Evaluation of Cost-Effectiveness Criteria in Supply Chain Management: Case Study

Hindawi Publishing CorporationAdvances in Decision SciencesVolume 2013 Article ID 873534 11 pageshttpdxdoiorg1011552013873534

Research ArticleEvaluation of Cost-Effectiveness Criteria in Supply ChainManagement Case Study

Reza Rostamzadeh12 Mahdi Sabaghi3 and Ahmad Esmaili4

1 Department of Management Faculty of Management and Human Resource Development Universiti Teknologi Malaysia 81310Skudai Johor Malaysia

2 Department of Management East Azarbaijan Science amp Research Branch Islamic Azad University Tabriz 51579-44533 Iran3Department of Mechanical Engineering Ecole Polytechnique de Montreal CP 6079 Succ Centre-Ville Montreal QC Canada H3C3A7

4Department of Industerial Management Faculty of Accounting andManagement Allameh Tabatabarsquoi University Tehran 1434863111Iran

Correspondence should be addressed to Reza Rostamzadeh rostamzadeh59gmailcom

Received 28 June 2013 Revised 13 September 2013 Accepted 14 September 2013

Academic Editor Wai Ki Ching

Copyright copy 2013 Reza Rostamzadeh et al This 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 aim of this paper is to evaluate and prioritize the proposed cost-effectiveness criteria in supply chain management using fuzzymultiple attribute decision-making (MADM) approach Over the past few years the determination of suitable cost-effectivenesscriteria in the supply chain has become a key strategic issue However the nature of these kinds of decisions is usually complexand unstructured Many quantitative and qualitative factors must be considered to determine the suitable criteria As the humandecision-making process usually contains fuzziness and vagueness a hierarchy ofMADMmodel based on fuzzy-sets theory is usedin this research Using a fuzzy analytic hierarchy process (FAHP) the weights of criteria and subcriteria are determined and thenthe final ranking is determined by technique for order preference by similarity to ideal solution (TOPSIS) Finally fuzzy TOPSIS(FTOPSIS) is employed to compare the results with classic TOPSIS This paper concludes that the subcriteria in all the items are inthe same rank

1 Introduction

Supply chain plays a critical role for a company to gain com-petitive advantage since the supply chain affects customerservice inventory and distribution costs and response tothe ever-changing markets directly Furthermore this rolebecomes more critical in todayrsquos distributed manufacturingenvironment inwhich companies focus on core competenciesand outsource supportive tasks which in turn create largesupply networks In an international marketplace an increas-ingly tough competition results in a companyrsquos attempt tofind strategies which give them more competitive advantagethan their rivals [1] In fact the competition is among supplychains not companies [2] Typically supply chain inventorymanagement studies are classified into three stages which aresupply production and distribution [3] however the main

focus is usually placed on the coordination between only twoof them

Themain objective of this research is to propose a system-atic evaluationmodel which eases the way for manufacturingcompanies to select and find the most important cost-effective criteria in supply chain management (SCM) underfuzzy multievaluator and multicriteria environment Hencethis study utilizes multicriteria decision-making method todetermine the importance weights of evaluation criteria inlinguistic terms parameterized with triangular fuzzy num-bers This approach is employed for four reasons (a) it isrational and understandable (b) the computation processesare straightforward (c) the concept permits the pursuit ofthe best alternatives for each criterion depicted in a simplemathematical form and (d) the importance weights areincorporated into the comparison procedures [4 5]

2 Advances in Decision Sciences

The remainder of this paper is organized as followsSection 2 presents the literature review of the supply chainmodelling In Section 3 methodologies of TOPSIS andFTOPSIS are given An application of case study is givenin Section 4 And finally in Section 5 the results of theapplication with two approaches (TOPSIS and FTOPSIS) arepresented and suggestions for the future studies are clarified

