Research Article Decision Making for Third Party Logistics...

Research ArticleDecision Making for Third Party Logistics SupplierSelection in Semiconductor Manufacturing IndustryA Nonadditive Fuzzy Integral Approach

Bang-Ning Hwang1 and Yung-Chi Shen2

1Department and Graduate Institute of Business Administration National Yunlin University of Science amp TechnologyNo 123 University Road Section 3 Douliou Yunlin 64002 Taiwan2Department of BioBusiness Management National Chiayi University No 580 Sinmin Road Chiayi 600 Taiwan

Correspondence should be addressed to Yung-Chi Shen sycmailncyuedutw

Received 22 August 2014 Accepted 6 January 2015

Academic Editor Salvatore Alfonzetti

Copyright copy 2015 B-N Hwang and Y-C ShenThis is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The semiconductor industry has a unique vertically disintegrated structure that consists of various firms specializing in a narrowrange of the value chain To ensure manufacturing and logistics efficiency the semiconductor manufacturers considerably relyon 3PL suppliers to achieve supply chain excellence However 3PL supplier selection is a complex decision-making processinvolving multiple selection criteria The goal of this paper is to identify the key 3PL selection criteria by employing thenonadditive fuzzy integral approach Unlike the traditional multicriterion decision-making (MCDM)methods which often assumeindependence among criteria and additive importance weights the nonadditive fuzzy integral is a more effective approach tosolve the dependency among criteria vagueness in information and essential fuzziness of human judgment In this paper wedemonstrate an empirical case that employs the nonadditive fuzzy integral to evaluate the importance weight of selection criteriaand choose the most appropriate 3PL supplier The research result can become a valuable reference for manufacturing companiesoperating in comparable situations Moreover the systematic framework presented in this study can be easily extended to theanalysis of other decision-making domains

1 Introduction

The third-party logistics (3PL) involves the use of exter-nal companies to perform logistics functions traditionallymanaged by the manufacturing firms Outsourcing isolatedlogistics activities such as transportation and warehousingto external service suppliers is not a new idea in theindustry Such outsourcing is based on simple make-or-buyconsiderations and choosing the cheapest alternative thatmeets preestablished service requirements [1] However dueto the increasing supply chain complication global compe-tition and customer demand for timeliness and flexibility ofgoodsservices delivery the role of 3PL has changed both incontent and in complexity While the previous driving forcesfor a firm to employ 3PL were to reduce operation costs andfocus a firmrsquos capital investment on its core competencies

the impetus today has a more strategic thrust to increasemarket coverage improve the level of service and increaseflexibility towards the changing requirements of customers[1ndash3] Therefore the decision of competent suppliers is ofcentral importance for successful supply chain management[4ndash6]

3PL supplier selection is a complex analytical processessentially A supplier selection problem usually involvesmore than one criterion and criteria often conflict witheach other [7] Basically the nature of the supplier selectionis as a type of multicriterion decision-making (MCDM)problem based on the relative priority assigned to eachselection criterion [8] In MCDM it is usually assumedthat the criteria are independent however in real life theavailable information in a decision-making process is usuallyuncertain vague or imprecise and the criteria are not

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 918602 12 pageshttpdxdoiorg1011552015918602

2 Mathematical Problems in Engineering

necessarily independent [7]The traditionalMCDMmethodsused to determine the importance of selection criteria oftenassume additive weights and independence among criteriaBut an additivemodel is not always suitable due to the varyingdegrees of interactions among selection criteria [9] On thecontrary the fuzzy measures do not need to assume theindependence among criteriaThe nonadditive fuzzy integralmethod based on the fuzzy measures has been developed toaddress the degree of interaction among diversified criteriaand the vagueness existing in human subjective judgments[10 11] Due to the advantage of better revealing the realenvironment we employed the nonadditive fuzzy integralapproach in this study to construct the 3PL supplier selectionassessment process

The remainder of this paper is organized as followsSection 2 presents a review of the relevant literature of 3PLand its significance to the semiconductor manufacturingindustry Section 3 introduces the nonadditive fuzzy integralresearch method Section 4 presents the empirical study thatemploys the research method to evaluate the importanceweight of selection criteria and choose the most appropriate3PL supplier Finally Section 5 discusses the research resultand concludes the paper

2 Literature Review

21 3PL and 3PL Selection Criteria 3PL functions encompassthe entire logistics process or selected activities within thatprocess [12] Typical logistics activities performed by a 3PLsupplier are warehousing transportation distribution cus-tomer service inventory packaging cross docking logisticsmanagement and reverse logistics [13 14] The relationshipbetween a 3PL supplier and its customers is that the firstparty is the client who purchases the logistics service and thesecond party is the clientrsquos customer(s) thus the third partyis the service supplier and acts as a middleman by takingtitle not to the products but to which logistics activities areoutsourced [15]

Initially 3PL services were relatively limited in scope[16] Over time 3PL suppliers began offering an increas-ingly integrated set of logistics activities and have becomea mainstream in current business environment [17] Mostmanufacturing companies are fond of 3PL suppliers as theyare alternatives with greater flexibility cost saving increasedoperational efficiency better customer service improvedexpertise reengineering of logistics processes and access tonew technologies [18 19] A meta-analysis evidenced thatthe employment of 3PL providers was in favor of a firmrsquosperformance [20] Moreover engaging logistics service of3PL suppliers permits a manufacturing firm a better focuson its core businesses [21] However achieving a successfulimplementation of logistics outsourcing to 3PL is not aneasy task [22] Often-cited difficulties that concern a 3PLsupplierrsquos performance include a lack of understanding ofclientrsquos supply chain needs lack of adequate expertise inspecific products and markets inadequate description ofservices and service levels lack of 3PL innovation and lackof logistics cost awareness [22 23] Therefore an efficientsupplier management that begins with the identification

of potential suppliers is prerequisite for successful logisticsoutsourcing

Academia started research regarding the supplier selec-tion of logistics services in the sixties [24 25] Among recentstudies one of the most comprehensive works is the onecarried out by Ho et al [8] The study was based on thereview of 78 papers related to supplier selection the authorsexhaustively addressed the issue of both qualitative andquantitative criteria that have to be considered when viablesuppliers are to be ranked Considering the nature of 3PL inparticular Coltman et al [26] added selection criteria such ascustomer interaction track-and-trace service recovery sup-ply chain flexibility and capability professionalism proactiveinnovation and relationship orientation Some researchersexamined the key selection factors for 3PL suppliers fromparticular perspectives For example Murphy and Poist [27]analyzed the key factors in a successful relationship fromboth supplier and user perspectives whereas Gotzamaniet al [28] paid special attention to quality-related factors anddeliberated the relationship between quality managementand financial performance of 3PL suppliers Chen et al[29] employed transport cost frequency of shipments ITcommunication quality performance and order to shop timeas 3PL selection criteria for apparel retailer industry

As supplier selection is viewed to be a multicrite-rion decision-making process for most companies someresearchers have developed research frameworks that orga-nize selection criteria according to a hierarchical structureFor example Ku et al [30] constructed a hierarchical frame-work to deal with the problem of global supplier selectionWu and Tsai [31] applied 7major criteria and 30 subcriteria toevaluate the suppliers for auto spare parts industry Govindanet al [32] listed 34 subcriteria and grouped them into sevencriteria Kang et al [33] developed a multilevel hierarchy tosupport the supplier selection decision by considering fivecriteria and thirteen subcriteria Vaidyanathan [34] proposeda 3PL evaluation framework that comprised sixmajor criteriaof IT quality assurance cost services performance andintangibles Sean [35] identified service-quality experienceand service-quality credence as dual-role factors when select-ing third-party reverse logistics suppliers In conclusionthe 3PL supplier selection is based on multiple criteriacomprising both quantitative and qualitative criteria

Incorporating many of these relevant criteria for theselection of a 3PL supplier Table 1 summarizesmost common3PL selection criteria and groups them in six general cate-gories suggested by Vaidyanathan [34]

22 Semiconductor Manufacturing Industry in Taiwan Tai-wanrsquos entire semiconductor industry is currently the fourthlargest in the world behind only the USA Japan andKorea According to the publication IC Insight Taiwan hasbecome the largest semiconductor foundry manufacturersecond largest semiconductor designer and the fourth largestsemiconductor producer in the world In contrast to thevertically integrated conglomerates dominating the industryin Korea and Japan Taiwanrsquos semiconductor industry hasa unique vertically disintegrated structure that consists ofmany small-to-medium firms specializing in a narrow range

Mathematical Problems in Engineering 3

IC design(263) Masking (3)

Manufacturing equipment

IC manufacturingfab (15)

IC packaging(30)

Final testing(36)

Raw wafer(11) materials

Chemical

(36)

Lead frameand motherboard (11)

Figure 1 Semiconductor industry supply chain

Table 1 3PL selection criteria summary

Performance

On-time deliveryDocument AccuracyTransportation safetyShipment error rate

Hertz and Alfredsson[15] Vaidyanathan [34]Gol and Catay [38]Jharkharia and Shankar[39] Ordoobadi [40]

Service

Customer supportserviceProblem-solvingcapabilityValue-added service

Hertz and Alfredsson[15] Murphy and Poist[27] Vaidyanathan [34]Jharkharia and Shankar[39] Ordoobadi [40]Bottani and Rizzi [41]Sheen and Tai [42]

CostContinuous costreductionPrice

Vaidyanathan [34]Bottani and Rizzi [41]Sheen and Tai [42]Daim et al [43]Selviaridis and Spring[44]

Qualityassurance

ContinuousimprovementKPI trackingISO compliance

Gotzamani et al [28]Vaidyanathan [34] Goland Catay [38]Jharkharia and Shankar[39] Ordoobadi [40]Gol and Catay [38]

IT

System stabilitySystem scalabilityData securityFunction coverage

Vaidyanathan [34]Bottani and Rizzi [41]Daim et al [43]McGinnis [45]

Intangible

ExperienceFinancial stabilityGlobal scopeGeneral reputation

Murphy and Poist [27]Vaidyanathan [34] Goland Catay [38]Ordoobadi [40] Bottaniand Rizzi [41] Gol andCatay [38] Daim et al[43] Selviaridis andSpring [44]

of the value chain such as semiconductor integrated circuit(IC) design mask production and foundry manufacturingpackaging and testing [36] Figure 1 illustrates the five majorsegments that constitute the semiconductor industry supplychain The number shown in the box represents the numberof companies operating in that specific segment in Taiwan

According to statistical data [37] there are more than 400companies operating in the five major areas of the Taiwansemiconductor industry in 2010 among which there were263 design houses 3 mask makers 15 fabrication companies66 packaging and testing companies and 58 raw materialsuppliers In a sense Taiwanrsquos semiconductor industry isorganized as an industrial network with a strong connectionto each other as well as to the global semiconductor anddownstream electronics markets

As shown in Figure 1 the semiconductor manufacturingsegment is located at the center of the supply chain and hasthe greatest number of logistics interactionswith its upstreamand downstream partners To ensure manufacturing andlogistics efficiency the semiconductor manufacturers needto collaborate closely with their partners both up and downthe value chain [46] Since logistics is not a core competencyfor semiconductor manufacturers they outsource most of itto 3PL suppliers to create competitive resource bundles Itis without a doubt that advances in science and technologyoperating under the evolving industry vertical disintegrationmodel have been the main contributors to Taiwanrsquos semi-conductor manufacturing industry success [36] howeverthe effective global logistics performed by the 3PL supplierswhich seamlessly integrate the product and information flowamong the significant number of semiconductor companiesintra- and internationally in a timely manner also plays acritical role in enabling global production networks

