Constructing a Travel Risks' Evaluation Model for Tour Freelancers Based on the ANP Approach

14 Pages·2016·2.09 MB·English

Hindawi Publishing Corporation
Advances in Operations Research
Volume 2016, Article ID 7968792, 13 pages
http://dx.doi.org/10.1155/2016/7968792
Research Article
Constructing a Travel Risks’ Evaluation Model for Tour
Freelancers Based on the ANP Approach
Chin-TsaiLin1andShih-ChiehHsu1,2
1DepartmentofBusinessAdministration,MingChuanUniversity,5F,No.130,JiheRoad,TaipeiCity11162,Taiwan
2DepartmentofTourismManagement,TaHwaUniversityofScienceandTechnology,No.1,DahuaRoad,
QionglinShiangHsinchuCounty30740,Taiwan
CorrespondenceshouldbeaddressedtoChin-TsaiLin;[email protected]
Received31December2015;Accepted28March2016
AcademicEditor:MhandHifi
Copyright©2016C.-T.LinandS.-C.Hsu. This is an open access article distributed under the Creative Commons Attribution
License,whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperly
cited.
Thisstudyconstructsanewtravelrisks’evaluationmodelforfreelancerstoevaluateandselecttourgroupsbyconsideringthe
interdependenciesoftheevaluationcriteriaused.Firstofall,theproposedmodeladoptstheNominalGroupTechnique(NGT)
toidentifysuitableevaluationcriteriaforevaluatingtravelrisks.Sixevaluationcriteriaand18subcriteriaareobtained.Thesix
evaluationcriteriaarefinancialrisk,transportationrisk,socialrisk,hygienerisk,sightseeingspotrisk,andgeneralriskforfreelancer
tourgroups.Secondly,themodelusestheanalyticnetworkprocess(ANP)todeterminetherelativeweightofthecriteria.Finally,
examplesofgrouppackagetours(GPTs)areusedtodemonstratethetravelriskevaluationprocessforthismodel.Theresultsshow
thattheTokyoGPTisthebestgrouptour.Theproposedmodelhelpsfreelancerstoeffectivelyevaluatetravelrisksanddecision-
making,makingithighlyapplicabletoacademiaandtourgroups.
1.Introduction arises.Therefore,freelancersplayanimportantroleinGPTs.
Freelancer GPT travel risk evaluation involves multicriteria
Typically, travel agencies put together several services pro- decision-making (MCDM). MCDM is designed to employ
vided by several distinct travel-related industries to offer a a set of criteria for a decision problem [9–13]. Thus, this
favourable tour experience [1–3]. The group package tour paper focuses on the evaluation of travel risk and how the
(GPT),ortheorganizedmasstour,isoneofthemajorforms selection of best GPTs meets the freelancer’s needs. These
ofoutboundtravelinmanypartsofAsia[1,2,4–7].Themost needs are met by reducing travel risk gaps introduced by
distinctivefeatureoftheGPTisthepresenceofatourleader, interdependence and feedback problems occurring among
who provides various services to the tour participants [7]. thedifferentcriteriaandsubcriteria,allowingahighevalua-
Thesetypesofoutboundtravelprovidetourparticipantswith tionleveltobeachievedandpromotingfreelancers’abilityto
aconvenientandfastexcursionenvironmentthatalsooffers providetourparticipantswithfavourabletourexperiences.It
certainqualityproductsandservices,savingthetouristtime isessentialforfreelancerstoknowthatthesuccessofleadinga
andmoney. grouptourdependsoneffectivemanagementandthecareful
Nowadays,competitionamongtravelagenciesisintense. preparationoftasksbeforehand.
Inordertoeconomiseonpersonnel-relatedcosts,manytravel Thereareothertermsusedtodescribeatourleaderwhich
agencies employ experienced freelancers, who exclusively aretourmanager,tourescort,tourconductor,tourdirector,
servicetourgroupsinthepeakseason.GevaandGoldman andtourcourier[14].Tourleadersarebothfront-lineservice
[8]haveindicatedthatoneofthemostimportanttasksforthe providers,whosepresentationcanmakeorbreakatour,and
tourleaderistosolveproblemsandtoescorttourparticipants administrators,whocarryoutvariousdutiesinthetourdura-
so that the tour leader can maintain a tour’s quality and tion[7,15].Thetourleaders canbedividedintotwotypes:
keepthemsatisfiedifsomethinggoeswrongoratravelrisk employees and freelancers [16]. The employee tour leader
2 AdvancesinOperationsResearch
is a company’s full-time employee. The freelancer is a self- Table1:Proposedcriterionandtheirrelatedsubcriteria.
