selectionofin-flightduty-freeproductsuppliersusinga … · 2021. 3. 23. · method and fuzzy ahp....

Research ArticleSelection of In-Flight Duty-Free Product Suppliers Using aCombination Fuzzy AHP Fuzzy ARAS and MSGP Methods

Yan-Kai Fu 1 Chung-Jen Wu 2 and Chin-Nung Liao 3

1Department of Aviation Service and Management China University of Science and Technology No 200 Zhonghua StHengshan Township Hsinchu County 312 Taiwan2Department of International Business and Marketing China University of Science and TechnologyNo 245 Sec 3 Academia Rd Nankang Taipei 115 Taiwan3Department of Business Administration China University of Science and Technology No 245 Sec 3 Academia Rd NankangTaipei 115 Taiwan

Correspondence should be addressed to Yan-Kai Fu yankaifucccustedutw

Received 13 June 2020 Revised 1 March 2021 Accepted 4 March 2021 Published 23 March 2021

Academic Editor Dylan F Jones

Copyright copy 2021 Yan-Kai Fu et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Over a billion people travel by air all over the world every year and there are many in-flight retailing opportunities for the airlineindustry is paper proposes a novel integration fuzzy analytical hierarchy process (FAHP) fuzzy additive ratio assessment(FARAS) and multisegment goal programming (MSGP) methods to select the best supplier for in-flight duty-free product inairline industry e advantage of this proposed method is that it allows decision makers (DMs) to set multisegment aspirationvague levels considering both the qualitative and quantitative criteria for supplier selection simultaneously To the best of ourknowledge a simultaneous consideration of qualitative and quantitative criteria for supplier selection of in-flight duty-freeproduct has never been applied under the airline retail industry contextis research will fill into the gaps of supplier selection inin-fight duty-free product for airline industry e integrated model is illustrated by an example in an airline company in Taiwan

1 Introduction

Each day millions of people travel by air us the air tourhas expanded into a large market and is no longer a wealthonly for the rich [1] For instance in Taiwan according tothe annual report of the Civil Aeronautics Administration(CAA) [2] from 2008 the number of passengers enteringand leaving the 17 airports (including inbound outboundand transit passengers) was 3524 (10000 persons) By 2017the number of passengers entering and leaving these airportsincreased to 6598 (10000 persons) From 2008 to 2017 thenumber of visitors to the three major international airportsin Taiwan increased significantly e growth rate of TaiwanTaoyuan International Airport (TITA) was 51 the growthrate of Taiwan Kaohsiung International Airport (TKIA) was36 and the growth rate of Taiwan Taipei InternationalAirport (TTIA) was 48 e average growth rate of thethree major airports was 45 in Taiwan (see Table 1)

In other words air tourism has many passengers andbusiness opportunities As a result in-flight retailing offers acritical growth area for the airlines industry and manymultiple channel retailers in Taiwan erefore in-flightretail product revenue has become an essential key to thecompetitiveness and long-term survival of the airline in-dustry Besides consumer satisfaction is one index used toevaluate product qualityvariety and service performanceBased on the in-flight shopperrsquos experience reviews andconsidering the unique nature of retailing at flight a con-sumer satisfaction category is established and divided intofive extrinsic values quality product variety price infor-mation and services sold in the sky e quality and varietyof services sold in the sky are essential factors to passengerslooking for an enjoyable and satisfying experience duringflight [3 4] However considering the importance of qualityairlines must consider in-flight duty-free product supplyresources such as supplier selection

HindawiMathematical Problems in EngineeringVolume 2021 Article ID 8545379 13 pageshttpsdoiorg10115520218545379

e importance of supplier selection has been increas-ingly recognized in supply chain management (SCM) SCMhas identified suppliers as significant based on consumersrsquopurchase decisions In recent years determining the bestsupplier in the supply chain has overwhelmingly become anessential strategy for business [5] e supplier selectionprocess is a multicriteria decision-making (MCDM) prob-lem due to the involvement of many conflicts in businessresources based on qualitative and quantitative criteria[6ndash8] erefore supplier selection is one of the sophisti-cated and many measures in the supply chain that has asignificant effect on the excellent capability of a business [9]However selecting the fittest supplier from many latentsuppliers is often a daunting work e sustainable supplierselection problem can be defined as the classical supplierselection issue that considers economic social and envi-ronmental criteria to select and monitor suppliersrsquo perfor-mances [10ndash12] For any manufacturer selecting the rightsupplier is crucial to success at the right supplier willsignificantly increase customer satisfaction reduce pur-chasing costs and improve competitive ability

ese years a large number of methodologies have beenused to decide the supplier evaluation problememethodsinclude goal programming (GP) linear programming (LP)statistical and probabilistic methods mathematical pro-gramming models multiple objective programming ana-lytic hierarchy process (AHP) analytic network process(ANP) techniques for order preference by similarity to idealsolution (TOPSIS) additive ratio assessment (ARAS) dataenvelopment analysis (DEA) cost-based methods (CBMs)decision-making trial and evaluation laboratory (DEMA-TEL) and neural networks (NNs) [13] Recently the inte-gration of different techniques within the supplier selectionprocess has received considerable attention in the SCMliterature for example Fu [14] focused on the performanceof AHP ARAS and MCGP approach in supplier selectionissues Additionally Memari et al [15] presented an intuitivefuzzy TOPSIS approach to select the right fit provider thatconsiders nine criteria and thirty subcriteria for an auto-motive spare parts manufacturer in relation to airlinecompanies Awasthi et al [16] used a fuzzy AHP-VIKOR-based approach for multi-tier sustainable global supplierselection Fallahpour et al [17] used the DEA decisionsupport model for sustainable supplier selection in sus-tainable supply chain management Liao et al [18] presenteda hybrid model for the selection of optimal online travelagencies (OTAs) using the fuzzy Delphi method (FDM)-DEMATEL-ANP Chaharsooghi and Ashrafi [11]

introduced a fuzzy MCDM approach using a neofuzzyTOPSIS method to find the best solution for sustainablesupplier selection based on the triple bottom line (TBL)approach in a supply chain Wang Chen [12] proposed acomprehensive fuzzy MCDM method for green supplierevaluation using fuzzy AHP and TOPSIS in the luminanceenhancement film (LEF) industry

In addition Shi et al [19] deployed a new integratedmodel based on interval-valued intuitionistic uncertainlinguistic sets (IVIULSs) and a grey relational analysis(GRA)-TOPSIS method for the selection of green suppliersTsui and Wen [20] proposed a hybrid multiple criteriagroup decision-making (MCGDM) method by using AHPentropy elimination and selection expressing the reality III(ELECTRE III) and the linear assignment method (LAM) toassist a thin film transistor liquid crystal display (TFT-LCD)manufacturer in choosing green suppliers Ulutas et al [21]develop a novel fuzzy multiattribute decision-making modelconsisting of a fuzzy extension of preference selection index(FPSI) and fuzzy extension of the range of value (FROV) todetermine the best supplier for a Turkish textile companyJauhar and Pant [22] integrated the DEA with DE andMODE for sustainable supplier selection problems Yu andWong [23] developed an agent-based CBM model forsupplier selection of multiple products with a synergisticeffect Rezaei et al [6] investigated supplier selection in theairline retail industry by using a conjunctive screeningmethod and fuzzy AHP Hsu et al [24] utilized theDEMATEL approach with an example in the green supplychain to improve the overall performance of supplier se-lection management Liao and Kao [25] integrated the AHPand MCGP model to solve the supplier selection issue eintegrated model uses source data provided for the airlineindustry to discuss the real world in supplier selectionHowever these techniques are not perfect for in-flight duty-free supplier evaluation and selection because the availableinformation in the airline context is inherently ambiguousinaccurate imprecise and uncertain by nature e novelintegration fuzzy AHP fuzzy ARAS and MSGP methodmay be useful for various MCDM problems is is a crucialcontribution to the paper

e remainder of this paper is structured as follows Inthe next section a detailed review of the criteria for supplierselection-related literature is presented Section 3 explainsthe proposed combined FAHP FARAS and MSGPmethods Section 4 used the integrated method to thesupplier selection for in-flight duty-free product with anumerical example to the airline firm In Section 5 the paperfinishes with concluding suggestions for future research

2 Literature Review

Many researchers have proposed different criteria to eval-uate the sustainability of supplier selectionere are variousimportant factors to consider when selecting suppliers in-cluding price discounts delivery time service level aquantity discount transportation cost carbon emission taxcurrency exchange rate supplier capacity and lead time[26 27] Rao and Zhang [28] summarized the supplier

Table 1 Number and growth rate of passengers entering andleaving in the top three airports in 2008 to 2017 in Taiwan (unitpersons)

YearAirports

TITA TKIA TTIA2008 21936083 4160515 31018542016 44878703 6479183 5943153Growth rate 51 36 48Resource Civil Aeronautics Administration (CAA) Annual Report (2017)

2 Mathematical Problems in Engineering

selection problems and proposed that the most importantcriteria are quality price cost and delivery performanceKannan et al [29] applied fuzzy AHP and TOPSIS to selectthe best suppliers ey applied quality cost deliverytechnology capability and environmental competency cri-teria for supplier selection Bankian-Tabrizi et al [30]proposed five primary evaluation criteria for suppliersservice financial competencies and organization skillsGheidar Kheljani et al [31] considered the costs of both thebuyer and the suppliers to minimize the overall costs of thesupply chain Furthermore Zimmer et al [32] reviewed theliterature concerning supplier selection issues ey exam-ined 143 peer-reviewed papers from 1997 to 2014 to sum-marize relationship research areas Based on their survey thetop 10 economic environmental and social criteria areshown in Table 2 [15]

Also many elements affect an airlinersquos decision to selecta cooperation supplier For example Fu [14] used criteriaincluding product quality service delivery time businessimage and food safety for catering supplier selectionChiappa et al [33] used fuzzy theory and the TOPSIS ap-proach and applied criteria including price quality ofproducts location and internal atmosphere proximityfriendliness of staff and speed of service to evaluate airportretailers Rezaei et al [6] considered costprice serviceproduct quality delivery financial patience and corporatesocial responsibility (CSR) and applied an assortment ofsupplier selection methodologies to airline retail Hsu andLiou [34] applied the DANP (DEMATEL-based ANP) ap-proach to select the suppliers in the airline industry in-cluding on-time rate costprice service quality skillscustomer relationship client satisfaction flexibility andinformation partake Vijayvargy [35] applied cost servicedelivery performance relationship business reputationmeal hygiene and safety to evaluate providers in the airlineretail industry Chang and Lee [36] examined a multipleobject goal programming method to select the airportsupplier by using price product quality service qualityexperience reputation and consumer satisfaction in orderto obtain the best overall optimal performance

In previous studies many researchers have discussedairline supplier selection problems However most of theliterature on the supplier selection method considers onlythe qualitative criteria To the best of researcherrsquos knowledgequalitative and quantitative criteria for supplier selectionthe in-flight duty-free product have never been appliedsimultaneously in the airline retail industry case e mainaim of this paper is based on the airlinersquos context to suggest anew integrated method using the combined FAHP FARASand MSGP methods to fill this gap in the airline retail tradeliterature

3 Proposed Supplier Selection Method

31 Fuzzy Analytical Hierarchy Process Peng et al [37] useda fuzzy AHPmethod to solveMCDM inmanagement issuese problem of MCDM is to decide the best selections usinga fuzzy set of complete alternatives that are assessed inconflicting criteria Determining the relative importance of

different criteria in MCDM problems involves a high degreeof personal preference judgment from DMs [38] Howeverthe linguistic measure of peoplersquos judgments is often vaguein other words it is in interval value rather than that stablevalue judgment erefore FAHP theory can deal withinformation that is usually uncertain imprecise and vaguein decision-making problems [39]

FTNs are popular in fuzzy AHP applications A fuzzynumberA is described as a fuzzy subset of the real lineXwitha member function such as uA which represents uncer-tainty is membership function is defined in a universe ofdiscourse of [0 1] us a fuzzy triangular number (Fig-ure 1) can be defined as a triplet (a b c) where ale ble c themembership function of the fuzzy number A can be shownin Figure 1 and equation (1) denotation for algebraic op-erations on fuzzy numbers [40]

uA

(x minus a)

(b minus a) x isin [a b]

(c minus x)

(c minus b) x isin [b c]

0 otherwise

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(1)

1113957a (a1 b2 c3) and 1113957b (a1 b2 c3) are two fuzzytriangular numbers (FTNs) then the basic calculation ofFTNs 1113957a and 1113957b can be defined as follows [41]

addition 1113957a + 1113957b a1 + a2 b1 + b2 c1 + c2( 1113857

subtraction 1113957a minus 1113957b a1 minus c2 b1 minus b2 c1 minus a2( 1113857

multiplication 1113957a times 1113957b a1 times a2 b1 times b2 c1 times c2( 1113857

division 1113957adivide1113957b a1dividec2 b1divideb2 c1dividea2( 1113857

multiplication by constant k1113957a ka1 kb2 kc3( 1113857

inverse (1113957a)minus 1

1c1

1b1

1a1

1113888 1113889

(2)If a decision group has kDMs and the fuzzy ratings (FRs)

of all DM preferences are the FTNs 1113957Rk(ak bk ck) nextthe aggregated FRs will be obtained from 1113957R(a b c)

where a min ak b

1113937Kk1 bk

K

1113969

and c max ck withk 1 2 K

e FRs and importance weight of the kth(k 1 2 middot middot middot K) and the DMs are 1113957xijk (aijk bijk cijk) and1113957wjk (1113957wjk1 1113957wjk2 1113957wjk3) respectively where i 1 2 mand j 1 2 n erefore the fuzzy group ratings 1113957xij ofith alternatives with pertaining to jth criterion will be ob-tained from 1113957xij (aij bij cij) where aij min aijk

bij 1113937

Kk1 bijk

K

1113969 and cij max cijk and the fuzzy group

weights 1113957wj of each criterion will be obtained from 1113957wj

(wj1 wj2 wj3) where wi1 minwjk1 wj2 1113937

Kk1 wjk2

K

1113969

and wj3 maxwjk3

Mathematical Problems in Engineering 3

In addition the consistency index (CI) and consistencyratio (CR) are calculated as CI (λmax minus n)(n minus 1) λmax isthe maximum given eigenvector of the comparative matrixand n is the number of criteria in the matrixe consistencyratio (CR) is used to estimate directly the consistency ofpairwise comparisons e CR is computed by dividing theCI by a value obtained from a table of Random ConsistencyIndex (RI) CRCIRI If the CR is less than 010 thecomparisons are acceptable otherwise not RI is the averageindex for randomly generated weights

32 Fuzzy Additive Ratio Assessment A new fuzzy ARAStechnique was put forward by Zavadskas et al [42]e stepsof the fuzzy ARAS approach can be precisely described asfollows [40 43 44]

e first stage is establishing a fuzzy decision-makingmatrix for each criterion e typical form of the fuzzyMCDM discrete issue which contains m alternatives and ncriteria (i 0 1 m and j 1 2 n) can be shown ina fuzzy decision-making matrix as