3 Research Method

This section describes the background of the nonadditivefuzzy integral method and its suitability to our researchfollowed by a brief explanation of principle and operationprocess of the research method

Basically the nature of the supplier selection is as atype of multicriterion decision-making (MCDM) problembased on the relative priority assigned to each selectioncriterion [8] A considerable number of decision modelshave been developed based on the MCDM theory suchas preference ranking organization method (PROMETHEE)[47] analytical hierarchy process (AHP) [48ndash50] analyticnetwork process (ANP) [51] discrete choice analysis (DCA)[52] total cost ownership (TCO) [53] elimination et choicetranslating reality (ELECTRE) [54] and data envelopment


analysis (DEA) [55 56] In MCDM it is usually assumed thatthe criteria are independent and additive hence the weightedaverage method is often applied to aggregate the importanceweight of those criteria [57] However these assumptionsare not always suitable in many real world applications [757] In the context of 3PL supplier selection for examplethe price charged by a supplier is dependent on its servicequality delivery lead time and contract term and conditionwhich are all common criteria when considering supplierselection Besides the cost risk and quality of supplierare often interdependent for the supplier selection decision[58] The ignorance of the interdependency effects couldproduce assessment bias and leads to ineffective decisions[59] Moreover most decision makers cannot give exactnumerical values to assess the qualitative criteria such as sup-plierrsquos flexibility experience and reputation The judgmentsof the decision makers tend to be subjective and informalwhich are difficult to define and interpret accurately [60]In summary the available information for most supplierselection decisions in real life is usually uncertain vague orimprecise and the criteria are not necessarily independent[7] To solve the abovementioned problems Sugeno [61]proposed the fuzzy integral method which applied fuzzymeasures [62] to deal with the problems of human subjectiveperception and uncertainty as well as to address the levelof interdependency effects among criteria The results offuzzy measures can be further applied to assess the per-formance of interested alternatives [63] The fuzzy integralmethod provides an alternative computational scheme foraggregating information [11] Unlike the traditional additive-assessment methods not considering the interdependencyeffects between selection criteria [59] and adhering to theldquoadditivityrdquo property (ie the importance of two criteriain a probability framework can be nothing else than thesum of the importance of individual criteria) the fuzzymeasure is more flexible in a way that it accepts greater orlower value than simply the sum of importance of multipleindividual criteria That is the fuzzy integral method allowsthe modeling of interaction between criteria [64 65] Infuzzy set theory the linguistic variables are for expressingdecision makersrsquo vague and imprecise semantics Linguisticvariable is very useful in dealing with complex situationsthat are difficult to be reasonably described in conventionalquantitative expressions [66 67] Applying the linguisticvariables the nonadditive fuzzy integral approach enablesresearchers to handle the vague and imprecise semanticsand solve the interdependence among criteria to eliminatesubjective judgment problems involved in a decision-makingcomplex

The nonadditive fuzzy integral method has been popu-larly applied in diverse fields including cost analysis [68 69]location selection [57 70 71] eco-tour plan selection [7273] performance evaluation [74ndash78] performance and riskmeasurement [79] operating model evaluation [80] supplierselection [81 82] risk assessment [83] strategy development[84 85] technology innovation [86] and data selectionfor hyperspectral image sensing [87] In summary due tothe advantage of better revealing the real environment in

px

0 02 04 06 08 10

VP P MP F MG G VG

120583P(p)

10

Figure 2 Membership function for importance degree and perfor-mance value

a multicriterion decision-making complex the nonadditivefuzzy integral approach is employed in this study

The principle and operation process of the nonadditivefuzzy integral are described as follows

31 Step 1 Determine the Importance Degree of DecisionFactors Based on the fuzzy logic linguistic variables are usedto determine the importance degree of decision factors Theconcept of linguistic variablewas presented byZadeh [66 67]A linguistic variable is a variable whose values are wordsor sentences in natural or artificial language For exampleldquoperformancerdquo is a linguistic variable its values are very poor(VP) poor (P) median poor (MP) fair (F) median good(MG) good (G) and very good (VG) This study adoptstriangular fuzzy numbers of seven intervals that is from verypoor (VP) to very good (VG) to describe these linguisticimportance terms expressed by decision makers Their fuzzynumbers are defined as (00 00 01) (00 015 03) (02 0304) (03 05 07) (06 07 08) (07 085 10) and (09 0910) respectively The fuzzy numbers for importance degreeof decision factors are shown as in Figure 2

Making a decision in a multicriterion situation decisionmakersrsquo perceptions of criteria vary in terms of the eval-uations of linguistic variables with respect to importanceweighting on decision factors Given 119898 decision makers theevaluated values of importance are expressed as 119908

119894 119894 =

1 2 119898 One way to integrate decision makersrsquo options onimportance weights that are expressed by linguistic variablescan be done by applying the fuzzy arithmetic which wasproposed by Dubois and Prade [80] The aggregation ofimportance weights determined by 119898 decision makers ispresented by three vertices of triangular fuzzy number withthe following equation

119894119895= (119871119908119894119895119872119908119894119895119877119908119894119895)

= (

(sum119898

119901=1119908119901

119894119895)

119898

(sum119898

119901=1119908119901

119894119895)

119898

(sum119898

119901=1119908119901

119894119895)

119898

)

(1)

where 119894119895= (119871119908119894119895119872119908119894119895119877119908119894119895) is triangular fuzzy numbers

and their points on the left middle and right positions119871119908119894119895


119872119908119894119895 and

119877119908119894119895denote the importance of dimension 119894 and

criterion 119895However the fuzzy importance weights of decision fac-

tors need to be converted into crisp numbers for sequent uti-lization Many defuzzificationmethods have been developedincluding center of sum center of gravity mean of maximaand 120572-cut The defuzzification method proposed by Chenand Klein [81] is a highly sensitive and effective approachBy using the Chen and Klein [81] defuzzying approachthe crisp value of importance weight can be obtained andfurther imported to fuzzy integral to aggregate the overallperformance of alternatives Chen and Klein [81] employed amethod utilizing fuzzy subtraction of a referential rectangle from a fuzzy number 119883 the rectangle is derived bymultiplying the height of the membership function of 119883by the distance between the two crisp maximizing andminimizing barriers Here can be considered a fuzzynumber Fuzzy subtraction of the referential rectangle fromthe fuzzy number119883 can be performed at level 120572

119894as follows

119883120572119894⟨minus⟩ = [119897119894

119903119894] [minus] [119888 119889] = [119897119894

minus 119889 119903119894minus 119888]

119894 = 0 1 2 infin

(2)

where ⟨minus⟩ and [minus] represent fuzzy subtraction and intervalsubtraction operators respectively 119897

119894and 119903119894denote the left

and right loci of and 119888 and 119889 are the left and right barriersrespectively The defuzzification rating of the fuzzy numbercan be obtained with the following equation

119863(119883) =

sum119899

119894=0119903119894minus 119888

sum119899

119894=1(119903119894minus 119888) minus sum

119899

119894=0(119897119894minus 119889)

119899 997888rarr infin (3)

where 119899 denotes the number of 120572-cuts as 119899 approachesinfinthe sum is the measured area In (3) sum119899

119894=1(119903119894minus 119888) is positive

sum119899

119894=1(119897119894minus 119889) is negative and 0 le 119863(119883) le 1 if 0 le 119909 le 1

32 Step 2 Evaluate the Performance Values of AlternativesTo evaluate the performance value on a set of decision factorsthe same fuzzy numbers of seven intervals as presented inFigure 2 are applied Similarly the aggregation of119898 decisionmakersrsquo opinions on the performance of decision factors isobtained with the following equation

119894119895= (119871119901119894119895119872119901119894119895119877119901119894119895)

= (

(sum119898

119901=1119901119901

119894119895)

119898

(sum119898

119901=1119901119901

119894119895)

119898

(sum119898

119901=1119901119901

119894119895)

119898

)

(4)



119872119901119894119895 and

119877119901119894119895represent the overall average ratings of deci-

sion factors on aspect 119894 and criteria 119895 over119898 decisionmakersThe same defuzzification approach developed by Chen andKlein [81] is adopted to convert the fuzzy performance valuesinto crisp numbers for sequent fuzzy integral

After obtaining the performance values on decision fac-tors we can aggregate the overall performance of alternativesand determine the degrees of importance for fuzzy decisionfactors Fuzzy measure can be explicated as the subjectiveimportance of a criterion during the evaluation processSugeno and Terano [82] incorporated the 120582-additive axiom tosimplify information accumulation In fuzzy measure space(X 120573 119892) let 120582 isin (minus1infin) If 119860 isin 120573 119861 isin 120573 119860 cap 119861 = 120601then the fuzzy measure 119892 is 120582-additive This particular fuzzymeasure is termed as 120582-fuzzymeasure because it has to satisfy120582 additively and is known as the Sugeno measure [61]

Assume that X = 1199091 1199092 119909

119899 and 119875(X) is the power

set ofX the set function 119892119875(119883) rarr [0 1] is a fuzzymeasurewhich is nonadditive and preserves the following propertiesforall119860 119861 isin 120573(X) 119860 cap 119861 = 120601 and 119892

120582(119860 cup 119861) = 119892

120582(119860) +

119892120582(119861) + 120582119892

120582(119860)119892120582(119861) for minus1 lt 120582 lt infin To differentiate

this measure from other fuzzy measures 119892120582denotes 120582-fuzzy

measure When 120582 = 0 the 120582-fuzzy measure 119892 is nonadditiveotherwise 120582 = 0means that the 120582-fuzzymeasure 119892 is additiveand there is no interaction between decision factors [83]Additionally the 120582-fuzzy measure of the finite set can bederived from fuzzy densities as indicated in the followingequation [84 85]

119892120582(1199091 1199092 119909

119899)

=

119899

sum

119894=1

119892119894+ 120582

119899minus1

sum

1198941=1

119899

sum

1198942=1198941+1

11989211989411198921198942+ sdot sdot sdot + 120582

119899minus111989211198922 119892

119899

=

1

120582

1003816100381610038161003816100381610038161003816100381610038161003816

119899

prod

119894=1

(1 + 120582119892119894) minus 1

1003816100381610038161003816100381610038161003816100381610038161003816

for minus 1 lt 120582 lt infin

(5)

Based on the boundary conditions in (1) 119892120582(X) = 1 120582

can be determined via the following equation

120582 + 1 =

119899

prod

119894=1

(1 + 120582119892119894) (6)

In fuzzy measure space (X 120573 119892) let ℎ denote a measur-able function from X to [0 1] The fuzzy integral of ℎ over 119860with respect to 119892 is then defined as

int

119860

ℎ (119909) 119889119892 = sup120572isin[01]

[120572 and 119892 (119860 cap 119865120572)] (7)

where 119865120572= 119909 | ℎ(119909) ge 120572 [9] and 119860 represents the domain

of a fuzzy integral When 119860 = 119883 the fuzzy integral can bepresented as int ℎ 119889119892 For simplicity consider a fuzzy measure119892 of (X 119875(X)) where X is a finite set Let ℎ X rarr [0 1] andassume without loss of generality that the function ℎ(119909

119894) is

monotonically decreasing in 119894 for instance ℎ(1199091) ge ℎ(119909

2) ge

sdot sdot sdot ge ℎ(119909119899) To ensure that the elements inX are renumbered

we get the following equation

intℎ (119909) 119892 =

119899

⋁

119894=1

[ℎ (119909119894) and 119892 (119867

119894)] (8)


where 119867119894= 119909

1 1199092 119909

119899 119894 = 1 2 119899 In practice

ℎ can be regarded as a given alternativersquos performance ona particular decision factor and 119892 represents the subjectiveimportance weight of each decision factor The nonadditivefuzzy integral of ℎ(119909) with respect to 119892 gives the overallassessment of the attribute To simplify the calculation thesame fuzzy measure of Choquet integral is expressed asfollows