employedpersonandisnotcommittedtoanemployerlong-
Criteria Subcriteria
term.Leadingagrouptourisacomplextask,encompassing
risksthatcanariseinrestaurants,hotels,attractions,airlines, Financialrisk Travelagencygoesbankrupt(C11),
and motorcoaches or while shopping or being involved in (C1) pocket-picker(C12)
amusement activities and optional tours, and so forth [6]. Safetyoftransportation(C21),
Nowadays, increasing number of travel risk issues leads to Transportation safetyofdriving(C22),
convenienttelecommunicationfacilities
more consumer concerns. Some traditional experiences are risk(C2) (C23),
unabletobemet;thus,bytravelriskevaluationforfreelancers
publictransitdelayedorcanceled(C24)
notonlycantheypromoteabetter,moreefficientevaluation
Politicalandeconomicinstability(C31),
ofthedecision-makingprocess,buttheyalsoeasilymaintain Socialrisk(C3) possibilityofterroristactivities(C32),
thequalityofatourgroupwhileimprovingtheirearnings. assistanceavailableofaccident(C33)
Previoustravelrisksstudieshavefocusedonthetourist’s Hygienerisk Hygieneofcateringconditions(C41),
perspective[16–20],thetourleader’sperspective[6,21],the (C4) possibilityofinfectiousdiseases(C42)
effectsofreligiousaffiliation[22],andtheeffectsofdiseases Sightseeingspot Safetyofrecreationalfacilities(C51),
and viruses [23, 24]. Additional studies have addressed the risk(C5) prearrangedmeetingpoint/time(C52)
pervasiveness of tourists’ judgements of food-related risks Checkitineraryandflightstatus(C61),
[25]. In general, research has examined adventure tourism Generalrisk ensuremeetingpointandtimes(C62),
otopuerriasttos’rvsoilnunrtealarytiorinskt-otatkoiunrgisbtehacacviidoeunrtss[2a7n]d,oirncjuorniseusm[2e6r]s,’ (C6) cimusatgoemoefrtchoemcopulanitnrtys/(dCes63ti)n,ation(C64),
different cognition of perceived risk attributes [28]. In the hotelsecuritysystem(C65)
literature,therearefewMCDMtheoriesaimedatevaluating
the travel risk model. There exists, so far, no complete set
NGT requires less time and resources than the Delphi
of travel risk evaluation models of the tourism market for
technique [32]. We adopt NGT [32, 33] to determine the
freelanceroperations,eventhoughthetourismindustryhas
hierarchicalcriteriasetandtheirinterdependenceproperties
rapidlygrown.Thisstudyattemptstousetheanalyticnetwork
tohelpafreelanceridentifytravelrisksprioritymeasureindi-
process(ANP)approachtodeterminetherelativeweightsof
catorsofGPT.
multiple evaluation criteria and then decide what the best
Delbecqetal.[32]suggestedfivetoeightindividualsasan
alternatives of GPT are in terms of an overall evaluation
appropriatenumberofmembersinanNGT,and,thus,this
criteria set. As a method, the ANP reconstructs a complex
studyemployedadecision-makinggroupcomprisingseven
MCDMproblemasahierarchy[29].Thus,thisstudyprovides
experts. To simplify the process and avoid any misunder-
an effective rationale model for a freelancer to evaluate the
standing,theinteractionbetweenanyofthesecriteriaisnot
GPTtravelrisks.
considered in the first instance. Six evaluation criteria and
18 subcriteria are determined through the NGT process, as
2.Methodology showninTable1.Thecriteriasetmaynotincludeallofthe
decisionfactorsintheGPTtravelriskevaluation.However,
2.1. Nominal Group Technique (NGT). The importance of theyarethemostmeaningfulmeasuresinourcaseandhave
tour leader’s views is now increasingly recognised, partic- beenstressedinnumerousleadingarticles.
ularly as customers are more likely to use a service that
meets their specific needs. Given the growing emphasis on
2.2.AnalyticNetworkProcess(ANP). ANPisacomprehen-
addressing the rising rates of travel risks and customers
sive decision-making technique that has the capability to
complaints,tourmanagersaremorelikelytoseekfreelancers’
includealltherelevantcriteriainarrivingatadecision[34].
opinions and priorities. However, opinion varies as to the
ANP is an extension of analytic hierarchy process (AHP)
best method(s) to elicit freelancer evaluations [30]. When
and allows for more complex interdependent relationships
collectingopinionforaneeds’evaluation,prioritizingneeds,
between elements [34]. AHP models assume that there are
or making recommendations for action based on needs
unidirectional relationships between elements of different
evaluation findings, the nominal group technique can be a
decisionlevelsalongthehierarchyanduncorrelatedelements
valuabletoolforfacilitatinggroupdecision-making.
withineachclusteraswellasbetweenclusters.Itisnotappro-
NGTisastructuredvariationofasmall-groupdiscussion priate for models that specify interdependent relationships
aimed at reaching consensus, where all ideas have equal in AHP. Therefore, this study includes this advantage using
importance. The indicators are decided not only according theANP.Thestructuraldifferencebetweenahierarchyand
to the criteriaadopted by modifying/deletingfromrelevant anetworkisdepictedinFigure1.ANPcomprisesfourmajor
prior research but also according to criteria selected by a steps[35,36].
