loca-tionproblemisconsideredinthispaper.Anewstructuredapproach isproposedtoresolvedecisionproblemofthescrappedaircraft withdrawalplanlocationconsideringanewflexiblebipolar con-text.Abipolarwayisproposedtoconsiderpositiveandnegative aspectsdistinctlyinordertoidentifythebestalternativeorthe mostsatisficingone.Thepotentialinteractionofdecisionelements andtheimpactofhumanbehavioronthefinaldecisionaretaken intoaccount.Giventhelargevolumeofdatainvolvedinsolvingthe scrappedaircraftwithdrawalplanlocationproblem,thispaper pro-posestoresolveitbyusingamulti-criteria/multi-objectivedecision approachbasedonAHPmethodwhichoffersarobust hierarchi-calstructure.TheAHPprocessisadjustedtomeettheneedsand tominimizecomplications.BOCRanalysisbuiltuponthebipolar notionofsupportingandrejectingthatcharacterizedrelationships betweenattributesandobjectivesisdemonstratingitspowerasa structuringtoolfordecisionanalysis,seeforinstance[65–69]for somemodelingmethodsandapplicationsbasedonthisnotion.The BOCRanalysisconsideringbenefit,opportunity,costandrisk fac-torsisassociatedtoAHPmethodinordertoconsideruncertainty aspectinadequatewithdrawalplanidentification.Thisapproach allowsdistributingthedataacrossfourdistinctfactorsthusforming lessvoluminousclustersreducingthenumberofpairwise compar-isonattheoperationallevel.Thepotentialinteractionsbetween problemcharacteristicsareconsideredusingChoquetintegral.The proposedmodelallowsalternativestobecharacterizedby hetero-geneouscriteriaandmanageincomparabilitybetweenalternatives intermsofPareto-equilibriausingsatisficinggametheoryin rec-ommendationphasewhereafinalselectionisgivenaccordingto positiveandnegativecontribution.

1.1. Literaturereviewoffacilitylocationproblems

Thefacilitylocationframeworkcanconsiderdifferentcontexts involvingmultiproductandmultistagereverselogisticsnetwork problemfor the return products [14], evaluating green supply chainalternatives[15,16],recoveryplanninglikethe determina-tionofthedisassemblylevel [17],or theelaborationof catalog distributorstoreducecostsfromreturnsprocessing[18].The facil-itylocation problems includingremanufacturing are frequently encounteredintheliteratureandsolvedusingseveralapproaches goingfromoptimizationtomulticriteriaevaluation.Forexample, in [19], authors used p-median methodto calculate the mini-mumweighteddistancefrompmanufacturing/remanufacturing facilitiesto n demandlocations consideringthe minimum effi-cientscaleforenvironmentalandeconomicperformance.In[20], authorsproposesaconceptualframework,ananalyticalmodel,and athree-stagealgorithmicsolutionbasedonp-medianapproach. Theobjectivewastodeterminetheoptimalnumberandlocation ofreceivingcantersandthecorrectfinancialincentiveinorderto stimulatecollectionofusedorunrecoverableproductstoarequired

degree.Inordertolocaterecyclingcentersandtoassigncollection depotstothosecenters,authorsin[21]propose2-stagelocationset coveringproblem–p-medianintegratedmodelthatobtainsexact solutions using heuristic algorithms onthe basis of set opera-tions.TheMixedintegerprogrammingmodel[22–24]isanother optimizationapproachusedtocapture,forexample,component commonalityamongdifferentproductstohavetheflexibilityto incorporateallplausiblemeansintacklingproductreturnsusing amulti-commodityformulationanduseareversebillofmaterials

[25].Insomefacilitylocationproblems,fuzzycontextisconsidered

[26–28]totakeintoaccountriskwhichinfluencesthesupplychain designandmanagementandwhichcanberelatedtouncertainty embeddedinthemodelparameters(whichaffectstheproblemof balancingsupplyanddemand)and/or,naturaldisasters,strikesand economicdisruptions,orterroristicacts.Theoptimization meth-odsoffercomplextechnicalresolutionleadingtoafinal‘optimal’ solutioncharacterizingtheinstructiongivenbytheanalystonce theresolutioniscomplete.However,thesemethodsarenotalways applicableandflexibleforcomplexproblemswithalargevolume ofdata.Forp-medianmethodforexample,itisdifficulttosolve theinstancesofverylargesizesandtheassociatedclassicallinear relaxationtothisproblem.Formixedintegerprogrammingmodel usingintegervariablesmakeanoptimizationproblemnon-convex andthereforefarmoredifficulttosolve.Memoryandsolutiontime mayriseexponentiallyasmoreintegervariablesareadded.

Themulticriteriacontextisproposedasanalternativeinsome studies withfuzzy TOPSISmethod [29], AHPapproach [30,31], ELECTREIIImethod[32],orfuzzycompromiseprogramming[33]

todealwiththevaguenessofhumanjudgmentsanddetermine marginalutilityfunctionforeachcriteriatoconsiderscalingand subjectiveweightingissues.Itisarguedthattheselectionofa facil-itylocationisamulti-criteriadecision-makingproblemincluding bothquantitativeandqualitativecriteria.Thissupportstheuseof multicriteriamethodsasthosegivenabove.However,some meth-odsalthougheasytoimplement,canberestrictive,dependingon theproblemconsidered.Forexample,TOPSISmethodbased on idealandnon-idealnotionhasthedisadvantageofonlyconsidering cardinalcriteriawherepreferencesarefixedaprioriandmethod providesthebestactionamongthepoorifallthealternativesare notsatisfactory.FortheAHPmethodbasedonhierarchical struc-tureandlinguisticscale,alargenumberofdecisionelementscan increasethenumberofpairwisecomparisonsandarankreversal problemcanoccurwheretwo actionscanviewtheirorder pri-orityreversedafteraddingordeletingoneorseveralactions.For outrankingELECTREIIImethodusingavetothreshold,the com-plexityliesinthelargenumber oftechnical parametersand in theinterpretationwhichmaybedifficult.Moregenerally,complex decisionproblemconsideringamultitudeofobjectives,avariety ofconflictingandoftenheterogeneouscriteriaandmultipleactors withdifferentopinionsandpersonalities,inapotentiallyuncertain environmentmakemulticriteriamodelingnecessarytoconsider simultaneouslyalltheseaspects.Compromisesarethenrequired toachievearesponse.However,themulticriteriamodeling pro-posedinliteratureconsidersgenerallythatelicitationofcriteria isindependentofalternativesandobjectives,whichisnotalways trueinpractice.Ontheotherhand,aggregationmethodsareused torepresentalternativewithauniquevalue.Thiscompensatory approachdoesnotdistinguishbetweenthepositiveandnegative aspectsthatalternativespresentregardingobjectives.

Theremainderofthis paperis organizedasfollows:Section

2introducesthecharacteristicsofdeconstructionprocesses. Sec-tion3 addressesthestructuredframework methodfor analysis developmentstartingwithanintroductionofproposedAHP-BOCR approachand, detailedthenthestepsofaggregationphaseand the basis of the satisficing game theory used on the recom-mendationphase.Section4providesanexampleofapplication.

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Section5concludesthearticleand discussessomeperspectives andguidelinesforfutureworks.

2. Deconstructionprocesscharacteristics

Deconstructionprocessisasystemthatinvolvesallactivities addressing the EOL system to ensureits disposal according to environmentalconstraintswhenseekinganeconomicoptimum. Itconsistsofasetofphysical,human,informationandenergy enti-ties.Hardwareresourcescanbestructuredhierarchicallyfollowing thedecompositionofthemainsystemsubassembliesand individ-ualcomponents[34].Thedevelopmentandimplementationofa deconstructionsystemisacomplextaskthatrequiresthe realiza-tionofadeconstructionproject.Ingeneral,adeconstructionproject aimstodefinethemanagementofEOLsystemsinordertoachieve objectivessuch as the valuationof their components, proposi-tionofregenerativeactiveproducts,themasteryofoperationsfor ensuringthesafety,disassemblyanddismantling,aswellasthe separationofhazardouscomponentstoensurethesafetyofthe environmentandtraceabilityofreusepartsfromdeconstruction.