2 The Literature Review

An integrated supply chain multi-objective model was devel-oped by Sabri and Beamon [6] and applied in strategicplanning and operational SC The objective of the strategicmodel was to minimize the costs of the chain while theobjective of operational level was to determine the amountof equipment purchased and distribution using the economicorder quantity A deterministic mixed integer nonlinearmathematical programmingmodel based on economic orderquantity (EOQ) technique was offered by Cohen and Lee [7]which extends the overall policy of resource deploymentThetotal profit after tax for manufacturing facilities and distribu-tion centers was maximized in the objective function Alsomanagement constraints logical consistency constraints andmaterial requirements and assignments for all the productswere considered Petrovic et al [8] describe fuzzy modelingand simulation of an SC in an uncertain environment Thegoal was to find the inventory levels and order quantities foreach inventory in an SC to ensure satisfactory performanceat a reasonable total cost for the entire SC Sources ofuncertainty in customerrsquos demand and external supply of rawmaterials have been taken into account and represented byfuzzy sets and then a special SC simulator was developedCurrently it does not consider the real scope of variables andconstraints in a supply chain network (SCN) The PLAN-WAR model developed by Pirkul and Jayaraman [9] is a newformulation of multiproduct multisite problem capacitationlocation of the facility intended to address a number of plantsand distribution centers so that the total operating costs forthe distribution network were minimized In fact they havedeveloped anMIPmodel for the plant and the problem of thewarehouse location In addition Vidal and Goetschalck [10]modeled a Global Logistics System (GLS) By using historicaldata the system approximates the probability that the sup-plier sends shipments on time and the reliability of suppliershas been modeled The effect of exchange rates changes indemand and international transit times were also investi-gated Analytical models have been proposed by Lee and Kim[11] to solve the integrated production-distribution problemsin supply chain management They proposed an integratedmultiperiod multiproduct and multishop production anddistribution model in supply chain to gratify the retailerrsquosdemand in the given time periods For the demand problemthey developed a hybrid method that combined the analysisand simulation model Analytical model minimizes the over-all costs of production distribution inventory holding andshortage costs subjected to various kinds of inventory andoperation time constraints Yin et al [12] proposed a modelfor supply chain by taking into account both multi-input and

multioutput data based on the concept of virtualmarketplacewith multiagents In addition independent production andproduction support were made by the bidding strategies ofdemandsupply officers The simulation experiment showsthe applicability of economic analysis of this framework ina dynamic environment

Nonino and Panizzolo [13] analyzed the problem ofintegrating production and distribution in a single place ofsupply and demand of several places with a focus on improv-ing and streamlining the distribution network and thenoffered effective solutions rather than considering the routingproblem at both strategic and operational perspectives Rossand Jayaraman [14] extended the work by Jayaraman andRoss [15] and provided an assessment of the new heuristicsolution procedures for the location of cross docks anddistribution centers in the network design of SCThe authorsdescribed two heuristic solutions as close to the optimaldesign of distribution systems Jeong et al [16] proposeda mixed model of supply network design and planningof productiondistribution The authors used Lagrangianheuristic for the design of SCN and implemented geneticalgorithm (GA) for the problem of integrated production-distribution planning However their model also ignores thedynamic environment in which demand forecasts changeover time but themodel was not well integrated because theyproposed separate models for the three subnetworks Yu et al[17] examined the inventory period of several deterministicrouting problems with a split delivery (IRPSD) All clientsrsquorequests were identified and met without being backorderedThe model only describes the solution in each period whenthe quantity was delivered to each customer carried by eachdirected arc and the number of times it was visited by vehiclesin the transportation thereof

Seliaman [18] developed a four-stage serial supply chaininventory model with planned backorders This chain con-sists of a supplier a manufacturer a distributor and an endretailer Production and inventory decisions are made at thesuppliermanufacturer anddistributor levelsTheproductionand demand rates were assumed as finite In additionbackorders were permitted for demands that were not met atthe retailer The problem occurs in coordinating productionand inventory decisions across the supply chain so that thetotal cost of the system was minimized Amirteimoori andKhoshandam [19] applied a DEA model for measuring theperformance of suppliers and manufacturers in supply chainoperations Additive efficiency decomposition for suppliersand manufacturers in supply chain operations was proposed

Based on the literature review for the concept of supplychain models there are a few researches on the researchtopic and most of them have been conducted by focusingon production and distribution criteria There is a closeconnection between the design and management of thesupply chain flow (product information and funds) andthe success of a supply chain which can be partly statedthat many of e-businesses failures are due to the weaknessesin their supply chain design and planning Regarding theliterature review this research proposes new cost-orientedcriteria for evaluation in SCM using fuzzy MADM to help anorganization to make unified and satisfactory decisions

Advances in Decision Sciences 3

3 Methodology

In this section firstly TOPSIS method is summarized andthen followed by summary of FTOPSIS method

