Evaluating the Sustainability of Community-Based Long-Term Care Programmes

19 Pages·2016·3.12 MB·English

sustainability
Article
Evaluating the Sustainability of Community-Based
Long-Term Care Programmes: A Hybrid
Multi-Criteria Decision Making Approach
BaoanSong1,QiyuSun1,2,*,YingLi2andChuanqiQue1
1 SchoolofPhilosophyandSociety,JilinUniversity,ChangChun130012,China;[email protected](B.S.);
[email protected](C.Q.)
2 SchoolofSocialWork,UniversityofMichigan,1080S.University,RoomB660,AnnArbor,MI48109-1106,
USA;[email protected]
* Correspondence:[email protected];Tel.:[phone]
AcademicEditor:KannanGovindan
Received:2May2016;Accepted:4July2016;Published:12July2016
Abstract: Sustainability is a crucial factor in Long-Term Care (LTC) programmes, which implies
whether the programmes have the capability of sustaining a quality service over the long term.
Toevaluatethesustainabilityofcommunity-basedLTCprogrammes,anovelhybridframeworkhas
beendemonstratedwithamixedMulti-CriteriaDecisionMaking(MCDM)technique. Accordingto
extensiveliteraturereviewandthefuzzyDelphimethod,fourpillarsofinitialcriteriaandtwelve
sub-criteriahavebeendetermined. ThenaweightedhierarchyhasbeenconstructedwithAnalytic
HierarchyProcess(AHP)toconstitutetheevaluationindexsystem. Inordertoproveourframework,
acasestudyoffourcommunity-basedLTCprogrammesinMichiganispresentedbyapplyingthe
fuzzytechniquefororderpreferencebysimilaritytoanidealsolution(TOPSIS)method. Theresults
indicatethatprogrammeP2hasthebestpotentialofsustainability,andsub-criteriaassociatedwith
economyoutweighothersub-criteria. Thesensitivityanalysisverifiesthattheresultoftheranking
remainsstableregardlessofthefluctuationinsub-criteriaweights,whichprovestheevaluationresults
andproposedmodeltobeaccurateandeffective. Thisstudydevelopsacomprehensiveandeffective
frameworkforevaluatingcommunity-basedLTCprogrammesfromthesustainabilityperspective.
Keywords: community-basedLTCprogrammes; sustainabilityevaluation; hybridMCDM;fuzzy
Delphi;AHP;fuzzyTOPSIS
1. Introduction
Globalagingisaninevitabletrend,withtheincreasedagingpopulation,itisanticipatedthatthe
longtermcareneed(LTC)forfrailanddisabledseniorsisgrowing[1]. Nowadays,over12million
AmericancitizensofallageswithfunctionalimpairmentsrelyonpersonalassistanceandotherLTC
services, and varied programmes have been established to deliver services. However, a dramatic
projected increase in LTC in the coming decades will confront significant constraints in resources
availabletoprovideLTCservices[2].
The current LTC system depends almost exclusively on government programmes and
out-of-pocket spending [3]. Sustainability has been an issue in many public programmes, which
incursignificantstart-upcostsinhuman,fiscalandtechnicalresources,andmanyprogrammessee
their resources withdrawn before activities have reached full fruition [4]. However, while there
havebeennumerouscontributionsintermsofthedevelopmentandimplementationofhealthcare
programmesfromthetheoretical,empirical,andpracticalperspectives,lessconcernhasbeendrawn
fromasustainabilityperspectiveinthisfield.
Sustainability2016,8,657;doi:10.3390/su8070657 www.mdpi.com/journal/sustainability
Sustainability2016,8,657 2of19
Sustainability is a multi-dimensional issue in programme evaluation. However, there is no
“Goldstandard”forsustainabilitysincetheprogrammetype,settingorresourcescanbevaried[5].
Previous studies on the sustainability of LTC programmes mostly drew on a single perspective.
Considering that this article aims to develop a framework with multi-dimensional indicators
to evaluate the sustainability of community-based LTC programmes, we extended Scheirer and
Dearing’s[6]conceptualframeworkofprogrammesustainabilityandinvolvedfourpillarsinthisarticle
toexaminethesustainabilityoftheLTCprogramme,namelyeconomy,policy,organizationalsetting
andcommunityenvironment. Theeconomydimensionincludesvariedfinancialresources,sufficient
fundingandunitcostofservice. Thepolicydimensionrequiresthateffectivecollaboration,policy
stimulationandinstitutionalinnovationareconsidered. Fortheorganizationalsettingdimension,four
indicatorsareinvolved,namelyinstitutionalstrength,staffinvolvementandintegration,leadership
competenceandorganizationalculture. Thecommunityenvironmentdimensionindicatescommunity
supportandkeycommunityneedsincoordinationtobeevaluatedintheLTCprogramme.
Since this study evaluates the sustainability of the LTC programme with four aspects, we
employed the Multiple Criteria Decision Making (MCDM) method to measure the alternatives
systematically under various criteria. In order to define a comprehensive list of selection criteria,
theindicatorshavebeenselectedfromtheexistingliteraturecombinedwiththefuzzyDelphimethod.