paneloftourismexpertstodeterminethehierarchicalcriteria
set.Theprocessforceseveryonetoparticipate,andnodom- Step 1 (model construction and problem structuring). The
inantpersonisallowedtocontroltheproceedings.Further- problem should be stated clearly and transformed into a
more,NGTismorelikelytoreachaclearoutcome,providing rationalsystemlikeanetwork.Thestructurecanbeobtained
a sense of achievement for participants [31]. Importantly, viatheopinionofdecision-makersthroughbrainstormingor
AdvancesinOperationsResearch 3
(a) (b)
Figure1:Structuraldifferencebetween(a)ahierarchyand(b)anetwork,Changetal.[29].
otherappropriatemethods.Figure1(b)showsanexampleof ≤0.1,thentheestimateisaccepted;otherwise,anewcompar-
thenetworkformat. isonmatrixissoliciteduntilCR≤0.1.
Step 2 (pairwise comparisons of matrices and priority vec- Step 3 (supermatrix formation). The supermatrix concept
tors). The normal procedure for a pairwise comparison resembles the Markov chain process [35]. To obtain global
involves inviting experts to compare a series of pairwise priorities in a system with interdependent influences, the
comparisons in which two elements or two components at localpriorityvectorsareaddedtotheappropriatecolumnsof
a time are compared in terms of their contribution to their amatrix,knownasasupermatrix.Asupermatrixisactually
particularupperlevelcriterion[37].Therelativeimportance apartitionedmatrix,whereeachmatrixsegmentrepresentsa
valuesaredeterminedonascaleof1to9,where1represents relationshipbetweentwonodes(componentsorclusters)in
the equal importance of the two compared elements and 9 asystem[37].Letthecomponentsofadecisionsystembe𝐶𝑖,
indicates the heightened importance of one element (row 𝑖 = 1,2,...,𝑛,inwhicheachcomponent𝐶𝑖 has𝑗elements,
component in the matrix) versus the other one (column denoted as 𝑒𝑖𝑗, 𝑗 = 1,2,...,𝑚. The local priority vectors
componentinthematrix)[37].Areciprocalvalueisassigned obtained in Step 2 are grouped and located in appropriate
to the inverse comparison (i.e., 𝑎𝑗𝑖 = 1/𝑎𝑖𝑗, 𝑖 ≠ 𝑗; 𝑎𝑖𝑗 = 1, positionsinasupermatrixbasedontheflowofinfluencefrom
𝑖 = 𝑗,𝑖,𝑗 = 1,2,...,𝑛),where𝑎𝑖𝑗 denotestheimportanceof one component to another or from a component to itself,
𝑖thelementcomparedto𝑗thelement.Apairwisecomparison as in the loop. Equation (4) presents a standard form of a
in ANP is made in the framework of a matrix, and a supermatrix[35].Consider
localpriorityvectorcanbeobtainedtoestimatetherelative
importanceoftheelementsbeingcomparedbyapplyingthe
𝐶 𝐶 ⋅⋅⋅ 𝐶
followingequation: 1 2 𝑖
𝑒 𝑒 ⋅⋅⋅𝑒 𝑒 𝑒 ⋅⋅⋅𝑒 ⋅⋅⋅ 𝑒 𝑒 ...𝑒
𝐴⋅𝑤=𝜆max⋅𝑤, (1) 𝑒11 11 12𝑤11 1𝑗 21 2𝑤212 2𝑗 ⋅⋅⋅ 𝑖1𝑤𝑖21𝑗 𝑖𝑗
twIhfhe𝐴eerdiegeen𝐴novitseesctthaoecr,opanansidriswt𝜆eismnecaxycoimsmtahptreairxlia,srotghneesnmteeaiitggreeicnnevvsea,cl𝑤utoerroe𝑋fp𝐴rceas[ne3n8bt]es. 𝐶...1 𝑒1...2 [[[[[[ ]]]]]]
[ ]
determinedusing (𝐴−𝜆max𝐼)𝑋=0. (2) 𝑒𝑒211𝑗 [[[[[[𝑤21 𝑤22 ⋅⋅⋅ 𝑤2𝑗]]]]]]
Saaty[38]proposedadoptingtheconsistencyindex(CI) 𝑊= 𝐶2 𝑒22 [[[ ]]] . (4)
and consistency ratio (CR) to verify the consistency of the ... [[ ]]
[ ]
comparisonmatrix.TheCIandRIaredefinedasfollows: 𝑒 [[ ]]
. 2𝑗 [ ]
CI= (𝜆(m𝑛a−x−1)𝑛), .. ... [[[[[ ... ... d ... ]]]]]
(3) 𝑒 [ ]
𝐶 𝑖1 [ ]
CR= CI, 𝑖 𝑒 [[ ]]
RI ..𝑖2 [[[ ]]]
whereRIdenotestheaverageconsistencyindexfornumerous . [ ]
randomentriesofthesameorderreciprocalmatrices.IfCR 𝑒𝑖𝑗 [ 𝑤𝑖1 𝑤𝑖2 ⋅⋅⋅ 𝑤𝑖𝑗 ]
4 AdvancesinOperationsResearch
As an example, the supermatrix representation in a
hierarchywiththreelevelsisshownas Goal
0 0 0
[ ]
𝑊ℎ =[𝑤21 0 0], (5)
[ 0 𝑤32 𝐼] Criteria
where𝑤21isavectorthatrepresentstheeffectofthegoalon
thecriteria,𝑤32 isamatrixdenotingtheeffectofcriteriaon
eachofthealternatives,𝐼istheidentitymatrix,andentriesof Subcriteria
zerosindicateelementsthathavenoinfluence.Fortheabove
example,ifthecriteriaareinterrelated,the(2,2)entryof𝑊𝑛
given by 𝑤22 would indicate the interdependency, and the
supermatrixwouldbe[35]
Alternatives
0 0 0
[ ]
𝑊𝑛 =[𝑤21 𝑤22 0]. (6) Figure2:Networkformforthispaper.