(119888) int ℎ 119889119892 = ℎ (119909119899) 119892 (119867

119899) + [ℎ (119909

119899minus1) minus ℎ (119909

119899)] 119892 (119867

119899minus1)

+ sdot sdot sdot + [ℎ (1199091) minus ℎ (119909

2)] 119892 (119867

1)

= ℎ (119909119899) [119892 (119867

119899) minus 119892 (119867

119899minus1)]

+ ℎ (119909119899minus1) [119892 (119867

119899minus1) minus 119892 (119867

119899minus2)]

+ sdot sdot sdot + ℎ (1199091) 119892 (119867

1)

(9)

where 0 le ℎ(1199091) le ℎ(119909

2) le sdot sdot sdot le ℎ(119909

119899) le 1 119867

1= 1199091 and

1198672= 1199091 1199092 119867

119899= 1199091 1199092 119909

119899 = X In literature the

fuzzy integral defined by int ℎ 119889119892 is termed a nonadditive fuzzyintegral and denotes the overall performance of alternatives

4 Empirical Study in SemiconductorManufacturing Industry

An empirical study was conducted to identify the key 3PLselection criteria in the semiconductormanufacturing indus-try Firstly we constructed a decision hierarchy consisting ofthree levels of selection criteria as described in Section 41Next we conducted a field survey within semiconductormanufacturing companies to obtain the importance degreeof identified selection criteria in Section 42 Subsequentlywe demonstrated how a company applied the obtainedimportance degree of identified selection criteria to select themost appropriate 3PL supplier from a series of alternativesin Section 43 The practice of the nonadditive fuzzy integralmethod is illustrated in Sections 42 and 43

41 Define theDecisionHierarchy Derived from the selectioncriteria summarized in Table 1 a three-level hierarchy ofselection criteria comprising 6 criterion dimensions and 20subcriteria was developed as shown in Figure 3The top levelof the hierarchy denoted by level 1 represents the ultimategoal of the research which is to identify the determinants of3PL selection criteria The next two levels contain the 6 eval-uation criterion dimensions and 20 subcriteria respectively

The criteria listed in Figure 3 have both quantitative andqualitative variables and some of them have dependency rela-tionship For example the criteria such as the shipment errorrate (119909

13) or contract price (119909

31) are quantitative Conversely

other criteria such as commitment of continuous improve-ment (119909

43) and general reputation (119909

64) are qualitative

therefore their evaluation by most decision makers tendsto be subjective and imprecise The dependency relationshipamong criteria exists in a scene in which a 3PL supplierrsquosshipment error rate would cause impacts to the contract

price with its client and to a certain degree a 3PL supplierrsquosgeneral reputation depends on its delivery performancequality assurance and problem-solving capability To addressthe dependency among criteria vagueness in informationand essential fuzziness of human judgment the nonadditivefuzzy integral method is applied successively

42 Determine the Importance Degree of Selection Criteria Inline with the developed three-level hierarchy of 3PL selectioncriteria we designed a questionnaire complying with thefuzzy integral format The convenient sampling techniquewas adopted in this study due to the fact that it permittedresearchers to survey qualified experts more easily Thesequestionnaires targeted managers and senior staff respon-sible for importexport purchasing warehousing materialsmanagement or logistics outsourcing in the semiconductormanufacturing industry There were ten domain expertsresponding to the survey The average length of respondentsrsquowork experience was more than 10 years

In the nonadditive fuzzy integral method the criteriaweighting begins from the bottom level of decision hierarchyIn the hierarchical structure every item comprises an answerto a question and the associated importance weight Forexample in this empirical study the criterion dimensionof performance would have four answered questions andassociated importance weight values for its associated foursubcriteria that is on-time delivery transportation safetyshipment error rate and document accuracy respectivelyDuring the survey process the importance values of criteriawere weighted by using the fuzzy number In the beginningthe survey respondents evaluated the importance of selectioncriteria via a questionnaireTheir evaluation values were thenconverted into triangular fuzzy numbers by using linguisticvariables as shown in Figure 2 Subsequently the importanceweights of selection criteria were calculated by aggregatingsurvey respondentsrsquo evaluation values via (1) Finally wecould derive the importance weights by using (3) the resultis shown in Table 2 As we can see in Table 2 the criteriondimension of performance has the highest rank with aweightof 0909 followed by cost and service (both of them have thesame importance weight of 0769) then by quality assuranceand intangible with the same importanceweight of 0667 andlastly by IT with the weight of 0500 Within each criteriondimension the weights of belonging subcriteria indicatetheir importance ranking For example the subcriterion ofdocument accuracy in the dimension of performance hasthe highest ranking (0877) followed by transportation safety(0867) shipment error rate (0833) and on-time delivery(0815)

43 Evaluate the Performance Values of Alternatives Basedon the importance weights of 3PL selection criteria obtainedin Table 2 a major semiconductor manufacturing companyin Taiwan conducted a group decision meeting of 3PLsupplier selection For confidentiality reasons a fictitiousname Company X is used to represent the case companyone of the top 10 semiconductor manufacturing companiesin the world Company X has more than 10 manufacturing


3PL

supp

lier s

elect

ion

Level 1 goal Level 2 criterion dimensions Level 3 subcriteria

Performance (D1)

Service (D2)

Cost (D3)

Quality assurance (D4)

IT (D5)

Intangible (D6)

On-time delivery (x11)

Transportation safety (x12)

Shipment error rate (x13)

Document accuracy (x14)

Value-added service (x21)

Customer support service (x22)

Problem-solving capability (x23)

Price (x31)

Continuous cost reduction (x32)

ISO compliance (x41)

Key performance indicators tracking (x42)

Continuous improvement (x43)

System stability (x51)

System scalability (x52)

Data security (x53)

Function coverage (x54)

Experience (x61)

Financial stability (x62)

Global scope (x63)

General reputation (x64)

Figure 3 The hierarchy of 3PL provider selection

plants in Taiwan China Singapore and the USA As of 2013the company served more than 400 worldwide customerswith more than 7000 products manufacturing for a varietyof electronic applications in computer communication andconsumer markets Four 3PL suppliers were considered forthe study they were all large operations with global networksof services UPS DHL two distinguished American logisticscompanies Nippon Express a notable Japanese companyand Morrison the largest 3PL supplier in Taiwan We maskthe identities of the four candidates by labelling them suppli-ers A B C and D with random sequence

At the outset the selection teammembers evaluated thesealternativesrsquo performance according to the selection criteriashown in Figure 3 With the performance results collectedfrom the selection team we then aggregated them as fuzzyperformance values by using (4) and converted them into

crisp numbers by using (3) The value 120582 of each dimensionwas calculated by using (6) with corresponding measuredensity 119892

119894 the importance weight of each subcriterion

Finally we can get the Choquet integral value and 120582-value forthe overall performance of one alternative by using (9)

Table 3 shows the fuzzy measure and aggregated value forone of the 3PL suppliers the supplier A The 4th column119892119894(sdot) in Table 3 inherited from the last column in Table 2

presents the importance weights of subcriteria The crispperformance value ℎ(sdot) the 3rd column in Table 3 showsthe given 3PL suppliersrsquo performance on each subcriterionThe 120582-value of the 5th column presents the fuzzy measureand the Choquet integral value (119888) int ℎ(sdot)119889119892

120582 the last column

represents the overall perceived performance of the selectionteamrsquos perception on the entire selection criteria As shownin Table 3 the criterion dimension 119863

2has the highest


Table 2 Weights of 6 criterion dimensions and 20 subcriteria

Dimension Weight (119892119894(sdot)) Criterion Weight (119892

119894(sdot))

Performance (1198631) 0909

On-time delivery (x11) 0815Transportation safety (x12) 0867Shipment error rate (x13) 0833Document accuracy (x14) 0877

Service (1198632) 0769

Value-added service (x21) 0789Customer support service (x22) 0714Problem-solving capability (x23) 0838

Cost (1198633) 0769 Price (x31) 0794

Continuous cost reduction (x32) 0877

Quality assurance (1198634) 0667

ISO compliance (x41) 0762Key performance indicators tracking (x42) 0805

Continuous improvement (x43) 0702

IT (1198635) 0500

System stability (x51) 0722System scalability (x52) 0693Data security (x53) 0779

Function coverage (x54) 0800

Intangible (1198636) 0667

Experience (x61) 0800Financial stability (x62) 0742Global scope (x63) 0726

General reputation (x64) 0752

Table 3 Fuzzy measure and aggregated values for 3PL supplier A

Dimensions Subcriteria ℎ(sdot) 119892119894(sdot) 119892

120582(sdot) (119888) int ℎ(sdot)119889119892

120582(sdot) (120582-value)

1198631

x11 0769 0815 119892120582(x14) 0867

0767 (minus0999)x12 0769 0867 119892120582(x14 x13) 0976

x13 0667 0833 g120582(x14 x13 x11) 0997x14 0500 0877 119892

120582(x14 x13 x11 x12) 1000

1198632

x21 0769 0789 119892120582(x21) 0714

0869 (minus0989)x22 0909 0714 119892120582(x21 x23) 0960

x23 0769 0838 119892120582(x21 x23 x22) 1000

1198633

x31 0769 0794 119892120582(x31) 0877 0770 (minus0963)

x32 0769 0877 119892120582(x31 x32) 1000

1198634

x41 0745 0762 119892120582(x41) 0702

0768 (minus0984)x42 0769 0805 119892120582(x41 x42) 0951

x43 0769 0702 119892120582(x41 x42 x43) 1000

1198635

x51 0667 0722 119892120582(x51) 0800

0768 (minus0996)x52 0769 0693 119892120582(x51 x52) 0958

x53 0769 0779 119892120582(x51 x52 x53) 0990

x54 0769 0800 119892120582(x51 x52 x53 x54) 1000

1198636

x61 0769 0800 119892120582(x62) 0726

0766 (minus0996)x62 0667 0742 119892120582(x62 x64) 0947

x63 0769 0726 119892120582(x62 x64 x61) 0990

x64 0720 0752 119892120582(x62 x64 x61 x63) 1000

Choquet integral value of 0869 among all the six dimensionswhich indicates that supplier A performs best in the Serviceselection criterion dimension according to the judgment ofthe selection teamMoreover the 120582-value closing to minus1 meansthe existence of complete dependent and mutual influencerelationships among criteria

The Choquet integral value of each individual criteriondimension can be further aggregated to determine the overallperformance of supplier A As shown in Table 4 the ℎ(sdot)column inherited from Table 3 is supplier Arsquos performanceon each criterion dimension whereas the 119892

119894(sdot) column

inherited from Table 2 is the importance weight of the six


Table 4 Fuzzy measure and overall performance values for 3PL supplier A

3PL supplier Criterion group ℎ(sdot) 119892119894(sdot) 119892

120582(sdot) (119888) int ℎ(sdot)119889119892

120582(sdot) (120582-value)

A

D1 0767 0909 119892120582(1198636) 0769

0847 (minus0999)

D2 0869 0769 119892120582(11986361198631) 0980

D3 0770 0909 119892120582(119863611986311198634) 0994

D4 0768 0769 119892120582(1198636119863111986341198635) 0999

D5 0768 0667 119892120582(11986361198631119863411986351198633) 1000

D6 0766 0769 119892120582(119863611986311198634119863511986331198632) 1000

Table 5 3PL suppliersrsquo performance values and rankings

3PL supplier Performance value RankingA 0847 3B 0892 1C 0885 2D 0832 4

criterion dimensions Applying (6) and (9) we can get thefuzzy measure 120582-value of 119892