1113957X

1113957x01 middot middot middot 1113957x0j middot middot middot 1113957x0n

⋮ ⋱ ⋮ ⋱ ⋮

1113957xi1 middot middot middot 1113957xij middot middot middot 1113957xin

⋮ ⋱ ⋮ ⋱ ⋮

1113957xm1 middot middot middot 1113957xmj middot middot middot 1113957xmm

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(3)

where 1113957x0j denotes the optimal value of j criterion and 1113957xij

denotes a fuzzy value indicating the performance value of the

ialternative in terms of the jcriterion in which m is items ofalternatives and n is the item of criteria picture each al-ternative When the DMs do not have preferences theoptimal performance ratings are obtained by x0j max xij

j isin Ωmax and x0j minxij j isin Ωmin where x0j denotes theoptimal performance rating to the jth criterionx0j max xij indicates benefit criteria for optimization di-rection are maximization and x0j min

ixij represents cost

criteria for optimization direction are minimizedIn the second stage the decision of a fuzzy normalized

matrix for the initial value is computed e initial values ofall criteria are normalized and the initial values 1113957xijofnormalized decision-making matrix 1113957X are as

1113957X


⋮ ⋱ ⋮ ⋱ ⋮1113957xi1 middot middot middot 1113957xij middot middot middot 1113957xin

⋮ ⋱ ⋮ ⋱ ⋮1113957xm1 middot middot middot 1113957xm1 middot middot middot 1113957xmn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

i 0 1 m j 1 2 n

(4)When the criteria whose preferable values are maxima

(eg benefit criteria) they are normalized as shown in thefollowing formula

1113957xij 1113957xij

1113936mi0 1113957xij

(5)

where j isin Ωmax when the criteria whose preferable valuesare minima (eg cost criteria) the normalized are shown asfollows

1113957xij 11113957xij

1113936mi0 11113957xij

j isin Ωmin (6)

e third stage is to obtain the weight of fuzzy nor-malized decision matrix as follows

11139571113954X



⋮ ⋱ ⋮ ⋱ ⋮11139571113954xm1 middot middot middot 11139571113954xmj middot middot middot 11139571113954xmm

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

i 0 1 m j 1 2 n

(7)

e following formula obtains the fuzzy values of nor-malized weighted in all the criteria

Table 2 Suppliersrsquo selection criteria by Zimmer et al (2016)

Category Criteria

Economic Quality pricecostlowast lead timelowast flexibility relationship technical capability reverse logistics logistics costslowast rejectionratiolowast

Environmental Environmental management system resource consumption recycling reuses ecodesign controlling of ecologicalimpacts wastewater energy consumption air emissions and environmental code of conduct

SocialInvolvement of stakeholders social management commitment health and safety stakeholder relations the rights ofstakeholders staff training social code of conduct donations for sustainable projects safety practices annual number of

accidentslowast indicates quantitative criteria and all others are qualitative criteria

uA (x)

x

1

0α β γ

Figure 1 Triangular membership function fuzzy number


11139571113954xij 1113957xij times 1113957wj i 0 1 m j 1 2 n (8)

where 11139571113954xij is the weighted normalized performance rating ofthe ith alternative in relation to the jth criterion and 1113957wj is theweight (importance) of the j criterion

e following task is to compute the overall performanceindex for each alternative e overall performance index 1113957Si ofeach alternative can be obtained as the sum of weightednormalized performance ratings using the following formula

1113957Si 1113944n

j1

11139571113954xij i 0 1 m (9)

where 1113957Si is the value of the optimality function of the ithalternative then the highest value is the best and the lastone is the worst In addition the center-of-area method isthe most practical and simple to use

1113957Si 13

1113957Siα + 1113957Siβ + 1113957Sic1113872 1113873 i 0 1 m (10)

e final step is to calculate the utility degree to eachalternative e utility degree of an alternative Ai will beobtained using the following model

Qi Si

S0 i 0 1 m (11)

where S0 and Si are the optimal criterion values and obtainedfrom equation (10) Qi is the degree of utility of the ithalternative and the largest value of Qi is the best value

33 Multisegment Goal Programming Goal programming(GP) is the most powerful techniques that have been appliedto solve various decision-making issuers in which targetshave been assigned to all attributes and the DMs are thepreference in minimizing the not achievement of the rele-vant goal [45] However GP cannot solve some multi-aspiration levels of management and economic problemsLiao [46] put forward a multisegment goal programming(MSGP) method to solve multisegment aspiration level(MSAL) problems and then the DMs can set multipleaspiration levels to each segment goal levels

e MSGP model has been formulated under no penaltyweight as the following achievement function [40 46]

MSGP model

Min Z 1113944n

i1d

+i + d

minusi( 1113857

st fi(x) + d+i minus d

minusi gi

fi(x) 1113944m

j1sijBij(b) times xi

sij si1 or si2 or or sim

sijBij(b) isin Ri(x) i 0 1 n j 1 2 m

d+i d

minusi ge 0 i 0 1 n

X isin F(F is a feasible set)

(12)

where d+i and dminus

i represent positive and negative devia-tions respectively attached to the ith goal |fi(x) minus gi| andsij is a decision variable coefficient which represents themultisegment aspiration levels of the jth segment of the ithgoal In addition Bij(b) represents a function of a binaryserial number and Ri(x) is the function of resourcelimitations

Following Changrsquos [47] fuzzy GP idea the MSGP modelcan be reformulated as follows

MinZ 1113944n

i1d

+i + d

minusi( 1113857 + e

+i + e

minusi( 1113857 (13)

st 1113944m

j1sijBij(b) times xi + d

+i minus d

minusi gi

1Li

bismaxij + 1 minus bi( 1113857s

minij1113872 1113873 minus e

+i + e

minusi

(14)

1Li

smaxij or s

minij1113872 1113873 (15)

Li smaxij minus s

minij1113872 1113873

sijBij(b) isin Ri(x) bi isin 0 1 d+i d

minusi e

+i e

minusi ge 0


(16)

where e+i and eminus

i are the positive and negative deviationsrespectively attached to the ith goal |yi minus smax

ij | or |yi minus sminij |

αi represents the weights attached to the sum of the devi-ations (e+

i + eminusi ) and smax

ij and sminij are the lower and upper

bounds of the ith goal respectively All other variables aredetermined in the MSGP model

In this case a new approach combining FAHP FARASand MSGP is integrated to solve the problem of supplierselection for in-flight duty-free product First fuzzy AHP isused to compute the relative weight for each criterion basedon the subjective determination from DMs from the airlinecompany (eg EVA Air) Second FARAS technology cal-culates a closeness coefficient (CC) for the capability of eachalternative supplier with respect to each criterion Finallyquantitative constraints (ie those related to benefit cost orbusiness strategic demand criteria) are merged into theMSGP pattern to identify the optimality supplier e in-tegration method steps are as follows

FAHP step

(1) Identify criteria of supplier selection and pairwisecomparison of criteria for each supplier

(2) Determine criteria weights for each candidate

FARAS step using the weights obtained from FAHPstep into FARAS to calculate closeness coefficient foreach alternative with respect to each criterionIntegration step formulate the main goals of supplerselection into FAHP FARAS and MSGP modelsAlso the process of this integration is shown inFigure 2


4 Supplier Selection for In-Flight Duty-FreeProduct Application

e proposed method is applied to the largest and well-knownairline in Taiwan EVA Air (BR) is airline seeks the bestsupplier for their in-fight duty-free product in order to achievea competitive advantage and increase the number of passengerssatisfied with the aviation industrymarket An EVAAir projectdecision committee comprised five members such as CEO topmarketing manager and top purchase say (D1 D2 and D3)respectively and two in-fight retail experts (D4 and D5) etwo experts were invited to participate in this committee andprovide their valuable opinions

e following criteria used to evaluate the suppliershad to be set up for the project decision committee Basedon a literature review from the committee and retail ex-perts using the nominal group technique (NGT) methodthe supplierrsquos evaluation qualitative criteria have beendecided as follows

(i) 1113957c1 product quality(ii) 1113957c2 delivery performance

(iii) 1113957c3 brand image

(iv) 1113957c4 pricecost level

(v) 1113957c5 financial stability

Meanwhile the market survey has five suppliers S1S2 S3 S4 and S5 remaining for further evaluation andselection e FAHP hierarchical structure of the sup-plierrsquos selection decision-making problem is shown inFigure 3

In general airlines have provided in-flight duty-freeproduct for the customer to purchase pending their flightMany airlines offer the customer the opportunity to pur-chase from a wider goods range and place orders prior todeparture [6] e general airline retail products categorycan be divided into different items of related goods forexample EVA Air offers in-flight duty-free products asshown in Table 3 and EVA Airrsquos sales share in revenuegeneration 2018 is presented in Figure 4

In the first stage by applying formula in Section 31CI (λmax minus n)(n minus 1) and CRCIRI e consistencyproperty of each DMrsquos comparison results is examined bycalculating the CR From consistency ratio CR 0083 itshows that the judgment matrix processes consistencyFurthermore the DMs use the fuzzy membership func-tion (FMF) for linguistic values as shown in Figure 5 andthe corresponding linguistic term for the supplierrsquosevaluation is displayed in Table 4 to evaluate the im-portance of the criteria In addition the importance offuzzy weights of the criteria decided by DMs is displayedin Table 5

Using FARAS to calculate closeness coefficient for each alternative with respect to

each criterion

Fined the optimal suppliers for in-fight retailer product

FAHP

Determine criteria weights for each candidate

Yes

Consistency check CR lt 01

No

Weight calculation

Identify criteria of supplier selection and pairwise

comparison of criteria for each supplier

Computation with LINGO for suppliersrsquo

evaluation

Formulate the main goals of supplier selection into FAHP

FARAS and MSGP models

Quantitative goals demand by company

- Goal 1hellip- Goal 2hellip

- Goal nhellip

Supplier candidates of in-fight retail products

Figure 2 An integrated FAHP-FARAS-MSGP procedure for supplier selection


In the second stage the DMs use the correspondinglinguistic term for the supplierrsquos evaluation shown in Table 4to assess the rating of each candidate about each criterionand then the ratings are shown in Table 6

In the third stage a fuzzy weighted decision matrix iscreated using the weights of each criterion (Wi) in Table 5and the linguistic evaluations are shown in Table 6 which arepresented in Table 7 displaying the decision values of fuzzyweighted

S1 S2 S3 S4 S5

Supplier selection for in-flight retail products

Product quality

c1~

Delivery performance

c2~

Assortment capability

c3~

Pricecost level

c4~

Financial stability

c5~

Figure 3 FAHP hierarchy structure of supplier selection problem

Table 3 Airline retail product categories by Eva Air (BR)

Product category In-flight retail products itemsSkincare products 84Necklace jewelry 30Watches 21Perfume 18Liquor 14Walletbeltleather bag 12Beauty products 12Health food 7Others (scarves and travel gadgets) 6Pen 5Sunglasses 43C products 4Resource Eva Air (BR) internal document 2018

Skin care products (39)

Necklace jewelry (14)

Watches (10)

Perfume (8)

Liquor (6)

Walletbelt leather bag

(5)

Beauty products (6)

Health food (3)

Others (scarves and travel gadgets)

(3)

Pen (2)

Sunglasses (2)

3C products (2)

Figure 4 Eva Airrsquos sales share in revenue generation 2018

0 01 02 03 04 05 06 07 08 09

N VL L FL ML M MG FG G VG E

1

Figure 5 Fuzzy membership function for linguistic values

Table 4 Corresponding linguistic term for supplierrsquos evaluation

Linguistic terms (abbreviation) Fuzzy preferenceNone (N) (0 0 01)Very low (VL) (0 01 02)Low (L) (01 02 03)Fairly low (FL) (02 03 04)More or less low (ML) (03 04 05)Medium (M) (04 05 06)More or less good (MG) (05 06 07)Fairly good (FG) (06 07 08)Good (G) (07 08 09)Very good (VG) (08 09 1)Excellent (E) (09 1 1)


In the fourth stage by using equations (3) and (4) thefuzzy decision matrix of five alternatives is derived andshown in Table 8

In the fifth stage using equations (5) and (6) and Table 8the decision-making of the normalized fuzzy matrix isconstructed and displayed in Table 9

In the following stage by using equations (7)ndash(11) thefuzzy decision-making matrix of normalized weighted andsolution results are derived and displayed in Table 10

e final stage in line with the normalized weights(Qi i 1 2 5) obtained for each supplier in Table 10 isused as a priority value to set up the integrated fuzzy

Table 5 Aggregated fuzzy weight of criteria by decision makers (DMs)

Fuzzy criterionDecision makers (DMs)

Fuzzy group weight 1113957wiD1 D2 D3 D4 D5Ratings

1113957c1 (05 06 07) (04 05 06) (08 09 1) (08 09 1) (08 09 1) (04 071 1)1113957c2 (04 05 06) (05 06 07) (04 05 06) (06 07 08) (07 08 09) (04 061 09)1113957c3 (08 09 1) (07 08 09) (06 07 08) (05 06 07) (06 07 08) (05 073 1)1113957c4 (07 08 09) (03 04 05) (05 06 07) (03 04 05) (04 05 06) (03 052 09)1113957c5 (05 06 07) (02 03 04) (09 1 1) (08 09 1) (05 06 07) (02 063 1)

Table 6 e rating of five criteria by DMs

Fuzzy criterion Decision makers (DMs)Alternatives

S1 S2 S3 S4 S5Ratings

1113957c1

D1 (04 05 06) (06 07 08) (05 06 07) (04 05 06) (06 07 08)D2 (04 05 06) (03 04 05) (07 08 09) (04 05 06) (09 1 1)D3 (07 08 09) (03 04 05) (03 04 05) (07 08 09) (05 06 07)D4 (05 06 07) (05 06 07) (03 04 05) (06 07 08) (04 05 06)D5 (03 04 05) (07 08 09) (04 05 06) (04 05 06) (07 08 09)

1113957c2

D1 (07 08 09) (03 04 05) (06 07 08) (05 06 07) (04 05 06)D2 (03 04 05) (04 05 06) (07 08 09) (07 08 09) (05 06 07)D3 (04 05 06) (06 07 08) (05 06 07) (04 05 06) (07 08 09)D4 (07 08 09) (03 04 05) (09 1 1) (08 09 1) (04 05 06)D5 (04 05 06) (04 05 06) (04 05 06) (04 05 06) (07 08 09)

1113957c3

D1 (07 08 09) (05 06 07) (05 06 07) (07 08 09) (05 06 07)D2 (07 08 09) (04 05 06) (04 05 06) (09 1 1) (07 08 09)D3 (05 06 07) (06 07 08) (07 08 09) (07 08 09) (04 05 06)D4 (04 05 06) (06 07 08) (03 04 05) (07 08 09) (03 04 05)D5 (04 05 06) (06 07 08) (04 05 06) (03 04 05) (07 08 09)

1113957c4

D1 (06 07 08) (04 05 06) (05 06 07) (04 05 06) (05 06 07)D2 (03 04 05) (05 06 07) (04 05 06) (07 08 09) (04 05 06)D3 (04 05 06) (04 05 06) (07 08 09) (04 05 06) (08 09 1)D4 (03 04 05) (07 08 09) (03 04 05) (06 07 08) (07 08 09)D5 (04 05 06) (05 06 07) (04 05 06) (06 07 08) (04 05 06)