0 𝑤 𝐼
[ 32 ]
supermatrix,butallthecolumnsofthelimitsupermatrixare
Note that any zero in the supermatrix can be replaced
thesame.Normalisingeachblockofthesupermatrixresults
by a matrix if there is an interrelationship of the elements
inthefinalprioritiesofalltheelementsbeingobtained.
in a component or between two components. Since inter-
dependence generally exists among clusters in a network, a
Step4(selectionofthebestalternatives). Ifthesupermatrix
supermatrixusuallyhasmultiplecolumns.Thesupermatrix formed in Step 3 covers the whole network, the priority
must be transformed first to make it stochastic; after being
weightsofalternativescanbefoundinthecolumnofalter-
restated, each column of the matrix adds up to unity. This
nativesinthenormalisedsupermatrix.Ontheotherhand,if
studyusedtheANPtoweighthecriteriaandsubcriteria,and
asupermatrixonlycomprisesinterrelatedcomponents,addi-
ttohu𝑊st󸀠h𝑛:eequationsupermatrix𝑊𝑛 mustbemodifiedslightly tpiroinoarilticeaslcouflathtieonalstemrnuasttivbees.pTherfeoramlteerdnatotivoebwtaiitnhtthheeolavregreasltl
0 0 0 overallpriorityshouldbetheoneselected.Thisstudyapplies
𝑊󸀠𝑛 =[[𝑤21 𝑤22 0 ]], (7) the first method, and a supermatrix that covers the whole
network,asshownbythebracketinFigure2,isthenformed.
0 𝑤 𝑤
[ 32 33]
where the criteria and subcriteria are interrelated, 𝑤22 and 3.ConstructingtheTravelRisks
𝑤33indicatetheinterdependency,andanetworkreplacesthe EvaluationModel
hierarchy.
ArecommendedapproachbySaaty[35]istodetermine The research problems were determined by a literature
the relative importance of the clusters in the supermatrix, review.Inordertoacquiremorecomprehensiveassessments,
withthecolumncluster(block)asthecontrollingcomponent we established an expert group to assign the evaluation
[37]. That is, the row components with nonzero entries for criteriaandsubcriteria.
their blocks in that column block are compared according
to their impact on the component of that column block 3.1.DesignationoftheGroupofExperts. Expertswereinvited
[35]. An eigenvector can be obtained from the pairwise to assess the content and relevance among the criteria and
comparisonmatricesoftherowcomponentswithrespectto subcriteria. To avoid biases occurring, an expert group
thecolumncomponent.Thisprocessproducesaneigenvector comprisingsevenprofessionalexpertsfromtourism-related
for each column block. For each column block, the first industrieswasformed.Wespenttwomoremonthsbetween
entry of the respective eigenvector is multiplied by all the August and October 2015 gathering sufficient information.
elements in the first block of that column and the second AlloftheexpertswereinvolvedintheGPTtravelriskeval-
ismultipliedbyalltheelementsinthesecondblockofthat uation model of the criteria selecting process. The tourism
column, and so on. In this way, the block in each column expertsselectedinthisstudycomprisedonedoctorateholder
of the supermatrix is weighted, and the result is known as whousedanemployedtourleaderinatravelagencyforten
the weighted supermatrix, which is stochastic. Increasing a years, one route control (RC) department manager from a
matrix to powers gives the long-term relative influence of wholesale travel agency, two scholars working in a tourism
theelementsononeanother.Toachieveconvergenceofthe management department, and three senior freelancers who
importance weights, the weighted supermatrix is increased hadbeenworkingforatravelagencyfor22,16,and14years,
tothepowerof2𝑘+1,where𝑘isanarbitrarilylargenumber, respectively. Therefore, the experts were able to consider
andthisnewmatrixistermedthelimitsupermatrix[35].The variousissuesandthenevaluatewhichonewasthebestbased
limit supermatrix possesses the same form as the weighted ontheirpracticalexperience.