31 TOPSIS Hwang and Yoon [20] originally proposedthe order performance technique based on similarity toideal solution (TOPSIS) in which the chosen alternativeshould not only have the shortest distance from the positiveideal reference point (PIRP) but also the longest distancefrom the negative ideal reference point (NIRP) to solve themulticriteria decision-making (MCDM) problems Chen [21]extended TOPSIS method to the fuzzy environment Wangand Elhag [22] suggested a fuzzy TOPSIS model whereratings of alternatives under the criteria and importanceweights of criteria are assessed in linguistic values representedby fuzzy numbers Wang and Chang [23] applied the fuzzyMCDM method to determine the importance weights ofevaluation criteria and to synthesize the ratings of candidatersquosaircraft then TOPSIS is employed to obtain a crisp overallperformance value for each alternative to make a finaldecision Other studies can be found in Yang and Hung [24]Wang and Lee [25] Kahraman et al [26] Dagdeviren et al[27] Gumus [28] Sun and Lin [29] Torfi and Rashidi [30]Armero et al [31] In this study TOPSIS method is used forthe final ranking of the cost-effectiveness criteria and thenthe results are compared with fuzzy TOPSIS The steps inTOPSIS are given as follows

Step 1 Decision matrix is normalized via

119903119894119895=

119908119894119895

radicsum119869

119895=11199082

119894119895

119895 = 1 2 3 119869 119894 = 1 2 3 119899 (1)

Step 2 The weighted normalized decision matrix is formedby

V119894119895= 119908119894lowast 119903119894119895 119895 = 1 2 3 119869 119894 = 1 2 3 119899 (2)

Step 3 Positive ideal solution (PIS) and negative ideal solu-tion (NIS) will be determined by

119860+= V+1 V+2 V+3 119899 max values

119860minus= Vminus1 Vminus2 Vminus3 119899 min values

(3)

Step 4 The distance of each alternative from PIS and NIS iscalculated as

119889+

119894= radic

119899

sum

119895=1

(V119894119895minus V+119895)

2

119895 = 1 2 119869

119889minus

119894= radic

119899

sum

119895=1

(V119894119895minus Vminus119895)

2

119895 = 1 2 119869

(4)

Step 5 The closeness coefficient of each alternative is calcu-lated as

CC119894=

119889minus

119894

119889+

119894+ 119889minus

119894

119894 = 1 2 119869 (5)

Step 6 By comparing CC119894values the ranking of alternatives

is determined

32 Fuzzy TOPSIS Here the steps of fuzzy TOPSIS devel-oped by Chen and Hwang [32] are given First a decisionmatrix (119863) of119898 times 119899 dimension is defined as in

1199091

119909119895

119909119899

119863 =

1198601

119860119894

119860119898

(

11990911

1199091119895

1199091119899

1199091198941

119909119894119895

119909119894119899

1199091198981

119909119898119895

119909119898119899

)

(6)

where 119909119894119895 forall119894119895may be crisp or fuzzy If 119909

119894119895is fuzzy it is

represented by a triangular fuzzy number (TFN) as 119909119894119895=

(119886119894119895 119887119894119895 119888119894119895) The fuzzy weights can be described by

119882 = (1199081 119908

119895 119908

119899) 119908

119895= (120572119895 120573119895 120594119895) (7)

The problem is solved using the following steps

Step 1 Normalize the decision matrix The decision matrixmust be first normalized so that the elements are unit-free Alinear normalization method was used as

119903119894119895=

119909119894119895 () 119909+

119895= (

119886119894119895

119888+

119895

119887119894119895

119887+

119895

119888119894119895

119886+

119895

) forall119895 119909119895 is a benefit attribute

119909minus

119895() 119909119894119895 = (

119886minus

119895

119888119894119895

119887minus

119895

119887119894119895

119888minus

119895

119886119894119895

) forall119895 119909119895 is a cost attribute

(8)

By applying (3) we can rewrite the decision matrix in (6) asin

1199091

119909119895

119909119899

1198631015840=

1198601

119860119894

119860119898

(

11990311

1199031119895

1199031119899

1199031198941

119903119894119895 119903

119894119899

1199031198981

119903119898119895

119903119898119899

)

(9)

Step 2 Calculate the weighted normalized fuzzy decisionmatrix The weighted normalized value V