1113957c5

D1 (04 05 06) (05 06 07) (06 07 08) (03 04 05) (05 06 07)D2 (09 1 1) (04 05 06) (04 05 06) (09 1 1) (04 05 06)D3 (06 07 08) (07 08 09) (04 05 06) (03 04 05) (07 08 09)D4 (04 05 06) (04 05 06) (07 08 09) (07 08 09) (04 05 06)D5 (07 08 09) (05 06 07) (04 05 06) (04 05 06) (09 1 1)

Table 7 e fuzzy decision matrix of five alternatives

Fuzzy criterionAlternatives


1113957c1 (03 054 1) (03 056 09) (03 052 08) (04 059 09) (05 077 1)1113957c2 (03 058 09) (03 049 08) (05 07 1) (04 064 1) (04 063 09)1113957c3 (04 063 09) (04 063 08) (03 054 09) (03 073 1) (03 06 09)1113957c4 (03 049 08) (04 059 098) (03 034 09) (04 063 09) (04 064 1)1113957c5 (04 067 1) (04 059 09) (04 059 0 9) (03 058 1) (04 063 1)


Table 8 e change in fuzzy decision matrix of five alternatives


TotalS0 S1 S2 S3 S4 S5Ratings

1113957c1 100 (03 054 1) (03 056 09) (03 052 08) (04 059 09) (05 077 1) (28 398 56)1113957c2 100 (03 058 09) (03 049 08) (05 07 1) (04 064 1) (04 063 09) (29 403 56)1113957c3 100 (04 063 09) (040 63 08) (03 0540 9) (03 073 1) (03 0609) (27 413 55)1113957c4 100 (03 049 08) (04 059 098) (03 034 09) (04 063 09) (04 064 1) (28 389 55)1113957c5 100 (04 067 1) (04 059 09) (04 059 09) (03 058 1) (04 063 1) (29 406 58)

Table 9 e normalized fuzzy decision-making matrix


S0 S1 S2 S3 S4 S5Ratings

1113957c1 (018 025 036) (005 014 036) (005 014 032) (005 013 029) (007 015 032) (009 019 036)1113957c2 (018 025 034) (005 014 031) (005 012 028) (009 017 034) (007 016 034) (007 016 031)1113957c3 (018 024 037) (007 015 033) (007 015 030) (005 013 033) (005 018 037) (005 014 033)1113957c4 (018 026 036) (005 013 029) (007 015 032) (005 014 032) (007 016 032) (007 016 036)1113957c5 (017 025 034) (007 017 034) (007 015 031) (007 014 031) (005 014 034) (007 016 034)

Table 10 e normalized weights fuzzy decision-making matrix and FARAS solution results as figures



1113957c1 (007 019 036) (002 01 036) (002 01 032) (002 01 029) (003 011 032) (004 014 036)1113957c2 (007 015 031) (002 009 028) (002 007 025) (004 011 031) (003 010 031) (003 009 028)1113957c3 (0 018 037) (004 01 033) (004 011 03) (003 010 033) (003 013 037) (003 011 033)1113957c4 (005 013 032) (002 007 026) (002 008 029) (002 007 029) (002 008 029) (002 009 032)1113957c5 (003 015 034) (001 01 034) (001 009 031) (001 009 031) (001 009 034) (001 01 034)1113957Si (032 08 17) (011 047 157) (011 046 147) (011 046 153) (012 051 164) (013 053 164)

Alternatives

032

080

170

011

047

157

011

046

147

011

046

153

012

051

164

013

053

164

000020040060080100120140160180

aA0b c a b c a b c a b c a b c a b c

A1 A2 A3 A4 A5

Si 0943 0717 0680 0702 0754 0763Qi 1 076 072 074 080 081

1000

076 072 074 080 081

0000

0200

0400

0600

0800

1000

1200

Q0 Q1 Q2 Q3 Q4 Q5


MSGP method to get the best supplier selectionprocedure

Furthermore following the business strategy by EVAAir the top managers of EVA Air established other goals todetermine the supplier selection criteria as follows

G1 minimizes average purchase cost such asf1(x)le 5300 (NT$ 1000month)

G2 more services capability items such asf2(x)ge 5items

G3 more operation experience such as f3(x)ge 12 yearsG4 the highest weighted of supplier such asf4(x) 1To select the best in-flight duty-free product supplier

EVA Air outsources market research of the suppliersrsquo sales

records from the last five years e relation coefficients ofvariables in the supplier profiles are displayed in Table 11which indicates the data set and ranges for all suppliers

Consider the quantitative criteria in Table 10 and theintegration of fuzzy MSGP method for supplier selectiondecision issue adapted from equation (13) to allow one-sideddeviations as follows

MinZ d+1 + d

minus2 + d

minus3 + d

+4 + d

minus4 + e

+1 + e

+2 + e

minus3 + e

minus4 + e

minus5

(17)

Satisfy all obligatory goals

st 4500b1 + 5200 1 minus b1( 1113857( 1113857x1 + 4620x2 + 3450b2 + 3800 1 minus b2( 1113857( 1113857x3 + 4200x4 + 5350x5 minus d+1 + d

minus1 5300 (18)

For purchase cost minimization goal1

700 4500b1 + 5200 1 minus b1( 1113857( 1113857minus e

+1 + e

minus1 743 (19)

Minimization of purchase cost for S11

350 3450b2 + 3800 1 minus b2( 1113857( 1113857minus e

+2 + e

minus2 1085 (20)


4b3 + 7 1 minus b3( 1113857x1 + 3b4+( 5 1 minus b4( 1113857x2 + 5x3(

+ 2b5 + 6 1 minus b5( 1113857x4 + 5x5 minus d+2 + d

minus2 5(

(21)

Maximization of service capability items

13 4b3 + 7 1 minus b3( 1113857( 1113857

minus e+3 + e

minus3 333 (22)

Maximization of service capability items for S11

2 3b4 + 5 1 minus b4( 1113857( 1113857minus e

+4 + e

minus4 350 (23)


4 2b5 + 6 1 minus b5( 1113857( 1113857minus e

+5 + e

minus5 250 (24)


14x1 + 10x2 + 8x3 + 11x4 + 9x5 minus d+3 + d

minus3 12 (25)

Maximization of operation experience

076x1 + 072x2 + 074x3 + 080x4 + 081x5 + dminus4 1

(26)

For weighing supplier goal

bi isin o 1 i 1 2 3 5 (27)

represents the binary number

d+i d

minusi ge 0 i 1 2 4

e+i e

minusi ge 0 i 1 2

(28)

represents the deviation from the targete integration fuzzy MSGP model was solved using

LINGO software [48] on a Pentium (R) 4 CPU 200 GHz-based microcomputer in a few seconds of computer pro-cessing time e solutions are as follows

x2 1

x1 0

x3 0

x4 0

x5 0

(29)

erefore according to the results based on the in-volvement of quantitative criteria survey in the best supplierto EVAAir the S2 should be selected as the in-fight duty-freeproduct supplieris result differs from the previous resultssince the integration fuzzy MSGP method considers qual-itative and quantitative criteria at the same time as thedecision supplier

Table 11 Five supplierrsquos data from Eva Airrsquos outsource research

SuppliersQuantitative criteria

Average purchase cost (NT$1000month) Service capability items Operation experience (years)S1 4500ndash5200 4ndash7 14S2 4620 3ndash5 10S3 3450ndash3800 5 8S4 4200 2ndash6 11S5 5350 4 9


5 Conclusions

e air travel market in Taiwan has witnessed both domesticand international competitions in recent years ereforein-flight retail product revenue has become an essential keyto the competitiveness and long-term survival of the airlineindustry e appropriate selection of a sustainable supplieris important to ensure the quality of in-flight duty-freeproducts to increase consumer satisfactionis paper offersa new integration method using a combination of fuzzyAHP fuzzy ARAS and MSGP to select the best supplier inthe airline industry

e supplier selection problem comprises many multi-segment aspiration levels that may exist such as supplierrsquosaverage purchase cost thus this integrated approach allowsthe DMs to set multiaspiration levels for supplier evaluatione contribution of this integrated method is it enables si-multaneous consideration of both tangible (qualitative) andintangible (quantitative) criteria as well as both ldquohigher isbetterrdquo (eg benefit criteria) and ldquolower is betterrdquo (eg costcriteria) in in-flight retailing supplierrsquos selection problem Tothe best of our knowledge no researcher has been performedto solve supplier selection problems using an integrated fuzzyview of AHP ARAS and MSGP approaches Table 12 showsthe superiority of this proposedmethodwith othersemainadvantage of this paper is to propose an efficient and simplereference method to help airlines in selecting the best in-flightduty-free product supplier e findings show that whenconsidering qualitative criteria by using FARAS method thebest supplier was identified as S1 However if qualitative andquantitative criteria (eg four tangible constraints) wereincorporated into the FARAS-MSGP model the best supplieris calculated as S2

e main limitation of the proposed method is that itmay complicate the supplier selection problem because ofmore complicated vagueness and imprecision of goalsconstraints and parameters in decision-making ere-fore future work could link the fuzzy MSGP approach insupplier selection problems Moreover the proposed ap-proach can be useful for many fuzzy MCDM issues forexample supplier-related activity selection supplier seg-mentation or in-flight shopping marketing and airlineproject management when available information is vagueimprecise and uncertain In addition in future research

can consider combining DEMATEL MSGP and TOPSISmethods into the proposed model to reduce the number ofcriteria comparisons and achieve a more objective direc-tion [49 50]

Abbreviation

LPGP Linear programminggoal programmingAHPANP Analytical hierarchy processanalytical

network processDEA Data envelopment analysisCBM Cost-based methodNN Neural networkDEMATEL Decision-making trial and evaluationTOPSIS Techniques for order preference by similarity

to ideal solutionFAHP Fuzzy analytical hierarchy process (FAHP)FARAS Fuzzy additive ratio assessmentMSGP Multisegment goal programming

Data Availability

e data used to support the findings of this study are in-cluded within the article

Disclosure

e research did not receive any specific funding but wasperformed as part of Department of Aviation Managementand Services China University of Science and Technology

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] E Sezgen K J Mason and R Mayer ldquoVoice of airlinepassenger a text mining approach to understand customersatisfactionrdquo Journal of Air Transport Management vol 77pp 65ndash74 2019

[2] Civil Aeronautics Administration (CAA) Civil Air Trans-portation Statistics Annual Report Ministry of Transportationand Communications Taiwan 2017

Table 12 Comparison of supplier selection methods

MethodslowastSelection criteria

Multisegment aspiration levelsQualitative Quantitative

LPGP No Yes NoAHPANP Yes No NoDEA No Yes NoCBE No Yes NoNN Yes No NoDEMATEL No Yes NoTOPSIS Yes No NoAHP (or ANP)+TOPSIS Yes No NoFuzzy ARAS Yes No Nois proposed method (FAHP+FARAS+MSGP) Yes Yes YeslowastPlease see Appendix A for all these abbreviations


[3] S-W Perng C-C Chow and W-C Liao ldquoAnalysis ofshopping preference and satisfaction with airport retailingproductsrdquo Journal of Air Transport Management vol 16no 5 pp 279ndash283 2010

[4] W Li S Yu H Pei C Zhao and B Tian ldquoA hybrid approachbased on fuzzy AHP and 2-tuple fuzzy linguistic method forevaluation in-flight service qualityrdquo Journal of Air TransportManagement vol 60 pp 49ndash64 2017

[5] H H Hsu W L Huang Y K Fu and C N Liao ldquoA fuzzymodel to green supplier selection using AHP ARAS andMCGP approachrdquo Transylvanian Review vol XXIV no 82016

[6] J Rezaei P B M Fahim and L Tavasszy ldquoSupplier selectionin the airline retail industry using a funnel methodologyconjunctive screening method and fuzzy AHPrdquo Expert Sys-tems with Applications vol 41 no 18 pp 8165ndash8179 2014

[7] O Jadidi S Zolfaghari and S Cavalieri ldquoA new normalizedgoal programming model for multi-objective problems a caseof supplier selection and order allocationrdquo InternationalJournal of Production Economics vol 148 no 2 pp 158ndash1652014

[8] I Sultana I Ahmed and A Azeem ldquoAn integrated approachfor multiple criteria supplier selection combining FuzzyDelphi Fuzzy AHP and Fuzzy TOPSISrdquo Journal of Intelligentand Fuzzy Systems vol 29 no 4 pp 1273ndash1287 2015

[9] S V Parkouhi A S Ghadikolaei and H F Lajimi ldquoResilientsupplier selection and segmentation in grey environmentrdquoJournal of Cleaner Production vol 207 pp 1123ndash1137 2019

[10] H G Goren ldquoA decision framework for sustainable supplierselection and order allocation with lost salesrdquo Journal ofCleaner Production vol 183 pp 1156ndash1169 2018

[11] S K Chaharsooghi and M Ashrafi ldquoSustainable supplierperformance evaluation and selection with Neofuzzy TOPSISmethodrdquo International Scholarly Research Notices vol 2014Article ID 434168 10 pages 2014

[12] H M Wang Chen S Y Chou Q D Luu and T H K Yu ldquoAfuzzy MCDM approach for green supplier selection from theeconomic and environmental aspectsrdquo Mathematical Prob-lems in Engineering vol 2016 Article ID 8097386 10 pages2016

[13] C-N Liao and H-P Kao ldquoAn integrated fuzzy TOPSIS andMCGP approach to supplier selection in supply chainmanagementrdquo Expert Systems with Applications vol 38 no 9pp 10803ndash10811 2011

[14] Y-K Fu ldquoAn integrated approach to catering supplier se-lection using AHP-ARAS-MCGP methodologyrdquo Journal ofAir Transport Management vol 75 pp 164ndash169 2019

[15] A Memari A Dargi M R Akbari Jokar R Ahmad andA R Abdul Rahim ldquoSustainable supplier selection a multi-criteria intuitionistic fuzzy TOPSIS Methodrdquo Journal ofManufacturing Systems vol 50 pp 9ndash24 2019

[16] A Awasthi K Govindan and S Gold ldquoMulti-tier sustainableglobal supplier selection using a fuzzy AHP-VIKOR basedapproachrdquo International Journal of Production Economicsvol 195 pp 106ndash117 2018

[17] A Fallahpour E Udoncy Olugu S Nurmaya Musa K YewWong and S Noori ldquoA decision support model for sus-tainable supplier selection in sustainable supply chain man-agementrdquo Computers and Industrial Engineering vol 105pp 391ndash410 2017

[18] S K Liao H Y Hsu and K L Chang ldquoOTAs selection for hotspring hotels by a hybrid MCDM modelrdquo MathematicalProblems in Engineering vol 2019 p 9 Article ID 42513622019

[19] H Shi M-Y Quan H-C Liu and C-Y Duan ldquoA novelintegrated approach for green supplier selection with interval-valued intuitionistic uncertain linguistic information a casestudy in the agri-food industryrdquo Sustainability vol 10 no 3p 733 2018