120582(sdot) and the Choquet integral

value (119888) int ℎ(sdot)119889119892120582 respectively The Choquet integral value

of 0847 is the overall performance of supplier AApplying the same calculation process to the remaining

three 3PL supplier alternatives we could obtain their overallperformance values as shown in Table 5 The result showsthat supplier B is the one with the highest performance value(0892) followed by suppliers C (0885) A (0847) and D(0832) respectively Therefore supplier B is the best choicewith the considerations of the multiplicative effects of criteriaand dimensions

5 Discussion and Conclusion

Through the nonadditive fuzzy integral operation pro-cess aforementioned we demonstrated how the importancedegree of the 3PL supplier selection criteria was obtainedand how the most appropriate 3PL supplier was determinedfrom a series of alternatives The results shown in Table 2reveal that the criterion dimension of performance has thehighest rank with a weight of 0909 followed by cost (0769)service (0769) quality assurance (0667) intangible (0667)and IT (0500) The fact that all the top three criteriondimensions namely performance cost and service have ashigh as more than 75 percent of importance weight indi-cates that a 3PL supplier that can deliver high-performancelogistics functions combined with thorough cost controlcapability and high-quality customer services is appealingto the semiconductor manufacturing industry most At thedetailed-level the document accuracy (0877) ranks number1 within 20 subcriteria The justification of such high rankingis because the main documents required for contemporaryinternational logistics include as many as 200 or more dataelements that are keyed in multiple times by various parties[86] Without accurate documentation goods shipmentscould remain in customsrsquo possession which incurs high

shipment error rates and thus jeopardizes on-time deliveryThis interdependency relationship explains why documentaccuracy is ranked ahead of shipment error rate and on-time delivery in the performance dimension that is whenthe requirement of document accuracy is fulfilled the resultsof shipment error and on-time delivery rates are improvedaccordingly

3PL supplier selection is a complex analytical processand involves a wide range of quantitative and qualitativeselection criteria Within a multicriterion decision-makingsituation decision criteria have to be defined and weightedalternatives need to be evaluated and finally best satisfyingalternative could be identified The information available foruse in multicriterion decision-making complex is usuallyuncertain vague or imprecise and the criteria are notnecessarily independent In addition if a criterion containsadditional subcriteria there would be a stronger possibil-ity of correlation among subcriteria Unlike the traditionalMCDM methods which often assume independence amongcriteria and additive importance weights the nonadditivefuzzy integral is a more effective approach to solve thedependency among criteria vagueness in information andessential fuzziness of human judgment

In terms of managerial implications this research pro-vides insights for decision makers in both semiconductormanufacturing and 3PL companies For the semiconductormanufacturing companieswith global supply chain and logis-tics outsourcing needs this research result provides themwith perceivable and holistic information so that they caneasily focus on the most important 3PL selection criteria Forthe 3PL companies aiming to persist in competitive advantagein the high-tech industries this research enlightens themthat the superior performance satisfying customer servicesand detailed cost-control conform most to the semicon-ductor manufacturersrsquo requirements Additionally althoughthis research is based on a sample of the semiconductormanufacturing industry the experience of selecting 3PLproviders uncovered in this research could be a valuablereference for other industries with similar characteristics ofglobal supply chain complex heavy capital investment shortproduct life cycle and dynamic market demands

The main contributions of this study are that it presentsa comprehensive 3PL supplier selectionrsquos decision frameworkand produces the importance weights of each selection cri-terion by considering the interdependent relationship amongthose selection criteria and eliminating the ambiguous andimprecise nature embedded in decision-makersrsquo subjective


judgments The research result can become a valuable refer-ence for manufacturing companies operating in comparablesituations Moreover the systematic framework presented inthis study can be easily extended to the analysis of otherdecision-making domains

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research is supported by the National Science CouncilTaiwan (Project no NSC101-2410-H-224-040-) The authorswould also like to thank the reviewers for their constructivecomments to improve the overall quality of this paper

References

[1] T Skjoett-Larsen ldquoThird party logisticsmdashfrom an interor-ganizational point of viewrdquo International Journal of PhysicalDistribution and Logistics Management vol 30 no 2 pp 112ndash127 2000

[2] M Knemeyer T M Corsi and P R Murphy ldquoLogisticsoutsourcing relationships customer perspectivesrdquo Journal ofBusiness Logistics vol 24 no 1 pp 77ndash109 2003

[3] ZG ZachariaN R Sanders andNWNix ldquoThe emerging roleof the third-party logistics provider (3PL) as an orchestratorrdquoJournal of Business Logistics vol 32 no 1 pp 40ndash54 2011

[4] R Lasch and C G Janker ldquoSupplier selection and controllingusing multivariate analysisrdquo International Journal of PhysicalDistribution and Logistics Management vol 35 no 6 pp 409ndash425 2005

[5] K Goffin F Lemke and M Szwejczewski ldquoAn exploratorystudy of lsquoclosersquo supplier-manufacturer relationshipsrdquo Journal ofOperations Management vol 24 no 2 pp 189ndash209 2006

[6] D A Carrera and R V Mayorga ldquoSupply chain management amodular Fuzzy Inference System approach in supplier selectionfor new product developmentrdquo Journal of Intelligent Manufac-turing vol 19 no 1 pp 1ndash12 2008

[7] J L Yang H N Chiu G-H Tzeng and R H Yeh ldquoVendorselection by integrated fuzzy MCDM techniques with indepen-dent and interdependent relationshipsrdquo Information Sciencesvol 178 no 21 pp 4166ndash4183 2008

[8] W Ho X Xu and P K Dey ldquoMulti-criteria decision makingapproaches for supplier evaluation and selection a literaturereviewrdquo European Journal of Operational Research vol 202 no1 pp 16ndash24 2010

[9] Z Wang K Leung and J Wang ldquoA genetic algorithm fordetermining nonadditive set functions in information fusionrdquoFuzzy Sets and Systems vol 102 no 3 pp 463ndash469 1999

[10] M Grabisch ldquoFuzzy integral in multicriteria decision makingrdquoFuzzy Sets and Systems vol 69 no 3 pp 279ndash298 1995

[11] J H Chiang ldquoChoquet fuzzy integral-based hierarchical net-works for decision analysisrdquo IEEE Transactions on Fuzzy Sys-tems vol 7 no 1 pp 63ndash71 1999

[12] R Lieb and B A Bentz ldquoThe use of third-party logisticsservices by large American manufacturers the 2004 surveyrdquoTransportation Journal vol 44 no 2 pp 5ndash15 2005

[13] L Jiang Y Wang and X Yan ldquoDecision and coordinationin a competing retail channel involving a third-party logisticsproviderrdquo Computers amp Industrial Engineering vol 76 pp 109ndash121 2014

[14] A C Suyabatmaz F T Altekin and G Sahin ldquoHybridsimulation-analytical modeling approaches for the reverselogistics network design of a third-party logistics providerrdquoComputers amp Industrial Engineering vol 70 no 1 pp 74ndash892014

[15] S Hertz and M Alfredsson ldquoStrategic development of thirdparty logistics providersrdquo Industrial Marketing Managementvol 32 no 2 pp 139ndash149 2003

[16] M J Maloni and C R Carter ldquoOpportunities for research inthird-party logisticsrdquo Transportation Journal vol 45 no 2 pp23ndash38 2006

[17] S Jharkharia and R Shankar ldquoSelection of logistics serviceprovider an analytic network process ANP approachrdquo Omegavol 35 no 3 pp 274ndash289 2007

[18] T Solakivi J Toyli and L Ojala ldquoLogistics outsourcing itsmotives and the level of logistics costs in manufacturing andtrading companies operating in Finlandrdquo Production Planningand Control vol 24 no 4-5 pp 388ndash398 2013

[19] W Liu H Xu X Sun Y Yang and Y Mo ldquoOrder allocationresearch of logistics service supply chain with mass customiza-tion logistics servicerdquo Mathematical Problems in Engineeringvol 2013 Article ID 957260 13 pages 2013

[20] R Leuschner C R Carter T J Goldsby and Z S RogersldquoThird-party logistics a meta-analytic review and investigationof its impact on performancerdquo Journal of Supply ChainManage-ment vol 50 no 1 pp 21ndash43 2014

[21] A H Bask ldquoRelationships among TPL providers and membersof supply chainsmdasha strategic perspectiverdquo Journal of Business ampIndustrial Marketing vol 16 no 6-7 pp 471ndash486 2001

[22] R Wilding and R Juriado ldquoCustomer perceptions on logis-tics outsourcing in the European consumer goods industryrdquoInternational Journal of Physical Distribution and LogisticsManagement vol 34 no 8 pp 628ndash644 2004

[23] B Baki and IM Ar ldquoA comparative analysis of 3PL applicationsin manufacturing firms from seven countriesrdquo Supply ChainForum vol 10 no 1 pp 16ndash30 2009

[24] G Busch ldquoNew twist on supplier evaluationrdquo Purchasing vol55 pp 102ndash103 1962

[25] G W Dickson ldquoAn analysis of vendor selection systems anddecisionsrdquo Journal of Purchasing vol 2 no 1 pp 5ndash17 1966

[26] T R Coltman T M Devinney and B W Keating ldquoBest-worstscaling approach to predict customer choice for 3PL servicesrdquoJournal of Business Logistics vol 32 no 2 pp 139ndash152 2011

[27] P R Murphy and R F Poist ldquoThird-party logistics some userversus provider perspectivesrdquo Journal of Business Logistics vol21 no 1 pp 121ndash133 2000

[28] K D Gotzamani P Longinidis and F Vouzas ldquoThe logisticsservices outsourcing dilemma quality management and finan-cial performance perspectivesrdquo Supply Chain Management vol15 no 6 pp 438ndash453 2010

[29] Y M Chen M-J Goan and P-N Huang ldquoSelection processin logistics outsourcingmdasha view from third party logisticsproviderrdquo Production Planning and Control vol 22 no 3 pp308ndash324 2011

[30] C-Y Ku C-T Chang and H-P Ho ldquoGlobal supplier selectionusing fuzzy analytic hierarchy process and fuzzy goal program-mingrdquo Quality and Quantity vol 44 no 4 pp 623ndash640 2010


[31] H H Wu and Y N Tsai ldquoUsing AHP to evaluate the criteria ofauto spare parts industryrdquoQuality amp Quantity vol 45 no 1 pp969ndash983 2011

[32] K Govindan J Sarkis and M Palaniappan ldquoAn analyticnetwork process-basedmulticriteria decisionmakingmodel fora reverse supply chainrdquo The International Journal of AdvancedManufacturing Technology vol 68 no 1ndash4 pp 863ndash880 2013

[33] H-Y Kang A H I Lee and C-Y Yang ldquoA fuzzy ANP modelfor supplier selection as applied to IC packagingrdquo Journal ofIntelligent Manufacturing vol 23 no 5 pp 1477ndash1488 2012

[34] G Vaidyanathan ldquoA Framework for evaluating third-partylogisticsrdquo Communications of the ACM vol 48 no 1 pp 89ndash94 2005

[35] R F Sean ldquoA newmodel for selecting third-party reverse logis-tics providers in the presence of multiple dual-role factorsrdquoTheInternational Journal of Advanced Manufacturing Technologyvol 46 no 1ndash4 pp 405ndash410 2010