119894119895calculated by

V119894119895= 119903119894119895 (sdot) 119908+

119895= (

119886119894119895

119888lowast

119895

120572119895

119887119894119895

119887lowast

119895

120573119895

119888119894119895

119886lowast

119895

120594119895) (10)

V119894119895= 119903119894119895 (sdot) 119908minus

119895= (

119886minus

119895

119888119894119895

120572119895

119887minus

119895

119887119894119895

120573119895

119888minus

119895

119886119894119895

120594119895) (11)

Equation (10) is used when the 119895th attribute is a benefitattribute Equation (11) is used when the 119895th attribute is a costattribute The result can be summarized as in

1198831

119883119895

119883119899

V =1198601

119860119894

119860119898

(

V11

V1119895

V1119899

V1198941

V119894119895

V119894119899

V1198981

V119898119895

V119898119899

)

(12)


Step 3 Identify (PIS) (119860+) and (NIS) (119860minus) solutionsV+119895and Vminus

119895may be obtained through some ranking pro-

cedures Chen and Hwang [32] used Lee and Lirsquos rankingmethod for comparison of fuzzy numbersThe V+

119895and Vminus

119895are

the fuzzy numbers with the largest and the smallest gen-eralized mean respectively The generalized mean for fuzzynumber V

119894119895 forall119895 119895 is defined as

119872(V119894119895) =

minus1198862

119894119895+ 1198882

119894119895minus 119886119894119895sdot 119887119894119895+ 119888119894119895sdot 119887119894119895

3 (minus119886119894119895+ 119888119894119895)

(13)

For each column 119895 we find a V119894119895whose greatest mean

is V+119895and lowest mean is Vminus

119895

Step 4 Calculate the distance of each alternative from 119860+

and 119860minus For fuzzy data the difference between two fuzzy

numbers is explained as given in

119863+

119894119895= 1 minus sup

119909min [propV119894119895

(119909) propV+119895

(119909)]

119863minus

119894119895= 1 minus sup

119909min [propV119894119895

(119909) propVminus119895

(119909)]

(14)

in which this equation is extendable for FTNs as followsIf V+119895= (119886+ 119887+ 119888+) and Vminus

119895= (119886minus 119887minus 119888minus) then

119863+

119894119895=

1 minus

119888119894119895minus 119886+

119887++ 119888119894119895minus 119886+minus 119887119894119895

for (119887119894119895lt 119887+)

1 minus

119888+minus 119886119894119895

119887119894119895+ 119888+minus 119886119894119895minus 119887+

for (119887+lt 119887119894119895)

119863minus

119894119895=

1 minus

119888minusminus 119886119894119895

119887119894119895+ 119888minusminus 119886119894119895minus 119887minus

for (119887minuslt 119887119894119895)

1 minus

119888119894119895minus 119886minus

119887minus+ 119888119894119895minus 119886minusminus 119887119894119895

for (119887119894119895lt 119887minus)

(15)

Note that both119863+119894119895and119863minus

119894119895are crisp numbers

Step 5 Compute the relative closeness to ideals This index isused to combine 119878+

119894and 119878minus119894indices calculated in Step 4 Since

119878+

119894and 119878minus119894are crisp numbers they can be combined

CC119894=

119878minus

119894

119878+

119894+ 119878minus

119894

119894 = 1 2 119868 (16)

Step 6 Rank preference order Choose an alternative withmaximum CC+

119894or rank alternatives according to CCminus

119894in

descending order

4 Case Study

SCM has influenced human lives thoughts and actions formore than a decade Practitioners and academicians havespent several years in comprehending and exploring thecomplexity of SCM The evolution has been slow but stablefrom logistic tomaterialmanagement to SCMThe 1990s have

been the stormiest period leading to large-scale acceptance ofSCM concept The change in power from the manufacturerto the consumer accessibility and technology the arrival ofthe omnipresent Internet and economic deregulation leadingto firmrsquos competition are just some of the characteristicsof this new age This in turn prompted change from theobligation of making profit and wealth from the market(external environment outside the manufacturerrsquos control) tothe organization itself (within the manufacturerrsquos control)The tools and techniques of SCM have appeared to be themanufacturerrsquos lifelineThe benefits of SCMaremultiples andlong term [33]