Theobjectivesofadeconstructionprojectaremainlyexpressed intermsofoperationscontrolforensuringthesafety, disassem-blyanddismantling,recoveryofmaterials(formulatedasrecovery ratesgenerallyrangingfrom70%to95%)andtraceabilityofreuse ofpartsfromdecommissioning.Toachievetheseobjectives,three phasescanbedistinguishedinadeconstructionprocess[34,37]

(seeFig.1):

1.Reverselogisticsphase:thefirststepdealswithreverselogistics activities;theEOLsystemisoutofservice,stored,cleanedand, dependingonthetypeofsystem,decontaminatedandsecured untilitsmanagement.TheobjectivehereistorepatriatetheEOL systemsatlowestcostconsideringgeographicaloptimizationof treatmentcenters,thinkingaboutparkingplaces,ortransport modes.

2.Dismantlingphase:whentheEOLsystemarrivestotheselected site, dismantling activities can be implemented. First, parts whichcanbereusedarerecoveredand sentinarepair shop beforebeingrecycled.TheDislocationisthenrealizedby sep-arating the system components according to the nature of

materials,theirformattingforhandling(cutting,batchtraining). Thedislocationcanalsodealswithdrainingthesystemandthe removalofpollutantsandhazardousmaterials.Thegoalisto recoverthecomponents(suchasengine,landinggear, equip-ment)thatcanbepotentiallyreusedononehandand,incaseit isnotpossibleornoteconomicallyworthy,toextractreusable materials(suchasaluminum,alloys,plastics).Thisstepallows theproductionofvaluableproductsrepresentinganaddedvalue intheprocess.

3.Valorizationphase:wheretreatmentofEOLsystempartor mate-rialisrealizedtogivethemavalue.Therearegenerallyfourtypes ofrecovery.

-functionalrecycling:reinstatetheproductsresultingfromthe deconstruction;

-materialrecycling:reusingthematerialcomponentsoftheEOL system;

-energy recovery: incinerating of non-recyclable products obtainedfromdeconstructiontoproduceenergy;

-packagingandstorageofhazardousproductsandproductsthat cannotbevaluedinenvironmentalfriendlyconditions.

Our workis a partofthe implementationofthe firstphase of deconstruction process. The objective is to ensure optimal geographicaldeploymentof deconstructionsitewithlowercost considering,geographicoptimizationoftreatmentcenters, reflec-tiononparkingsite,transportmodes,andtrafficpattern.

The determination ofdeconstruction site is a complex deci-sionproblemrequiringtoconsidercontradictoryobjectivesusually relatedtoeconomic,ecologicalandsocialnotions.Thefirst res-olution phaseconsists to form a committee of experts and to defineparametersand characteristicsoftheproblem. Consider-ingfixedobjectivesandinvolvedaspectsintheproblemselection, theidentificationofpotentialsitesisbasedonparameterssuch as;thelogisticschainoperations,resourcesneededtocarry opera-tions,possibletransportationmethods,thestoragecapacity,the economic parameters(suchas thecostand profitgenerated by eachpotentialsite),socialparameters(suchastheemployment creation) and environmental parameters (such as the level of pollutiongenerated).Toevaluatecharacteristicsofpotential with-drawalsites,severalcriteriarelatedtoeconomicprofit,valorization

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rate,and ecologicalbalancehavetobetaken intoaccount[13]. Basedonliteraturereviewsand practicalexperiences, the com-mitteeofexpertsdefineasetofindicatorssuchasthosesuggested below.

Economicindicators:relatedtocostsandrevenuesgenerated bythedevelopmentofadeconstructionsite.Costindicatorsinclude logisticcosts(suchastransportandconditioning),productioncost (deconstructioncost),managementcostsandadministrativecost. Revenuesindicatorsimplygenerallyvalorizationrevenuesrelated totheexpectedsalesforecasts,quantitiesofcomingproductsand monetaryvalues. Other revenues related to the potential ben-efits with the corresponding incomes as components sale and savingtaxescanbeconsidered.Theseindicatorscanbedetailed inquantifiablecriteriaforevaluation.Inlogisticcostsfor exam-ple,theevaluation of transport cost canconsider distance and cost/kmcriteriaincludingfuelcosts,transportationmaintenance, tolls,transportationtaxes(fixedcosts),andrentalcost-relatedto resources,travelinsurance,payrollserviceproviders–costof use-relatedtodepreciationof machineryor tools–travel time and resourceefficiency(variablescosts). Forconditioningcosts, sev-eralcriteriacanbeconsidered; theratioof qualifiedworkforce workcaninformsonthedegreeofworkcomplexityandthelabor costs,cost/hincludingenergyasfuel,gasandelectricity,rentalcost includingtariffsfor incurredservicesand toolsforconditioning (shearsorcranes).

Environmentalindicators:canbedividedintoqualitativeand quantitativeeconomicandnon-economicindicatorsfocusingon themeasurement ofphysical data,i.e.emissions,waste,energy andtransportation[36],orresidualwasteandenergy[24].Inthis paper,toassesstheimpactofthedismantlingprojectonindividuals andthebioticandabioticenvironmentaccordingtoenvironmental regulations,thepollutionindicatorsareconsideredinthe evalua-tionprocess.Therevalorizationandtreatmentindicatorssuchas recyclingandconfinementareproposedtoestimatebenefitsof dismantlingproject.

Thepollutionindicatorsconsidersomecriteriasuchas,pollution sources(tanks,vessels,piping,storageareasandwarehousing– drums,cans,bags–chronicoraccidentalspills,orwasteburied contaminatedsoil),transfermodeofpollution (possiblevectors arewatersurfaces,groundwater,air–spreadbythewind)and tar-getthreatenedor affected(humanbeings, faunaandflora).The impacton humans can bevisual (disruption duration, number ofaffectedpersons),respiratory(levelof airquality,number of affectedpersons),oracoustic(averagedecibel,numberofaffected persons).Theimpactonenvironment canbeestimated consid-eringquantityofwasteand itsimpact(onair quality,pollution of water sources, or soil pollution), or transport mode (fuels consumption).

The revalorization and treatment indicators can be evaluated consideringrecyclingcriteria(%recycledmaterials,%reused mate-rials),powergenerationandcontainmentofhazardousmaterials, numberofaccidentsperyear,averageseverityofaccidents,number ofemployeesinvolved,orlevelofstakeholdersatisfaction.

Social indicators: proposed to characterize the social per-formanceoftheprojectconsideringpositive (employment)and negativeimpact(perturbationsoraccidents)oftheprojectonthe society.Criteriaasvisual,acoustic,respiratoryperturbationsand accidentscanbeconsideredfornegativeimpactwhere positive impactcanbeestimatedconsideringsatisfactionlevelof stakehol-dersandnumberofhiredemployees.Thecompletelistofproposed criteriafordismantlinglactationproblemissummarizedinthelast section.

Theevaluationcommitteecanbecomposedbyseveralactors participatingin thedefinitionof dismantlingprocess. Themost importantstakeholdersmayberepresentedbythefollowing enti-ties[13].

Operatingcompanies:theyhaveexploitationrightsoftheEOF aircrafts withoutnecessarily being theirowners. The operating companyisthestartingpointofthedismantlingprocess.

Theownercompany:ithastheaircraftanditisresponsiblefor theselectionofdeconstructionsiteafteralternativesevaluation.

Dismantlingcompany:thecompanythatdealswith deconstruc-tion.Itdeconstructstheaircraftinaccordancewiththeowner.The Negotiationparametersincludecosts,dates,orprofits.

Otheractors:transportcompanies,cleaning,insurance, govern-mentorganizationsand/orNGOs.