Intermsofsettingupaweightedmodel,theAnalyticalHierarchyProcess(AHP)hasbeenapplied
to decide and give weight to each criterion. The technique for order preference by similarity to
anidealsolution(TOPSIS)isawell-knownMCDMmethodthatselectsthebestalternativeamong
many flexible alternatives, by computing the distances from the positive ideal and the negative
ideal solution. Nevertheless, the traditional TOPSIS is controversial for its weakness in solving
uncertainties. Whensolvingtherealworldproblems,crispvaluesaredifficulttohandletheambiguity
andsubjectivityofhumanjudgement. Afuzzymethodisadaptedtoembracethefuzzynatureofthe
comparisonorevaluationprocessandenhancethecomprehensivenessandrationalityofthedecision
makingprocess. Therefore,ourstudyemployedasyntheticmethodologywithFDM,AHPandfuzzy
TOPSIStoevaluatethesustainabilityoftheLTCprogrammeinMichigan.
Therestofthispaperiscomposedasfollows: Section2reviewstheliteraturerelatedtotheissue
ofprogrammesustainability,programmeevaluationcriteriaandmethods. Thenweillustratethemajor
contributionofthisresearch. Section3istheintroductionoftheresearchmethod,thetheoryofFDM,
AHPandfuzzyTOPSISmethodshasbeenelaboratedinthispart. Section4buildsuptheevaluation
frameworkofLTCprogrammesustainability.Section5illustratestheindexsystemforLTCprogramme
sustainabilityevaluation;Section6conductsanempiricalstudyoffourLTCprogrammesinMichigan
under the research framework. Results are discussed and the sensitivity analysis is implemented
tocheckvalidityandsoundnessoftheproposedmodel;Finally,theconclusionhasbeendrawnin
Section8.
2. LiteratureReview
Sustainabilitymeanstakingdifferentfactorslikesocial,environmental,financial,economic,and
politicalfactorsintoconsiderationtoguaranteethesurvivalinthelongterm.[7]. However,itremains
a multi-dimensional, multi-factorial notion that is used somewhat inconsistently or ambiguously
and takes on different meanings at various times or contexts [5]. Scheirer and Dearing define the
sustainabilityofpublichealthprogrammesas“thecontinueduseofprogrammecomponentsand
activities(beyondtheirinitialfundingperiod)forthecontinuedachievementofdesirableprogramme
andpopulationoutcomes”[6,8]. Someresearchersviewsustainabilityasasetofprocessesthatoccur
duringtheearlierstagesofalifecycleofaprogramme[9,10],butScheirercriticizesthattheprocess
definitionofsustainabilitywillpresentchallengesforplanningresearchorevaluationonthisissue
sincewithoutexplicateddefinitionsofoutcomevariablesandmeasures,itisdifficultforresearchersto
accumulateordisconfirmfindingsaboutpredictorsofsustainability[6].
Sustainability2016,8,657 3of19
Therearenumerouspredictorsinfluencingprogrammesustainability,thoughsomesimilaritiesin
factorsidentificationandorganizingstructurescouldbefound,thewayhowtheauthorscategorize
thesepredictorsaredifferential. Stirmanetal. proposedtheframeworkofinfluencesonsustainability
asinnovationcharacteristics,context,capacity,processesandinteractions[11]. WhileFleiszeretal.[5]
sortedtheindicatorsasinnovation,context,leadershipandprocess. Buchananetal.[12]approacheda
synthesis with the influences on sustainability categorized as substantial, individual, managerial,
financial, leadership, organizational, cultural, political, processual, contextual and temporal.
Someauthorsindicatethatthereisoverlapbetweencategoriesofindicators,forexample,leadership
and process, and process and context. The interactive effect makes it hard to set up the relative
importanceofeachfactor[8,13].
Many studies set up a framework based on categories and sub-criteria for programme
sustainabilityevaluation. InSavayaandSpiro’s[14]study,33predictorsweretestedwithbivariate
analyses and multivariate analyses, and the results indicated the significance and co-relation
between indicators and manifestations. However, its inherited bias is that the research design
was based on relatively weak self-reports, as the informants who were the key person in the
involved projects would lead to the rating being inflated. Mancini and Marek [15] constructed
a framework to evaluate community-based programme sustainability with seven major elements
includinga29-itemProgramSustainabilityIndex(PSI).However,theinterplayofeachsustainability
elementshowedthatsomeprecedeotherfactors,sincetheyputalltheindicatorsinanequivalent
relationship. Considering that a weighting system should be established to build the scientific
evaluationsystem,Maheretal.[16] developed an instrument based on the National Health Service
Institute for Innovation and Improvement’s Health Service Sustainability model with multilevel
measurement. Eventhoughtheauthorsbelievedthatthisqualityandserviceimprovementtoolcould
be applied at any phase of a project, it could be more appropriate to apply it at the early stage to
evaluate the possibility of sustainability. Furthermore, this tool cannot be applied to estimate the
degreeofsustainability,sinceitisnotpossibletomakeacomparisonofdifferentprogrammeswith
thisevaluationmodel.