[36] S-H Chen ldquoGlobal production networks and informationtechnology the case of Taiwanrdquo Industry and Innovation vol9 no 3 pp 249ndash266 2002

[37] ITRI Taiwan Semiconductor Industry Yearbook Industrial Eco-nomics amp Knowledge Center Taipei Taiwan 2011

[38] H Gol and B Catay ldquoThird-party logistics provider selectioninsights from a Turkish automotive companyrdquo Supply ChainManagement vol 12 no 6 pp 379ndash384 2007

[39] S Jharkharia and R Shankar ldquoSelection of logistics serviceprovider an analytic network process (ANP) approachrdquo TheInternational Journal of Management Sciences vol 35 no 3 pp274ndash289 2007

[40] S M Ordoobadi ldquoDevelopment of a supplier selection modelusing fuzzy logicrdquo Supply Chain Management vol 14 no 4 pp314ndash327 2009

[41] E Bottani and A Rizzi ldquoA fuzzy TOPSIS methodology tosupport outsourcing of logistics servicesrdquo Supply Chain Man-agement vol 11 no 4 pp 294ndash308 2006

[42] G J Sheen and C T Tai ldquoA study on decision factors and thirdparty selection criterion of logistics outsourcing an exploratorystudy of direct selling industryrdquo Journal of American Academyof Business vol 9 no 2 pp 331ndash337 2006

[43] T U Daim A Udbye andA Balasubramanian ldquoUse of analytichierarchy process AHP for selection of 3PL providersrdquo JournalofManufacturing TechnologyManagement vol 24 no 1 pp 28ndash51 2013

[44] K Selviaridis and M Spring ldquoThird party logistics a literaturereview and research agendardquo International Journal of LogisticsManagement vol 18 no 1 pp 125ndash150 2007

[45] M A McGinnis ldquoA comparative evaluation of freight trans-portationmodelsrdquoTransportation Journal vol 29 no 2 pp 36ndash46 1989

[46] B-N Hwang S-C Chang H-C Yu and C-W Chang ldquoPio-neering e-supply chain integration in semiconductor industrya case studyrdquo International Journal of Advanced ManufacturingTechnology vol 36 no 7-8 pp 825ndash832 2008

[47] J-P Brans and P Vincke ldquoA preference ranking organizationmethodrdquoManagement Science vol 31 no 6 pp 647ndash656 1985

[48] R L Nydick and R P Hill ldquoUsing the analytic hierarchy processto the supplier selection problemrdquo Journal of Purchasing andMaterials Management vol 28 pp 31ndash36 1992

[49] S H Ghodsypour and C OrsquoBrien ldquoA decision support systemfor supplier selection using an integrated analytic hierarchyprocess and linear programmingrdquo International Journal ofProduction Economics vol 56-57 no 20 pp 199ndash212 1998

[50] Z Li W K Wong and C K Kwong ldquoAn integrated modelof material supplier selection and order allocation using fuzzyextended AHP and multiobjective programmingrdquo Mathemat-ical Problems in Engineering vol 2013 Article ID 363718 14pages 2013

[51] C-M Wu C-L Hsieh and K-L Chang ldquoA hybrid multiplecriteria decision making model for supplier selectionrdquo Mathe-matical Problems in Engineering vol 2013 Article ID 324283 8pages 2013

[52] R Verma and M E Pullman ldquoAn analysis of the supplierselection processrdquo Omega vol 26 no 6 pp 739ndash750 1998

[53] Z Degraeve E Labro and F Roodhooft ldquoEvaluation of vendorselection models from a total cost of ownership perspectiverdquoEuropean Journal of Operational Research vol 125 no 1 pp 34ndash58 2000

[54] C-W Tsui and U-P Wen ldquoA hybrid multiple criteria groupdecision-making approach for green supplier selection in theTFT-LCD industryrdquoMathematical Problems in Engineering vol2014 Article ID 709872 13 pages 2014

[55] C A Weber J R Current and A Desai ldquoAn optimizationapproach to determining the number of vendors to employrdquoSupply Chain Management vol 5 no 2 pp 90ndash98 2000

[56] R Narasimhan S Talluri and D Mendez ldquoSupplier evaluationand rationalization via data envelopment analysis an empiricalexamplerdquoThe Journal of Supply Chain Management vol 37 no3 pp 28ndash37 2001

[57] G-H Tzeng Y-P Ou Yang C-T Lin and C-B Chen ldquoHier-archical MADM with fuzzy integral for evaluating enterpriseintranet web sitesrdquo Information Sciences vol 169 no 3-4 pp409ndash426 2005

[58] J J H Liou and G-H Tzeng ldquoComments on lsquoMultiplecriteria decision making (MCDM) methods in economics anoverviewrsquordquo Technological and Economic Development of Econ-omy vol 18 no 4 pp 672ndash695 2012

[59] Y C Kuo S T Lu G H Tzeng Y C Lin and Y SHuang ldquoUsing fuzzy integral approach to enhance site selectionassessmentmdasha case study of the optoelectronics industryrdquoProcedia Computer Science vol 17 pp 306ndash313 2013

[60] C-S Lai H-L Lee and Y-C Pan ldquoApplying fuzzy multi-criteria decision-making model to ecotour plan selectionrdquoQuality amp Quantity vol 47 no 2 pp 1125ndash1141 2013

[61] M SugenoTheory of Fuzzy Integrals and Its Applications TokyoInstitute of Technology Tokyo Japan 1974

[62] R E Bellman and L A Zadeh ldquoDecision-making in a fuzzyenvironmentrdquoManagement Science vol 17 pp B141ndashB164 1970

[63] C-H Wang I-Y Lu and C-B Chen ldquoIntegrating hierarchicalbalanced scorecard with non-additive fuzzy integral for evalu-ating high technology firm performancerdquo International Journalof Production Economics vol 128 no 1 pp 413ndash426 2010

[64] M Grabisch ldquoFuzzy integral as a flexible and interpretabletool of aggregationrdquo in Aggregation and Fusion of ImperfectInformation vol 12 pp 51ndash72 Physica Heidelberg Germany1998

[65] M Sugeno and S H Kwon ldquoA clusterwise regression typemodel for subjective evaluationrdquo Journal of Japan Society forFuzzy Theory and Systems vol 7 pp 291ndash310 1995

[66] L A Zadeh ldquoThe concept of a linguistic variable and itsapplication to approximate reasoningrdquo Information Sciencesvol 8 no 3 pp 199ndash249 1975

[67] L A Shah A Etienne A Siadat and F Vernadat ldquoDecision-making in the manufacturing environment using a value-riskgraphrdquo Journal of Intelligent Manufacturing 2014


[68] Y-W Chen and G-H Tseng ldquoUsing fuzzy integral for evalu-ating subjectively perceived travel costs in a traffic assignmentmodelrdquo European Journal of Operational Research vol 130 no3 pp 653ndash664 2001

[69] G Buyukozkan O Feyzioglu and M Sakir Ersoy ldquoEvaluationof 4PL operating models a decision making approach based on2-additive Choquet integralrdquo International Journal of Produc-tion Economics vol 121 no 1 pp 112ndash120 2009

[70] T Demirel N C Demirel and C Kahraman ldquoMulti-criteriawarehouse location selection using Choquet integralrdquo ExpertSystems with Applications vol 37 no 5 pp 3943ndash3952 2010

[71] R Florez-Lopez ldquoStrategic supplier selection in the added-valueperspective a CI approachrdquo Information Sciences vol 177 no 5pp 1169ndash1179 2007

[72] S-J Chen and C-L Hwang Fuzzy Multiple Attribute DecisionMaking Methods and Applications Springer Berlin Germany1992

[73] M-L Tseng J H Chiang and L W Lan ldquoSelection of optimalsupplier in supply chain management strategy with analyticnetwork process and choquet integralrdquo Computers amp IndustrialEngineering vol 57 no 1 pp 330ndash340 2009

[74] H-K Chiou and G-H Tzeng ldquoFuzzy multiple-criteriadecision-making approach for industrial green engineeringrdquoEnvironmental Management vol 30 no 6 pp 816ndash830 2002

[75] G Buyukozkan and D Ruan ldquoChoquet integral based aggre-gation approach to software development risk assessmentrdquoInformation Sciences vol 180 no 3 pp 441ndash451 2010

[76] W T Lin S C Chen H F Jang and H H Wu ldquoPerfor-mance evaluation of introducing QS-9000 to the Taiwanesesemiconductor industryrdquo International Journal of AdvancedManufacturing Technology vol 27 no 9-10 pp 1011ndash1020 2006

[77] H-K Chiou G-H Tzeng and D-C Cheng ldquoEvaluatingsustainable fishing development strategies using fuzzy MCDMapproachrdquo Omega vol 33 no 3 pp 223ndash234 2005

[78] F-M Tseng and Y-J Chiu ldquoHierarchical fuzzy integral statedpreference method for Taiwanrsquos broadband service marketrdquoOmega vol 33 no 1 pp 55ndash64 2005

[79] C-H Wang I-Y Lu and C-B Chen ldquoEvaluating firm techno-logical innovation capability under uncertaintyrdquo Technovationvol 28 no 6 pp 349ndash363 2008

[80] D Dubois and H Prade Fuzzy Sets and Systems Theory andApplications Academic Press New York NY USA 1980

[81] C B Chen and C M Klein ldquoAn efficient approach to solvingfuzzy MADM problemrdquo Fuzzy Sets and Systems vol 88 no 1pp 51ndash67 1997

[82] M Sugeno and T Terano ldquoA model of learning based on fuzzyinformationrdquo Kybernetes vol 6 no 3 pp 157ndash166 1977

[83] G J Klir Z Wang and D Harmanec ldquoConstructing fuzzymeasures in expert systemsrdquo Fuzzy Sets and Systems vol 92 no2 pp 251ndash264 1997

[84] R L Keeney and H Raiffa Decisions with Multiple ObjectivesPreferences and Value Tradeoffs Wiley New York NY USA1976

[85] K Leszczynski P Penczek and W Grochulski ldquoSugenorsquos fuzzymeasure and fuzzy clusteringrdquo Fuzzy Sets and Systems vol 15no 2 pp 147ndash158 1985

[86] PM Byrne ldquoCross-border trade redefining high performancerdquoLogistics Management vol 44 no 3 pp 25ndash27 2005

[87] H Gao L Xu C Li A Shi F Huang and Z Ma ldquoA newfeature selection method for hyperspectral image classification

based on simulated annealing genetic algorithm and choquetfuzzy integralrdquoMathematical Problems in Engineering vol 2013Article ID 537268 13 pages 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Differential EquationsInternational Journal of

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Stochastic AnalysisInternational Journal of


necessarily independent [7]The traditionalMCDMmethodsused to determine the importance of selection criteria oftenassume additive weights and independence among criteriaBut an additivemodel is not always suitable due to the varyingdegrees of interactions among selection criteria [9] On thecontrary the fuzzy measures do not need to assume theindependence among criteriaThe nonadditive fuzzy integralmethod based on the fuzzy measures has been developed toaddress the degree of interaction among diversified criteriaand the vagueness existing in human subjective judgments[10 11] Due to the advantage of better revealing the realenvironment we employed the nonadditive fuzzy integralapproach in this study to construct the 3PL supplier selectionassessment process

The remainder of this paper is organized as followsSection 2 presents a review of the relevant literature of 3PLand its significance to the semiconductor manufacturingindustry Section 3 introduces the nonadditive fuzzy integralresearch method Section 4 presents the empirical study thatemploys the research method to evaluate the importanceweight of selection criteria and choose the most appropriate3PL supplier Finally Section 5 discusses the research resultand concludes the paper