[20] W Tsui and U P Wen ldquoA hybrid multiple criteria groupdecision-making approach for green supplier selection in theTFT-LCD industryrdquo Mathematical Problems in Engineeringvol 2014 Article ID 709872 13 pages 2014

[21] A Ulutas A Topal and R Bakhat ldquoAn application of fuzzyintegrated model in green supplier selectionrdquo MathematicalProblems in Engineering vol 2019 Article ID 425635911 pages 2019

[22] S K Jauhar and M Pant ldquoIntegrating DEA with DE andMODE for sustainable supplier selectionrdquo Journal of Com-putational Science vol 21 pp 299ndash306 2017

[23] C Yu and T N Wong ldquoAn agent-based negotiation modelfor supplier selection of multiple products with synergy ef-fectrdquo Expert Systems with Applications vol 42 no 1pp 223ndash237 2015

[24] C-W Hsu T-C Kuo S-H Chen and A H Hu ldquoUsingDEMATEL to develop a carbon management model ofsupplier selection in green supply chain managementrdquoJournal of Cleaner Production vol 56 pp 164ndash172 2013

[25] C-N Liao and H-P Kao ldquoSupplier selection model usingTaguchi loss function analytical hierarchy process and multi-choice goal programmingrdquo Computers and Industrial Engi-neering vol 58 no 4 pp 571ndash577 2010

[26] K Hallmann S Muller S Feiler C Breuer and R RothldquoSuppliersrsquo perception of destination competitiveness in awinter sport resortrdquo Tourism Review vol 67 no 2 pp 13ndash212012

[27] R Hammami C Temponi and Y Frein ldquoA scenario-basedstochastic model for supplier selection in global context withmultiple buyers currency fluctuation uncertainties and pricediscountsrdquo European Journal of Operational Researchvol 233 no 1 pp 159ndash170 2014

[28] C Rao and N Zhang ldquoMulti-attribute decision model ofgreen supplier selection under the low-carbon economyrdquo inProceedings of the International Conference on Applied Scienceand Engineering Innovation ASEI Jinan China August 2015

[29] D Kannan R Khodaverdi L Olfat A Jafarian and A DiabatldquoIntegrated fuzzy multi criteria decision making method andmulti-objective programming approach for supplier selection andorder allocation in a green supply chainrdquo Journal of CleanerProduction vol 47 pp 355ndash367 2013

[30] B Bankian-Tabrizi K Shahanaghi and M Saeed JabalamelildquoFuzzy multi-choice goal programmingrdquo Applied Mathe-matical Modelling vol 36 no 4 pp 1415ndash1420 2012

[31] J Gheidar Kheljani S H Ghodsypour and C OrsquoBrienldquoOptimizing whole supply chain benefit versus buyerrsquos benefitthrough supplier selectionrdquo International Journal of Pro-duction Economics vol 121 no 2 pp 482ndash493 2009

[32] K Zimmer M Frohling and F Schultmann ldquoSustainablesupplier management - a review of models supporting sus-tainable supplier selection monitoring and developmentrdquoInternational Journal of Production Research vol 54 no 5pp 1412ndash1442 2016

[33] G D Chiappa J C Martin and C Roman ldquoService quality ofairportsrsquo food and beverage retailers A fuzzy approachrdquo Journal ofAir Transport Management vol 53 pp 105ndash113 2016

[34] C-C Hsu and J J H Liou ldquoAn outsourcing provider decisionmodel for the airline industryrdquo Journal of Air TransportManagement vol 28 pp 40ndash46 2013


[35] L Vijayvargy ldquoModeling of intangibles an application insupplier selection in supply chain - a case study of multi-national food industryrdquo International Journal of Managementand Innovation vol 5 no 1 pp 61ndash79 2013

[36] Y-C Chang and N Lee ldquoA multi-objective goal program-ming airport selection model for low-cost carriersrsquo networksrdquoTransportation Research Part E Logistics and TransportationReview vol 46 no 5 pp 709ndash718 2010

[37] Y Peng G Kou G Wang W Wu and Y Shi ldquoEnsemble ofsoftware defect predictors an AHP-based evaluationmethodrdquo International Journal of Information Technology ampDecision Making vol 10 no 1 pp 187ndash206 2011

[38] V Kersuliene and Z Turskis ldquoIntegrated fuzzy multiplecriteria decision making model for architect selectionrdquoTechnological and Economic Development of Economy vol 17pp 645ndash666 2011

[39] D Bozanic D Pamucar and D Bojanic ldquoModification of theanalytic hierarchy process (AHP) method using fuzzy logicfuzzy AHP approach as a support to the decision makingprocess concerning engagement of the group for additionalhinderingrdquo Serbian Journal of Management vol 10pp 151ndash171 2015

[40] C N Liao Y K Fu and L C Wu ldquoIntegrated FAHP ARAS-F and MSGP methods for green supplier evaluation andselectionrdquo Technological and Economic Development ofEconomy vol 22 no 5 pp 651ndash669 2016

[41] C-T Chen C-T Lin and S-F Huang ldquoA fuzzy approach forsupplier evaluation and selection in supply chain manage-mentrdquo International Journal of Production Economicsvol 102 no 2 pp 289ndash301 2006

[42] E K Zavadskas Z Turskis and T Vilutiene ldquoMultiple criteriaanalysis of foundation instalment alternatives by applying Ad-ditive Ratio Assessment (ARAS) methodrdquo Archives of Civil andMechanical Engineering vol 10 no 3 pp 123ndash141 2010

[43] Z Turskis and E K Zavadskas ldquoA new fuzzy additive ratioassessment method (Aras-f ) Case study the analysis of fuzzymultiple criteria in order to select the logistic centers loca-tionrdquo Transport vol 25 no 4 pp 423ndash432 2010

[44] D Stanujkic and R Jovanovic ldquoMeasuring a quality of facultywebsite using ARAS methodrdquo Contemporary Issues in Busi-ness Management and Education pp 545ndash554 2012

[45] C-N Liao ldquoA fuzzy approach to business travel airline se-lection using an integrated AHP-TOPSIS-MSGP methodol-ogyrdquo International Journal of Information Technology andDecision Making vol 12 no 01 pp 119ndash137 2013

[46] C-N Liao ldquoFormulating the multi-segment goal program-mingrdquo Computers and Industrial Engineering vol 56 no 1pp 138ndash141 2009

[47] C-T Chang ldquoMulti-choice goal programmingrdquo Omegavol 35 no 4 pp 389ndash396 2007

[48] L Schrage LINGO Release 80 LINDO System Inc ChicagoIL USA 2002

[49] R-X Nie Z-P Tian J-Q Wang H-Y Zhang andT-L Wang ldquoWater security sustainability evaluation ap-plying a multistage decision support framework in industrialregionrdquo Journal of Cleaner Production vol 196 pp 1681ndash1704 2018

[50] L Wang X K Wang J J Peng and J Q Wang ldquoe dif-ferences in hotel selection among various types of travellers acomparative analysis with a useful bounded rationalitybehavioural decision support modelrdquo Tourism Managementvol 76 Article ID 103961 2020


e importance of supplier selection has been increas-ingly recognized in supply chain management (SCM) SCMhas identified suppliers as significant based on consumersrsquopurchase decisions In recent years determining the bestsupplier in the supply chain has overwhelmingly become anessential strategy for business [5] e supplier selectionprocess is a multicriteria decision-making (MCDM) prob-lem due to the involvement of many conflicts in businessresources based on qualitative and quantitative criteria[6ndash8] erefore supplier selection is one of the sophisti-cated and many measures in the supply chain that has asignificant effect on the excellent capability of a business [9]However selecting the fittest supplier from many latentsuppliers is often a daunting work e sustainable supplierselection problem can be defined as the classical supplierselection issue that considers economic social and envi-ronmental criteria to select and monitor suppliersrsquo perfor-mances [10ndash12] For any manufacturer selecting the rightsupplier is crucial to success at the right supplier willsignificantly increase customer satisfaction reduce pur-chasing costs and improve competitive ability

ese years a large number of methodologies have beenused to decide the supplier evaluation problememethodsinclude goal programming (GP) linear programming (LP)statistical and probabilistic methods mathematical pro-gramming models multiple objective programming ana-lytic hierarchy process (AHP) analytic network process(ANP) techniques for order preference by similarity to idealsolution (TOPSIS) additive ratio assessment (ARAS) dataenvelopment analysis (DEA) cost-based methods (CBMs)decision-making trial and evaluation laboratory (DEMA-TEL) and neural networks (NNs) [13] Recently the inte-gration of different techniques within the supplier selectionprocess has received considerable attention in the SCMliterature for example Fu [14] focused on the performanceof AHP ARAS and MCGP approach in supplier selectionissues Additionally Memari et al [15] presented an intuitivefuzzy TOPSIS approach to select the right fit provider thatconsiders nine criteria and thirty subcriteria for an auto-motive spare parts manufacturer in relation to airlinecompanies Awasthi et al [16] used a fuzzy AHP-VIKOR-based approach for multi-tier sustainable global supplierselection Fallahpour et al [17] used the DEA decisionsupport model for sustainable supplier selection in sus-tainable supply chain management Liao et al [18] presenteda hybrid model for the selection of optimal online travelagencies (OTAs) using the fuzzy Delphi method (FDM)-DEMATEL-ANP Chaharsooghi and Ashrafi [11]

introduced a fuzzy MCDM approach using a neofuzzyTOPSIS method to find the best solution for sustainablesupplier selection based on the triple bottom line (TBL)approach in a supply chain Wang Chen [12] proposed acomprehensive fuzzy MCDM method for green supplierevaluation using fuzzy AHP and TOPSIS in the luminanceenhancement film (LEF) industry

In addition Shi et al [19] deployed a new integratedmodel based on interval-valued intuitionistic uncertainlinguistic sets (IVIULSs) and a grey relational analysis(GRA)-TOPSIS method for the selection of green suppliersTsui and Wen [20] proposed a hybrid multiple criteriagroup decision-making (MCGDM) method by using AHPentropy elimination and selection expressing the reality III(ELECTRE III) and the linear assignment method (LAM) toassist a thin film transistor liquid crystal display (TFT-LCD)manufacturer in choosing green suppliers Ulutas et al [21]develop a novel fuzzy multiattribute decision-making modelconsisting of a fuzzy extension of preference selection index(FPSI) and fuzzy extension of the range of value (FROV) todetermine the best supplier for a Turkish textile companyJauhar and Pant [22] integrated the DEA with DE andMODE for sustainable supplier selection problems Yu andWong [23] developed an agent-based CBM model forsupplier selection of multiple products with a synergisticeffect Rezaei et al [6] investigated supplier selection in theairline retail industry by using a conjunctive screeningmethod and fuzzy AHP Hsu et al [24] utilized theDEMATEL approach with an example in the green supplychain to improve the overall performance of supplier se-lection management Liao and Kao [25] integrated the AHPand MCGP model to solve the supplier selection issue eintegrated model uses source data provided for the airlineindustry to discuss the real world in supplier selectionHowever these techniques are not perfect for in-flight duty-free supplier evaluation and selection because the availableinformation in the airline context is inherently ambiguousinaccurate imprecise and uncertain by nature e novelintegration fuzzy AHP fuzzy ARAS and MSGP methodmay be useful for various MCDM problems is is a crucialcontribution to the paper

e remainder of this paper is structured as follows Inthe next section a detailed review of the criteria for supplierselection-related literature is presented Section 3 explainsthe proposed combined FAHP FARAS and MSGPmethods Section 4 used the integrated method to thesupplier selection for in-flight duty-free product with anumerical example to the airline firm In Section 5 the paperfinishes with concluding suggestions for future research

2 Literature Review

Many researchers have proposed different criteria to eval-uate the sustainability of supplier selectionere are variousimportant factors to consider when selecting suppliers in-cluding price discounts delivery time service level aquantity discount transportation cost carbon emission taxcurrency exchange rate supplier capacity and lead time[26 27] Rao and Zhang [28] summarized the supplier

Table 1 Number and growth rate of passengers entering andleaving in the top three airports in 2008 to 2017 in Taiwan (unitpersons)

YearAirports

TITA TKIA TTIA2008 21936083 4160515 31018542016 44878703 6479183 5943153Growth rate 51 36 48Resource Civil Aeronautics Administration (CAA) Annual Report (2017)









uA

(x minus a)


(c minus x)


0 otherwise

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(1)








1c1

1b1

1a1

1113888 1113889



where a min ak b

1113937Kk1 bk

K

1113969



bij 1113937

Kk1 bijk

K




Kk1 wjk2

K

1113969

and wj3 maxwjk3





1113957X


⋮ ⋱ ⋮ ⋱ ⋮


⋮ ⋱ ⋮ ⋱ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(3)








1113957X




⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

i 0 1 m j 1 2 n



1113957xij 1113957xij

1113936mi0 1113957xij

(5)


1113957xij 11113957xij

1113936mi0 11113957xij

j isin Ωmin (6)


11139571113954X




⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

i 0 1 m j 1 2 n

(7)



Category Criteria





uA (x)

x

1

0α β γ






1113957Si 1113944n

j1

11139571113954xij i 0 1 m (9)


1113957Si 13

1113957Siα + 1113957Siβ + 1113957Sic1113872 1113873 i 0 1 m (10)


Qi Si

S0 i 0 1 m (11)




MSGP model

Min Z 1113944n

i1d

+i + d

minusi( 1113857


minusi gi

fi(x) 1113944m




d+i d

minusi ge 0 i 0 1 n


(12)




MinZ 1113944n

i1d

+i + d

minusi( 1113857 + e

+i + e

minusi( 1113857 (13)

st 1113944m


+i minus d

minusi gi

1Li


minij1113872 1113873 minus e

+i + e

minusi

(14)

1Li

smaxij or s

minij1113872 1113873 (15)

Li smaxij minus s

minij1113872 1113873


minusi e

+i e

minusi ge 0


(16)









FAHP step
















each criterion


FAHP


Yes


No

Weight calculation




evaluation





- Goal nhellip






S1 S2 S3 S4 S5


Product quality

c1~


c2~


c3~

Pricecost level

c4~

Financial stability

c5~






Watches (10)

Perfume (8)

Liquor (6)


(5)

Beauty products (6)

Health food (3)


(3)

Pen (2)

Sunglasses (2)

3C products (2)


0 01 02 03 04 05 06 07 08 09


1












1113957c1 (05 06 07) (04 05 06) (08 09 1) (08 09 1) (08 09 1) (04 071 1)1113957c2 (04 05 06) (05 06 07) (04 05 06) (06 07 08) (07 08 09) (04 061 09)1113957c3 (08 09 1) (07 08 09) (06 07 08) (05 06 07) (06 07 08) (05 073 1)1113957c4 (07 08 09) (03 04 05) (05 06 07) (03 04 05) (04 05 06) (03 052 09)1113957c5 (05 06 07) (02 03 04) (09 1 1) (08 09 1) (05 06 07) (02 063 1)