In order to prepare the study to explore the sustainability of evidence-informed practice
improvementprogrammesintheLTCsector,wenotedthattheliteraturerelatedtoLTCprogramme
sustainabilityisinsufficient. Oneofthefewstudieswefoundconductedalongitudinalcasestudy
by Demiglio and Williams [17] to examine the sustainability of the shared care model among five
alternativecareteams. Theureretal. studiedthemutualsupportgroupinterventioninlong-term
carehomesandaddressedreplicationandsustainability[18]. BurackandReinhardt[19]conducted
a research on the cultural change model in long-term care communities, and the result indicated
thattheperson-centredcareinterventioncontributestoapositiveimpactonlongtermsustainability.
Simmons [3] also tested the person-centred model for elderly people with Alzheimer’s disease in
acommunity-basedLTCsustainablelivingarrangement. Slaghuisetal.[20]setupaconceptualized
frameworkwithroutinizationandinstitutionalizationanddevelopedameasurementtoevaluatethe
sustainabilityofworkpracticesinLTCprogrammes. MostoftheliteraturerelatedtoLTCsustainability
focusedonthefiscalsustainabilityandpolicyperspective[21–24]. However,alltheliteratureabove
juststudiedthesustainabilityoftheLTCprogrammefromasingleperspectivesuchasorganizational
formulation,internalhumanresources,economyandpolicy;nostudyintegratedalltheperspectives
ordiscussedthesustainabilityoftheLTCprogrammeonabroaderscale.
ItwasnotedthattheevaluationofsustainabilityinLTCprogrammesrequiresaconsiderationof
multiple criteria, and so a multiple criteria decision-making strategy could be introduced in this
research. The MCDM method has been applied by researchers and practitioners in evaluating,
assessingandrankingalternativeswithanumberofstudies[25].Manymulti-attributedecisionmaking
(MADM)methodshavebeendevelopedtosolveevaluationissues,suchastheAnalyticalNetwork
Process(ANP),AnalyticalHierarchyProcess(AHP),VIKOR,andthePreferenceRankingOrganisation
MethodforEnrichmentEvaluations(PROMETHEE)[26]. TOPSISisoneoftheprominentevaluation
Sustainability2016,8,657 4of19
techniquesanditiswellrespectedintheliterature[27–29].However,inarealdecision-makingprocess,
uncertainty and vagueness of the concepts associated with human beings’ subjective judgements,
includinglinguisticterms,satisfactiondegree,andimportancedegreeneedaprevalencephenomenon.
To tackle this issue, fuzzy set theory is proposed by Zadeh [30] to measure the equivocalness and
uncertainness of the concepts. Upon this issue, the fuzzy TOPSIS technique can be introduced as
an effective measurement in evaluating the sustainability of LTC programmes. Some researchers
attemptedtointegrateMCDMwithdifferentweightingmechanisms;forexample,combinationsAHP
andTOPSIS,ANPandTOPSIS,etc. Sincetheevaluationcriteriacouldbearrayedintoahierarchy,
we conduct an AHP-fuzzy TOPSIS approach in evaluating the LTC programmes. This approach
extendsthefuzzyTOPSISmethodtoahierarchicaloneandhasbeenconductedbymanyresearchers,
also named as hierarchical fuzzy TOPSIS method [31–33]. This method inherits the hierarchy
mechanismofAHPmethodandprovidesgreatersuperioritytoclassicalfuzzyTOPSISmethods[34,35].
ThehierarchicalfuzzyTOPSISdoesnothavethedisadvantagesofthepairwisecomparisonsamong
criteria,sub-criteriaandalternatives,whileitalsosimultaneouslyovercomesthedisadvantagesfor
thenecessitytoassignaninitialweightinfuzzyTOPSIS[31]. WiththeintegratedapplicationofAHP
andfuzzyTOPSISmethods,theevaluationprocesshasadvantagesofthetwomethodsandeffectively
avoidtheinsufficienciesofeachmethod[28].
Themaincontributionsofthisstudy:
1. Previousstudiesevaluatingthesustainabilityofpublicprogramsmostlydrawattentiontohealth
care;theissuesrelatedtoLTCprogrammesustainabilityarelimitedandmerelyaddressasingle
aspectofsustainabilityinLTCprojects. Meanwhile,studiesfortheevaluationofsustainability
inpublichealthcareprogrammesdonotprovideaneffectiveweightingframeworkandinherit
thebiasfromsubjectiveself-report. Inordertocopethematters,weconductedafuzzyDelphi
method(FDM)involvingthescholarsandpractitionersinLTCareastoestablishanevaluation
frameworkbasedtheirknowledgeandexperiencecombinedwiththeexistedliterature.
2. AhybridMCDMmethodbasedonFDM-AHP-FuzzyTOPSIShasbeenpilotconductedinthis
study. This is a novel research method for evaluating community-based LTC programmes.
Thisresearchmethodovercomesthedefectsofpreviousstudiesthatlackaweightingstrategy
within indicators, and it could be applied to measure the degree of sustainability and make
effectivescoringandratingamongdifferentprogrammes.