Modelingadeconstructionsitelocationproblemmustintegrate all of the above elements and provide support for the imple-mentationofanoptimizationmethod.Indeed,forlargesystems withmanyrecoverytrajectories(alternatives),thedataevaluates potentialsolutionscanbeverylargeandautomatedsearchforan idealsolutioncanbenecessary.Tofindthewithdrawalplanthat meetsthefixedobjectiveswithoutviolatingtheregulations,the followingsectionproposetoconsiderthedismantlingsitelocation problemasamulticriteriadecisionproblemandresolveitusing bipolarapproachbasedonAnalyticHierarchyProcessandBOCR analysis.

3. Structuredframeworkforanalysis

Considering dismantlingsites aspotentialalternativesnoted A={a1,a2,...,an},theevaluationmethodmustquantifythe

capac-ityofeachsitetomeettheobjectivesofdecisionmakersnoted O={o1,o2,...,oq}.Toresolvemulticriteriadecisionproblem,the

literaturepresentsgenerallyalternativesbyacommonsetof crite-riaforallobjectives.However,inpracticetherearecaseswhere thecriteriaaredependentonalternativesand/orobjectives.The proposedapproachoffersthepossibilityofconductingelicitation ofcriteriaforeachpair(alternative,objective)inorderto quan-tifyalternativepotentialtoachievetheobjectives.Asetofcriteria for(ol,ai)isnotedCol(ai)={c₁oI,co₂I,...,cmoI}.Indecisionproblems,

characteristicsof alternatives maybe detailed in severallevels throughdetailedcriteriagoingformgeneraltooperationallevel. Oncequantifiablecriteriaevaluated,theoppositepathistakenby aggregating subsetsofeach level inorder toquantify potential ofalternatives(seeFig.2).Theformulationofcriteria hierarchi-cally,hasbecomethemainfeatureoftheanalytichierarchyprocess (AHP)developedbySaaty[37].Thishierarchyofcriteriaallowsthe analysttostructurethedecisionproblemprovidingusersabetter understandingandallowingthemtofocusonallocationofweights tothecriteriaandsub-criteria.Weproposeinthenextsectionto useAHPprocessinmodelingandevaluationphasesofproposed approach.Theevaluationresultsateachlevelareassumed nor-malizedintherange[0,1]in ordertomaintainasameorderof magnitudeforevaluations.Itisassumedthatalternative perfor-mancecan beassessedthrough a setof indicatorsnoted Io_l_(a

i)

toestimatethedegreeofachievementofobjectiveolconsidering

alternativeai(Eq.(1)).

Io_l_(a

i)=ϕol(col(ai)) (1)

where ϕo_l _represents_an_aggregation _measure_of _{correspondent}

component.

Theproposedapproachconsidersasocialchoiceproblemwhere decisionmakersseektoobtainafinaldecisionincollectiveway.In thiscase, basedontheproposedframework bytheanalyst,the roleofstakeholdersistoelicitcommonlytheproblem character-isticsintheelicitationphaseandthenevaluatethemdepending ontheirdiscipline,knowledgeandexperience.Theselection pro-cessesofcriteriaarestructuredhierarchicallywhereglobalcriteria aredetaileduntiloperationallevel.Thenumberofconsidered crite-riaisnotlimitedinthisapproach.However,itisclearthatalarge

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Fig.2.Hierarchicalstructurationofcriteria.

numberofparameterswouldmaketheprocessmorecomplicated andlengthy.

Thestagesofthecorrespondingdecisionmakingproblemareas follows:

1.Actorsselectobjectivesandindicatorstomeasuretheirdegree ofachievement.

2.Potentialalternativesareidentifiedbyactors.

3.For each pair(objective, alternative),actorscan determinea setofcriteriathatpermittheevaluationofanalternativewith regardtoanobjective.

4.Alternativesareevaluatedwithregardtoobjectivesfor recom-mendations.

TheaimofthispaperistodevelopanewAHP-BOCRapproach basedonqualitativeandquantitativeevaluationstostructureand solvedismantlingsitelocationproblem.Theanalytichierarchy pro-cess(AHP)proposedby Saaty[38] allows solvingcomplex and unstructureddecisionproblems froma pairwise comparison of relativecriteriaunderahierarchicalstructure.Toevaluatethe fea-sibilityofdismantlingsitesinstallation,aBOCRanalysis(seefor instance[65]),isassociatedtoAHPmethodtoanalyzealternatives basedonBenefit(B),Opportunity(O),Cost(C)andRisk(R)aspects simultaneously.In theproposed bipolar approach, the positive criteriaofbenefit (certain)and opportunity(uncertain)andthe negativecriteriaofcost(certain)andrisk(uncertain)are synthetiz-ingdistinctivelythroughtheselectabilityandrejectabilitynotions in order to rankalternatives considering positive and negative impactsrespectively,beforetherecommendations.Wedefine pos-itive/negativecriteriain termsof supporting/rejectingobjective achievementascriteriapositively/negativelycorrelatedwiththe variationofconsideredobjective.Elicitationofpositive/negative criteriainBOCRframeworkcanbedonebyansweringquestions as“whatarethecertain/uncertaincharacteristicsthatrepresent

a benefit/opportunity(cost/risk) in using the alternative ‘ai’ to

achieveobjective‘ol’?”.Twodistinctgroupsareidentified:

-thesetofcriteriasupportingtheachievementof objective‘ol’

noted Co_l

s(ai),whereCsol(ai)=C_bol(ai)∪Cool(ai).This setincludes

benefits criteria noted Co_l

b (ai) and opportunity criteria noted

Co_l

o(ai).

-the set of criteria rejecting the achievement of objective ‘ol’

noted Co_l

o(ai)where Crol(ai)=Ccol(ai)∪Crol(ai).This setincludes

costcriterianotedCo_l

c (ai)andriskcriterianotedCrol(ai).

The AHP-BOCRevaluation method and therecommendation phasearedevelopedinthenextsection.

3.1. AHP-BOCRevaluationapproach

First introduced by Saaty in the 70s, theanalytic hierarchy process hasbecome one of themost commonly usedmethods inmulticriteriadecisionliterature[38].TheprincipleoftheAHP methodis todecompose a decisionproblemintodifferent ele-ments grouped in clusters, in a linear hierarchy starting from generaltoparticular.Criteriaare detailed untilreaching opera-tional level that allows alternatives evaluation [39]. Saaty also proposedaBOCRanalysismethodtoletdecisionmakersdealing withbenefits,opportunities,costs,andrisks[40–42].Thedegree ofobjectiveachievementmaybedescribedbythesefourfactors

[43]whereeachoneisrepresentedbyasetofcriteriadetailedin subhierarchygoingfromgeneraltooperationallevel.Considering bipolarrelationships,strengthassessmentusingAHP-BOCR analy-sisisobtainedbydistinguishingpositive(selectabilitynotion)and negative(rejectabilitynotion)factors.Pairwisecomparisonis car-riedouttoquantifytherelativeimportanceofeachelementwith respecttotheobjectiveachievement(Fig.2).

Therelativeimportanceisobtainedforeachelementbya pair-wisecomparisonwithrespecttoanelementoftheupperhierarchy

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Table1

AHPscale.

Qualitativescale Numericalvalues

Equallyimportant 1

Moderatelymoreimportant 3

Stronglymoreimportant 5

Verystronglymoreimportant 7

Extremelymoreimportant 9

Intermediatescales(compromise) 2,4,6,8

Fig.3. ParametersofproposedAHP-BOCRapproach.

levelusingaratioscalesuchasanAHPscaleshowedinTable1. Unlikeintervalscales[44],theratioscaledoesnotrequireanyunit. Theevaluationcanbemadefromaverbaljudgmentrepresenting arelativevalueorsameunitquantityfraction.Thisapproachhas beenwelcomed bypsychologists whoconsidereasierand more accuratetoexpresstheiropinionbyconsideringonlytwoelements insteadofasetofelementssimultaneously[45].

In theevaluationphase,a setofparametersmustbe quanti-fiedbydecisionmakers(Fig.3)todeterminetheperformanceof eachalternative.The detailedevaluation oftheseparameters is discussedbelow.