2 Literature Review

21 3PL and 3PL Selection Criteria 3PL functions encompassthe entire logistics process or selected activities within thatprocess [12] Typical logistics activities performed by a 3PLsupplier are warehousing transportation distribution cus-tomer service inventory packaging cross docking logisticsmanagement and reverse logistics [13 14] The relationshipbetween a 3PL supplier and its customers is that the firstparty is the client who purchases the logistics service and thesecond party is the clientrsquos customer(s) thus the third partyis the service supplier and acts as a middleman by takingtitle not to the products but to which logistics activities areoutsourced [15]

Initially 3PL services were relatively limited in scope[16] Over time 3PL suppliers began offering an increas-ingly integrated set of logistics activities and have becomea mainstream in current business environment [17] Mostmanufacturing companies are fond of 3PL suppliers as theyare alternatives with greater flexibility cost saving increasedoperational efficiency better customer service improvedexpertise reengineering of logistics processes and access tonew technologies [18 19] A meta-analysis evidenced thatthe employment of 3PL providers was in favor of a firmrsquosperformance [20] Moreover engaging logistics service of3PL suppliers permits a manufacturing firm a better focuson its core businesses [21] However achieving a successfulimplementation of logistics outsourcing to 3PL is not aneasy task [22] Often-cited difficulties that concern a 3PLsupplierrsquos performance include a lack of understanding ofclientrsquos supply chain needs lack of adequate expertise inspecific products and markets inadequate description ofservices and service levels lack of 3PL innovation and lackof logistics cost awareness [22 23] Therefore an efficientsupplier management that begins with the identification

of potential suppliers is prerequisite for successful logisticsoutsourcing

Academia started research regarding the supplier selec-tion of logistics services in the sixties [24 25] Among recentstudies one of the most comprehensive works is the onecarried out by Ho et al [8] The study was based on thereview of 78 papers related to supplier selection the authorsexhaustively addressed the issue of both qualitative andquantitative criteria that have to be considered when viablesuppliers are to be ranked Considering the nature of 3PL inparticular Coltman et al [26] added selection criteria such ascustomer interaction track-and-trace service recovery sup-ply chain flexibility and capability professionalism proactiveinnovation and relationship orientation Some researchersexamined the key selection factors for 3PL suppliers fromparticular perspectives For example Murphy and Poist [27]analyzed the key factors in a successful relationship fromboth supplier and user perspectives whereas Gotzamaniet al [28] paid special attention to quality-related factors anddeliberated the relationship between quality managementand financial performance of 3PL suppliers Chen et al[29] employed transport cost frequency of shipments ITcommunication quality performance and order to shop timeas 3PL selection criteria for apparel retailer industry

As supplier selection is viewed to be a multicrite-rion decision-making process for most companies someresearchers have developed research frameworks that orga-nize selection criteria according to a hierarchical structureFor example Ku et al [30] constructed a hierarchical frame-work to deal with the problem of global supplier selectionWu and Tsai [31] applied 7major criteria and 30 subcriteria toevaluate the suppliers for auto spare parts industry Govindanet al [32] listed 34 subcriteria and grouped them into sevencriteria Kang et al [33] developed a multilevel hierarchy tosupport the supplier selection decision by considering fivecriteria and thirteen subcriteria Vaidyanathan [34] proposeda 3PL evaluation framework that comprised sixmajor criteriaof IT quality assurance cost services performance andintangibles Sean [35] identified service-quality experienceand service-quality credence as dual-role factors when select-ing third-party reverse logistics suppliers In conclusionthe 3PL supplier selection is based on multiple criteriacomprising both quantitative and qualitative criteria

Incorporating many of these relevant criteria for theselection of a 3PL supplier Table 1 summarizesmost common3PL selection criteria and groups them in six general cate-gories suggested by Vaidyanathan [34]

22 Semiconductor Manufacturing Industry in Taiwan Tai-wanrsquos entire semiconductor industry is currently the fourthlargest in the world behind only the USA Japan andKorea According to the publication IC Insight Taiwan hasbecome the largest semiconductor foundry manufacturersecond largest semiconductor designer and the fourth largestsemiconductor producer in the world In contrast to thevertically integrated conglomerates dominating the industryin Korea and Japan Taiwanrsquos semiconductor industry hasa unique vertically disintegrated structure that consists ofmany small-to-medium firms specializing in a narrow range





IC packaging(30)

Final testing(36)


Chemical

(36)




Performance



Service





Qualityassurance



IT



Intangible






3 Research Method






px

0 02 04 06 08 10

VP P MP F MG G VG

120583P(p)

10






119894 119894 =


119894119895= (119871119908119894119895119872119908119894119895119877119908119894119895)

= (

(sum119898

119901=1119908119901

119894119895)

119898

(sum119898

119901=1119908119901

119894119895)

119898

(sum119898

119901=1119908119901

119894119895)

119898

)

(1)




119872119908119894119895 and




119894as follows

119883120572119894⟨minus⟩ = [119897119894

119903119894] [minus] [119888 119889] = [119897119894

minus 119889 119903119894minus 119888]

119894 = 0 1 2 infin

(2)




119863(119883) =

sum119899

119894=0119903119894minus 119888

sum119899

119894=1(119903119894minus 119888) minus sum

119899

119894=0(119897119894minus 119889)

119899 997888rarr infin (3)



sum119899



119894119895= (119871119901119894119895119872119901119894119895119877119901119894119895)

= (

(sum119898

119901=1119901119901

119894119895)

119898

(sum119898

119901=1119901119901

119894119895)

119898

(sum119898

119901=1119901119901

119894119895)

119898

)

(4)



119872119901119894119895 and




Assume that X = 1199091 1199092 119909



120582(119860 cup 119861) = 119892

120582(119860) +

119892120582(119861) + 120582119892




119892120582(1199091 1199092 119909

119899)

=

119899

sum

119894=1

119892119894+ 120582

119899minus1

sum

1198941=1

119899

sum

1198942=1198941+1

11989211989411198921198942+ sdot sdot sdot + 120582

119899minus111989211198922 119892

119899

=

1

120582

1003816100381610038161003816100381610038161003816100381610038161003816

119899

prod

119894=1

(1 + 120582119892119894) minus 1

1003816100381610038161003816100381610038161003816100381610038161003816


(5)



120582 + 1 =

119899

prod

119894=1

(1 + 120582119892119894) (6)


int

119860

ℎ (119909) 119889119892 = sup120572isin[01]

[120572 and 119892 (119860 cap 119865120572)] (7)



119894) is


2) ge



intℎ (119909) 119892 =

119899

⋁

119894=1

[ℎ (119909119894) and 119892 (119867

119894)] (8)


where 119867119894= 119909

1 1199092 119909

119899 119894 = 1 2 119899 In practice


(119888) int ℎ 119889119892 = ℎ (119909119899) 119892 (119867

119899) + [ℎ (119909

119899minus1) minus ℎ (119909

119899)] 119892 (119867

119899minus1)


2)] 119892 (119867

1)

= ℎ (119909119899) [119892 (119867

119899) minus 119892 (119867

119899minus1)]

+ ℎ (119909119899minus1) [119892 (119867

119899minus1) minus 119892 (119867

119899minus2)]

+ sdot sdot sdot + ℎ (1199091) 119892 (119867

1)

(9)

where 0 le ℎ(1199091) le ℎ(119909


119899) le 1 119867

1= 1199091 and

1198672= 1199091 1199092 119867

119899= 1199091 1199092 119909











64) are qualitative







3PL

supp

lier s

elect

ion


Performance (D1)

Service (D2)

Cost (D3)


IT (D5)

Intangible (D6)








Price (x31)







Data security (x53)


Experience (x61)


Global scope (x63)












2has the highest




119894(sdot))



Service (1198632) 0769


Cost (1198633) 0769 Price (x31) 0794





IT (1198635) 0500








120582(sdot) (119888) int ℎ(sdot)119889119892

120582(sdot) (120582-value)

1198631

x11 0769 0815 119892120582(x14) 0867

0767 (minus0999)x12 0769 0867 119892120582(x14 x13) 0976

x13 0667 0833 g120582(x14 x13 x11) 0997x14 0500 0877 119892

120582(x14 x13 x11 x12) 1000

1198632

x21 0769 0789 119892120582(x21) 0714

0869 (minus0989)x22 0909 0714 119892120582(x21 x23) 0960

x23 0769 0838 119892120582(x21 x23 x22) 1000

1198633

x31 0769 0794 119892120582(x31) 0877 0770 (minus0963)

x32 0769 0877 119892120582(x31 x32) 1000

1198634

x41 0745 0762 119892120582(x41) 0702

0768 (minus0984)x42 0769 0805 119892120582(x41 x42) 0951

x43 0769 0702 119892120582(x41 x42 x43) 1000

1198635

x51 0667 0722 119892120582(x51) 0800

0768 (minus0996)x52 0769 0693 119892120582(x51 x52) 0958

x53 0769 0779 119892120582(x51 x52 x53) 0990

x54 0769 0800 119892120582(x51 x52 x53 x54) 1000

1198636

x61 0769 0800 119892120582(x62) 0726

0766 (minus0996)x62 0667 0742 119892120582(x62 x64) 0947

x63 0769 0726 119892120582(x62 x64 x61) 0990

x64 0720 0752 119892120582(x62 x64 x61 x63) 1000



119894(sdot) column





120582(sdot) (119888) int ℎ(sdot)119889119892

120582(sdot) (120582-value)

A

D1 0767 0909 119892120582(1198636) 0769

0847 (minus0999)

D2 0869 0769 119892120582(11986361198631) 0980

D3 0770 0909 119892120582(119863611986311198634) 0994

D4 0768 0769 119892120582(1198636119863111986341198635) 0999

D5 0768 0667 119892120582(11986361198631119863411986351198633) 1000

D6 0766 0769 119892120582(119863611986311198634119863511986331198632) 1000


















Acknowledgments


References


































































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













IC packaging(30)

Final testing(36)


Chemical

(36)




Performance



Service





Qualityassurance



IT



Intangible






3 Research Method






px

0 02 04 06 08 10

VP P MP F MG G VG

120583P(p)

10






119894 119894 =


119894119895= (119871119908119894119895119872119908119894119895119877119908119894119895)

= (

(sum119898

119901=1119908119901

119894119895)

119898

(sum119898

119901=1119908119901

119894119895)

119898

(sum119898

119901=1119908119901

119894119895)

119898

)

(1)




119872119908119894119895 and




119894as follows

119883120572119894⟨minus⟩ = [119897119894

119903119894] [minus] [119888 119889] = [119897119894

minus 119889 119903119894minus 119888]

119894 = 0 1 2 infin

(2)




119863(119883) =

sum119899

119894=0119903119894minus 119888

sum119899

119894=1(119903119894minus 119888) minus sum

119899

119894=0(119897119894minus 119889)

119899 997888rarr infin (3)



sum119899



119894119895= (119871119901119894119895119872119901119894119895119877119901119894119895)

= (

(sum119898

119901=1119901119901

119894119895)

119898

(sum119898

119901=1119901119901

119894119895)

119898

(sum119898

119901=1119901119901

119894119895)

119898

)

(4)



119872119901119894119895 and




Assume that X = 1199091 1199092 119909



120582(119860 cup 119861) = 119892

120582(119860) +

119892120582(119861) + 120582119892




119892120582(1199091 1199092 119909

119899)

=

119899

sum

119894=1

119892119894+ 120582

119899minus1

sum

1198941=1

119899

sum

1198942=1198941+1

11989211989411198921198942+ sdot sdot sdot + 120582

119899minus111989211198922 119892

119899

=

1

120582

1003816100381610038161003816100381610038161003816100381610038161003816

119899

prod

119894=1

(1 + 120582119892119894) minus 1

1003816100381610038161003816100381610038161003816100381610038161003816


(5)