3. Since experts with specialist knowledge backgrounds might select subjective orders on their
preferred aspects, we, accordingly, conduct a sensitivity analysis to examine the impact of
alternativeweightsonthefinalscores. Thisisthefirstattempttoresearchtheeconomy,policy,
organizationalsettingandcommunityenvironmentaspectsofthesustainabilityevaluationin
community-basedLTCprogrammesthroughweightsfluctuation.
3. ResearchMethod
ThissectionillustratesindetailthefuzzyDelphimethod,AHPandfuzzyTOPSISmethod.
3.1. FuzzyDelphiMethod
Inordertomakethedecisionprocesseffective,systematicandobjectivetocomposetheframework
and criteria, experts’ perspectives have to be applied to decide the influential evaluation factors.
Dijk[36]indicatesthattheDelphiMethod(DM)isanappropriatecommunicativetechniqueonthe
subjectivebaseofnormsandopinionsinsocialresearch;itcanbeappliedtogenerateaprofessional
consensusforambiguous, complicatedandcontentiousissues[37]. FirstproposedbyDalkeyand
Helmer[38]in1963,thistechniquehasbeenappliedindecision-makingpredictionstogetthemost
reliableconsensuswithsomegroupsofexperts. However,thetraditionalDMisatime-consuming
method, whichisdifficulttoconvergethroughrepetitivesurvey. Aimingtohandlethedeficiency
in processing equivocalness and uncertainness within the expert survey, the fuzzy logic set was
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introduced to upgrade the Delphi method to the fuzzy Delphi method (FDM) to overcome the
disadvantagesinthetraditionalDelphimethod. WiththeFDMtechnique,expertswillprovidetheir
opinions with three-point estimates by using triangular fuzzy numbers (TFNs), and not need to
modifythemrepetitively[39]. Sinceallthejudgementscouldbeefficientlyconsideredbymembership
degrees,alltheimportantinformationcouldbepreserved. Owingtothesemeritsinsummoninggroup
decisions,FDMhasbeenemployedinalargenumberofresearchestoconstituteevaluation. Inorder
tofindthekeyindicatorsforthesustainabilityevaluationofLTCprogrammes,theFDMisapplied
inthisstudy. Inpreviousstudies,duetoalackofsystematicclassification,somecriteriamighthave
interactiveeffects. Inordertoavoidtheinterdependencyofthecriteria,alltheindicatorsshouldpass
ascreeningprocessbyexpertstomakesurethepotentialinterdependentindicatorsareexcluded.
3.2. AHPMethod
Developed by Thomas Saaty in 1980, AHP is one of the predominant MCDM approaches.
It involves the structuring criteria for multiple opinions within a system hierarchy. Moreover, it
containsthecomparingalternatives,relativevaluesforcriteria,anddefiningtheaverageimportance
ofalternatives. Ononehand,itencouragestheactiveparticipationofstakeholders[8]. Ontheother
hand,itprovidespractitionersarationalfoundationtowardwhichtomakedecisions[40]. AHPbuilds
astructureforthedecomposingproblemintodifferentlevelsthatcorrespondtohowoneunderstands
the goals, criteria, sub-criteria and alternatives [41]. The elements of each layer are compared as
pairsregardingtheirimportanceinthedecision-makingprocess. AlinguisticscaleisappliedinAHP
thathelpstheevaluatorstoincorporatesubjectivity,experienceandknowledgeinapresentativeand
naturalway. Matricesarecreatedaftercomparisonandrelativeweightsaregeneratedfromthevarious
indicators. Compositeweightswerecalculatedbyaggregatingtheweightsthroughoutthesystem.
Theoutcomeisanormalizedeigenvectoroftheglobalweightoftheindicators. TheAHPmethod
enablesdecision-makerstobreakdownacomplexproblemintoamulti-hierarchyandrateagreat
numbersofquantitativeandqualitativeelementsinasystem[42].
3.3. FuzzyTOPSISMethod
The TOPSIS method is proposed by Hwang and Yoon [27], which is a technique for order
preferencebysimilaritytoidealsolutions. TheTOPSISapproachselectsthealternativethatisnotonly
closesttothepositiveidealsolution,butalsofarthestfromthenegativeidealsolution. Thepositive
idealsolution(PIS)consistsoftheoptimalperformancevaluesforallcriteriawhereasthenegative
idealsolution(NIS)composesoftheworstperformancevalues. However,sincetheTOPSISmethod
cannottackletheinherentuncertaintyandimprecisionoftheevaluators’insightwithcrispvalues,
ithasbeencriticizedinhandlingrankingissuesinrealsituations[43,44]. Personaljudgementsare
scoredcrispnumbersinconventionalTOPSISwhilethehumanpreferencemodelisunpredictable
andevaluatorsmightbeunabletoallocateacrispvaluetocomparativejudgementsinmanypractical
cases [45]. Therefore, in order to cope with the defects of traditional TOPSIS, linguistic values are
incorporatedwithTOPSIStohandleuncertainfactorsinafuzzysolution[46].