Company 119883 is an Iranian firm which is active in thetoy industries Toy business is tremendously unstable andseasonal in nature which is relatively different from theindustries like chemical telecommunication agriculturepharmaceutical automobile and so on [34] The volatilityin the toy industry is caused by variables and disorganizeddemands very short and specific selling-windows and shortproduct-life cycles Hence investors and practitioners knowvery well that the toy industry is far from tranquil [35]Compared to other industries toy industry has sufferedcomparatively higher costs on outdated inventory lost salesand markdown These are the distinctive consequences ofvolatility in the toy supply chains similar to the fashionclothing industry [36] In facing a very unique challengethese industries need to survive by providing the right toysat the right quantity and at the right stores during very shortselling windows and also to frequently provide creative andyet price-competitive toys

Over the past few years the determination of suitablecost-effectiveness criteria in the supply chain has become akey strategic issue However the nature of these decisionsis usually complex and unstructured In general manyquantitative and qualitative factors must be considered todetermine suitable criteria The managers and analysts of thecompany decided to evaluate their supply chain situation tomake strategic decisions for the future and gain a strongbusiness relationship with the suppliers The most importantcost-effectiveness criteria from three areas including supplyproduction and distribution sections have been collectedthrough the interview with the managers and experts of thecompany To determine the reliability of the questionnairetest-retest method was used In this way the researcherrandomly chose five samples from managers at two differ-ent times (at least two weeks) then questionnaires weredistributed to them After that Spearman rank correlationcoefficient analysis andmeaningful test of samplingwere con-ducted Reliability test of the questionnaire was conductedat 97 confidence coefficient level As the results show thequestionnaire has acceptable reliability After determiningthe criteria and subcriteria decision tree of the problemwas designed Figure 1 shows the hierarchical process of costcriteria

There is a main goal in the first level which is anevaluation of the cost-effectiveness criteria in supply chain3 criteria at the second level and at the third level 20subcriteria have been located in 3 different groupsThe aim ofthis research is the evaluation and prioritization of proposed


Cost-effective criteria for SCM

Distribution Production Supply

cit cjt

hitp hjtp

Πjt

ΠJjt

Πiit

Πit

Πrt

Πrrt

hrpt

crt

Spjpt

Sppjpt

TCjd

SSPjpt

SSPrpt

SSPipt

TCis

fcoqYis

Figure 1 Hierarchal process for the criteria

Parts and

materialssuppliers

Sale agencies

W3

W2 W4W1

CKDProduction lines

Outsourcerrsquos production lines

Pre-montage

Final montage

Figure 2 Supply chain of the company

cost-effectiveness criteria in supply chain management Thisresearch has been done in three stages In the first stage todetermine the weights of criteria FAHP was used and forthe final ranking of the same criteria TOPSIS was appliedThen fuzzy TOPSIS was applied to compare the results withthe classic TOPSISThe supply chain of the company is shownin Figure 2

The raw materials of parts are obtained through fourways which are domestic suppliers international suppliersinternal production and outsourcing All materials are heldin warehouse (W1) at the entry point and then the mate-rials are separated accordingly Raw materials are stored inwarehousing (W2) while semimanufactured parts are stored

in warehouses (W3) The parts which are made inside thefactory and the parts that are made by the outsourcers aretransferred to the Complete Knock Down (CKD) warehouseThe parts are then transferred from CKD to the montageand premontage workshopsThe finished products are trans-ported to the finished products warehouse (W4) and afterthat they are sent to the sales agencies for distribution to thecustomers Regarding the above description the indices usedin this research are defined as Indices Section

41 Application of FAHP The respondents of this researchwere managers assistant managers analysts and experts ofthe company (which is a manufacturing firm) Questionnaire


Table 1 Linguistic scale of importance

Linguistic scale forimportance

Triangular fuzzyscale

Triangular fuzzyreciprocal scale

Equal (1 1 1) (1 1 1)Weak (12 1 32) (23 1 2)Fairly strong (32 2 52) (25 12 23)Very strong (52 3 72) (27 13 25)Absolute (72 4 92) (29 14 27)

was used to gather the data needed for FAHP tables In thisresearch we have asked for managersrsquo and expertsrsquo opinionsthrough questionnaires to rank the cost-effectiveness criteriain SCM Table 1 shows the linguistic scales of the importantcriteria Then the criteria were calculated using FAHPCalculations of subcriteria were done in the same manner InTable 2 the fuzzy evaluation matrix sample for main criteriaof supply is given