AdvancesinOperationsResearch 5
Goal Criteria Subcriteria Alternative
Financial risk (C1) Travel Paogceknecty- pgiocekse rb a(Cnk12ru)pt (C11)
Safety of transportation (C21)
Transportation risk (C2) Safety of driving (C22)
Convenient telecommunication facilities (C23) TYO GPT
ct the Public transit delayed or canceled (C24) (A1)
ele Political and economic instability (C31)
ers evaluate and sbest travel risk HSyogciieanl er irsiksk ( C(C3)4) PAPHoosyssssgisisiibetbainilnlieitct yoye f ooa cfvf a iatnteielfrraeribcontlrgeiio socutof s ana cdcdticiisvtiediioateisnneessts ((((CCCC43341232)))) HK(GA 2G)PT
c
Freelan Sightseeing spot risk (C5) CPShraeefacerktry ai tonifng reeedrca mrreyae ateintoidnn gafl lip gfoahcitni lstit/tatiietmus s(e C( (CC5165)12)) KW(AL 3G)PT
Ensure meeting point and times (C62)
General risk (C6) Customer complaints (C63)
Image of the country/destination (C64)
Hotel security system (C65)
Figure3:Hierarchicalstructureoftravelriskevaluationmodelforfreelancers.
Sightseeing
Financial Transportation Social risk Hygiene risk General risk
risk (C1) risk (C2) (C3) (C4) spo(Ct r5i)sk (C6)
Figure4:Interdependencecriteriaofresearchmodel.
3.2. Determining the Evaluation Criteria Set and Travel Risk criteria 𝐶11 and 𝐶12, 𝐶12 and 𝐶21,..., and 𝐶62 and 𝐶63 are
Model. This study seeks to assess GPT travel risk, which independent.
usually consists of multiple dimensions and criteria, and to
determinetheinfluentialweightsofthosecriteria.Basedon
4.EmpiricalStudyandDiscussion
the experts’ opinions, we constructed a GPT travel risks’
evaluation model for freelancers in this study. Figure 3
Duetotheinterdependenceexistingamongthecriteriaset,
illustrates the hierarchical model of the GPT travel risk
the ANP approach was adapted to compute the relative
evaluationcriteria(i.e.,sixcriteriaand18subcriteria).
weightsofthecriteria.SuperDecisionsoftwareisusedtorank
According to the experts’ suggestions, Figures 4 and 5
thealternativesandselectthebesttravelrisks.Afterentering
show the interdependence among the criteria set based on
thenormalisedvaluesintothesupermatrixandcompleting
the hierarchical structure. The slender arrows imply a one-
thestochasticcolumn,thepowerofthesupermatrixisraised
or two-way relationship. For example, the arrow that goes
untilconvergenceoccurs[35,36].
from financial risk and feeds into transportation risk infers
that the criterion “financial risk” influences the criterion
“transportation risk.” Figure 4 shows that all of the criteria 4.1. Demonstrating the Empirical Study. In this study, we
have an inner dependence relationship, except for hygiene assumed that the group size, tour duration, and earnings
risk and sightseeing spot risk. Similarly, Figure 5 shows were the same among the various GPTs. The criteria were
theinnerdependencebetweenthesubcriteria.Forexample, setforfreelancersdecidingonthebestgrouptouritinerary.
6 AdvancesinOperationsResearch
Table2:Pairwisecomparisonmatricesforcriteriaoflevel2.
Criteria Financial(C1) Transportation(C2) Social(C3) Hygiene(C4) ScenicSpot(C5) General(C6) Weights
Financial(C1) 1 0.796 1.171 1.186 1.472 3.630 0.203
Transportation(C2) 1.256 1 1.483 1.515 1.863 4.601 0.257
Social(C3) 0.854 0.674 1 1.012 1.276 3.104 0.174
Hygiene(C4) 0.843 0.660 0.988 1 1.252 3.077 0.172
Scenicspot(C5) 0.679 0.537 0.784 0.799 1 2.469 0.138
General(C6) 0.275 0.217 0.322 0.325 0.405 1 0.056
𝜆max=6.000;CI=0;andCR=0.000≤0.1consistency.
C C C C C C C C C C C C C C C C C C
11 12 21 22 23 24 31 32 33 41 42 51 52 61 62 63 64 65
Figure5:Interdependencesubcriteriaofresearchmodel.
Consequently, the empirical study represents three famous Table3:Pairwisecomparisonmatricesforcriteriaoflevel3.