Fuzzysettheoryisemployedtoovercomeambiguityduringdecision-makingprocessesowning
totheinsufficientinformation.Insteadofprecisevalues,itapplieslinguisticvaluestofigureevaluators’
preferences,whichcansimplifythedecisionprocess[47]. Therefore,fuzzyTOPSISanditsextensions
aredevelopedtotacklerankingandjustificationproblems.Theelementarytheoryisthateachindicator
r
has a membership degree belonging to a fuzzy set. A fuzzy set A in a universe of discourse X is
describedbyamembershipfunctionµra. Thismembershipfunctionassociateswitheachelementxin
Xarealnumberwithin[0,1]. Tobespecific,whenthemembershipvalueequalsto1,itmeansthatthis
indicatortotallyattributestothefuzzyset. Onthecontrary,iftheindicatordoesnotaffiliatetothis
fuzzyset,themembershipvalueequalsto0.
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Owing to the simple calculation process, fuzzy linguistic values are always represented by
r
triangularfuzzynumbers(TFN),definedasatripleta“ra1,a2,a3s. Themembershipfunctionµrapxqis
definedas: $
’’’’’&0 xă a1
x´a1 a ă xă a
µrapxq“’’’’’%aax22´´´aaa313 a12 ă xă a23 (1)
0 xě a
3
In Equation (1), a ,a ,a are crisp numbers p´8ă a ď a ď a ă8q, a and a are the
1 2 3 1 2 3 1 3
boundariesofavailableareaforperformanceevaluation.
The linguistic value should be switched into TFN. Table 1 indicates the regulations of the
transformation.
Table1.LinguisticscalesandtheTFN.
LinguisticScales TFN
VL(VeryLow) (0,0,0.2)
L(Low) (0,0.2,0.4)
F(Fair) (0.3,0.5,0.7)
H(High) (0.6,0.8,1)
VH(VeryHigh) (0.8,1,1)
4. TheResearchFramework
TheproposedmodelforevaluatingsustainabilityinLTCprogrammesbasedonhybridMCDM
includesthefollowingthreesteps,asshowninFigure1.
Step1: DefinetheevaluationcriteriaaccordingtotheliteraturereviewandfuzzyDelphimethod.
At this stage, the decision-making group was set up by selecting experts from a related research
backgroundordirectmanagersofLTCprogrammes.Anextensiveliteraturereviewhasbeenconducted
togeneralizethemajorcriteriaandalternativestodesignthequestionnairefortheFDM.Basedonthe
decision-makers’opinionandthecharacteristicsofLTCprogrammes,theevaluatingcriterionsare
votedthroughFDM.
Step2: DecideweightsoftheevaluationcriterionthroughAHPmethod. Afterdeterminingthe
vitalevaluationcriteriawithFDM,ahierarchyhasbeenformulatedwiththreelayers: Thetoplayer
standsforthegoal;thesecondlayerstandsforthemajorcriteria;thesub-criteriaisindicatedbythe
third layer. The AHP technique has been applied to weight the criteria: Initially, relative weights
are rated by experts through pairwise comparison. Then, the weight of each alternative has been
calculated. Finally,thenormalizedeigenvectoroftheglobalweightshasbeencomputedasaresult.
Step 3: Evaluate the sustainability of LTC programmes with fuzzy TOPSIS method. In the
beginning, assembling the initial fuzzy decision matrix where the experts distribute the linguistic
ratingstoallthealternativesaccordingtotheirsubjectivevalues. Next,assemblingthefuzzyratings
ofthealternativesrelatedtotheobjectivecriteriabasedontheobjectiveconditions. Afterthat,fuzzy
TOPSIStechniqueisintroducedtoassemblecriteriaratingsandcomputetheevaluationresultsofthe
alternatives. TheresultsofLTCprogrammesareillustratedindecreasedorderintermsofthecloseness
coefficientvaluesofallthealternatives.
There are three advantages in evaluating the LTC programmes with a hybrid evaluation
model. First,theFDMtechniquehelpstoconstructascientificevaluationframeworkwithcriteria
and alternatives particularly designed for community-based LTC programmes. Likewise, these
criteriacanreflectacomprehensiveevaluationfrommulti-perspectivesespeciallyinsustainability.
Otherthanthat,thefuzzytechniquecombinedwithDelphimethodisconfidenttosolvethevagueness
anduncertaintyoftheexperts’judgements. Second,theAHPmethodendowstheweightsofcriteria
withthedecisionfromtheexpertgroup,whichmakestheevaluationmorefeasibleforscoringand
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rankingamongdifferentcommunity-basedLTCprogrammes. Finallyyetimportantly,fuzzyTOPSIS
isaneffectivetoolinhandlingrankingalternativeswithmultiplecriteriaenhancedfuzzytheoryinthe
fieldofsustainabilityevaluation.
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Phase 1：Establish evaluation index
system for evaluating the community
based LTC programmes
Establish the expert decision group
Set up evaluation index system for Phase 3：Evaluate the sustainability of
evaluating the community based LTC
community based LTC programmes using
programmes from the perspective of
fuzzy TOPSIS .
sustainability
Assemble the fuzzy ratings for criteria
performance of all alternatives.