Step1.Identificationofweightparameters

TheevaluationofthedecisionproblembytheAHPprocedure startswiththeassessmentoftheobjectiveimportanceconsidering theoverallgoal[39].Apairwisecomparisonofthesetof objec-tivesisachievedbyansweringquestionssuch“howimportantis objective‘ok’comparedtotheobjective‘ol’withregardtothe

over-alldecisiongoalnotedO.”TheAHPscalegiveninTable1isused toobtainapairwisecomparisonmatrix noted(˝O_(l,_l′₎₎

q×q (see

below),where˝O_(l,_l′₎_corresponds_to_relative_importance_of_the

objectiveolcomparedtotheobjectiveol′.

˝O₌ o1 o2 ... oq o1 o2 .. . oq







1 ˝_1,2k,O ... ˝k,O_1,q ˝k,O_2,1 ... ˝k,O_l,l′ ... .. . ˝k,O_l′,l =1/˝ k,O l′,l ... ... ˝k,O_q,1 ... ... 1







Thismatrixmustbeconsistentandsatisficingtransitivity condi-tiononallcomparisons.Thismeansthatthematrix˝O_must_satisfy

thefollowingconditions˝O_(l,_l)₌_1,_˝O_(l,_l′₎₌_1/˝O_(l′_,_l)_and_˝O_(l,

l′₎₌_˝O_(l,_l′′₎_·_˝O_(l′′_,_l′₎_(for_more_details_see_[46,45]_)._If_the_matrix

isperfectlyconsistent,theconditionoftransitivity˝O_(l,_l′₎₌_˝O_(l,

l′′₎_·_˝O_(l_’_’_,_l′₎_is_satisfied_on_all_comparisons._To_avoid_checking_the

consistencyafteranarbitrarymatrixconstruction,weproposea straightforwardapproachthatleadstoaconsistentmatrix[39]: -selectapivotobjectivenotedop

-compareotherobjectivestothispivottoobtainscores

v

(l,p)(from Table1)forallotherobjectivesj=/ p

-generatethematrix˝O_with;

˝O_(l,_{p) =}_(l,_{p) ,}_˝O_(p,_{l) =}_{1/ (l,}_{p) ,}_˝O _l,_l′′

=˝O(l,p) ˝O _p,_l′′

=˝O(l,p) /˝O _l′′_,_p

₍₂₎

Therelativecomparisonvector‘ωo_’_is_calculated_using_Eq.₍₃₎_.

ωO_(o l)= 1 q q

X

l′′₌₁

!

˝O_(l,_l′′₎

P

i=1 q ˝O(i,l′′)

"

(3) TherelativeimportanceofindicatorsIo_l_(a

i)givenanobjective

ol,

∀

ol∈O,isthenevaluatedbythewayofapairwisecomparison.

Foreachalternativeai,therelativeimportancevectorof

indica-torsIo_l_(a

i)forobjectiveolisnotedωiol.Thisvectorisobtainedfrom

aconsistentmatrixnoted˝ol

i (Eq.(3)).InBOCRframework,the

degreeofrelativeimportanceofcriteriawithrespecttothe objec-tivesisnotedωo_l

×whereωo×l(cj)representstherelativeimportance

ofcj∈C×ol(ai)foreachcategory×=b,o,c,r.Thevectorωo×l canbe

obtainedinthesamewayasvectorsωo_l

i andω

O_.

Step2.Alternativeevaluation

Theevaluationmatrixofthealternativenotedo_l

×considering

differentsub-setsofcriteriaCo_l

×(×=b,o,c,r)canbeobtainedin

twoways:

Foragivencriteria,iftheevaluationofthealternativeis quan-titativewithco_l

j (ai)theperformanceofalternativeaiwithregard

toco_l

j ,thenthepairwisecomparisonmatrix˝ col

j

× foreachcategory

×=b,o,c,risobtainedthroughEq.(4). ˝colj

× (ai,ai′)=c_jol(ai)/cjol(ai′) (4)

Otherwise,thepairwisecomparisonmatrix˝c×olj foreach

cate-gory×=b,o,c,rcanbeobtainedusingAHPmethodbyanswering questionslike“whatistheperformanceofthealternativeaiin

com-parisontoalternativeai′ consideringthecriteriaC_jol?”.Thevalues

oftheevaluationmatriceso_l

×arecalculatedfromtheEq.(5)[39].

ol ×(ai,cojl)= 1 n n

X

i′₌₁





˝c ol j × (ai,ai′)

P

i′′˝ col j × (ai′′,ai′)





(5)

OncetheAHPprocedurehasbeencarriedoutconsideringBOCR analysis,theperformanceevaluationofalternativesisrepresented byb,o,c,rfactorsobtainedafteraggregation.Theproposed aggre-gationphaseisdevelopedinthenextpart.

3.2. Aggregationphase

Theaggregationconceptisacommonfeatureforall multicri-teriadecisionproblemsevaluationproceduressuchas;thetheory ofmulti-criteriautility(MAUT)andoutrankingmethods.InMAUT procedure,one-dimensionalutilityfunctionsareaggregatedinto anoverallutilityfunctionbycombiningallthecriteria,whereas in outranking methods (such as ELECTRE), preference relations areaggregatedbypairalternatives(see[47,48]).Toaggregatea setofdataandrepresentthembyasinglevalue,themostused aggregationmethodistheaverageweightedarithmetic[49–51]. Thismethodhasthedrawbackofignoringtheinteractionbetween

(8)

theaggregatecomponents,asthesynergy,redundancyor inde-pendence. To remedy this, fuzzy integrals were then put up. Consideringpositiveandnegativeaspectsdistinctlyinproposed approachpromotessynergisticrelationshipsbetweenthecriteria ofeachcluster.Inthiscontext,weproposetheuseofChoquet inte-gral[52,47]asaggregationtooltoconsidertheconceptofsynergy ineachset.

3.2.1. TheuseofChoquetintegralinproposedapproach

TheChoquetintegral isgivenby‘GustaveChoquet’(Choquet 1954)andintroducedintothefuzzymeasurecommunityby ‘Muro-fushiandSugeno’[53].Itisconsideredasanadequatesubstitute totheweightedarithmeticmeanbecauseitproposestodefinea weighttoeachelementandeachsubsetofelements[49].Theuseof theChoquetintegralasanaggregationtoolofinteractingelements inmulticriteriadecisionproblemshasbeenproposedbyseveral authors[54–57,47].Weproposetousethisintegraltoaggregatea dataoftheproposedbipolarhierarchicalapproach.

LetX={x1,x2,...,xn}bethesetofnumericallyvaluedelements

toaggregatebyChoquetintegral,toconsiderpotentialinteractions, afuzzyorcapacitymeasurenoted‘

v

’mustbedefinedasfollows:

Definition1(:). Let2x_be_the_power_set_of_X,_a_function

_v

_:₂x_→

[01]isacapacityorafuzzymeasureoverXifitverifies: i)v(∅)=0,v(X)=1,

ii)S⊆T⇒v(S)≤v(T),

∀

S,T⊆X

iii)For eachS⊆X,v(S)canbeinterpretedastheweightofthe importanceofthecombinationofelementsofthesetS(relative weightstoS).TheChoquetintegralofvectorxofelementsof thesetXassociatedtothecapacityorfuzzymeasureisgiven byEq.(6).

Cv(x):=

n

X

i=1

{

v

(A_(i))(x_(i)−x(i−1))} (6)

where(.)isapermutationoverasetXsuchasx(1)≤...≤x(n),x(0)= 0andA(i)={(i),...,(n)}.

FormoredetailsontheaxiomaticcharacterizationsofChoquet integrals,interestedreaderscanconsultthefollowingreferences:

[58,52,50].ThedifficultyofcomputingChoquetintegralistodefine afuzzymeasureoverthesetXthatnecessitatesobtaining2x₋₂

coefficientsthatrepresentthemeasureofsubsetsofXotherthan ∅and X.Whentheclassificationofelementscanberealizedby assigningthemrelativeimportancenormalizedweights,we pro-posetouseaweightedcardinalfuzzymeasure(WCFM)thatleadsto astraightforwardformulaforthecorrespondingChoquetintegral

[54].