120582 + 1 =

119899

prod

119894=1

(1 + 120582119892119894) (6)


int

119860

ℎ (119909) 119889119892 = sup120572isin[01]

[120572 and 119892 (119860 cap 119865120572)] (7)



119894) is


2) ge



intℎ (119909) 119892 =

119899

⋁

119894=1

[ℎ (119909119894) and 119892 (119867

119894)] (8)


where 119867119894= 119909

1 1199092 119909

119899 119894 = 1 2 119899 In practice


(119888) int ℎ 119889119892 = ℎ (119909119899) 119892 (119867

119899) + [ℎ (119909

119899minus1) minus ℎ (119909

119899)] 119892 (119867

119899minus1)


2)] 119892 (119867

1)

= ℎ (119909119899) [119892 (119867

119899) minus 119892 (119867

119899minus1)]

+ ℎ (119909119899minus1) [119892 (119867

119899minus1) minus 119892 (119867

119899minus2)]

+ sdot sdot sdot + ℎ (1199091) 119892 (119867

1)

(9)

where 0 le ℎ(1199091) le ℎ(119909


119899) le 1 119867

1= 1199091 and

1198672= 1199091 1199092 119867

119899= 1199091 1199092 119909











64) are qualitative







3PL

supp

lier s

elect

ion


Performance (D1)

Service (D2)

Cost (D3)


IT (D5)

Intangible (D6)








Price (x31)







Data security (x53)


Experience (x61)


Global scope (x63)












2has the highest




119894(sdot))



Service (1198632) 0769


Cost (1198633) 0769 Price (x31) 0794





IT (1198635) 0500








120582(sdot) (119888) int ℎ(sdot)119889119892

120582(sdot) (120582-value)

1198631

x11 0769 0815 119892120582(x14) 0867

0767 (minus0999)x12 0769 0867 119892120582(x14 x13) 0976

x13 0667 0833 g120582(x14 x13 x11) 0997x14 0500 0877 119892

120582(x14 x13 x11 x12) 1000

1198632

x21 0769 0789 119892120582(x21) 0714

0869 (minus0989)x22 0909 0714 119892120582(x21 x23) 0960

x23 0769 0838 119892120582(x21 x23 x22) 1000

1198633

x31 0769 0794 119892120582(x31) 0877 0770 (minus0963)

x32 0769 0877 119892120582(x31 x32) 1000

1198634

x41 0745 0762 119892120582(x41) 0702

0768 (minus0984)x42 0769 0805 119892120582(x41 x42) 0951

x43 0769 0702 119892120582(x41 x42 x43) 1000

1198635

x51 0667 0722 119892120582(x51) 0800

0768 (minus0996)x52 0769 0693 119892120582(x51 x52) 0958

x53 0769 0779 119892120582(x51 x52 x53) 0990

x54 0769 0800 119892120582(x51 x52 x53 x54) 1000

1198636

x61 0769 0800 119892120582(x62) 0726

0766 (minus0996)x62 0667 0742 119892120582(x62 x64) 0947

x63 0769 0726 119892120582(x62 x64 x61) 0990

x64 0720 0752 119892120582(x62 x64 x61 x63) 1000



119894(sdot) column





120582(sdot) (119888) int ℎ(sdot)119889119892

120582(sdot) (120582-value)

A

D1 0767 0909 119892120582(1198636) 0769

0847 (minus0999)

D2 0869 0769 119892120582(11986361198631) 0980

D3 0770 0909 119892120582(119863611986311198634) 0994

D4 0768 0769 119892120582(1198636119863111986341198635) 0999

D5 0768 0667 119892120582(11986361198631119863411986351198633) 1000

D6 0766 0769 119892120582(119863611986311198634119863511986331198632) 1000


















Acknowledgments


References


































































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












px

0 02 04 06 08 10

VP P MP F MG G VG

120583P(p)

10






119894 119894 =


119894119895= (119871119908119894119895119872119908119894119895119877119908119894119895)

= (

(sum119898

119901=1119908119901

119894119895)

119898

(sum119898

119901=1119908119901

119894119895)

119898

(sum119898

119901=1119908119901

119894119895)

119898

)

(1)




119872119908119894119895 and




119894as follows

119883120572119894⟨minus⟩ = [119897119894

119903119894] [minus] [119888 119889] = [119897119894

minus 119889 119903119894minus 119888]

119894 = 0 1 2 infin

(2)




119863(119883) =

sum119899

119894=0119903119894minus 119888

sum119899

119894=1(119903119894minus 119888) minus sum

119899

119894=0(119897119894minus 119889)

119899 997888rarr infin (3)



sum119899



119894119895= (119871119901119894119895119872119901119894119895119877119901119894119895)

= (

(sum119898

119901=1119901119901

119894119895)

119898

(sum119898

119901=1119901119901

119894119895)

119898

(sum119898

119901=1119901119901

119894119895)

119898

)

(4)



119872119901119894119895 and




Assume that X = 1199091 1199092 119909



120582(119860 cup 119861) = 119892

120582(119860) +

119892120582(119861) + 120582119892




119892120582(1199091 1199092 119909

119899)

=

119899

sum

119894=1

119892119894+ 120582

119899minus1

sum

1198941=1

119899

sum

1198942=1198941+1

11989211989411198921198942+ sdot sdot sdot + 120582

119899minus111989211198922 119892

119899

=

1

120582

1003816100381610038161003816100381610038161003816100381610038161003816

119899

prod

119894=1

(1 + 120582119892119894) minus 1

1003816100381610038161003816100381610038161003816100381610038161003816


(5)



120582 + 1 =

119899

prod

119894=1

(1 + 120582119892119894) (6)


int

119860

ℎ (119909) 119889119892 = sup120572isin[01]

[120572 and 119892 (119860 cap 119865120572)] (7)



119894) is


2) ge



intℎ (119909) 119892 =

119899

⋁

119894=1

[ℎ (119909119894) and 119892 (119867

119894)] (8)


where 119867119894= 119909

1 1199092 119909

119899 119894 = 1 2 119899 In practice


(119888) int ℎ 119889119892 = ℎ (119909119899) 119892 (119867

119899) + [ℎ (119909

119899minus1) minus ℎ (119909

119899)] 119892 (119867

119899minus1)


2)] 119892 (119867

1)

= ℎ (119909119899) [119892 (119867

119899) minus 119892 (119867

119899minus1)]

+ ℎ (119909119899minus1) [119892 (119867

119899minus1) minus 119892 (119867

119899minus2)]

+ sdot sdot sdot + ℎ (1199091) 119892 (119867

1)

(9)

where 0 le ℎ(1199091) le ℎ(119909


119899) le 1 119867

1= 1199091 and

1198672= 1199091 1199092 119867

119899= 1199091 1199092 119909











64) are qualitative







3PL

supp

lier s

elect

ion


Performance (D1)

Service (D2)

Cost (D3)


IT (D5)

Intangible (D6)








Price (x31)







Data security (x53)


Experience (x61)


Global scope (x63)












2has the highest




119894(sdot))



Service (1198632) 0769


Cost (1198633) 0769 Price (x31) 0794





IT (1198635) 0500








120582(sdot) (119888) int ℎ(sdot)119889119892

120582(sdot) (120582-value)

1198631

x11 0769 0815 119892120582(x14) 0867

0767 (minus0999)x12 0769 0867 119892120582(x14 x13) 0976

x13 0667 0833 g120582(x14 x13 x11) 0997x14 0500 0877 119892

120582(x14 x13 x11 x12) 1000

1198632

x21 0769 0789 119892120582(x21) 0714

0869 (minus0989)x22 0909 0714 119892120582(x21 x23) 0960

x23 0769 0838 119892120582(x21 x23 x22) 1000

1198633

x31 0769 0794 119892120582(x31) 0877 0770 (minus0963)

x32 0769 0877 119892120582(x31 x32) 1000

1198634

x41 0745 0762 119892120582(x41) 0702

0768 (minus0984)x42 0769 0805 119892120582(x41 x42) 0951

x43 0769 0702 119892120582(x41 x42 x43) 1000

1198635

x51 0667 0722 119892120582(x51) 0800

0768 (minus0996)x52 0769 0693 119892120582(x51 x52) 0958

x53 0769 0779 119892120582(x51 x52 x53) 0990

x54 0769 0800 119892120582(x51 x52 x53 x54) 1000

1198636

x61 0769 0800 119892120582(x62) 0726

0766 (minus0996)x62 0667 0742 119892120582(x62 x64) 0947

x63 0769 0726 119892120582(x62 x64 x61) 0990

x64 0720 0752 119892120582(x62 x64 x61 x63) 1000



119894(sdot) column





120582(sdot) (119888) int ℎ(sdot)119889119892

120582(sdot) (120582-value)

A

D1 0767 0909 119892120582(1198636) 0769

0847 (minus0999)

D2 0869 0769 119892120582(11986361198631) 0980

D3 0770 0909 119892120582(119863611986311198634) 0994

D4 0768 0769 119892120582(1198636119863111986341198635) 0999

D5 0768 0667 119892120582(11986361198631119863411986351198633) 1000

D6 0766 0769 119892120582(119863611986311198634119863511986331198632) 1000


















Acknowledgments


References


































































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










119872119908119894119895 and




119894as follows

119883120572119894⟨minus⟩ = [119897119894

119903119894] [minus] [119888 119889] = [119897119894

minus 119889 119903119894minus 119888]

119894 = 0 1 2 infin

(2)




119863(119883) =

sum119899

119894=0119903119894minus 119888

sum119899

119894=1(119903119894minus 119888) minus sum

119899

119894=0(119897119894minus 119889)

119899 997888rarr infin (3)



sum119899



119894119895= (119871119901119894119895119872119901119894119895119877119901119894119895)

= (

(sum119898

119901=1119901119901

119894119895)

119898

(sum119898

119901=1119901119901

119894119895)

119898

(sum119898

119901=1119901119901

119894119895)

119898

)

(4)



119872119901119894119895 and




Assume that X = 1199091 1199092 119909



120582(119860 cup 119861) = 119892

120582(119860) +

119892120582(119861) + 120582119892




119892120582(1199091 1199092 119909

119899)

=

119899

sum

119894=1

119892119894+ 120582

119899minus1

sum

1198941=1

119899

sum

1198942=1198941+1

11989211989411198921198942+ sdot sdot sdot + 120582

119899minus111989211198922 119892

119899

=

1

120582

1003816100381610038161003816100381610038161003816100381610038161003816

119899

prod

119894=1

(1 + 120582119892119894) minus 1

1003816100381610038161003816100381610038161003816100381610038161003816


(5)



120582 + 1 =

119899

prod

119894=1

(1 + 120582119892119894) (6)


int

119860

ℎ (119909) 119889119892 = sup120572isin[01]

[120572 and 119892 (119860 cap 119865120572)] (7)



119894) is


2) ge



intℎ (119909) 119892 =

119899

⋁

119894=1

[ℎ (119909119894) and 119892 (119867

119894)] (8)


where 119867119894= 119909

1 1199092 119909

119899 119894 = 1 2 119899 In practice


(119888) int ℎ 119889119892 = ℎ (119909119899) 119892 (119867

119899) + [ℎ (119909

119899minus1) minus ℎ (119909

119899)] 119892 (119867

119899minus1)


2)] 119892 (119867

1)

= ℎ (119909119899) [119892 (119867

119899) minus 119892 (119867

119899minus1)]