Construct the initial fuzzy decision
matrix.
Phase 2：Decide the criteria weights
according to
AHP approach. Normalize the initial fuzzy decision
matrix.
Construct the hierarchical structure.
Set up the weighted normalized fuzzy
decision matrix.
Compare all indicators with Saaty’s
pairwise comparisons. Determine the fuzzy PIS and the fuzzy
NIS.
Calculate the local weights of elements
and check the consistency of crisp Calculate the distances of each
pairwise comparisons. alternative from the fuzzy PIS and the
fuzzy NIS.
Calculate the global weights of
elements. Calculate the closeness coefficient of
each alternative
Figure 1. The framework for sustainability evaluation of Community based LTC programmes.
Figure1.TheframeworkforsustainabilityevaluationofCommunitybasedLTCprogrammes.
Step 1: Define the evaluation criteria according to the literature review and fuzzy Delphi
meth5o.dE. vAatl uthatiiso sntaIgned,e txhSe ydsetecimsiofonr-mLTakCinPgr oggrroaumpm weaSsu ssetta iunpa bbiyli tsyelecting experts from a related
research background or direct managers of LTC programmes. An extensive literature review has
Inordertoconstructacomprehensiveandscientificframeworkfortheevaluation,theselection
been conducted to generalize the major criteria and alternatives to design the questionnaire for the
of the evaluation criteria is of great importance. Since the sustainability evaluation requires
FDM. Based on the decision-makers’ opinion and the characteristics of LTC programmes, the
multi-dimensions including internal and external factors of the LTC programmes with varied
evaluating criterions are voted through FDM.
alternatives ranging from economy, society, environment, organization, culture, policy, etc., while
Step 2: Decide weights of the evaluation criterion through AHP method. After determining the
previousstudiesrelatedtotheevaluationofprogrammesustainabilitydonotprovideaconfident
vital evaluation criteria with FDM, a hierarchy has been formulated with three layers: The top layer
researchframework,weemployedanexpertgrouptohelpussetuptheevaluationindexsystem.
stands for the goal; the second layer stands for the major criteria; the sub-criteria is indicated by the
First of all, 16 experts in related fields are invited to set up the decision-making group.
third layer. The AHP technique has been applied to weight the criteria: Initially, relative weights are
The background of our experts is LTC programme managers, professors and researchers who are
rated by experts through pairwise comparison. Then, the weight of each alternative has been
familiar with programme evaluation and LTC services. Then, based on the extended conceptual
calculated. Finally, the normalized eigenvector of the global weights has been computed as a result.
framework of programme sustainability by Scheirer and Dearing and characteristics of the LTC
Step 3: Evaluate the sustainability of LTC programmes with fuzzy TOPSIS method. In the
programmes,33initialcriteriawerecollectedbasedonspecificLTCprogrammesandagreementsfrom
beginning, assembling the initial fuzzy decision matrix where the experts distribute the linguistic
thedecisiongroup,inwhicheconomy,policy,organizationalsettingandcommunityenvironment
ratings to all the alternatives according to their subjective values. Next, assembling the fuzzy ratings
perspectivesareinvolved.Finally,thefinalevaluationsub-criteriaaredecidedfromtheFDMtechnique.
of the alternatives related to the objective criteria based on the objective conditions. After that, fuzzy
TOPSIS technique is introduced to assemble criteria ratings and compute the evaluation results of
the alternatives. The results of LTC programmes are illustrated in decreased order in terms of the
closeness coefficient values of all the alternatives.
There are three advantages in evaluating the LTC programmes with a hybrid evaluation model.
First, the FDM technique helps to construct a scientific evaluation framework with criteria and
Sustainability2016,8,657 8of19
Decision-making group contributes their views upon the importance of sub-criteria by
conservativeandoptimisticvalues. Thenscoresthesub-criteriafrom0to10atthefirststage. Next,the
conservativeTFNandoptimisticTFNarecomputed(Table2). Thenverifytheconsistencyofexperts’
agreementandrepeatuntilall Mi´Zi valuesareabove0. Lastly,determinethefinalsub-criterions
accordingtotheconsensusvalueGi. Inthisstudy,thethresholdvalue6.0hasbeenagreedby90%of
thedecisionmakers. Consequently,12finalcriteriaaredecidedtomeasurethesustainabilityofLTC
pSursotaginraabmilimty e20s1.6T, 8h,e x finalevaluationindexsystemispresentedinFigure2. 9 of 21
Evaluate the sustainability of
community based LTC programmes
Organizational Community
Criteria Economy Policy
Setting environment
Varied financial Institutional Community Effective
resources(C11) strength(C21) support(C31) Collaboration(C41)
Sub-criteria Sufficient Organizational Key community needs Policy
funding(C12) culture(C22) incoordination(C32) stimulation(C42)
Unit cost of Staff involvement and Institutional
service(C13) integration(C23) innovation(C43)
Leadership
competence(C24)

FFiigguurree 22.. EEvvaalluuaattiioonn iinnddeexx ssyysstteemm ffoorrs suusstataininaabbiliiltiytye evvaaluluataitoionno fofc ocmommmunuintyit-yb-absaesdedLT LCTCpr ogrammes.
programmes.