GPTsasalternativecaseswhichisdependentontheexperts’
suggestions, comprising 𝐴1: a five-day itinerary of Tokyo Travelagency Pocket-picker
M(TaYcOau),(JHapKaGn,),𝐴H2:onagfivKeo-ndgay, aitninder𝐴ar3y: aoffiHveo-ndgayKiotningeraanrdy Subcriteria goes(bCa1n1k)rupt (C12) Weights
Travelagency
ofGuangxiGuilin(KWL),China.Theresearchersgathered
goesbankrupt 1 0.690 0.408
data from October to December 2015. In total, research
(C11)
on 35 freelancer tour leaders was conducted. The results
Pocket-picker
present the overall scores and the order of alternatives. 1.449 1 0.592
The ranking was obtained and validated though the above- (C12)
describedanalyticalprocess,whichconsidersthatfreelancers 𝜆max=2.000;CI=0;andCR=0.000≤0.1consistency.
evaluateGPTtravelrisksintravelagenciesaccordingtothe
methodandsummarisedthecomputationalprocedurewith
the related importance of the subcriteria in terms of their
thefollowingsteps.
upperlevelcriteria.Thepairwisecomparisonmatricesforthe
criteriaandsubcriteriaareshowninTables2and3.
Step 1 (establish the pairwise comparison matrices and
determine weights). This study uses six evaluation criteria
Theweightsforlevel2to level3 listsinTable 4include
and18subcriteriaasthemodelforestablishingatravelrisks’ the respective weights of the six evaluative criteria (𝑤21)
evaluationcriteriaset.Firstly,theimportanceoftheweights
and the respective weights of the 18 evaluative subcriteria
of the criteria and subcriteria had to be obtained. For this (𝑤32).Assumingthatthereisnointerdependenceamongthe
reason,theexpertswereaskedtoassessallproposedcriteria criteriaandsubcriteria,whichcriteriaandsubcriteriashould
and subcriteria in a pairwise fashion while assuming that be emphasised more in determining their respective upper
no interdependence existed. The normalised weights were level criterion?As indicatedin Table 4, thecriticalorderof
calculatedasauniquesolutionasrepresentedby𝑤21,which thesixevaluationcriteriaforthetravelriskevaluationmodel
showstherelatedlocalpriorityofthecriteria.𝑤32represents isfinancialrisk(0.203),transportationrisk(0.257),socialrisk
AdvancesinOperationsResearch 7
Table4:Weightsforlevel2andlevel3. (0.174),hygienerisk(0.172),sightseeingspotrisk(0.138),and
generalrisk(0.056).
Weightsof Weightsof
Criteria criteria(𝑤21) Subcriteria subcriteria(𝑤32) Step2(establishthesupermatrixandthelimitmatrix,which
C1 0.203 C11 0.408 are listed as columns in Tables 5–7). The supermatrix con-
C12 0.592 sideringinterdependencecanthenbeobtainedbycombining
C2 0.257 CC2212 00..226884 tThaeblrees5u.lTtsabolbet5ainpreedsebnyts𝑤t2h1e, 𝑤su2p2,er𝑤m32a,trainxd,i𝑤n3a3d,daistisohnowtonthine
C23 0.176 respective vectors and matrices previously obtained. Since
C24 0.272
C3 0.174 C31 0.340 the supermatrix includes interactions between clusters, for
C32 0.282 example, inner dependence exists between criteria, not all
C33 0.378 ofthecolumnsadduptoone.Additionally,thedependence
C4 0.172 C41 0.534 betweentheselectioncriteriaandsubcriteriawasconsidered
C42 0.466 andanalysed,whileANPisintroducedwithinthisframework
C51 0.510 to obtain the weights of the criteria. The experts separately
C5 0.138 C52 0.490 examined the impact of all the criteria using a pairwise
C61 0.240 comparison. The normalised weights for these matrices are
C6 0.056 CC6623 00..223240 calculated and presented as 𝑤22 and 𝑤33, where zeros are
assigned to the weights of the criteria and subcriteria on
C64 0.088
whichagivencriterionisbased:
C65 0.218
𝐶 𝐶 𝐶 𝐶 𝐶 𝐶
1 2 3 4 5 6
𝐶 0 0 0.260 0 0 0.294
1
[ ]
𝐶 [0.420 0 0.300 0 0 0.376]
2 [ ]
[ ]
𝑤 = 𝐶 [ 0 0.460 0 0.463 0.446 0.331],
22 3 [ ]
[ ]
𝐶 [0.257 0 0.207 0 0 0 ]
4 [ ]
𝐶5 [[0.322 0 0 0 0 0 ]]
𝐶6 [ 0 0.540 0.233 0.537 0.554 0 ]
𝑤
33
𝐶 𝐶 𝐶 𝐶 𝐶 𝐶 𝐶 𝐶 𝐶 𝐶 𝐶 𝐶 𝐶 𝐶 𝐶 𝐶 𝐶 𝐶
11 12 21 22 23 24 31 32 33 41 42 51 52 61 62 63 64 65
𝐶11 0 0 0 0 0 0 0 0 0.141 0 0 0 0 0 0 0.117 0 0
𝐶12 [[[ 0 0 0 0 0 0 0 0 0.122 0 0 0 0 0 0 0 0.104 0.211]]]
𝐶21 [[0.122 0 0 0.373 0 0.415 0 0 0.151 0 0 0 0 0 0 0 0.079 0 ]]
[ ]
𝐶22 [[0.141 0 1 0 0 0.369 0 0 0 0 0 0 0 0 0 0.082 0.088 0 ]]
𝐶23 [[[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.075 0 0.082]]] (8)
𝐶24 [[ 0 0 0 0 0 0 0 0 0.160 0 0 0 0 0.416 0.294 0.121 0 0 ]]
[ ]
𝐶31 [[0.297 0.484 0 0 0 0 0 0.469 0.127 0 0 0 0 0.289 0 0 0.097 0.135]]
𝐶32 [[[ 0 0 0 0.292 0 0.217 0.504 0 0.153 0 0 1 0.430 0.294 0.193 0 0.093 0.161]]]
= 𝐶33 [[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.121 0.108 0 ]].