1113957c1

D1 (04 05 06) (06 07 08) (05 06 07) (04 05 06) (06 07 08)D2 (04 05 06) (03 04 05) (07 08 09) (04 05 06) (09 1 1)D3 (07 08 09) (03 04 05) (03 04 05) (07 08 09) (05 06 07)D4 (05 06 07) (05 06 07) (03 04 05) (06 07 08) (04 05 06)D5 (03 04 05) (07 08 09) (04 05 06) (04 05 06) (07 08 09)

1113957c2

D1 (07 08 09) (03 04 05) (06 07 08) (05 06 07) (04 05 06)D2 (03 04 05) (04 05 06) (07 08 09) (07 08 09) (05 06 07)D3 (04 05 06) (06 07 08) (05 06 07) (04 05 06) (07 08 09)D4 (07 08 09) (03 04 05) (09 1 1) (08 09 1) (04 05 06)D5 (04 05 06) (04 05 06) (04 05 06) (04 05 06) (07 08 09)

1113957c3

D1 (07 08 09) (05 06 07) (05 06 07) (07 08 09) (05 06 07)D2 (07 08 09) (04 05 06) (04 05 06) (09 1 1) (07 08 09)D3 (05 06 07) (06 07 08) (07 08 09) (07 08 09) (04 05 06)D4 (04 05 06) (06 07 08) (03 04 05) (07 08 09) (03 04 05)D5 (04 05 06) (06 07 08) (04 05 06) (03 04 05) (07 08 09)

1113957c4

D1 (06 07 08) (04 05 06) (05 06 07) (04 05 06) (05 06 07)D2 (03 04 05) (05 06 07) (04 05 06) (07 08 09) (04 05 06)D3 (04 05 06) (04 05 06) (07 08 09) (04 05 06) (08 09 1)D4 (03 04 05) (07 08 09) (03 04 05) (06 07 08) (07 08 09)D5 (04 05 06) (05 06 07) (04 05 06) (06 07 08) (04 05 06)

1113957c5

D1 (04 05 06) (05 06 07) (06 07 08) (03 04 05) (05 06 07)D2 (09 1 1) (04 05 06) (04 05 06) (09 1 1) (04 05 06)D3 (06 07 08) (07 08 09) (04 05 06) (03 04 05) (07 08 09)D4 (04 05 06) (04 05 06) (07 08 09) (07 08 09) (04 05 06)D5 (07 08 09) (05 06 07) (04 05 06) (04 05 06) (09 1 1)




1113957c1 (03 054 1) (03 056 09) (03 052 08) (04 059 09) (05 077 1)1113957c2 (03 058 09) (03 049 08) (05 07 1) (04 064 1) (04 063 09)1113957c3 (04 063 09) (04 063 08) (03 054 09) (03 073 1) (03 06 09)1113957c4 (03 049 08) (04 059 098) (03 034 09) (04 063 09) (04 064 1)1113957c5 (04 067 1) (04 059 09) (04 059 0 9) (03 058 1) (04 063 1)





1113957c1 100 (03 054 1) (03 056 09) (03 052 08) (04 059 09) (05 077 1) (28 398 56)1113957c2 100 (03 058 09) (03 049 08) (05 07 1) (04 064 1) (04 063 09) (29 403 56)1113957c3 100 (04 063 09) (040 63 08) (03 0540 9) (03 073 1) (03 0609) (27 413 55)1113957c4 100 (03 049 08) (04 059 098) (03 034 09) (04 063 09) (04 064 1) (28 389 55)1113957c5 100 (04 067 1) (04 059 09) (04 059 09) (03 058 1) (04 063 1) (29 406 58)




1113957c1 (018 025 036) (005 014 036) (005 014 032) (005 013 029) (007 015 032) (009 019 036)1113957c2 (018 025 034) (005 014 031) (005 012 028) (009 017 034) (007 016 034) (007 016 031)1113957c3 (018 024 037) (007 015 033) (007 015 030) (005 013 033) (005 018 037) (005 014 033)1113957c4 (018 026 036) (005 013 029) (007 015 032) (005 014 032) (007 016 032) (007 016 036)1113957c5 (017 025 034) (007 017 034) (007 015 031) (007 014 031) (005 014 034) (007 016 034)




1113957c1 (007 019 036) (002 01 036) (002 01 032) (002 01 029) (003 011 032) (004 014 036)1113957c2 (007 015 031) (002 009 028) (002 007 025) (004 011 031) (003 010 031) (003 009 028)1113957c3 (0 018 037) (004 01 033) (004 011 03) (003 010 033) (003 013 037) (003 011 033)1113957c4 (005 013 032) (002 007 026) (002 008 029) (002 007 029) (002 008 029) (002 009 032)1113957c5 (003 015 034) (001 01 034) (001 009 031) (001 009 031) (001 009 034) (001 01 034)1113957Si (032 08 17) (011 047 157) (011 046 147) (011 046 153) (012 051 164) (013 053 164)

Alternatives

032

080

170

011

047

157

011

046

147

011

046

153

012

051

164

013

053

164

000020040060080100120140160180


A1 A2 A3 A4 A5

Si 0943 0717 0680 0702 0754 0763Qi 1 076 072 074 080 081

1000

076 072 074 080 081

0000

0200

0400

0600

0800

1000

1200

Q0 Q1 Q2 Q3 Q4 Q5










MinZ d+1 + d

minus2 + d

minus3 + d

+4 + d

minus4 + e

+1 + e

+2 + e

minus3 + e

minus4 + e

minus5

(17)



minus1 5300 (18)


700 4500b1 + 5200 1 minus b1( 1113857( 1113857minus e

+1 + e

minus1 743 (19)


350 3450b2 + 3800 1 minus b2( 1113857( 1113857minus e

+2 + e

minus2 1085 (20)




minus2 5(

(21)


13 4b3 + 7 1 minus b3( 1113857( 1113857

minus e+3 + e

minus3 333 (22)


2 3b4 + 5 1 minus b4( 1113857( 1113857minus e

+4 + e

minus4 350 (23)


4 2b5 + 6 1 minus b5( 1113857( 1113857minus e

+5 + e

minus5 250 (24)


14x1 + 10x2 + 8x3 + 11x4 + 9x5 minus d+3 + d

minus3 12 (25)


076x1 + 072x2 + 074x3 + 080x4 + 081x5 + dminus4 1

(26)


bi isin o 1 i 1 2 3 5 (27)


d+i d

minusi ge 0 i 1 2 4

e+i e

minusi ge 0 i 1 2

(28)



x2 1

x1 0

x3 0

x4 0

x5 0

(29)






5 Conclusions





Abbreviation




Data Availability


Disclosure




References

































































uA

(x minus a)


(c minus x)


0 otherwise

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(1)








1c1

1b1

1a1

1113888 1113889



where a min ak b

1113937Kk1 bk

K

1113969



bij 1113937

Kk1 bijk

K




Kk1 wjk2

K

1113969

and wj3 maxwjk3





1113957X


⋮ ⋱ ⋮ ⋱ ⋮


⋮ ⋱ ⋮ ⋱ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(3)








1113957X




⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

i 0 1 m j 1 2 n



1113957xij 1113957xij

1113936mi0 1113957xij

(5)


1113957xij 11113957xij

1113936mi0 11113957xij

j isin Ωmin (6)


11139571113954X




⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

i 0 1 m j 1 2 n

(7)



Category Criteria





uA (x)

x

1

0α β γ






1113957Si 1113944n

j1

11139571113954xij i 0 1 m (9)


1113957Si 13

1113957Siα + 1113957Siβ + 1113957Sic1113872 1113873 i 0 1 m (10)


Qi Si

S0 i 0 1 m (11)




MSGP model

Min Z 1113944n

i1d

+i + d

minusi( 1113857


minusi gi

fi(x) 1113944m




d+i d

minusi ge 0 i 0 1 n


(12)




MinZ 1113944n

i1d

+i + d

minusi( 1113857 + e

+i + e

minusi( 1113857 (13)

st 1113944m


+i minus d

minusi gi

1Li


minij1113872 1113873 minus e

+i + e

minusi

(14)

1Li

smaxij or s

minij1113872 1113873 (15)

Li smaxij minus s

minij1113872 1113873


minusi e

+i e

minusi ge 0


(16)









FAHP step
















each criterion


FAHP


Yes


No

Weight calculation




evaluation





- Goal nhellip






S1 S2 S3 S4 S5


Product quality

c1~


c2~


c3~

Pricecost level

c4~

Financial stability

c5~






Watches (10)

Perfume (8)

Liquor (6)


(5)

Beauty products (6)

Health food (3)


(3)

Pen (2)

Sunglasses (2)

3C products (2)


0 01 02 03 04 05 06 07 08 09


1












1113957c1 (05 06 07) (04 05 06) (08 09 1) (08 09 1) (08 09 1) (04 071 1)1113957c2 (04 05 06) (05 06 07) (04 05 06) (06 07 08) (07 08 09) (04 061 09)1113957c3 (08 09 1) (07 08 09) (06 07 08) (05 06 07) (06 07 08) (05 073 1)1113957c4 (07 08 09) (03 04 05) (05 06 07) (03 04 05) (04 05 06) (03 052 09)1113957c5 (05 06 07) (02 03 04) (09 1 1) (08 09 1) (05 06 07) (02 063 1)




1113957c1

D1 (04 05 06) (06 07 08) (05 06 07) (04 05 06) (06 07 08)D2 (04 05 06) (03 04 05) (07 08 09) (04 05 06) (09 1 1)D3 (07 08 09) (03 04 05) (03 04 05) (07 08 09) (05 06 07)D4 (05 06 07) (05 06 07) (03 04 05) (06 07 08) (04 05 06)D5 (03 04 05) (07 08 09) (04 05 06) (04 05 06) (07 08 09)

1113957c2

D1 (07 08 09) (03 04 05) (06 07 08) (05 06 07) (04 05 06)D2 (03 04 05) (04 05 06) (07 08 09) (07 08 09) (05 06 07)D3 (04 05 06) (06 07 08) (05 06 07) (04 05 06) (07 08 09)D4 (07 08 09) (03 04 05) (09 1 1) (08 09 1) (04 05 06)D5 (04 05 06) (04 05 06) (04 05 06) (04 05 06) (07 08 09)

1113957c3

D1 (07 08 09) (05 06 07) (05 06 07) (07 08 09) (05 06 07)D2 (07 08 09) (04 05 06) (04 05 06) (09 1 1) (07 08 09)D3 (05 06 07) (06 07 08) (07 08 09) (07 08 09) (04 05 06)D4 (04 05 06) (06 07 08) (03 04 05) (07 08 09) (03 04 05)D5 (04 05 06) (06 07 08) (04 05 06) (03 04 05) (07 08 09)

1113957c4

D1 (06 07 08) (04 05 06) (05 06 07) (04 05 06) (05 06 07)D2 (03 04 05) (05 06 07) (04 05 06) (07 08 09) (04 05 06)D3 (04 05 06) (04 05 06) (07 08 09) (04 05 06) (08 09 1)D4 (03 04 05) (07 08 09) (03 04 05) (06 07 08) (07 08 09)D5 (04 05 06) (05 06 07) (04 05 06) (06 07 08) (04 05 06)

1113957c5

D1 (04 05 06) (05 06 07) (06 07 08) (03 04 05) (05 06 07)D2 (09 1 1) (04 05 06) (04 05 06) (09 1 1) (04 05 06)D3 (06 07 08) (07 08 09) (04 05 06) (03 04 05) (07 08 09)D4 (04 05 06) (04 05 06) (07 08 09) (07 08 09) (04 05 06)D5 (07 08 09) (05 06 07) (04 05 06) (04 05 06) (09 1 1)




1113957c1 (03 054 1) (03 056 09) (03 052 08) (04 059 09) (05 077 1)1113957c2 (03 058 09) (03 049 08) (05 07 1) (04 064 1) (04 063 09)1113957c3 (04 063 09) (04 063 08) (03 054 09) (03 073 1) (03 06 09)1113957c4 (03 049 08) (04 059 098) (03 034 09) (04 063 09) (04 064 1)1113957c5 (04 067 1) (04 059 09) (04 059 0 9) (03 058 1) (04 063 1)





1113957c1 100 (03 054 1) (03 056 09) (03 052 08) (04 059 09) (05 077 1) (28 398 56)1113957c2 100 (03 058 09) (03 049 08) (05 07 1) (04 064 1) (04 063 09) (29 403 56)1113957c3 100 (04 063 09) (040 63 08) (03 0540 9) (03 073 1) (03 0609) (27 413 55)1113957c4 100 (03 049 08) (04 059 098) (03 034 09) (04 063 09) (04 064 1) (28 389 55)1113957c5 100 (04 067 1) (04 059 09) (04 059 09) (03 058 1) (04 063 1) (29 406 58)




1113957c1 (018 025 036) (005 014 036) (005 014 032) (005 013 029) (007 015 032) (009 019 036)1113957c2 (018 025 034) (005 014 031) (005 012 028) (009 017 034) (007 016 034) (007 016 031)1113957c3 (018 024 037) (007 015 033) (007 015 030) (005 013 033) (005 018 037) (005 014 033)1113957c4 (018 026 036) (005 013 029) (007 015 032) (005 014 032) (007 016 032) (007 016 036)1113957c5 (017 025 034) (007 017 034) (007 015 031) (007 014 031) (005 014 034) (007 016 034)




1113957c1 (007 019 036) (002 01 036) (002 01 032) (002 01 029) (003 011 032) (004 014 036)1113957c2 (007 015 031) (002 009 028) (002 007 025) (004 011 031) (003 010 031) (003 009 028)1113957c3 (0 018 037) (004 01 033) (004 011 03) (003 010 033) (003 013 037) (003 011 033)1113957c4 (005 013 032) (002 007 026) (002 008 029) (002 007 029) (002 008 029) (002 009 032)1113957c5 (003 015 034) (001 01 034) (001 009 031) (001 009 031) (001 009 034) (001 01 034)1113957Si (032 08 17) (011 047 157) (011 046 147) (011 046 153) (012 051 164) (013 053 164)

Alternatives

032

080

170

011

047

157

011

046

147

011

046

153

012

051

164

013

053

164

000020040060080100120140160180


A1 A2 A3 A4 A5

Si 0943 0717 0680 0702 0754 0763Qi 1 076 072 074 080 081

1000

076 072 074 080 081

0000

0200

0400

0600

0800

1000

1200

Q0 Q1 Q2 Q3 Q4 Q5










MinZ d+1 + d

minus2 + d

minus3 + d

+4 + d

minus4 + e

+1 + e

+2 + e

minus3 + e

minus4 + e

minus5

(17)



minus1 5300 (18)


700 4500b1 + 5200 1 minus b1( 1113857( 1113857minus e

+1 + e

minus1 743 (19)


350 3450b2 + 3800 1 minus b2( 1113857( 1113857minus e

+2 + e

minus2 1085 (20)




minus2 5(

(21)


13 4b3 + 7 1 minus b3( 1113857( 1113857

minus e+3 + e

minus3 333 (22)


2 3b4 + 5 1 minus b4( 1113857( 1113857minus e

+4 + e

minus4 350 (23)