+ ℎ (119909119899minus1) [119892 (119867

119899minus1) minus 119892 (119867

119899minus2)]

+ sdot sdot sdot + ℎ (1199091) 119892 (119867

1)

(9)

where 0 le ℎ(1199091) le ℎ(119909


119899) le 1 119867

1= 1199091 and

1198672= 1199091 1199092 119867

119899= 1199091 1199092 119909











64) are qualitative







3PL

supp

lier s

elect

ion


Performance (D1)

Service (D2)

Cost (D3)


IT (D5)

Intangible (D6)








Price (x31)







Data security (x53)


Experience (x61)


Global scope (x63)












2has the highest




119894(sdot))



Service (1198632) 0769


Cost (1198633) 0769 Price (x31) 0794





IT (1198635) 0500








120582(sdot) (119888) int ℎ(sdot)119889119892

120582(sdot) (120582-value)

1198631

x11 0769 0815 119892120582(x14) 0867

0767 (minus0999)x12 0769 0867 119892120582(x14 x13) 0976

x13 0667 0833 g120582(x14 x13 x11) 0997x14 0500 0877 119892

120582(x14 x13 x11 x12) 1000

1198632

x21 0769 0789 119892120582(x21) 0714

0869 (minus0989)x22 0909 0714 119892120582(x21 x23) 0960

x23 0769 0838 119892120582(x21 x23 x22) 1000

1198633

x31 0769 0794 119892120582(x31) 0877 0770 (minus0963)

x32 0769 0877 119892120582(x31 x32) 1000

1198634

x41 0745 0762 119892120582(x41) 0702

0768 (minus0984)x42 0769 0805 119892120582(x41 x42) 0951

x43 0769 0702 119892120582(x41 x42 x43) 1000

1198635

x51 0667 0722 119892120582(x51) 0800

0768 (minus0996)x52 0769 0693 119892120582(x51 x52) 0958

x53 0769 0779 119892120582(x51 x52 x53) 0990

x54 0769 0800 119892120582(x51 x52 x53 x54) 1000

1198636

x61 0769 0800 119892120582(x62) 0726

0766 (minus0996)x62 0667 0742 119892120582(x62 x64) 0947

x63 0769 0726 119892120582(x62 x64 x61) 0990

x64 0720 0752 119892120582(x62 x64 x61 x63) 1000



119894(sdot) column





120582(sdot) (119888) int ℎ(sdot)119889119892

120582(sdot) (120582-value)

A

D1 0767 0909 119892120582(1198636) 0769

0847 (minus0999)

D2 0869 0769 119892120582(11986361198631) 0980

D3 0770 0909 119892120582(119863611986311198634) 0994

D4 0768 0769 119892120582(1198636119863111986341198635) 0999

D5 0768 0667 119892120582(11986361198631119863411986351198633) 1000

D6 0766 0769 119892120582(119863611986311198634119863511986331198632) 1000


















Acknowledgments


References


































































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










where 119867119894= 119909

1 1199092 119909

119899 119894 = 1 2 119899 In practice


(119888) int ℎ 119889119892 = ℎ (119909119899) 119892 (119867

119899) + [ℎ (119909

119899minus1) minus ℎ (119909

119899)] 119892 (119867

119899minus1)


2)] 119892 (119867

1)

= ℎ (119909119899) [119892 (119867

119899) minus 119892 (119867

119899minus1)]

+ ℎ (119909119899minus1) [119892 (119867

119899minus1) minus 119892 (119867

119899minus2)]

+ sdot sdot sdot + ℎ (1199091) 119892 (119867

1)

(9)

where 0 le ℎ(1199091) le ℎ(119909


119899) le 1 119867

1= 1199091 and

1198672= 1199091 1199092 119867

119899= 1199091 1199092 119909











64) are qualitative







3PL

supp

lier s

elect

ion


Performance (D1)

Service (D2)

Cost (D3)


IT (D5)

Intangible (D6)








Price (x31)







Data security (x53)


Experience (x61)


Global scope (x63)












2has the highest




119894(sdot))



Service (1198632) 0769


Cost (1198633) 0769 Price (x31) 0794





IT (1198635) 0500








120582(sdot) (119888) int ℎ(sdot)119889119892

120582(sdot) (120582-value)

1198631

x11 0769 0815 119892120582(x14) 0867

0767 (minus0999)x12 0769 0867 119892120582(x14 x13) 0976

x13 0667 0833 g120582(x14 x13 x11) 0997x14 0500 0877 119892

120582(x14 x13 x11 x12) 1000

1198632

x21 0769 0789 119892120582(x21) 0714

0869 (minus0989)x22 0909 0714 119892120582(x21 x23) 0960

x23 0769 0838 119892120582(x21 x23 x22) 1000

1198633

x31 0769 0794 119892120582(x31) 0877 0770 (minus0963)

x32 0769 0877 119892120582(x31 x32) 1000

1198634

x41 0745 0762 119892120582(x41) 0702

0768 (minus0984)x42 0769 0805 119892120582(x41 x42) 0951

x43 0769 0702 119892120582(x41 x42 x43) 1000

1198635

x51 0667 0722 119892120582(x51) 0800

0768 (minus0996)x52 0769 0693 119892120582(x51 x52) 0958

x53 0769 0779 119892120582(x51 x52 x53) 0990

x54 0769 0800 119892120582(x51 x52 x53 x54) 1000

1198636

x61 0769 0800 119892120582(x62) 0726

0766 (minus0996)x62 0667 0742 119892120582(x62 x64) 0947

x63 0769 0726 119892120582(x62 x64 x61) 0990

x64 0720 0752 119892120582(x62 x64 x61 x63) 1000



119894(sdot) column





120582(sdot) (119888) int ℎ(sdot)119889119892

120582(sdot) (120582-value)

A

D1 0767 0909 119892120582(1198636) 0769

0847 (minus0999)

D2 0869 0769 119892120582(11986361198631) 0980

D3 0770 0909 119892120582(119863611986311198634) 0994

D4 0768 0769 119892120582(1198636119863111986341198635) 0999

D5 0768 0667 119892120582(11986361198631119863411986351198633) 1000

D6 0766 0769 119892120582(119863611986311198634119863511986331198632) 1000


















Acknowledgments


References


































































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










3PL

supp

lier s

elect

ion


Performance (D1)

Service (D2)

Cost (D3)


IT (D5)

Intangible (D6)








Price (x31)







Data security (x53)


Experience (x61)


Global scope (x63)












2has the highest




119894(sdot))



Service (1198632) 0769


Cost (1198633) 0769 Price (x31) 0794





IT (1198635) 0500








120582(sdot) (119888) int ℎ(sdot)119889119892

120582(sdot) (120582-value)

1198631

x11 0769 0815 119892120582(x14) 0867

0767 (minus0999)x12 0769 0867 119892120582(x14 x13) 0976

x13 0667 0833 g120582(x14 x13 x11) 0997x14 0500 0877 119892

120582(x14 x13 x11 x12) 1000

1198632

x21 0769 0789 119892120582(x21) 0714

0869 (minus0989)x22 0909 0714 119892120582(x21 x23) 0960

x23 0769 0838 119892120582(x21 x23 x22) 1000

1198633

x31 0769 0794 119892120582(x31) 0877 0770 (minus0963)

x32 0769 0877 119892120582(x31 x32) 1000

1198634

x41 0745 0762 119892120582(x41) 0702

0768 (minus0984)x42 0769 0805 119892120582(x41 x42) 0951

x43 0769 0702 119892120582(x41 x42 x43) 1000

1198635

x51 0667 0722 119892120582(x51) 0800

0768 (minus0996)x52 0769 0693 119892120582(x51 x52) 0958

x53 0769 0779 119892120582(x51 x52 x53) 0990

x54 0769 0800 119892120582(x51 x52 x53 x54) 1000

1198636

x61 0769 0800 119892120582(x62) 0726

0766 (minus0996)x62 0667 0742 119892120582(x62 x64) 0947

x63 0769 0726 119892120582(x62 x64 x61) 0990

x64 0720 0752 119892120582(x62 x64 x61 x63) 1000



119894(sdot) column





120582(sdot) (119888) int ℎ(sdot)119889119892

120582(sdot) (120582-value)

A

D1 0767 0909 119892120582(1198636) 0769

0847 (minus0999)

D2 0869 0769 119892120582(11986361198631) 0980

D3 0770 0909 119892120582(119863611986311198634) 0994

D4 0768 0769 119892120582(1198636119863111986341198635) 0999

D5 0768 0667 119892120582(11986361198631119863411986351198633) 1000

D6 0766 0769 119892120582(119863611986311198634119863511986331198632) 1000


















Acknowledgments


References


































































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












119894(sdot))



Service (1198632) 0769


Cost (1198633) 0769 Price (x31) 0794





IT (1198635) 0500








120582(sdot) (119888) int ℎ(sdot)119889119892

120582(sdot) (120582-value)

1198631

x11 0769 0815 119892120582(x14) 0867

0767 (minus0999)x12 0769 0867 119892120582(x14 x13) 0976

x13 0667 0833 g120582(x14 x13 x11) 0997x14 0500 0877 119892

120582(x14 x13 x11 x12) 1000

1198632

x21 0769 0789 119892120582(x21) 0714

0869 (minus0989)x22 0909 0714 119892120582(x21 x23) 0960

x23 0769 0838 119892120582(x21 x23 x22) 1000

1198633

x31 0769 0794 119892120582(x31) 0877 0770 (minus0963)

x32 0769 0877 119892120582(x31 x32) 1000

1198634

x41 0745 0762 119892120582(x41) 0702

0768 (minus0984)x42 0769 0805 119892120582(x41 x42) 0951

x43 0769 0702 119892120582(x41 x42 x43) 1000

1198635

x51 0667 0722 119892120582(x51) 0800

0768 (minus0996)x52 0769 0693 119892120582(x51 x52) 0958

x53 0769 0779 119892120582(x51 x52 x53) 0990

x54 0769 0800 119892120582(x51 x52 x53 x54) 1000

1198636

x61 0769 0800 119892120582(x62) 0726

0766 (minus0996)x62 0667 0742 119892120582(x62 x64) 0947

x63 0769 0726 119892120582(x62 x64 x61) 0990

x64 0720 0752 119892120582(x62 x64 x61 x63) 1000



119894(sdot) column





120582(sdot) (119888) int ℎ(sdot)119889119892

120582(sdot) (120582-value)

A

D1 0767 0909 119892120582(1198636) 0769

0847 (minus0999)

D2 0869 0769 119892120582(11986361198631) 0980

D3 0770 0909 119892120582(119863611986311198634) 0994

D4 0768 0769 119892120582(1198636119863111986341198635) 0999

D5 0768 0667 119892120582(11986361198631119863411986351198633) 1000

D6 0766 0769 119892120582(119863611986311198634119863511986331198632) 1000


















Acknowledgments


References


































































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












120582(sdot) (119888) int ℎ(sdot)119889119892

120582(sdot) (120582-value)

A

D1 0767 0909 119892120582(1198636) 0769

0847 (minus0999)

D2 0869 0769 119892120582(11986361198631) 0980

D3 0770 0909 119892120582(119863611986311198634) 0994

D4 0768 0769 119892120582(1198636119863111986341198635) 0999

D5 0768 0667 119892120582(11986361198631119863411986351198633) 1000

D6 0766 0769 119892120582(119863611986311198634119863511986331198632) 1000


















Acknowledgments


References


































































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













Acknowledgments


References


































































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Research Article Decision Making for Third Party Logistics...

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Transcript of Research Article Decision Making for Third Party Logistics...