Table2.Theresultsofevaluationsub-criteria.
Table2. The results of evaluation sub-criteria.
Pessimistic Optimistic Geometric Consensus
Mi´Zi
Perspectives Sub-Criteria VPaelusesimistic OVaplutiemistic GMeoemanetric CVoanlsueensus
i i
M Z
Perspectives Sub-Criteria CViLalue CiU VOaiLlue OiU MCeiMan OiM VGaliue
Variedfinancialresources 1Ci 5Ci 7Oi O10i C4i.59 O8i.8 9 3.11 G6. 74>6.0
Affordablecostforcustomers 1 L 6 U 7 L 8U 4M.15 6M.27 2.73 5i.21<6.0
BeneVfitasrfioerds efirnvaicnecial 3 4 7 10 3.16 5.27 7.59 4.22<6.0
Sufficientfunding 11 65 77 190 4.45.937 8.879.8 4 3.121. 16 6.67.41 1>> 66.0.0
Economy Annureasloouperrcaetsio ncost 1 6 5 10 4.51 7.45 1.55 5.98<6.0
Annualincome 3 5 6 8 5.06 6.64 2.36 5.85<6.0
Affordable cost for
Unitcostofservice 21 86 77 81 0 4.51.514 6.277.5 9 2.713. 41 5.62.13 7<> 66.0.0
Totalciunsvteosmtmeernst 1 6 7 9 4.52 7.01 2.99 5.77<6.0
Benefits for service 3 4 7 10 3.16 5.27 7.59 4.22 < 6.0
Economy
Sufficient funding 1 6 7 9 4.37 7.84 2.16 6.11 > 6.0
Annual operation cost 1 6 5 10 4.51 7.45 1.55 5.98 < 6.0
Annual income 3 5 6 8 5.06 6.64 2.36 5.85 < 6.0
Unit cost of service 2 8 7 10 5.14 7.59 1.41 6.37 > 6.0
Total investment 1 6 7 9 4.52 7.01 2.99 5.77 < 6.0
Institutional strength 1 6 8 9 4.64 7.44 3.56 6.04 > 6.0
Prevailing
2 4 7 8 3.94 7.35 3.65 5.65 < 6.0
organizational climate
Organizational Workforce turnover
1 5 7 8 4.09 7.06 2.94 5.58 < 6.0
Setting rate
Clear policies and
2 5 7 10 4.68 5.64 6.36 5.16 < 6.0
procedures
Organizational culture 2 6 7 10 5.16 8.59 2.41 6.88 > 6.0
Sustainability2016,8,657 9of19
Table2.Cont.
Pessimistic Optimistic Geometric Consensus
Mi´Zi
Perspectives Sub-Criteria Value Value Mean Value
CiL CiU OiL OiU CiM OiM Gi
Institutionalstrength 1 6 8 9 4.64 7.44 3.56 6.04>6.0
Prevailing
2 4 7 8 3.94 7.35 3.65 5.65<6.0
organizationalclimate
Workforceturnoverrate 1 5 7 8 4.09 7.06 2.94 5.58<6.0
Clearpoliciesandprocedures 2 5 7 10 4.68 5.64 6.36 5.16<6.0
Organizationalculture 2 6 7 10 5.16 8.59 2.41 6.88>6.0
Staffinvolvement
Organizational 1 6 7 9 4.97 7.54 2.46 6.26>6.0
andintegration
Setting
Employeesatisfaction 4 5 6 7 3.96 7.85 0.15 5.91<6.0
Leadershipcompetence 2 6 6 10 3.75 8.26 1.74 6.01>6.0
Trainingand
2 6 7 9 3.64 6.84 3.16 5.24<6.0
promotionladder
Project
1 5 7 10 4.35 6.89 5.11 5.62<6.0
managementstructures
Relationshipamong
3 5 6 8 3.89 7.68 1.32 5.79<6.0
stakeholders
Communitysupport 3 7 7 10 4.64 8.04 1.96 6.34>6.0
Volunteerengagement 1 5 7 9 4.36 6.84 4.16 5.60<6.0
Perceivedhelpfulnessof
1 5 7 8 4.16 7.64 2.36 5.9<6.0
communityinvolvement
Connectiontothe
1 3 5 8 3.54 6.98 3.02 5.26<6.0
outsidecommunity
Community
Communityclimate 1 4 7 9 4.97 6.9 5.1 5.94<6.0
Environment
Localgovernmentsupport 2 7 5 9 5.11 6.16 0.84 5.98<6.0
Community
1 6 7 9 4.36 7.59 2.41 5.98<6.0
resourcesavailable
Keycommunityneeds
3 6 7 10 4.25 7.99 3.01 6.12>6.0
incoordination
Commitmentlevelof
2 8 6 10 4.84 7.04 0.96 5.94<6.0
thecommunity
EffectiveCollaboration 2 6 7 10 5.31 7.65 3.35 6.48>6.0
Deficientpolicystrategy 1 4 5 8 4.25 7.31 1.69 5.78<6.0
Policy Policystimulation 3 7 7 9 4.96 7.07 1.93 6.02>6.0
Legislativestabilization 2 5 7 9 3.75 5.68 5.32 4.72<6.0
Institutionalinnovation 4 6 7 9 4.59 7.65 2.35 6.12>6.0
5.1. EconomyCriteria
1. Variedfinancialresources: ReferstowhethertheLTCprogrammescangetavarietyoffinancial
resourcessuchasMedicaid,Medicare,insurancecompany,otherfoundations,oroutofpocket
paymentbythecostumers[48]. (C11)
2. Sufficientfunding: Referstowhetherthefundingoftheprogrammeissufficientforcurrentand
futureprogrammedevelopmentandimplementation. (C12)
3. Unitcostofservice: Referstotheaveragecostforservingeachcustomer,whichimpliesthecost
effectivenessoftheprogramme. (C13)