4 2b5 + 6 1 minus b5( 1113857( 1113857minus e

+5 + e

minus5 250 (24)


14x1 + 10x2 + 8x3 + 11x4 + 9x5 minus d+3 + d

minus3 12 (25)


076x1 + 072x2 + 074x3 + 080x4 + 081x5 + dminus4 1

(26)


bi isin o 1 i 1 2 3 5 (27)


d+i d

minusi ge 0 i 1 2 4

e+i e

minusi ge 0 i 1 2

(28)



x2 1

x1 0

x3 0

x4 0

x5 0

(29)






5 Conclusions





Abbreviation




Data Availability


Disclosure




References





























































1113957X


⋮ ⋱ ⋮ ⋱ ⋮


⋮ ⋱ ⋮ ⋱ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(3)








1113957X




⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

i 0 1 m j 1 2 n



1113957xij 1113957xij

1113936mi0 1113957xij

(5)


1113957xij 11113957xij

1113936mi0 11113957xij

j isin Ωmin (6)


11139571113954X




⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

i 0 1 m j 1 2 n

(7)



Category Criteria





uA (x)

x

1

0α β γ






1113957Si 1113944n

j1

11139571113954xij i 0 1 m (9)


1113957Si 13

1113957Siα + 1113957Siβ + 1113957Sic1113872 1113873 i 0 1 m (10)


Qi Si

S0 i 0 1 m (11)




MSGP model

Min Z 1113944n

i1d

+i + d

minusi( 1113857


minusi gi

fi(x) 1113944m




d+i d

minusi ge 0 i 0 1 n


(12)




MinZ 1113944n

i1d

+i + d

minusi( 1113857 + e

+i + e

minusi( 1113857 (13)

st 1113944m


+i minus d

minusi gi

1Li


minij1113872 1113873 minus e

+i + e

minusi

(14)

1Li

smaxij or s

minij1113872 1113873 (15)

Li smaxij minus s

minij1113872 1113873


minusi e

+i e

minusi ge 0


(16)









FAHP step
















each criterion


FAHP


Yes


No

Weight calculation




evaluation





- Goal nhellip






S1 S2 S3 S4 S5


Product quality

c1~


c2~


c3~

Pricecost level

c4~

Financial stability

c5~






Watches (10)

Perfume (8)

Liquor (6)


(5)

Beauty products (6)

Health food (3)


(3)

Pen (2)

Sunglasses (2)

3C products (2)


0 01 02 03 04 05 06 07 08 09


1












1113957c1 (05 06 07) (04 05 06) (08 09 1) (08 09 1) (08 09 1) (04 071 1)1113957c2 (04 05 06) (05 06 07) (04 05 06) (06 07 08) (07 08 09) (04 061 09)1113957c3 (08 09 1) (07 08 09) (06 07 08) (05 06 07) (06 07 08) (05 073 1)1113957c4 (07 08 09) (03 04 05) (05 06 07) (03 04 05) (04 05 06) (03 052 09)1113957c5 (05 06 07) (02 03 04) (09 1 1) (08 09 1) (05 06 07) (02 063 1)




1113957c1

D1 (04 05 06) (06 07 08) (05 06 07) (04 05 06) (06 07 08)D2 (04 05 06) (03 04 05) (07 08 09) (04 05 06) (09 1 1)D3 (07 08 09) (03 04 05) (03 04 05) (07 08 09) (05 06 07)D4 (05 06 07) (05 06 07) (03 04 05) (06 07 08) (04 05 06)D5 (03 04 05) (07 08 09) (04 05 06) (04 05 06) (07 08 09)

1113957c2

D1 (07 08 09) (03 04 05) (06 07 08) (05 06 07) (04 05 06)D2 (03 04 05) (04 05 06) (07 08 09) (07 08 09) (05 06 07)D3 (04 05 06) (06 07 08) (05 06 07) (04 05 06) (07 08 09)D4 (07 08 09) (03 04 05) (09 1 1) (08 09 1) (04 05 06)D5 (04 05 06) (04 05 06) (04 05 06) (04 05 06) (07 08 09)

1113957c3

D1 (07 08 09) (05 06 07) (05 06 07) (07 08 09) (05 06 07)D2 (07 08 09) (04 05 06) (04 05 06) (09 1 1) (07 08 09)D3 (05 06 07) (06 07 08) (07 08 09) (07 08 09) (04 05 06)D4 (04 05 06) (06 07 08) (03 04 05) (07 08 09) (03 04 05)D5 (04 05 06) (06 07 08) (04 05 06) (03 04 05) (07 08 09)

1113957c4

D1 (06 07 08) (04 05 06) (05 06 07) (04 05 06) (05 06 07)D2 (03 04 05) (05 06 07) (04 05 06) (07 08 09) (04 05 06)D3 (04 05 06) (04 05 06) (07 08 09) (04 05 06) (08 09 1)D4 (03 04 05) (07 08 09) (03 04 05) (06 07 08) (07 08 09)D5 (04 05 06) (05 06 07) (04 05 06) (06 07 08) (04 05 06)

1113957c5

D1 (04 05 06) (05 06 07) (06 07 08) (03 04 05) (05 06 07)D2 (09 1 1) (04 05 06) (04 05 06) (09 1 1) (04 05 06)D3 (06 07 08) (07 08 09) (04 05 06) (03 04 05) (07 08 09)D4 (04 05 06) (04 05 06) (07 08 09) (07 08 09) (04 05 06)D5 (07 08 09) (05 06 07) (04 05 06) (04 05 06) (09 1 1)




1113957c1 (03 054 1) (03 056 09) (03 052 08) (04 059 09) (05 077 1)1113957c2 (03 058 09) (03 049 08) (05 07 1) (04 064 1) (04 063 09)1113957c3 (04 063 09) (04 063 08) (03 054 09) (03 073 1) (03 06 09)1113957c4 (03 049 08) (04 059 098) (03 034 09) (04 063 09) (04 064 1)1113957c5 (04 067 1) (04 059 09) (04 059 0 9) (03 058 1) (04 063 1)





1113957c1 100 (03 054 1) (03 056 09) (03 052 08) (04 059 09) (05 077 1) (28 398 56)1113957c2 100 (03 058 09) (03 049 08) (05 07 1) (04 064 1) (04 063 09) (29 403 56)1113957c3 100 (04 063 09) (040 63 08) (03 0540 9) (03 073 1) (03 0609) (27 413 55)1113957c4 100 (03 049 08) (04 059 098) (03 034 09) (04 063 09) (04 064 1) (28 389 55)1113957c5 100 (04 067 1) (04 059 09) (04 059 09) (03 058 1) (04 063 1) (29 406 58)




1113957c1 (018 025 036) (005 014 036) (005 014 032) (005 013 029) (007 015 032) (009 019 036)1113957c2 (018 025 034) (005 014 031) (005 012 028) (009 017 034) (007 016 034) (007 016 031)1113957c3 (018 024 037) (007 015 033) (007 015 030) (005 013 033) (005 018 037) (005 014 033)1113957c4 (018 026 036) (005 013 029) (007 015 032) (005 014 032) (007 016 032) (007 016 036)1113957c5 (017 025 034) (007 017 034) (007 015 031) (007 014 031) (005 014 034) (007 016 034)




1113957c1 (007 019 036) (002 01 036) (002 01 032) (002 01 029) (003 011 032) (004 014 036)1113957c2 (007 015 031) (002 009 028) (002 007 025) (004 011 031) (003 010 031) (003 009 028)1113957c3 (0 018 037) (004 01 033) (004 011 03) (003 010 033) (003 013 037) (003 011 033)1113957c4 (005 013 032) (002 007 026) (002 008 029) (002 007 029) (002 008 029) (002 009 032)1113957c5 (003 015 034) (001 01 034) (001 009 031) (001 009 031) (001 009 034) (001 01 034)1113957Si (032 08 17) (011 047 157) (011 046 147) (011 046 153) (012 051 164) (013 053 164)

Alternatives

032

080

170

011

047

157

011

046

147

011

046

153

012

051

164

013

053

164

000020040060080100120140160180


A1 A2 A3 A4 A5

Si 0943 0717 0680 0702 0754 0763Qi 1 076 072 074 080 081

1000

076 072 074 080 081

0000

0200

0400

0600

0800

1000

1200

Q0 Q1 Q2 Q3 Q4 Q5










MinZ d+1 + d

minus2 + d

minus3 + d

+4 + d

minus4 + e

+1 + e

+2 + e

minus3 + e

minus4 + e

minus5

(17)



minus1 5300 (18)


700 4500b1 + 5200 1 minus b1( 1113857( 1113857minus e

+1 + e

minus1 743 (19)


350 3450b2 + 3800 1 minus b2( 1113857( 1113857minus e

+2 + e

minus2 1085 (20)




minus2 5(

(21)


13 4b3 + 7 1 minus b3( 1113857( 1113857

minus e+3 + e

minus3 333 (22)


2 3b4 + 5 1 minus b4( 1113857( 1113857minus e

+4 + e

minus4 350 (23)


4 2b5 + 6 1 minus b5( 1113857( 1113857minus e

+5 + e

minus5 250 (24)


14x1 + 10x2 + 8x3 + 11x4 + 9x5 minus d+3 + d

minus3 12 (25)


076x1 + 072x2 + 074x3 + 080x4 + 081x5 + dminus4 1

(26)


bi isin o 1 i 1 2 3 5 (27)


d+i d

minusi ge 0 i 1 2 4

e+i e

minusi ge 0 i 1 2

(28)



x2 1

x1 0

x3 0

x4 0

x5 0

(29)






5 Conclusions





Abbreviation




Data Availability


Disclosure




References





























































1113957Si 1113944n

j1

11139571113954xij i 0 1 m (9)


1113957Si 13

1113957Siα + 1113957Siβ + 1113957Sic1113872 1113873 i 0 1 m (10)


Qi Si

S0 i 0 1 m (11)




MSGP model

Min Z 1113944n

i1d

+i + d

minusi( 1113857


minusi gi

fi(x) 1113944m




d+i d

minusi ge 0 i 0 1 n


(12)




MinZ 1113944n

i1d

+i + d

minusi( 1113857 + e

+i + e

minusi( 1113857 (13)

st 1113944m


+i minus d

minusi gi

1Li


minij1113872 1113873 minus e

+i + e

minusi

(14)

1Li

smaxij or s

minij1113872 1113873 (15)

Li smaxij minus s

minij1113872 1113873


minusi e

+i e

minusi ge 0


(16)









FAHP step
















each criterion


FAHP


Yes


No

Weight calculation




evaluation





- Goal nhellip






S1 S2 S3 S4 S5


Product quality

c1~


c2~


c3~

Pricecost level

c4~

Financial stability

c5~






Watches (10)

Perfume (8)

Liquor (6)


(5)

Beauty products (6)

Health food (3)


(3)

Pen (2)

Sunglasses (2)

3C products (2)


0 01 02 03 04 05 06 07 08 09


1












1113957c1 (05 06 07) (04 05 06) (08 09 1) (08 09 1) (08 09 1) (04 071 1)1113957c2 (04 05 06) (05 06 07) (04 05 06) (06 07 08) (07 08 09) (04 061 09)1113957c3 (08 09 1) (07 08 09) (06 07 08) (05 06 07) (06 07 08) (05 073 1)1113957c4 (07 08 09) (03 04 05) (05 06 07) (03 04 05) (04 05 06) (03 052 09)1113957c5 (05 06 07) (02 03 04) (09 1 1) (08 09 1) (05 06 07) (02 063 1)




1113957c1

D1 (04 05 06) (06 07 08) (05 06 07) (04 05 06) (06 07 08)D2 (04 05 06) (03 04 05) (07 08 09) (04 05 06) (09 1 1)D3 (07 08 09) (03 04 05) (03 04 05) (07 08 09) (05 06 07)D4 (05 06 07) (05 06 07) (03 04 05) (06 07 08) (04 05 06)D5 (03 04 05) (07 08 09) (04 05 06) (04 05 06) (07 08 09)

1113957c2

D1 (07 08 09) (03 04 05) (06 07 08) (05 06 07) (04 05 06)D2 (03 04 05) (04 05 06) (07 08 09) (07 08 09) (05 06 07)D3 (04 05 06) (06 07 08) (05 06 07) (04 05 06) (07 08 09)D4 (07 08 09) (03 04 05) (09 1 1) (08 09 1) (04 05 06)D5 (04 05 06) (04 05 06) (04 05 06) (04 05 06) (07 08 09)

1113957c3

D1 (07 08 09) (05 06 07) (05 06 07) (07 08 09) (05 06 07)D2 (07 08 09) (04 05 06) (04 05 06) (09 1 1) (07 08 09)D3 (05 06 07) (06 07 08) (07 08 09) (07 08 09) (04 05 06)D4 (04 05 06) (06 07 08) (03 04 05) (07 08 09) (03 04 05)D5 (04 05 06) (06 07 08) (04 05 06) (03 04 05) (07 08 09)

1113957c4

D1 (06 07 08) (04 05 06) (05 06 07) (04 05 06) (05 06 07)D2 (03 04 05) (05 06 07) (04 05 06) (07 08 09) (04 05 06)D3 (04 05 06) (04 05 06) (07 08 09) (04 05 06) (08 09 1)D4 (03 04 05) (07 08 09) (03 04 05) (06 07 08) (07 08 09)D5 (04 05 06) (05 06 07) (04 05 06) (06 07 08) (04 05 06)

1113957c5

D1 (04 05 06) (05 06 07) (06 07 08) (03 04 05) (05 06 07)D2 (09 1 1) (04 05 06) (04 05 06) (09 1 1) (04 05 06)D3 (06 07 08) (07 08 09) (04 05 06) (03 04 05) (07 08 09)D4 (04 05 06) (04 05 06) (07 08 09) (07 08 09) (04 05 06)D5 (07 08 09) (05 06 07) (04 05 06) (04 05 06) (09 1 1)




1113957c1 (03 054 1) (03 056 09) (03 052 08) (04 059 09) (05 077 1)1113957c2 (03 058 09) (03 049 08) (05 07 1) (04 064 1) (04 063 09)1113957c3 (04 063 09) (04 063 08) (03 054 09) (03 073 1) (03 06 09)1113957c4 (03 049 08) (04 059 098) (03 034 09) (04 063 09) (04 064 1)1113957c5 (04 067 1) (04 059 09) (04 059 0 9) (03 058 1) (04 063 1)





1113957c1 100 (03 054 1) (03 056 09) (03 052 08) (04 059 09) (05 077 1) (28 398 56)1113957c2 100 (03 058 09) (03 049 08) (05 07 1) (04 064 1) (04 063 09) (29 403 56)1113957c3 100 (04 063 09) (040 63 08) (03 0540 9) (03 073 1) (03 0609) (27 413 55)1113957c4 100 (03 049 08) (04 059 098) (03 034 09) (04 063 09) (04 064 1) (28 389 55)1113957c5 100 (04 067 1) (04 059 09) (04 059 09) (03 058 1) (04 063 1) (29 406 58)