Definition2(:). Aweightedcardinalfuzzymeasure(WCFM)over Xassociatedtoarelativenormalizedweightsvectorω=[ω1,ω2,

...,ωn]isgivenbyEq.(7).

v

()= || |X|





X

j∈ ωj





(7) whereisasubsetofX.

Itisstraightforwardtoverifythatthisfunctionfulfillsconditions ofacapacityorfuzzymeasure.LetusdenotebyCω_(x),_the_Choquet

integralofnumericalndimensionvectorxassociatedtoaWCFM withrelativevector,thenthisintegral,isgivenbyEq.(8).

Cω_(x)₌

X

n k=1











_n₋(k₋1) n





X

j∈A_(k) ωj









(x(k)−x(k−1))







(8)

where (.) indicated a permutation on the set X such as x(1)≤...≤x(n),x(0)=0,andA(k)isdefinedbyA(k)={(k),...,(n)}.

UsingpresentedChoquetintegral,theaggregationlevelsof pro-posedmodelcanbesummarizedbythefollowingalgorithm.

Aggregationalgorithm

Inputdata

ωO_relative_importance_vector_of_objectives

ωol

i relativeimportancevectorofindicators

ωol

×relativeimportancevectorofcriteriacj∈Col

×(ai)foreachcategory×=b,o,

c,r

ol

×evaluationmatrixofthealternativeconsideringsub-setsofcriteria

Col

×,where×=b,o,c,r

Outputdata

B(ai),O(ai),C(ai),R(ai)benefit,opportunity,costandriskevaluationmeasures

ofalternativeai

1:Foreachalternativeai

2:Foreachobjectiveol

3:ForeachindicatorIol

×k∈I

ol

×,where×=b,o,c,randk=1,¯twheretis

dimensionofIol

×

4:Foreachcriteriacol

j ∈C×ol(ai),where×=b,o,c,r

5:Evaluationofalternativesperformanceconsideringcriteriaforeach

indicator Iol ×k(ai)=aggreg(c ol ×(ai)) Endforcol j(ai)

6:Evaluationalternativesperformanceforeachobjective

×ol(a_i)=aggreg(Iol ×_k(ai)),where×=b,o,c,r WhereIol ×(ai)=aggreg(Io×lk(ai))withI ol ×k(ai)=ϕ ol(col ×(ai)),×=b,o,c,r EndforIol ×k

7:Evaluationalternativesperformanceforeach×factor

×o_(a

i)=aggreg(×ol(ai))

Endforol

Endforai

Theselevelsofaggregationallowrepresentingeachalternative withb,o,c,rfactors.Theaggregationfunctionaggregisreplacedby theChoquetintegral.Forexample,theaggregationofcriteriaonan indicatorIo_l

×_kmaybegivenbythefollowingexpression:

Iol ×_k(ai)=aggreg(co×l(ai)) =

X

m× k=1











_m ×−(k−1) m×





X

col j ∈C×ol ωo_l ×(cojl)









ol ×(ai,cojl)_(i)−×ol(ai,cojl)_(i−1)







(9) where×=b,o,c,randm×isthedimensionoftheconsideredcriteria

set.

Giventhebipolarnatureofthecriteria,weproposetheuseof satisficinggametheoryasflexiblerecommendationtoolforfinal evaluationprocessinordertorepresenteachalternativewitha supportingmeasure(representedbybenefitandopportunity)and rejectingmeasure(representedbycostandrisk).Inthefollowing,a briefdescriptionofthesatisficinggametheoryispresentedbefore addressingtheapplicationexample.

3.3. Satisficinggametheory

Thephilosophybehindthemajorityofthetechniquesusedin theliteraturefortheconstructionofanevaluationmodelisbased onthesuperlativerationality[59]inwhichallalternativesmustbe comparedtoeachotherintheaimofoptimalityseeking.However, decisionmakersinsolvingrealworldproblemsdonotnecessarily seektheoptimalsolution,oftencostlyintermsoftimeandmoney, butasatisfactorysolutionwhosecapabilitiesareestimatedfairly goodregardingtoobjectiveachievement[60].Thesatisficinggame theoryisbasedonthisobservationandprovidesadequatetoolsfor theselectionofacceptablealternatives.Theconceptofbeinggood

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enoughissuitableforourapproach,whereanalternativecanbe consideredgoodenoughwhenitssupportingcontributionexceeds therejectingone.Tothisend,eachalternativeaiwillbe

charac-terizedbyaselectabilitymeasureS(ai)thatestimatestheextent

towhichaicomplieswiththeoverallgoalandrejectability

mea-surer(ai)thatrepresentsthecostassociatedwithalternativeai.

InBOCRframework,theselectabilitymeasurecorrespondstothe aggregationofbenefitandopportunityfactorsandtherejectability measurecorrespondstotheaggregationofcostandriskasshown inEqs.(10)and(11)[61].

s(ai)=ıB(ai)+(1−ı)O(ai) (10) r(ai)=(1−ı)C(ai)+ıR(ai) (11)

whereB(ai),O(ai),C(ai),R(ai)aretheevaluationresultsof

alterna-tiveaiconsideringrespectively,benefit,opportunity,costandrisk

factors.

0≤ı≤1:istheriskaversionindex.Itpermitstoconsiderthe riskaversionattitudeofadecisionmakeronselectionphase.The moreıiscloseto1,thegreateris therisk aversionofdecision makerwho,beingpessimistic,willtendtogivemoreimportance toriskthancostinrejectabilitymeasure(Eq.(11))andpenalize opportunityinfavorofbenefitinselectabilitymeasure(Eq.(10)). Inversely,whentheriskaversionindex tendsto0,thedecision makerisconsideredasoptimistic.Hewillfocusonopportunityto benefitintheselectabilitymeasure,andwilloverlookriskagainst costintherejectabilitymeasure.

Finally,selectabilityandrejectabilityfunctionsaregiven respec-tivelybythefollowingEqs.(12)and(13).

s(ai)= s (ai)

P

v i∈A s(

v

_i) (12) r(ai)=

P

r(ai) v i∈A r(

v

_i) (13)

Thesatisficinggametheoryischaracterizedbyseveralsetsthat canbeusedonrecommendationphasetoselecttheproposed solu-tion(s).

ThesatisficingsetSq⊆A(ataboldnessorcautionindexq)isthe

setofalternativesdefinedasfollowing(Eq.(14)).

Sq={ai∈A: s(ai)≥qr(ai)} (14)

q: is the caution index used to adjust the aspiration level. IncreasingqallowsreducingthesizeofsatisficingsetSq(iftoomany

alternativesaredeclaredsatisficing).Onthecontrarydecreasingq leadstoagrowingsatisficingset(ifSqisemptyforinstance)(Fig.4).

Asensitivityanalysiscanbeperformedtodeterminethe ‘thresh-old’valueofcautionindexnotedqminbelowwhichallalternatives

aresatisficingandthemaximumvalueofthecautionindexnoted qmax abovewhichnoalternativeis satisficing.For allsatisficing

Fig.4. Graphicalrepresentationofasatisficingset.

Fig.5. Graphicalrepresentationofnon-dominatedalternatives.

alternatives,theinequality(15)mustbecheckedsuchas,for cau-tionindexqthereisSq=A.

s(ai)≥qr(ai),

∀

ai∈A⇔q≤qmin=min ai∈A

_s(a i) r(ai)

(15) Onthecontrary,thereisnosatisfactoryalternativeSq=∅ifand

onlyiftheinequality(16)belowissatisfied. s(ai)hqr(ai)

∀

ai∈A⇔qiqmax=max

a_i∈A

_s(a_i)

r(ai)

(16) Letusnoticealsothatsometimessomesatisficingalternatives can be dominated by others alternatives presenting a higher selectabilitymeasureandalowerrejectabilitymeasure.Toidentify thesealternativesanequilibriumsetεisdefinedasfollows. ε={ai∈A:D(ai)=} (17)

whereD(ai)isthesetofalternativesthatarestrictlybetterthanai.