[ ]
𝐶41 [[ 0 0 0 0 0 0 0 0 0 0 0.613 0 0 0 0 0.139 0.139 0.103]]
𝐶42 [[[ 0 0 0 0 0 0 0.496 0 0 0.654 0 0 0 0 0 0 0.101 0.103]]]
𝐶51 [[0.235 0 0 0 0 0 0 0 0 0 0 0 0.361 0 0 0.094 0 0 ]]
[ ]
𝐶52 [[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.243 0.072 0 0 ]]
𝐶61 [[[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.270 0.066 0 0 ]]]
𝐶62 [[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]]
[ ]
𝐶63 [[ 0 0 0 0.335 1 0 0 0 0 0.346 0 0 0 0 0 0 0.088 0.129]]
𝐶64 [[0.205 0 0 0 0 0 0 0.269 0 0 0 0 0 0 0 0.049 0 0.078]]
𝐶65 [ 0 0.516 0 0 0 0 0 0.263 0.146 0 0.387 0 0.209 0 0 0.063 0.103 0 ]
Ifweintroducedasupermatrixforthecriteriabysimply components, and, hence, our entries became 0.5 for the
connecting each criterion to itself, our entries would nor- elements in the supermatrix [39]. A weighted supermatrix
mally be equal to one. However, our supermatrix needed is transformed first into a stochastic value, as presented in
to be stochastic to ensure convergence. To do that in Table 6. The current supermatrix reached convergence and
this case, we had to assign equal weights to the two obtaineduniqueweights.Table7showsthefinallimitmatrix,
8 AdvancesinOperationsResearch
C65000000000.211000.08200.1350.16100.1030.10300000.1290.0780
C64000000000.1040.0790.088000.0970.0930.1080.1390.10100000.08800.103
C6300000000.117000.0820.0750.121000.1210.13900.0940.0720.066000.0490.063
4 3 30
C620000000000000.2900.1900000.240.270000
694
C610000000000000.410.280.290000000000
C52000000000000000.4300000.361000000.209
C510000000000000010000000000
3 7
C4200000000000000000.6100000000.38
a
ri 4 6
criteC41000000000000000000.6500000.3400
b
IIIsuC3300000000.1410.1220.151000.1600.1270.1530000000000.146
9 93
x. C3200000000000000.460000000000.260.26
ri
ermat C31000000000000000.504000.4960000000
p
htedsu C240000000000.4150.3690000.2170000000000
eig C230000000000000000000000100
w
n
Theu C220000000000.37300000.29200000000.33500
e5: C210000000000100000000000000
l
b
a 4 6
T C1200000000000000.4800000000000.51
C110000000000.1220.141000.29700000.23500000.2050
C600.2940.3760.33100000000000000000.2040.2300.2560.1100.200
6 4 73
C500044005500000000000495000000
0. 0. 0.0.
3 7 37
eriaC40000.46000.530000000000.530.460000000
IIcritC30.2600.2600.30000.20700.2330000000.3800.2470.373000000000
0 0 4753
C20004600540021262427000000000000
0. 0. 0.0.0.0.
0 72 82
C1004202532039600000000000000000
0. 0.0. 0.0.
IGoal00.2030.2570.1740.1720.1380.056000000000000000000
LevelItemGoalC1C2C3C4C5C6C11C12C21C22C23C24C31C32C33C41C42C51C52C61C62C63C64C65
el
v
LeIII III
AdvancesinOperationsResearch 9
C65000000000.105000.04100.0670.08000.0510.05100000.0640.0390
C64000000000.0520.0400.044000.0480.0460.0540.0700.05100000.04400.052
C6300000000.059000.0410.0380.061000.06050.06900.0470.0360.033000.0240.032
C620000000000000.14700.09700000.1210.1350000
857
C610000000000000.200.140.140000000000
C52000000000000000.2150000.181000000.105
0
C51000000000000000.500000000000
6 4
riaC4200000000000000000.3000000000.19
bcriteC41000000000000000000.32700000.17300
u
IIIsC3300000000.0700.0610.076000.0800.0640.0760000000000.073
rix. C3200000000000000.2340000000000.1340.131
mat 2 8
per C31000000000000000.25000.240000000
u
s 74 8
hted C240000000000.200.180000.100000000000
g
wei C2300000000000000000000000.500
e
Th 6 6 8
6: C220000000000.1800000.1400000000.1600
e
abl C2100000000000.500000000000000
T
2 8
C1200000000000000.2400000000000.25
C110000000000.0610.070000.14900000.11700000.1030
C600.1470.1880.16500000000000000000.1020.1150.1280.0550.100
C5000223002770000000000024925100000
0. 0. 0.0.
