HAL Id: hal-01308899
https://hal.archives-ouvertes.fr/hal-01308899
Submitted on 28 Apr 2016
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of
sci-entific research documents, whether they are
pub-lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
Decision evaluation process in end-of-life systems
management
Yasmina Bouzarour-Amokrane, Ayeley Tchangani, François Pérès
To cite this version:
Yasmina Bouzarour-Amokrane, Ayeley Tchangani, François Pérès. Decision evaluation process in
end-of-life systems management. Journal of Manufacturing Systems, Elsevier, 2015, vol. 37 (n° 3), pp.
715-728. �10.1016/j.jmsy.2015.03.007�. �hal-01308899�
To link to this article: DOI:10.1016/j.jmsy.2015.03.007
http://dx.doi.org/10.1016/j.jmsy.2015.03.007
This is an author-deposited version published in:
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
O
pen
A
rchive
T
oulouse
A
rchive
O
uverte (
OATAO
)
OATAO is an open access repository that collects the work of Toulouse researchers and
makes it freely available over the web where possible.
Any correspondence concerning this service should be sent to the repository
administrator:
staff-oatao@listes-diff.inp-toulouse.fr
Technical
Paper
Decision
evaluation
process
in
end-of-life
systems
management
q
Yasmina
Bouzarour-Amokrane
a,
Ayeley
Tchangani
b,∗,
Franc¸
ois
Peres
a aUniversiteDeToulouse/INPT/LGP,47,Avenued’Azereix,BP1629,65016TarbesCedex,FrancebUniversitédeToulouse/IUTdeTarbes/LGP,1,rueLauréamont,65016TarbesCedex,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,
qPreliminaryversionofthispaperwaspresentedatIFACMIM2013asa 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
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
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
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 Iol(a
i)
toestimatethedegreeofachievementofobjectiveolconsidering
alternativeai(Eq.(1)).
Iol(a
i)=ϕol(col(ai)) (1)
where ϕol representsanaggregation measureof correspondent
component.
Theproposedapproachconsidersasocialchoiceproblemwhere
decisionmakersseektoobtainafinaldecisionincollectiveway.In
thiscase, basedontheproposedframework bytheanalyst,the
roleofstakeholdersistoelicitcommonlytheproblem
character-isticsintheelicitationphaseandthenevaluatethemdepending
ontheirdiscipline,knowledgeandexperience.Theselection
pro-cessesofcriteriaarestructuredhierarchicallywhereglobalcriteria
aredetaileduntiloperationallevel.Thenumberofconsidered
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 Col
s(ai),whereCsol(ai)=Cbol(ai)∪Cool(ai).This setincludes
benefits criteria noted Col
b (ai) and opportunity criteria noted
Col
o(ai).
-the set of criteria rejecting the achievement of objective ‘ol’
noted Col
o(ai)where Crol(ai)= Ccol(ai)∪ Crol(ai).This setincludes
costcriterianotedCol
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
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′)correspondstorelativeimportanceofthe
objectiveolcomparedtotheobjectiveol′.
˝O= o1 o2 ... oq o1 o2 .. . oq
1 ˝1,2k,O ... ˝k,O1,q ˝k,O2,1 ... ˝k,Ol,l′ ... .. . ˝k,Ol′,l = 1/˝ k,O l′,l ... ... ˝k,Oq,1 ... ... 1
Thismatrixmustbeconsistentandsatisficingtransitivity
condi-tiononallcomparisons.Thismeansthatthematrix˝Omustsatisfy
thefollowingconditions˝O(l,l)=1,˝O(l,l′)=1/˝O(l′,l)and˝O(l,
l′)=˝O(l,l′′)·˝O(l′′,l′)(formoredetailssee[46,45]).Ifthematrix
isperfectlyconsistent,theconditionoftransitivity˝O(l,l′)=˝O(l,
l′′)·˝O(l’’,l′)issatisfiedonallcomparisons.Toavoidcheckingthe
consistencyafteranarbitrarymatrixconstruction,weproposea
straightforwardapproachthatleadstoaconsistentmatrix[39]:
-selectapivotobjectivenotedop
-compareotherobjectivestothispivottoobtainscores
v
(l,p)(fromTable1)forallotherobjectivesj=/ p
-generatethematrix˝Owith;
˝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’iscalculatedusingEq.(3).
ωO(o l)= 1 q q
X
l′′=1!