ThesetD(ai)isdefinedwithEq.(18)(Fig.5).

D(ai)=Ds(ai)∪Dr(ai) (18)

whereDs(ai)andDr(ai)aredefinedasfollows:

Ds(ai)={ai′∈A:r(ai)<r(ai)ands(ai)≥s(ai)} (19)

Dr(ai)={ai′∈A:r(ai)≤r(ai)ands(ai)>s(ai)} (20)

Thesatisficingequilibriumsetεs

qisgivenbyEq.(21).

εs

q=ε∩Sq (21)

The satisficingequilibrium set εs

q constitutes a Pareto

equi-librium which means that the alternatives in this set are incomparable.Agraphicalrepresentationofthealternativescan bedoneintheplane(s(ai),r(ai))asshowninFig.6.The

sat-isficingParetosetisgivenbytheportionlocatedonthehatched curveabovethestraightlinebetweenthesatisficingandnot sat-isficingalternatives.Consideringadiscretenumberofalternatives, theproposedapproachisbasedonsimpleParetofrontalgorithm wheresatisficingalternativesareidentifiedfirstbycomparingtheir selectabilityandrejectabilitymeasures.Then,thenon-dominated setsofalternativesareidentifiedbyconsideringdistancesbetween alternatives.Theparetofrontierareobtainedthereafter consider-ingtheintersectionofsatisficingandnon-dominatedalternative.

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Intherecommendationphase,therankingortheselectionof finalsolution(s)canbeobtainedfromsatisficingequilibriumset usingaselectioncriterion.Theselectionandtherankingarethe relativeevaluationoperations thatcanbeperformedontheset ofalternativesAthrougha selectioncriterianoted‘cs’[62].The selectioncriteriacanbedeterminedbyavaluefunctionnoted(ai)

definedintermsofselectabilitymeasuresandrejectability

mea-surer,asfollows([39]).

(ai)=(s(ai),r(ai))

∀

ai∈εSq (22)

Thevaluefunction(ai)cantakeseveralformsdependingonthe

decisiongoal,forexample:

sc1: (ai)=s(ai)−qr(ai)

∀

ai∈εSq (23)

thatgivestheprioritytoalternativeswithlargedifferencebetween theselectabilitymeasureandtherejectabilitymeasuregiventhe indexofcautionq,or

sc2: (ai)=s(ai)/qr(ai)

∀

ai∈εSq (24)

thatconsidersalternativeswiththelargestindexofcaution,or (25)(ai)=s(ai)

respect·(ai)=r1(ai)

∀

ai∈εSqthat gives

prioritytoalternativeswiththelargestselectability(respect. low-estrejectability);thislatercaseissuitablewhenoneofthemeasure isuniformlydistributedoveralternatives.Thevaluefunctioncan thenbeusedtoselecttheultimatealternativea∗

i asfollows(Eq. (26)). a∗ i =argmax a_i∈εS q (ai) (26)

ortorankalternativesusingtherelationgivenbyEq.(27)

ai<ai′⇔(a_i)≥(a_i)

∀

a_i,a_i′∈εS_q (27)

Thepreferencerelation<indicatesthatalternativeaiisbetterthan

alternativeai′.

Aglobalsensitivityanalysiswouldstudythevariabilityofinputs andtheirimpactontheoutputresult.Thisanalysiscanbeused tovalidatethe proposedand guide researchefforts and devel-opmentmethod.Giventhehierarchicaldecomposition,variation calculusfromoperationalleveltofinalmeasuresisrenderedeasy inachainingprocess;sothatasensitivityanalysisschemecanbe easilyconsideredinordertomeasuretherobustnessofselected alternative.

4. Casestudy

Thedevelopedapproachisappliedtosolvethescrapped air-craftwithdrawalplanlocationproblem.Thispaperinvestigatinga centralizedreversesupplychainstructuredue tothesignificant economicadvantageit hasinthecontextof localization strate-gies[63].Indeed,thecentralizedstructureallowsminimizingthe investmentsofrestatementprocesswhichoftenrequiresspecific testequipmentandaqualifiedworkforce,asemphasizesonreverse logisticsliterature.Inaddition,theconcentrationofreturnsinone placeallowseconomiesofscalebyvolumeeffectandawiderrange ofpossibilitiesforreworkandthereforeadditionalrevenue oppor-tunities[64].

Considering a bipolar context where positive and negative aspectsareevaluateddistinctly,AHPprocedurecombinedtoBOCR analysisisusedtoselectthemostsatisficingaircraftdismantling siteamongsevenpotentiallocationsindecisionproblem,discussed initiallyin[13].Thematerialsofconsideredproblemareadapted andre-organizedtotheapproachestablishedinthispaper.The overallgoalof theproblemis torepatriateanEOLaircrafttoa dismantlingplatform.Economic,environmentalandsocial objec-tiveshavebeenfixedbythegroupdecision.Theindicatorsused

0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 a₁ a₂ a₃ a₄ a 5 a6 a₇ Rejectability measures S e lec ta b il it y m ea su res

Fig.7. Alternativerepresentationin(r,s)planefor(ı=0.5).

tocalculatetheachievementdegreeofobjectivesareelicitedby decisionmakers for each objective and detailed in quantifiable criteriacharacterizingthealternativesinBOCRanalysisframework (Tables2–4).

The evaluation of alternatives using proposed AHP-BOCR approachstartswiththedeterminationofthedecisionparameter weights(objectives,indicators,criteria)usingapairwise compar-isonineachhierarchicallevel,Eqs.(2)and(3)areusedtodeduce parameterweights.Thenumericalevaluationofalternativesisthen realized,thepairwisecomparisonmatrixinthiscasearededuced withEq.(4).TheNumericalevaluation(quantitativeand qualita-tive)ofalternativeconsideringeconomicobjectiveforexample,is giveninTable5.

ConsideringBOCRframework,fromdifferentperformanceand weightsmatrices,aproposedapproachthroughEq.(5)hasbeen donetoobtaintheevaluationofeachalternativewithregardto criteriaintermsofmatricesol

×foreachcategory.TheBOCRanalysis

ofobjectivesisdeducedusingproposedaggregationmethodand summarizedinTable6.

Finally, considering all objectives, the selectability measure (benefitandopportunity)andtherejectabilitymeasure(costand risks)arededucedbasedonthesatisficinggametheoryformalism throughEqs.(10)–(13).Consideringthatdecisionmakershavean averageriskaversion(ı=0.5)giventheequalimportancetocertain parameters(benefitandcost)anduncertainones(opportunityand risk),theresultsaresummarizedinTable7andthegraphical repre-sentationofthealternativesisshowninFig.7.Showingalternatives positionsintheplane(s,r)maybeofagreataidforanalysis

(mainlywhenthereisagreatnumberofalternatives)asthisallows tovisualizeequilibria,satisficing,notsatisficingalternatives.For aparticularalternativeonecandeterminealternativesthatmay dominateit;thisinformation canbeusedtoguideasensitivity analysisprocessfortrade-offseekingforinstanceandfacilitates dialogbetweentheanalystandthedecisiongroup.

Assumingthatthecautionindex(redlineinFig.7)isequalto1 (q=1)withq∈[0,481,46],analternativeisconsideredsatisfactory ifitsselectabilitymeasureisgreaterorequaltoitsrejectability measure,thus,thesatisficingequilibriumsetinthiscaseconsists onalternativesa1,a3,a5,a6 whicharenotdominatedandhave

selectabilitymeasuregreateroftheirrejectabilitymeasures(εs

1=

{a1,a3,a5,a6}).Thegraphicalrepresentationshowsalsothat

alter-nativea2,althoughsatisfactory,isnotinequilibriumsetbecauseof

itsdominationbyotheralternatives.Thealternativea4is

consid-eredunsatisfactoryontheotherhand.