1113957c1 (018 025 036) (005 014 036) (005 014 032) (005 013 029) (007 015 032) (009 019 036)1113957c2 (018 025 034) (005 014 031) (005 012 028) (009 017 034) (007 016 034) (007 016 031)1113957c3 (018 024 037) (007 015 033) (007 015 030) (005 013 033) (005 018 037) (005 014 033)1113957c4 (018 026 036) (005 013 029) (007 015 032) (005 014 032) (007 016 032) (007 016 036)1113957c5 (017 025 034) (007 017 034) (007 015 031) (007 014 031) (005 014 034) (007 016 034)




1113957c1 (007 019 036) (002 01 036) (002 01 032) (002 01 029) (003 011 032) (004 014 036)1113957c2 (007 015 031) (002 009 028) (002 007 025) (004 011 031) (003 010 031) (003 009 028)1113957c3 (0 018 037) (004 01 033) (004 011 03) (003 010 033) (003 013 037) (003 011 033)1113957c4 (005 013 032) (002 007 026) (002 008 029) (002 007 029) (002 008 029) (002 009 032)1113957c5 (003 015 034) (001 01 034) (001 009 031) (001 009 031) (001 009 034) (001 01 034)1113957Si (032 08 17) (011 047 157) (011 046 147) (011 046 153) (012 051 164) (013 053 164)

Alternatives

032

080

170

011

047

157

011

046

147

011

046

153

012

051

164

013

053

164

000020040060080100120140160180


A1 A2 A3 A4 A5

Si 0943 0717 0680 0702 0754 0763Qi 1 076 072 074 080 081

1000

076 072 074 080 081

0000

0200

0400

0600

0800

1000

1200

Q0 Q1 Q2 Q3 Q4 Q5










MinZ d+1 + d

minus2 + d

minus3 + d

+4 + d

minus4 + e

+1 + e

+2 + e

minus3 + e

minus4 + e

minus5

(17)



minus1 5300 (18)


700 4500b1 + 5200 1 minus b1( 1113857( 1113857minus e

+1 + e

minus1 743 (19)


350 3450b2 + 3800 1 minus b2( 1113857( 1113857minus e

+2 + e

minus2 1085 (20)




minus2 5(

(21)


13 4b3 + 7 1 minus b3( 1113857( 1113857

minus e+3 + e

minus3 333 (22)


2 3b4 + 5 1 minus b4( 1113857( 1113857minus e

+4 + e

minus4 350 (23)


4 2b5 + 6 1 minus b5( 1113857( 1113857minus e

+5 + e

minus5 250 (24)


14x1 + 10x2 + 8x3 + 11x4 + 9x5 minus d+3 + d

minus3 12 (25)


076x1 + 072x2 + 074x3 + 080x4 + 081x5 + dminus4 1

(26)


bi isin o 1 i 1 2 3 5 (27)


d+i d

minusi ge 0 i 1 2 4

e+i e

minusi ge 0 i 1 2

(28)



x2 1

x1 0

x3 0

x4 0

x5 0

(29)






5 Conclusions





Abbreviation




Data Availability


Disclosure




References





































































each criterion


FAHP


Yes


No

Weight calculation




evaluation





- Goal nhellip






S1 S2 S3 S4 S5


Product quality

c1~


c2~


c3~

Pricecost level

c4~

Financial stability

c5~






Watches (10)

Perfume (8)

Liquor (6)


(5)

Beauty products (6)

Health food (3)


(3)

Pen (2)

Sunglasses (2)

3C products (2)


0 01 02 03 04 05 06 07 08 09


1












1113957c1 (05 06 07) (04 05 06) (08 09 1) (08 09 1) (08 09 1) (04 071 1)1113957c2 (04 05 06) (05 06 07) (04 05 06) (06 07 08) (07 08 09) (04 061 09)1113957c3 (08 09 1) (07 08 09) (06 07 08) (05 06 07) (06 07 08) (05 073 1)1113957c4 (07 08 09) (03 04 05) (05 06 07) (03 04 05) (04 05 06) (03 052 09)1113957c5 (05 06 07) (02 03 04) (09 1 1) (08 09 1) (05 06 07) (02 063 1)




1113957c1

D1 (04 05 06) (06 07 08) (05 06 07) (04 05 06) (06 07 08)D2 (04 05 06) (03 04 05) (07 08 09) (04 05 06) (09 1 1)D3 (07 08 09) (03 04 05) (03 04 05) (07 08 09) (05 06 07)D4 (05 06 07) (05 06 07) (03 04 05) (06 07 08) (04 05 06)D5 (03 04 05) (07 08 09) (04 05 06) (04 05 06) (07 08 09)

1113957c2

D1 (07 08 09) (03 04 05) (06 07 08) (05 06 07) (04 05 06)D2 (03 04 05) (04 05 06) (07 08 09) (07 08 09) (05 06 07)D3 (04 05 06) (06 07 08) (05 06 07) (04 05 06) (07 08 09)D4 (07 08 09) (03 04 05) (09 1 1) (08 09 1) (04 05 06)D5 (04 05 06) (04 05 06) (04 05 06) (04 05 06) (07 08 09)

1113957c3

D1 (07 08 09) (05 06 07) (05 06 07) (07 08 09) (05 06 07)D2 (07 08 09) (04 05 06) (04 05 06) (09 1 1) (07 08 09)D3 (05 06 07) (06 07 08) (07 08 09) (07 08 09) (04 05 06)D4 (04 05 06) (06 07 08) (03 04 05) (07 08 09) (03 04 05)D5 (04 05 06) (06 07 08) (04 05 06) (03 04 05) (07 08 09)

1113957c4

D1 (06 07 08) (04 05 06) (05 06 07) (04 05 06) (05 06 07)D2 (03 04 05) (05 06 07) (04 05 06) (07 08 09) (04 05 06)D3 (04 05 06) (04 05 06) (07 08 09) (04 05 06) (08 09 1)D4 (03 04 05) (07 08 09) (03 04 05) (06 07 08) (07 08 09)D5 (04 05 06) (05 06 07) (04 05 06) (06 07 08) (04 05 06)

1113957c5

D1 (04 05 06) (05 06 07) (06 07 08) (03 04 05) (05 06 07)D2 (09 1 1) (04 05 06) (04 05 06) (09 1 1) (04 05 06)D3 (06 07 08) (07 08 09) (04 05 06) (03 04 05) (07 08 09)D4 (04 05 06) (04 05 06) (07 08 09) (07 08 09) (04 05 06)D5 (07 08 09) (05 06 07) (04 05 06) (04 05 06) (09 1 1)




1113957c1 (03 054 1) (03 056 09) (03 052 08) (04 059 09) (05 077 1)1113957c2 (03 058 09) (03 049 08) (05 07 1) (04 064 1) (04 063 09)1113957c3 (04 063 09) (04 063 08) (03 054 09) (03 073 1) (03 06 09)1113957c4 (03 049 08) (04 059 098) (03 034 09) (04 063 09) (04 064 1)1113957c5 (04 067 1) (04 059 09) (04 059 0 9) (03 058 1) (04 063 1)





1113957c1 100 (03 054 1) (03 056 09) (03 052 08) (04 059 09) (05 077 1) (28 398 56)1113957c2 100 (03 058 09) (03 049 08) (05 07 1) (04 064 1) (04 063 09) (29 403 56)1113957c3 100 (04 063 09) (040 63 08) (03 0540 9) (03 073 1) (03 0609) (27 413 55)1113957c4 100 (03 049 08) (04 059 098) (03 034 09) (04 063 09) (04 064 1) (28 389 55)1113957c5 100 (04 067 1) (04 059 09) (04 059 09) (03 058 1) (04 063 1) (29 406 58)




1113957c1 (018 025 036) (005 014 036) (005 014 032) (005 013 029) (007 015 032) (009 019 036)1113957c2 (018 025 034) (005 014 031) (005 012 028) (009 017 034) (007 016 034) (007 016 031)1113957c3 (018 024 037) (007 015 033) (007 015 030) (005 013 033) (005 018 037) (005 014 033)1113957c4 (018 026 036) (005 013 029) (007 015 032) (005 014 032) (007 016 032) (007 016 036)1113957c5 (017 025 034) (007 017 034) (007 015 031) (007 014 031) (005 014 034) (007 016 034)




1113957c1 (007 019 036) (002 01 036) (002 01 032) (002 01 029) (003 011 032) (004 014 036)1113957c2 (007 015 031) (002 009 028) (002 007 025) (004 011 031) (003 010 031) (003 009 028)1113957c3 (0 018 037) (004 01 033) (004 011 03) (003 010 033) (003 013 037) (003 011 033)1113957c4 (005 013 032) (002 007 026) (002 008 029) (002 007 029) (002 008 029) (002 009 032)1113957c5 (003 015 034) (001 01 034) (001 009 031) (001 009 031) (001 009 034) (001 01 034)1113957Si (032 08 17) (011 047 157) (011 046 147) (011 046 153) (012 051 164) (013 053 164)

Alternatives

032

080

170

011

047

157

011

046

147

011

046

153

012

051

164

013

053

164

000020040060080100120140160180


A1 A2 A3 A4 A5

Si 0943 0717 0680 0702 0754 0763Qi 1 076 072 074 080 081

1000

076 072 074 080 081

0000

0200

0400

0600

0800

1000

1200

Q0 Q1 Q2 Q3 Q4 Q5










MinZ d+1 + d

minus2 + d

minus3 + d

+4 + d

minus4 + e

+1 + e

+2 + e

minus3 + e

minus4 + e

minus5

(17)



minus1 5300 (18)


700 4500b1 + 5200 1 minus b1( 1113857( 1113857minus e

+1 + e

minus1 743 (19)


350 3450b2 + 3800 1 minus b2( 1113857( 1113857minus e

+2 + e

minus2 1085 (20)




minus2 5(

(21)


13 4b3 + 7 1 minus b3( 1113857( 1113857

minus e+3 + e

minus3 333 (22)


2 3b4 + 5 1 minus b4( 1113857( 1113857minus e

+4 + e

minus4 350 (23)


4 2b5 + 6 1 minus b5( 1113857( 1113857minus e

+5 + e

minus5 250 (24)


14x1 + 10x2 + 8x3 + 11x4 + 9x5 minus d+3 + d

minus3 12 (25)


076x1 + 072x2 + 074x3 + 080x4 + 081x5 + dminus4 1

(26)


bi isin o 1 i 1 2 3 5 (27)


d+i d

minusi ge 0 i 1 2 4

e+i e

minusi ge 0 i 1 2

(28)



x2 1

x1 0

x3 0

x4 0

x5 0

(29)






5 Conclusions





Abbreviation




Data Availability


Disclosure




References




























































S1 S2 S3 S4 S5


Product quality

c1~


c2~


c3~

Pricecost level

c4~

Financial stability

c5~






Watches (10)

Perfume (8)

Liquor (6)


(5)

Beauty products (6)

Health food (3)


(3)

Pen (2)

Sunglasses (2)

3C products (2)


0 01 02 03 04 05 06 07 08 09


1












1113957c1 (05 06 07) (04 05 06) (08 09 1) (08 09 1) (08 09 1) (04 071 1)1113957c2 (04 05 06) (05 06 07) (04 05 06) (06 07 08) (07 08 09) (04 061 09)1113957c3 (08 09 1) (07 08 09) (06 07 08) (05 06 07) (06 07 08) (05 073 1)1113957c4 (07 08 09) (03 04 05) (05 06 07) (03 04 05) (04 05 06) (03 052 09)1113957c5 (05 06 07) (02 03 04) (09 1 1) (08 09 1) (05 06 07) (02 063 1)




1113957c1

D1 (04 05 06) (06 07 08) (05 06 07) (04 05 06) (06 07 08)D2 (04 05 06) (03 04 05) (07 08 09) (04 05 06) (09 1 1)D3 (07 08 09) (03 04 05) (03 04 05) (07 08 09) (05 06 07)D4 (05 06 07) (05 06 07) (03 04 05) (06 07 08) (04 05 06)D5 (03 04 05) (07 08 09) (04 05 06) (04 05 06) (07 08 09)

1113957c2

D1 (07 08 09) (03 04 05) (06 07 08) (05 06 07) (04 05 06)D2 (03 04 05) (04 05 06) (07 08 09) (07 08 09) (05 06 07)D3 (04 05 06) (06 07 08) (05 06 07) (04 05 06) (07 08 09)D4 (07 08 09) (03 04 05) (09 1 1) (08 09 1) (04 05 06)D5 (04 05 06) (04 05 06) (04 05 06) (04 05 06) (07 08 09)

1113957c3

D1 (07 08 09) (05 06 07) (05 06 07) (07 08 09) (05 06 07)D2 (07 08 09) (04 05 06) (04 05 06) (09 1 1) (07 08 09)D3 (05 06 07) (06 07 08) (07 08 09) (07 08 09) (04 05 06)D4 (04 05 06) (06 07 08) (03 04 05) (07 08 09) (03 04 05)D5 (04 05 06) (06 07 08) (04 05 06) (03 04 05) (07 08 09)

1113957c4

D1 (06 07 08) (04 05 06) (05 06 07) (04 05 06) (05 06 07)D2 (03 04 05) (05 06 07) (04 05 06) (07 08 09) (04 05 06)D3 (04 05 06) (04 05 06) (07 08 09) (04 05 06) (08 09 1)D4 (03 04 05) (07 08 09) (03 04 05) (06 07 08) (07 08 09)D5 (04 05 06) (05 06 07) (04 05 06) (06 07 08) (04 05 06)

1113957c5

D1 (04 05 06) (05 06 07) (06 07 08) (03 04 05) (05 06 07)D2 (09 1 1) (04 05 06) (04 05 06) (09 1 1) (04 05 06)D3 (06 07 08) (07 08 09) (04 05 06) (03 04 05) (07 08 09)D4 (04 05 06) (04 05 06) (07 08 09) (07 08 09) (04 05 06)D5 (07 08 09) (05 06 07) (04 05 06) (04 05 06) (09 1 1)




1113957c1 (03 054 1) (03 056 09) (03 052 08) (04 059 09) (05 077 1)1113957c2 (03 058 09) (03 049 08) (05 07 1) (04 064 1) (04 063 09)1113957c3 (04 063 09) (04 063 08) (03 054 09) (03 073 1) (03 06 09)1113957c4 (03 049 08) (04 059 098) (03 034 09) (04 063 09) (04 064 1)1113957c5 (04 067 1) (04 059 09) (04 059 0 9) (03 058 1) (04 063 1)





1113957c1 100 (03 054 1) (03 056 09) (03 052 08) (04 059 09) (05 077 1) (28 398 56)1113957c2 100 (03 058 09) (03 049 08) (05 07 1) (04 064 1) (04 063 09) (29 403 56)1113957c3 100 (04 063 09) (040 63 08) (03 0540 9) (03 073 1) (03 0609) (27 413 55)1113957c4 100 (03 049 08) (04 059 098) (03 034 09) (04 063 09) (04 064 1) (28 389 55)1113957c5 100 (04 067 1) (04 059 09) (04 059 09) (03 058 1) (04 063 1) (29 406 58)