2 8 64
eriaC40000.23000.260000000000.260.230000000
crit 00 4 7 047
IIC300.130.1500.1000.110000000.190.120.18000000000
0 0 7437
C20000.23000.27000.100.130.120.13000000000000
C1000.21000.1290.16100.1990.3010000000000000000
IGoal00.2030.2570.1740.1720.1380.056000000000000000000
LevelItemGoalC1C2C3C4C5C6C11C12C21C22C23C24C31C32C33C41C42C51C52C61C62C63C64C65
el
v
LeIII III
10 AdvancesinOperationsResearch
C6500000000.0140.0330.0380.0590.0180.0180.1020.1200.0180.1260.1510.0160.0070.0070.0000.1010.0500.123
C6400000000.0140.0330.0380.0590.0180.0180.1020.1200.0180.1260.1510.0160.0070.0070.0000.1010.0500.123
C6300000000.0140.0330.0380.0590.0180.0180.1020.1200.0180.1260.1510.0160.0070.0070.0000.1010.0500.123
C6200000000.0140.0330.0380.0590.0180.0180.1020.1200.0180.1260.1510.0160.0070.0070.0000.1010.0500.123
C6100000000.0140.0330.0380.0590.0180.0180.1020.1200.0180.1260.1510.0160.0070.0070.0000.1010.0500.123
C5200000000.0140.0330.0380.0590.0180.0180.1020.1200.0180.1260.1510.0160.0070.0070.0000.1010.0500.123
C5100000000.0140.0330.0380.0590.0180.0180.1020.1200.0180.1260.1510.0160.0070.0070.0000.1010.0500.123
C4200000000.0140.0330.0380.0590.0180.0180.1020.1200.0180.1260.1510.0160.0070.0070.0000.1010.0500.123
riteriaC4100000000.0140.0330.0380.0590.0180.0180.1020.1200.0180.1260.1510.0160.0070.0070.0000.1010.0500.123
c
IIsubC3300000000.0140.0330.0380.0590.0180.0180.1020.1200.0180.1260.1510.0160.0070.0070.0000.1010.0500.123
I
C3200000000.0140.0330.0380.0590.0180.0180.1020.1200.0180.1260.1510.0160.0070.0070.0000.1010.0500.123
atrix. C3100000000.0140.0330.0380.0590.0180.0180.1020.1200.0180.1260.1510.0160.0070.0070.0000.1010.0500.123
m
super C2400000000.0140.0330.0380.0590.0180.0180.1020.1200.0180.1260.1510.0160.0070.0070.0000.1010.0500.123
elimit C2300000000.0140.0330.0380.0590.0180.0180.1020.1200.0180.1260.1510.0160.0070.0070.0000.1010.0500.123
Th
e7: C2200000000.0140.0330.0380.0590.0180.0180.1020.1200.0180.1260.1510.0160.0070.0070.0000.1010.0500.123
l
Tab C2100000000.0140.0330.0380.0590.0180.0180.1020.1200.0180.1260.1510.0160.0070.0070.0000.1010.0500.123
C1200000000.0140.0330.0380.0590.0180.0180.1020.1200.0180.1260.1510.0160.0070.0070.0000.1010.0500.123
C1100000000.0140.0330.0380.0590.0180.0180.1020.1200.0180.1260.1510.0160.0070.0070.0000.1010.0500.123
C600000000.0140.0330.0380.0590.0180.0180.1020.1200.0180.1260.1500.0160.0070.0070.0000.1010.0500.123
C500000000.0140.0330.0380.0590.0180.0180.1020.1200.0180.1260.1500.0160.0070.0070.0000.1010.0500.123
eriaC400000000.0140.0330.0380.0590.0180.0180.1020.1200.0180.1260.1500.0160.0070.0070.0000.1010.0500.123
IIcritC300000000.0140.0330.0380.0590.0180.0180.1020.1200.0180.1260.1500.0160.0070.0070.0000.1010.0500.123
C200000000.0140.0330.0380.0590.0180.0180.1020.1200.0180.1260.1500.0160.0070.0070.0000.1010.0500.123
C100000000.0140.0330.0380.0590.0180.0180.1020.1200.0180.1260.1500.0164.0000.0070.0000.1010.0500.123
IGoal00000000.0140.0330.0380.0590.0180.0180.1020.1200.0180.1260.1500.0160.0070.0070.0000.1010.0500.123
LevelItemGoalC1C2C3C4C5C6C11C12C21C22C23C24C31C32C33C41C42C51C52C61C62C63C64C65
el
v
LeIII III