Asensitiveanalysiscanberealizedbyvaryingindexcaution q∈[0,481,46]toidentifystablealternatives;consideringthat deci-sion maker presents a low caution (q=0.6 for example), only alternative a4 is not satisficingbecause ofits low performance

andasatisficingequilibriumsetconsistsonεs

0,6={a1,a3,a5,a6}.

Conversely,whendecisionmakerpresentsahighcaution(q=1.2 for example), cautionexpressedis reflected in theselection of

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Table2

Evaluationdataforeconomicalobjective.

Factors Indicators Criteria Unit

Benefit Recycledproducts %Ofmaterialstoberecycled %

Priceorvalueofmaterialstoberecycled Euro/kg

Reusedproducts %Ofpartsofsystemstobereused %

Resalevalueofspareparts Euro/un

Energyvalue %Ofwaste %

Energyvalue Euro/kg

Resources %Ofuseofresources %

Distancetraveledwith1Toffreightwith1loffuel kmt/l

Volumeofthematerial Units

%Ofskilledlabor %

Opportunity Forecastorders Forecastquantityofpartsandsystemcomponents Units

Frequencycomponentsrequired 1/year

Volumeofthematerial Unities

Possibleprofits Profittaxes Euros

Profitappropriation Euros

Cost Transportationcost Placeofdismantlingdistance km

Cost/km Euro/km

Traveltime Days

Locationcost Euro

Costofpackaging Costofownership(depreciation) Euros

Workinghours Days

Hourlycost Euros

Parkingtimepriortothedismantling Days

Costofproduction Servicelife Days

Servicecost Euros

Administrationcost Managementcosts(doc,training) Euros

Risk Opportunitycost %Ofskilledlabor %

Resourcesinthebestalternative Euros

Volumeofthematerial Units

Table3

Evaluationdataforenvironmentalobjective.

Benefit Recycling/reuse %Ofmaterialstoberecycled %

%Ofpartsofsystemstobereused %

%Waste %

Presenceofhazardousmaterials /

Volumeofthematerial Unit

Valuerecyclablematerials Euro/unit

Resalevalueofcoins Euro/unit

Resources %Ofuseofresourcesused %

%Ofskilledlabor %

Opportunity Gain Distancetraveledwith1Toffreightwith1loffuel km*t/l

Volumeofthematerial Unit

Levelofstakeholdersatisfaction /

Cost Recycling %Ofwasteuntreated %

Numberofpeopleaffected Persons

Packaging Hourlycost Euros

Workingtime Days

Parkingtimebeforethedeconstruction Days

Cost/km Euros/km

Traveltime Days

Rentalcost Euros

Others Costofservice Euros

Managementcosts Euros

Servicelife Days

Risks Pollution Levelofairquality /

Levelofpollutionofwaterresources /

Levelofsoilpollution /

Others kwhconsumedbytonofcommodity kwh/m2

(12)

Table4

Evaluationdataforsocialobjective.

Benefit Comfort Levelofairquality /

Employment Numberofemployees Persons

Levelofstakeholdersatisfaction /

Yield Traveltime Days

Workinghours Days

Servicelife Days

Opportunity Employment %ofskilledlabor %

Environment Levelofairquality /

Cost Accidents Frequencyrateofaccidentswithstop 1000%

Severityrate %

Soundincident Numberofpeopleaffected Persons

Averagedecibel Db

Risk Pollution Levelofpollutionofwaterresources /

Presenceofhazardousmaterials

Infections Numberofpeopleaffected Persons

Table5

Numericalevaluationofalternativesconsideringcriteriaofeconomicobjective.

Criteriaofeconomicobjective a1 a2 a3 a4 a5 a6 a7 Unit

%Ofmaterialstoberecycled 0.55 0.4 0.63 0.68 0.65 0.08 0.25 %

Priceorvalueofmaterialstoberecycled 50 30 45 25 60 35 35 Euros/kg

%Ofpartsofsystemstoreuse 0.35 0.4 0.3 0.2 0.25 0.15 0.6 %

Resalevalueofspareparts 150 100 300 500 200 150 100 Euros/unit

%Ofwaste 0.08 0.25 0.05 0.1 0.08 0.03 0.13 %

Energyvalue 15 10 15 13 1 12 10 Euro/kg

%Ofuseofresources 0.85 0.65 0.9 0.825 0.75 0.6 0.66 %

Distancetraveledwith1Toffreightwith1loffuel 50 45 80 200 250 70 50 kmt/l

Volumeofthematerial 10,000 120,000 150,000 17,000 13,000 70,000 10,000 Units

%Ofskilledlabor 0.3 0.6 0.85 0.75 0.6 0.9 0.5 %

Forecastquantityofpartsandsystemcomponents 10,000 10,000 10,000 15,000 12,000 70,000 80,000 Units

Requiredcomponentsfrequency 40 30 60 50 40 55 50 1/years

Profittaxes 2000 1000 3,000,000 2000 15,000 5,000,000 150,000 Euros

Profitappropriation 45,000 10,000 400 100 150,000 50 50 Euros

Placeofdismantlingdistance 1500 300 2000 8000 1000 500 1000 km

Cost/km 15 40 25 10 60 45 20 Euro/km

Traveltime 16 7 15 30 10 13 12 Days

Locationcost 25,000 30,000 75,000 5000 50,000 15,000 5000 Euros

Costofownership(depreciation) 1000 15 25 35 40 45 Euros

Workinghours 3 15 5 20 7 10 15 Days

Hourlycost 120 300 45 100 90 75 50 Euros

Parkingtimepriortothedismantling 200 100 50 90 130 250 200 Days

Servicelife 260 150 100 90 150 300 350 Days

Costofservice 2,000,000 3,500,000 1,500,000 4,000,000 2,000,000 1,500,000 3,000,000 Euros

Managementcosts 10,000 150,000 70,000 5000 10,000 15,000 120,000 Euros

%Ofskilledlabor 0.3 0.6 0.85 0.75 0.6 0.9 0.5 %

Resourcesinthebestalternative 2,500,000 3,000,000 3,000,000 3,000,000 3,000,000 3,000,000 3,000,000 Euros

Table6

AHPevaluationmatrixforb,o,c,rfactors.

Objectives ol × a1 a2 a3 a4 a5 a6 a7 Economicobjectives ×=b 0.13 0.15 0.17 0.18 0.15 0.10 0.12 ×=o 0.08 0.12 0.24 0.04 0.20 0.26 0.06 ×=c 0.15 0.21 0.14 0.10 0.11 0.11 0.18 ×=r 0.10 0.14 0.17 0.15 0.14 0.17 0.13 Environmental objectives ×=b 0.13 0.14 0.16 0.16 0.15 0.13 0.12 ×=o 0.09 0.18 0.19 0.16 0.15 0.14 0.08 ×=c 0.03 0.19 0.11 0.36 0.07 0.06 0.15 ×=r 0.09 0.13 0.15 0.16 0.13 0.21 0.14 Socialobjectives ×=b 0.16 0.14 0.13 0.18 0.11 0.14 0.13 ×=o 0.13 0.16 0.15 0.13 0.14 0.14 0.15 ×=c 0.09 0.04 0.09 0.52 0.10 0.08 0.09 ×=r 0.06 0.09 0.10 0.52 0.06 0.08 0.08

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Table7

Selectabilityandrejectabilitymeasuresfortheconsideredapplication(ı=0.5).

Bipolarmeasures a1 a2 a3 a4 a5 a6 a7

s(ai) 0.118 0.149 0.178 0.138 0.152 0.156 0.108

r(ai) 0.090 0.140 0.130 0.285 0.104 0.121 0.130

Table8

Rankedalternatives.