After the normalization of these values priority weightswith respect to main goal were calculated as 119882 =

(119878 119875 119863

0475 043 0095) Then weights of subcriteria were calculated

similarly Final weights of criteria and subcriteria using FAHPare given in Table 3 These weights will be used in TOPSISprocess

42 Application of TOPSIS In this stage TOPSIS is usedto obtain the final ranks of criteria For this reason wehave grouped the managers and analysts of the companyinto 3 groups of decision makers Decision makers fromdifferent backgrounds may define different weight vectorsThey usually cause not only imprecise evaluation but alsoserious persecution during the decision process [37] Thelinguistic evaluation is shown in Table 4 Also Table 5 repre-sents the importance weights of criteria from three decisionmakers Then the normalized-decision matrix and weightednormalized-decision matrix were constructed Table 6 showsthe final weights of criteria and subcriteria using TOPSIS

After normalizing via (1) 119877 will be obtained as follows

119877 =[

[

0672 0703 0329

0523 0502 0768

0523 0502 0548

]

]

(17)

The weights that we obtained from FAHP were used to getthe weighted decision matrix 119881 So weighted normalizeddecision matrix was formed by (2)

119881 =[

[

0317 0302 0031

0248 0215 0072

0248 0215 0052

]

]

(18)

Then positive ideal solution (PIS) and negative ideal solution(NIS) will be determined by (3)

119860+= 0317 0302 0072

119860minus= 0248 0215 0031

(19)

Table 2 The fuzzy evaluation matrix with respect to the goal

Cost-effectivenesscriteria Supply Production Distribution

Supply (1 1 1) (12 1 32) (32 2 52)Production (23 1 2) (1 1 1) (32 2 52)Distribution (25 12 23) (25 12 23) (1 1 1)

Table 3 Final weights of criteria and subcriteria using FAHP

Rank Supply (0475) Production (043) Distribution (0095)1 119888

119894119905(0331) prod 119894

119894119905(0154) Spp

119895119901119905(0409)

2 119891coq119884119894119904(0312) 119888

119895119905(0147) TC

119895119889(0298)

3 ℎ119894119905119901(0173) prod

119894119905(014) Sp

119895119901119905(0231)

4 SSP119894119901119905(0126) 119888

119903119905(011) SSP

119895119901119905(006)

5 TC119894119904(055) prod

119895119905(0098)

6 prod119895119895119905(0087)

7 prod119903119903119905(0074)

8 ℎ119903119901119905(0057)

9 prod119903119905(0046)

10 SSP119903119901119905(0043)

11 ℎ119895119905119901(0035)

The distance of each alternative from PIS and NIS wascalculated through (4)

119889+

1= 0041 119889

+

2= 0111 119889

+

3= 0112

119889minus

1= 0111 119889

minus

2= 0041 119889

minus

3= 0021

(20)

The closeness coefficients of each alternative were calculatedby (5)

119862+

1=

119889minus

1

119889+

1+ 119889minus

1

=

0111

0041 + 0111

= 073

119862+

2=

0041

0111 + 0041

= 0269

119862+

3=

0021

0112 + 0021

= 0157

(21)

Comparing CC119894values the ranking of main criteria was

determined as follows

1198621gt 1198622gt 1198623 (22)

So we can arrange the final weight of the main criteria asTable 6

43 Application of FTOPSIS In the third stage FTOPSIS wasimplemented to compare the results with classic TOPSISThelinguistic evaluations are shown in Tables 7 and 8 Mean-while Table 9 illustrates the importance weight of criteriafrom three groups of decision makers Tables 7 and 8 wereconverted into triangular fuzzy numbers to construct thefuzzy-decisionmatrix and determine the fuzzyweight of each


Table 4 Linguistic variables for the criteria weights

Very low (VL) 1Low (L) 3Medium (M) 5High (H) 7Very high (VH) 9

Table 5 Importance weight of criteria from three decision makersfor main criteria

Criteria Supply Production DistributionDecision makers1198631

9 7 31198632

7 5 71198633

7 5 5119882 0475 043 0095

criterion as shown in Table 10 Then the normalized fuzzy-decision matrix and weighted normalized fuzzy-decisionmatrix were constructed