5.2. OrganizationalSettingCriteria
1. Institutionalstrength: Referstotheintegrationoftheinstitutionandwhetherthegoalstructures
fitstheprojectgoals[4]. (C21)
2. Organizational culture: Refers to the shared belief, value and norms in the programme that
supportandorganizethestaffsandstakeholderstobeunitedandintegrated. (C22)
3. Staffinvolvementandintegration: Includethecommitted,qualifiedstaffinprogrammedesign,
implementation,evaluationanddecisionmaking[15]. (C23)
Sustainability2016,8,657 10of19
4. Leadershipcompetence: Referstotheabilityofprogrammechampionsespeciallytofocuson
programmeplanningandimplementation,financialmanagement,support,supervisingteamand
providingtraining. (C24)
5.3. CommunityEnvironmentCriteria
1. Community support: Involves identification of relevant stakeholders who actively support
programmegoalsandwhohaveclearlyidentifiedresponsibilities[24]. (C31)
2. Keycommunityneedsincoordination: Referstowhetherthemissionoftheprogrammeisnot
coordinatedwithkeyneedinthecommunity. (C32)
5.4. PolicyCriteria
1. Effectivecollaboration: Referstocollaborationaroundthepolicytosupporttheprogrammes,
andthecollaboratorsareinvolvedintheprogrammes. (C41)
2. Policy stimulation: Refers to the policy effectively promoting the development of the
programme.(C42)
3. Policyinnovation: Referstothepolicyfitstheorganizationalandprofessionalgoals,strategies
andprocedures. (C43)
6. EmpiricalAnalysis
Inthissection, weconductanempiricalstudywithfourcommunity-basedLTCprogrammes
inMichigan. Villageinthewoods(P1)isanewmodelofcommunity-basedLTCservice,whichis
organizedandoperatedbasedonthelocalelderlyandvolunteers. Itprovidesneighbour-to-neighbour
volunteer connections, social programming and concierge services with screened and discounted
providerstoassistthecommunitytoremainindependentandfullyengaged. HuronValleyPACE
(P2) provides members in the community the care and medical treatment they need in order to
help them live in their homes as long as they can. It offers a full package of services provided by
aprofessionalhealthcareteam. TheOaksadultdayprogramme(P3)isdesignedtoimprovesocial
interactionandmentalacuityforcopingwithcognitive,physicalormentaldisabilitiesfortheelderly
inthecommunity. Brookdaleseniorlivingcommunity(P4)isanassistedlivingcommunityproviding
personalizedassistedlivingandanAlzheimer’saswellasdementiacareserviceforseniors.
We combine the hierarchical fuzzy TOPSIS method to evaluate the sustainability of these
community-basedLTCprogrammes. SincethisMCDMissuehasbeenidentifiedasincludingfour
major criteria (Economy, Organization setting, Community environment, and Policy) and twelve
sub-criteria. With the aim of obtaining the criteria weights and the rating of sustainability of
community-basedLTCprogrammes,weorganizetheexpertsintofourgroupstoprocesstheevaluation.
Adetailedprocessislistedbelow:
6.1. DeterminetheCriteriaWeightsthroughAHP
1. After12evaluationcriteriawithfourperspectivesareselectedthroughFDM,themulti-layer
structureofthesustainabilityofLTCprogrammesisconstructed. Thehierarchycontainsthree
levels,asshowninFigure2.
2. Theexpertsintheexpertteamareinvitedtoformanindividualpairwisecomparisonmatrixby
applyingSaaty’spairwisecomparisonscale.
3. CalculatethevaluesofthevectorW. Table3indicatesthevaluesofpairwisecomparisonmatrix
i
provided by the decision makers. The vector of priorities is the principal eigenvector of the
matrix,whichgivestherelativepriorityofthecriteriameasuredonaratioscale. Thevalueis
definedasλ,whichistheprincipaleigenvalueofthematrix. CIistheconsistencyindexandCR
istheconsistencyratio,theyaregatheredthroughAHPprocess. TheresultofCIisnomorethan
0.1,sothattheestimatedvectorW isacceptable.
i