1113957c1 (018 025 036) (005 014 036) (005 014 032) (005 013 029) (007 015 032) (009 019 036)1113957c2 (018 025 034) (005 014 031) (005 012 028) (009 017 034) (007 016 034) (007 016 031)1113957c3 (018 024 037) (007 015 033) (007 015 030) (005 013 033) (005 018 037) (005 014 033)1113957c4 (018 026 036) (005 013 029) (007 015 032) (005 014 032) (007 016 032) (007 016 036)1113957c5 (017 025 034) (007 017 034) (007 015 031) (007 014 031) (005 014 034) (007 016 034)




1113957c1 (007 019 036) (002 01 036) (002 01 032) (002 01 029) (003 011 032) (004 014 036)1113957c2 (007 015 031) (002 009 028) (002 007 025) (004 011 031) (003 010 031) (003 009 028)1113957c3 (0 018 037) (004 01 033) (004 011 03) (003 010 033) (003 013 037) (003 011 033)1113957c4 (005 013 032) (002 007 026) (002 008 029) (002 007 029) (002 008 029) (002 009 032)1113957c5 (003 015 034) (001 01 034) (001 009 031) (001 009 031) (001 009 034) (001 01 034)1113957Si (032 08 17) (011 047 157) (011 046 147) (011 046 153) (012 051 164) (013 053 164)

Alternatives

032

080

170

011

047

157

011

046

147

011

046

153

012

051

164

013

053

164

000020040060080100120140160180


A1 A2 A3 A4 A5

Si 0943 0717 0680 0702 0754 0763Qi 1 076 072 074 080 081

1000

076 072 074 080 081

0000

0200

0400

0600

0800

1000

1200

Q0 Q1 Q2 Q3 Q4 Q5










MinZ d+1 + d

minus2 + d

minus3 + d

+4 + d

minus4 + e

+1 + e

+2 + e

minus3 + e

minus4 + e

minus5

(17)



minus1 5300 (18)


700 4500b1 + 5200 1 minus b1( 1113857( 1113857minus e

+1 + e

minus1 743 (19)


350 3450b2 + 3800 1 minus b2( 1113857( 1113857minus e

+2 + e

minus2 1085 (20)




minus2 5(

(21)


13 4b3 + 7 1 minus b3( 1113857( 1113857

minus e+3 + e

minus3 333 (22)


2 3b4 + 5 1 minus b4( 1113857( 1113857minus e

+4 + e

minus4 350 (23)


4 2b5 + 6 1 minus b5( 1113857( 1113857minus e

+5 + e

minus5 250 (24)


14x1 + 10x2 + 8x3 + 11x4 + 9x5 minus d+3 + d

minus3 12 (25)


076x1 + 072x2 + 074x3 + 080x4 + 081x5 + dminus4 1

(26)


bi isin o 1 i 1 2 3 5 (27)


d+i d

minusi ge 0 i 1 2 4

e+i e

minusi ge 0 i 1 2

(28)



x2 1

x1 0

x3 0

x4 0

x5 0

(29)






5 Conclusions





Abbreviation




Data Availability


Disclosure




References

































































1113957c1 (05 06 07) (04 05 06) (08 09 1) (08 09 1) (08 09 1) (04 071 1)1113957c2 (04 05 06) (05 06 07) (04 05 06) (06 07 08) (07 08 09) (04 061 09)1113957c3 (08 09 1) (07 08 09) (06 07 08) (05 06 07) (06 07 08) (05 073 1)1113957c4 (07 08 09) (03 04 05) (05 06 07) (03 04 05) (04 05 06) (03 052 09)1113957c5 (05 06 07) (02 03 04) (09 1 1) (08 09 1) (05 06 07) (02 063 1)




1113957c1

D1 (04 05 06) (06 07 08) (05 06 07) (04 05 06) (06 07 08)D2 (04 05 06) (03 04 05) (07 08 09) (04 05 06) (09 1 1)D3 (07 08 09) (03 04 05) (03 04 05) (07 08 09) (05 06 07)D4 (05 06 07) (05 06 07) (03 04 05) (06 07 08) (04 05 06)D5 (03 04 05) (07 08 09) (04 05 06) (04 05 06) (07 08 09)

1113957c2

D1 (07 08 09) (03 04 05) (06 07 08) (05 06 07) (04 05 06)D2 (03 04 05) (04 05 06) (07 08 09) (07 08 09) (05 06 07)D3 (04 05 06) (06 07 08) (05 06 07) (04 05 06) (07 08 09)D4 (07 08 09) (03 04 05) (09 1 1) (08 09 1) (04 05 06)D5 (04 05 06) (04 05 06) (04 05 06) (04 05 06) (07 08 09)

1113957c3

D1 (07 08 09) (05 06 07) (05 06 07) (07 08 09) (05 06 07)D2 (07 08 09) (04 05 06) (04 05 06) (09 1 1) (07 08 09)D3 (05 06 07) (06 07 08) (07 08 09) (07 08 09) (04 05 06)D4 (04 05 06) (06 07 08) (03 04 05) (07 08 09) (03 04 05)D5 (04 05 06) (06 07 08) (04 05 06) (03 04 05) (07 08 09)

1113957c4

D1 (06 07 08) (04 05 06) (05 06 07) (04 05 06) (05 06 07)D2 (03 04 05) (05 06 07) (04 05 06) (07 08 09) (04 05 06)D3 (04 05 06) (04 05 06) (07 08 09) (04 05 06) (08 09 1)D4 (03 04 05) (07 08 09) (03 04 05) (06 07 08) (07 08 09)D5 (04 05 06) (05 06 07) (04 05 06) (06 07 08) (04 05 06)

1113957c5

D1 (04 05 06) (05 06 07) (06 07 08) (03 04 05) (05 06 07)D2 (09 1 1) (04 05 06) (04 05 06) (09 1 1) (04 05 06)D3 (06 07 08) (07 08 09) (04 05 06) (03 04 05) (07 08 09)D4 (04 05 06) (04 05 06) (07 08 09) (07 08 09) (04 05 06)D5 (07 08 09) (05 06 07) (04 05 06) (04 05 06) (09 1 1)




1113957c1 (03 054 1) (03 056 09) (03 052 08) (04 059 09) (05 077 1)1113957c2 (03 058 09) (03 049 08) (05 07 1) (04 064 1) (04 063 09)1113957c3 (04 063 09) (04 063 08) (03 054 09) (03 073 1) (03 06 09)1113957c4 (03 049 08) (04 059 098) (03 034 09) (04 063 09) (04 064 1)1113957c5 (04 067 1) (04 059 09) (04 059 0 9) (03 058 1) (04 063 1)





1113957c1 100 (03 054 1) (03 056 09) (03 052 08) (04 059 09) (05 077 1) (28 398 56)1113957c2 100 (03 058 09) (03 049 08) (05 07 1) (04 064 1) (04 063 09) (29 403 56)1113957c3 100 (04 063 09) (040 63 08) (03 0540 9) (03 073 1) (03 0609) (27 413 55)1113957c4 100 (03 049 08) (04 059 098) (03 034 09) (04 063 09) (04 064 1) (28 389 55)1113957c5 100 (04 067 1) (04 059 09) (04 059 09) (03 058 1) (04 063 1) (29 406 58)




1113957c1 (018 025 036) (005 014 036) (005 014 032) (005 013 029) (007 015 032) (009 019 036)1113957c2 (018 025 034) (005 014 031) (005 012 028) (009 017 034) (007 016 034) (007 016 031)1113957c3 (018 024 037) (007 015 033) (007 015 030) (005 013 033) (005 018 037) (005 014 033)1113957c4 (018 026 036) (005 013 029) (007 015 032) (005 014 032) (007 016 032) (007 016 036)1113957c5 (017 025 034) (007 017 034) (007 015 031) (007 014 031) (005 014 034) (007 016 034)




1113957c1 (007 019 036) (002 01 036) (002 01 032) (002 01 029) (003 011 032) (004 014 036)1113957c2 (007 015 031) (002 009 028) (002 007 025) (004 011 031) (003 010 031) (003 009 028)1113957c3 (0 018 037) (004 01 033) (004 011 03) (003 010 033) (003 013 037) (003 011 033)1113957c4 (005 013 032) (002 007 026) (002 008 029) (002 007 029) (002 008 029) (002 009 032)1113957c5 (003 015 034) (001 01 034) (001 009 031) (001 009 031) (001 009 034) (001 01 034)1113957Si (032 08 17) (011 047 157) (011 046 147) (011 046 153) (012 051 164) (013 053 164)

Alternatives

032

080

170

011

047

157

011

046

147

011

046

153

012

051

164

013

053

164

000020040060080100120140160180


A1 A2 A3 A4 A5

Si 0943 0717 0680 0702 0754 0763Qi 1 076 072 074 080 081

1000

076 072 074 080 081

0000

0200

0400

0600

0800

1000

1200

Q0 Q1 Q2 Q3 Q4 Q5










MinZ d+1 + d

minus2 + d

minus3 + d

+4 + d

minus4 + e

+1 + e

+2 + e

minus3 + e

minus4 + e

minus5

(17)



minus1 5300 (18)


700 4500b1 + 5200 1 minus b1( 1113857( 1113857minus e

+1 + e

minus1 743 (19)


350 3450b2 + 3800 1 minus b2( 1113857( 1113857minus e

+2 + e

minus2 1085 (20)




minus2 5(

(21)


13 4b3 + 7 1 minus b3( 1113857( 1113857

minus e+3 + e

minus3 333 (22)


2 3b4 + 5 1 minus b4( 1113857( 1113857minus e

+4 + e

minus4 350 (23)


4 2b5 + 6 1 minus b5( 1113857( 1113857minus e

+5 + e

minus5 250 (24)


14x1 + 10x2 + 8x3 + 11x4 + 9x5 minus d+3 + d

minus3 12 (25)


076x1 + 072x2 + 074x3 + 080x4 + 081x5 + dminus4 1

(26)


bi isin o 1 i 1 2 3 5 (27)


d+i d

minusi ge 0 i 1 2 4

e+i e

minusi ge 0 i 1 2

(28)



x2 1

x1 0

x3 0

x4 0

x5 0

(29)






5 Conclusions





Abbreviation




Data Availability


Disclosure




References





























































1113957c1 100 (03 054 1) (03 056 09) (03 052 08) (04 059 09) (05 077 1) (28 398 56)1113957c2 100 (03 058 09) (03 049 08) (05 07 1) (04 064 1) (04 063 09) (29 403 56)1113957c3 100 (04 063 09) (040 63 08) (03 0540 9) (03 073 1) (03 0609) (27 413 55)1113957c4 100 (03 049 08) (04 059 098) (03 034 09) (04 063 09) (04 064 1) (28 389 55)1113957c5 100 (04 067 1) (04 059 09) (04 059 09) (03 058 1) (04 063 1) (29 406 58)




1113957c1 (018 025 036) (005 014 036) (005 014 032) (005 013 029) (007 015 032) (009 019 036)1113957c2 (018 025 034) (005 014 031) (005 012 028) (009 017 034) (007 016 034) (007 016 031)1113957c3 (018 024 037) (007 015 033) (007 015 030) (005 013 033) (005 018 037) (005 014 033)1113957c4 (018 026 036) (005 013 029) (007 015 032) (005 014 032) (007 016 032) (007 016 036)1113957c5 (017 025 034) (007 017 034) (007 015 031) (007 014 031) (005 014 034) (007 016 034)




1113957c1 (007 019 036) (002 01 036) (002 01 032) (002 01 029) (003 011 032) (004 014 036)1113957c2 (007 015 031) (002 009 028) (002 007 025) (004 011 031) (003 010 031) (003 009 028)1113957c3 (0 018 037) (004 01 033) (004 011 03) (003 010 033) (003 013 037) (003 011 033)1113957c4 (005 013 032) (002 007 026) (002 008 029) (002 007 029) (002 008 029) (002 009 032)1113957c5 (003 015 034) (001 01 034) (001 009 031) (001 009 031) (001 009 034) (001 01 034)1113957Si (032 08 17) (011 047 157) (011 046 147) (011 046 153) (012 051 164) (013 053 164)

Alternatives

032

080

170

011

047

157

011

046

147

011

046

153

012

051

164

013

053

164

000020040060080100120140160180


A1 A2 A3 A4 A5

Si 0943 0717 0680 0702 0754 0763Qi 1 076 072 074 080 081

1000

076 072 074 080 081

0000

0200

0400

0600

0800

1000

1200

Q0 Q1 Q2 Q3 Q4 Q5










MinZ d+1 + d

minus2 + d

minus3 + d

+4 + d

minus4 + e

+1 + e

+2 + e

minus3 + e

minus4 + e

minus5

(17)



minus1 5300 (18)


700 4500b1 + 5200 1 minus b1( 1113857( 1113857minus e

+1 + e

minus1 743 (19)


350 3450b2 + 3800 1 minus b2( 1113857( 1113857minus e

+2 + e

minus2 1085 (20)




minus2 5(

(21)


13 4b3 + 7 1 minus b3( 1113857( 1113857

minus e+3 + e

minus3 333 (22)


2 3b4 + 5 1 minus b4( 1113857( 1113857minus e

+4 + e

minus4 350 (23)


4 2b5 + 6 1 minus b5( 1113857( 1113857minus e

+5 + e

minus5 250 (24)


14x1 + 10x2 + 8x3 + 11x4 + 9x5 minus d+3 + d

minus3 12 (25)


076x1 + 072x2 + 074x3 + 080x4 + 081x5 + dminus4 1

(26)


bi isin o 1 i 1 2 3 5 (27)


d+i d

minusi ge 0 i 1 2 4

e+i e

minusi ge 0 i 1 2

(28)



x2 1

x1 0

x3 0

x4 0

x5 0

(29)






5 Conclusions





Abbreviation




Data Availability


Disclosure




References


































































MinZ d+1 + d

minus2 + d

minus3 + d

+4 + d

minus4 + e

+1 + e

+2 + e

minus3 + e

minus4 + e

minus5

(17)



minus1 5300 (18)


700 4500b1 + 5200 1 minus b1( 1113857( 1113857minus e

+1 + e

minus1 743 (19)


350 3450b2 + 3800 1 minus b2( 1113857( 1113857minus e

+2 + e

minus2 1085 (20)




minus2 5(

(21)


13 4b3 + 7 1 minus b3( 1113857( 1113857

minus e+3 + e

minus3 333 (22)


2 3b4 + 5 1 minus b4( 1113857( 1113857minus e

+4 + e

minus4 350 (23)


4 2b5 + 6 1 minus b5( 1113857( 1113857minus e

+5 + e

minus5 250 (24)


14x1 + 10x2 + 8x3 + 11x4 + 9x5 minus d+3 + d

minus3 12 (25)


076x1 + 072x2 + 074x3 + 080x4 + 081x5 + dminus4 1

(26)


bi isin o 1 i 1 2 3 5 (27)


d+i d

minusi ge 0 i 1 2 4

e+i e

minusi ge 0 i 1 2

(28)



x2 1

x1 0

x3 0

x4 0

x5 0

(29)






5 Conclusions





Abbreviation




Data Availability


Disclosure




References


























































5 Conclusions





Abbreviation




Data Availability


Disclosure




References


























































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