Selectioncriteria Alternatives

a1 a2 a3 a4 a5 a6 a7 cs1 4 5 1 7 2 3 6 cs2 3 5 2 7 1 4 6 cs3 6 4 1 5 3 2 7 1 6 4 7 2 3 4 Finalranking 4 5 1 7 2 3 6 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 a 1 a 2 a 3 a₄ a 5 a 6 a 7 Rejectability measures S e le ct a b il it y m e a su re s

Fig.8.Alternativerepresentationin(s,r)planefor(ı=0.8).

alternativesthathavethelowestlevelsofrejectability,inthiscase satisficingequilibriumsetisεs

1,2={a1,a3,a5,a6}whentherestof alternativesis considerednon-satisficing.Thefinal solutioncan bededucedusingproposedselectioncriteriawithEqs.(23)–(25)

fromsatisficingequilibriumset(εs

1=εs0,6=εs1,2={a1,a3,a5,a6})

asshown inTable8where theultimatedominancestructure is givenbyEq.(28).

a3<a5<a₆<a₁ (28) Theproposedapproachinvolvesexternalfactorsofcautionand riskaversiontoexpressahumanbehaviorthatcansignificantly alterthefinalselection.Toillustratethis,weproposetoconsider twoextremecases,whena‘pessimistic’decisionmakerexpresses astrongriskaversion(ı=0.8)andthecaseofanoptimisticdecision makerwhoserateofriskaversionislow(ı=0.2).

Astrongriskaversionpushesgenerallythedecisionmakerto focusonsomecertaingainwhileavoidingrisk.Suchbehavioris reflectedintheproposedapproachbygivenmoreimportanceto riskin rejectability measureand focus onbenefit in selectabil-itymeasure.Forpessimisticdecisionmakersfocusingonpositive certainelement(benefit) and negative uncertainelement(risk) (ı=0.8),thesetofsatisficingequilibriumcontainsthefollowing alternatives(εs

0,8={a2,a3,a5,a1}),Fig.8.Notethatthealternative

a6isreplacedinthiscasebyalternativea2inthesatisficing

equi-libriumset.Thisisexplainedbythefactthatthebenefitandrisk providedbythealternative2aremoreimportantthanthose pre-sentedbythealternative6.Howevertheopportunityofferedby thealternative6isgreaterthanalternative2.

In thesecondcase (ı=0.2),seeFig.9,thedecisionmakeris optimisticandbetsonthepotentialofalternative(opportunity) neglectingthepossible risk.Thisleadstopreferopportunityto benefitin selectability measure andcost torisk in rejectability measure.When decisionmakers have a low risk aversion, one willnotethat thesatisficingequilibriumsetcontains thesame

0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 a₁ a₂ a 3 a 4 a 5 a₆ a₇ Rejectability measures S e le ct a b il it y m e a su re s

Fig.9.Alternativerepresentationin(s,r)planfor(ı=0.2).

satisficingequilibriumsetasforı=0.5(εs

1=εs0.2={a1,a3,a5,a6})

which means that the selected alternatives present a good evaluationonbenefit,opportunity,costandriskfactors.

Considering a risk aversion index, the final solution can be obtainedbytheselectioncriteriadefinedintheprevioussection and/orasensitivityanalysiswhichwouldmakevarytherisk aver-sionindexandselectthemoststablealternatives.Inthiscase,one caneasilyobservethatalternativea3 issatisficinganddominant

regardlessofriskaversion,itcantherefore beconsideredasan ultimatesolutionwhichjoinedthefirstanalysisbasedonvariation indexcaution.Incaseofgroupdecisionconflict,simulationof pos-siblescenariosallowsabetteranalysisofthealternativeandhuman behaviorimpactforabetterreflectionforaconsistentchoice. 5. Conclusion

Thispaperaddressedtheproblemofselectinga sitefor dis-mantlinganEOLaircraft.Afterhavingdescribedthedismantling process,amethodologyhasbeenintroduced.Consideringthe prob-lemasamulti-criteria/multi-objectivesdecisionproblem,theAHP procedurecombinedwithBOCRanalysishavebeenproposedto structureandaddresstheproblemissue.Giventhebipolarnature ofcriteriadistributedaccordingtobenefit,opportunity,costand risk factors,the satisficinggamestheory hasbeenproposedas theanalysistoolforthefinalrecommendationprocess.Therisk aversionattitudethatdecisionmakersmaypresentistakeninto accountinthemodelthroughtheriskaversionindex.Themain contributionofthisworkisrelatedtothestructuringframework makingeasiertheelicitationofproblemcharacteristicsinorderto evaluatethedifferentalternativesinthedismantlingsitelocation problem.Thedevelopedapproachalsoproposesaflexible recom-mendationtoolthatintegratesthehumanfactorintheevaluation andallowsanalyzeitsimpactbyconsideringdifferentscenarios.In therecommendationphaseselectablityandrejectabilitymeasures

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werecalculatedintegratingtheconceptof riskaversiontotake intoaccounttheimpactofthedecisionmakernatureonthefinal ranking.Thisaggregationrevealsthesignificantimpactthatthe natureofindividualscanhaveontheirfinalchoice.Thisapproach provideseaseofimmersiveexcursionandcanbeassimilatedto non-expertstoolwherethegraphicalresultshelpfacilitatedialog betweenanalystanddecisionmakers.Thisproposalcanbeadapted todeal with complex decisionproblems including a multitude ofcharacteristicsconsideringdesignofreverselogisticsnetwork asmultiproductand/ormultistagereverselogisticnetwork prob-lemsandalsoingeneraldecisionfieldsinvolvinggroupdecision. Althoughtheproposedflexiblemodelhassomenewfeaturessuch asthoserelatedtobipolarhierarchicalstructure,elicitationof crite-riaconsideringeachobjectiveandalternativeandintegrationof thehumanfactor,someweaknesscanbefeltwhenapplyingthe approachdevelopedinthispaperparticularlyduetotheamountof parametersthathavetobeelicitatedandtheinterpretationissues bydecisionmakersmainlywhentheyaretrainedindifferent back-grounds.Butiftheprocessisconductedbyananalyststepbystep, thesedifficultiesmaybereduced.TheinfluenceofEOLaircrafts characteristicsinthereversesupplychainanddisassemblychoices canbeconsideredinmoregeneralmodel.

Futureworkscanaddressontheonehandsomeimprovement consideringmoreflexiblebipolarstructurationbasedongraphical modelsasBayesiannetworktoaddresstheevaluation approxima-tionsforexample.Ontheotherhand,theevaluationand recom-mendationmethodsforgroupdecisionmakingproblemscanbe developedconsideringthatalternativesarerepresentedwithlocal preferencesofeachdecisionmakers.Themoregeneralapproach basedonbipolarcontextcanbedevelopedconsideringtheimpact ofhumannature(fear,egoism,riskaversion,orinfluence)in evalu-ationprocess.Therepresentationofinteractionsbetweendecision elementscanbedoneusinggraphicalmodelssuchas Bayesian networksthatcanbeusedtoaddresstheapproximationsrelated toindividualassessmentsand/ortherepresentationofinfluences betweendecisionmakers.Toachieveacommonlegitimatesolution forthegroupdecision,theconsensusprocessescanalsobe devel-oped.Thesatisficinggametheoryisaninterestingmathematical tooltoconsidertherecommendationphase.Asensitiveanalysis canbedevelopedtoshowtheimpactofinputsdataandpotential influenceondecisionmakersconsideringgroupdecisiononfinal results.Thankstotheflexiblenatureofthepresentedapproach,it wouldalsobeinterestingtodevelopitinsolvingstrategicgames problems.Moreelaborateprocessofachievingequilibriummaybe subjectoffuturedevelopmentsincooperativegamesandthe vari-ouscasesofcoalitionsforexample.Non-cooperativegamesarealso anuntappedfieldofapplication.Theseperspectivescanbeoffered forsolvingreverselogisticsproblemsmentionedabovebutalso decisionmakingprobleminmoregeneralfields.

Contributors

Studyconception anddesign:YasminaBouzarour-Amokrane, Tchangani Ayeley, Franc¸ois Peres; Acquisition of data: Yas-minaBouzarour-Amokrane;Analysisandinterpretationofdata: Yasmina Bouzarour-Amokrane; Drafting of manuscript: Yas-mina Bouzarour-Amokrane; Criticalrevision: Tchangani Ayeley, Franc¸oisPeres.

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