˝O(l,l′′)P
i=1 q ˝O(i,l′′)"
(3)TherelativeimportanceofindicatorsIol(a
i)givenanobjective
ol,
∀
ol∈O,isthenevaluatedbythewayofapairwisecomparison.Foreachalternativeai,therelativeimportancevectorof
indica-torsIol(a
i)forobjectiveolisnotedωiol.Thisvectorisobtainedfrom
aconsistentmatrixnoted˝ol
i (Eq.(3)).InBOCRframework,the
degreeofrelativeimportanceofcriteriawithrespecttothe
objec-tivesisnotedωol
×whereωo×l(cj)representstherelativeimportance
ofcj∈C×ol(ai)foreachcategory×=b,o,c,r.Thevectorωo×l canbe
obtainedinthesamewayasvectorsωol
i andω
O.
Step2.Alternativeevaluation
Theevaluationmatrixofthealternativenotedol
×considering
differentsub-setsofcriteriaCol
×(×=b,o,c,r)canbeobtainedin
twoways:
Foragivencriteria,iftheevaluationofthealternativeis
quan-titativewithcol
j (ai)theperformanceofalternativeaiwithregard
tocol
j ,thenthepairwisecomparisonmatrix˝
col j
× foreachcategory
×=b,o,c,risobtainedthroughEq.(4).
˝colj
× (ai,ai′)=cjol(ai)/cjol(ai′) (4)
Otherwise,thepairwisecomparisonmatrix˝c×olj foreach
cate-gory×=b,o,c,rcanbeobtainedusingAHPmethodbyanswering
questionslike“whatistheperformanceofthealternativeaiin
com-parisontoalternativeai′ consideringthecriteriaCjol?”.Thevalues
oftheevaluationmatricesol
×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].
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(:). Let2xbethepowersetofX,afunction
v
:2x→[01]isacapacityorafuzzymeasureoverXifitverifies:
i)v(∅)=0,v(X)=1,
ii)S⊆ T⇒ v(S)≤ v(T),
∀
S,T⊆ Xiii)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),theChoquet
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
ωOrelativeimportancevectorofobjectives 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(ai)=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
indicatorIol
×kmaybegivenbythefollowingexpression:
Iol ×k(ai)=aggreg(co×l(ai)) =
X
m× k=1
m ×− (k− 1) m×
X
col j ∈C×ol ωol ×(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
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=maxai∈A
s(ai)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.
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 givesprioritytoalternativeswiththelargestselectability(respect.
low-estrejectability);thislatercaseissuitablewhenoneofthemeasure
isuniformlydistributedoveralternatives.Thevaluefunctioncan
thenbeusedtoselecttheultimatealternativea∗
i asfollows(Eq. (26)). a∗ i =argmax ai∈εS q (ai) (26)
ortorankalternativesusingtherelationgivenbyEq.(27)
ai<ai′⇔(ai)≥(ai)
∀
ai,ai′∈εSq (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
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.
Factors Indicators Criteria Unit
Benefit Recycling/reuse %Ofmaterialstoberecycled %
%Ofpartsofsystemstobereused %
%Waste %
Presenceofhazardousmaterials /
Frequencycomponentsrequired 1/year
Volumeofthematerial Unit
Valuerecyclablematerials Euro/unit
Resalevalueofcoins Euro/unit
Resources %Ofuseofresourcesused %
%Ofskilledlabor %
Opportunity Gain Distancetraveledwith1Toffreightwith1loffuel km*t/l
Volumeofthematerial Unit
Levelofstakeholdersatisfaction /
Frequencycomponentsrequired 1/year
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
Table4
Evaluationdataforsocialobjective.
Factors Indicators Criteria Unit
Benefit Comfort Levelofairquality /
Employment Numberofemployees Persons
Levelofstakeholdersatisfaction /
Yield Traveltime Days
Workinghours Days
Servicelife Days
Opportunity Employment %ofskilledlabor %
Environment Levelofairquality /
Levelofsoilpollution /
Cost Accidents Frequencyrateofaccidentswithstop 1000%
Severityrate %
Soundincident Numberofpeopleaffected Persons
Averagedecibel Db
Risk Pollution Levelofpollutionofwaterresources /
Levelofsoilpollution /
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
Volumeofthematerial 10,000 120,000 150,000 17,000 13,000 70,000 10,000 Units
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
Volumeofthematerial 10,000 120,000 150,000 17,000 13,000 70,000 10,000 Units
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
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
![Fig. 1. Disassembly process representation [35].](https://thumb-eu.123doks.com/thumbv2/123doknet/14245827.487515/5.892.185.727.774.1129/fig-disassembly-process-representation.webp)