Step 1 Normalize the decision matrixSupply Production Distribution

119909+

119895(08 1 1) (07 08 09) (06 07 08)

119909minus

119895(07 08 09) (06 07 08) (035 05 065)

11990311= 11990911 (

) 119909+

1= (

07

1

08

1

09

08

) = (07 08 1125)

(23)

Therefore the normalized matrix is

1199091

1199092

1199093

1198631015840=

119860111986021198603

(

(07 08 1125) (067 087 114) (075 1 133)

(08 1 125) (078 1 128) (043 071 108)

(07 08 1125) (078 1 128) (075 1 133)

)

(24)

Step 2 Calculate the weighted normalized fuzzy decisionmatrix

V11= 11990311 (

sdot) 119908+

11= (07 08 1125)

times (08 1 1) = (056 08 1125)

(25)

Therefore the weighted normalized matrix is as follows

1199091

1199092

1199093

119881 =

119860111986021198603

(

(056 08 1125) (0469 0696 1026) (045 07 1064)

(064 1 125) (0546 08 115) (0258 0497 0864)

(056 08 1125) (0546 08 115) (045 07 1064)

)

(26)

Table 6 Final weights of criteria and subcriteria using TOPSIS

Rank Supply (073) Production (0269) Distribution (0157)1 119891coq

119884119894119904(0209) prod 119894

119894119905(0098) Spp

119895119901119905(0253)

2 119888119894119905(0204) 119888

119895119905(0095) TC

119895119889(0215)

3 ℎ119894119905119901(0109) prod

119894119905(008) Sp

119895119901119905(0047)

4 SSP119894119901119905(0069) 119888

119903119905(0063) SSP

119895119901119905(0039)

5 TC119894119904(0021) prod

119895119905(00618)

6 prod119895119895119905(00612)

7 prod119903119903119905(0037)

8 prod119903119905(0035)

9 ℎ119903119901119905(0032)

10 SSP119903119901119905(0032)

11 ℎ119895119905119901(0015)


Very low (VL) (0 0 02)Low (L) (01 02 03)Medium low (ML) (02 03 04)Medium (M) (035 05 065)Medium high (MH) (06 07 08)High (H) (07 08 09)Very high (VH) (08 1 1)

Table 8 Linguistic variables for the ratings

Very poor (VP) (0 0 02)Poor (P) (01 02 03)Medium poor (MP) (02 03 04)Fair (F) (035 05 065)Medium good (MG) (06 07 08)Good (G) (07 08 09)Very good (VG) (08 1 1)

Table 9 Importance weight of criteria from three decision makers


H MH ML1198632

VH H M1198633

H H MH

Table 10 Fuzzy-decisionmatrix and fuzzy weights formain criteria

Criteria Supply Production Distribution1198631

(07 08 09) (06 07 08) (06 07 08)1198632

(08 1 1) (07 08 09) (035 05 065)1198633

(07 08 09) (07 08 09) (06 07 08)119882 (08 1 1) (07 08 09) (06 07 08)Bold font shows the Max value of matrix and the Italic one shows the Minvalue of matrix


Step 3 Identify positive ideal solution (PIS) (119860+) andnegative ideal solution (NIS) (119860minus) solutions

119872(V11) =(minus 056 times 08) minus 056

2+ 125

2+ (125 times 08)

3 (125 minus 056)

= 0828

119872 =

1003816100381610038161003816100381610038161003816100381610038161003816

0828 073 073

0963 0832 0539

0828 0832 073

1003816100381610038161003816100381610038161003816100381610038161003816

V+1

V+2

V+3

119860+= (064 1 125) (0546 08 115) (045 07 1064)

Vminus1

Vminus2

Vminus3

119860minus= (056 08 1125) (0469 0696 1026) (0258 0497 0864)

(27)


and 119860minus

119863+

11= 1 minus

1125 minus 064

1 + 1125 minus 064 minus 08

= 0291

119863+= (

0291 0 0

0291 0178 0329

0 0 0

)

119863minus

33= 1 minus

0864 minus 045

07 + 0864 minus 045 minus 0497

= 0329

119863minus= (

0 0 0329

0 0178 0

0291 0178 0329

)

119878+

1= 0291 + 0 + 0 = 0291

119878+

2= 0291 + 0178 + 0329 = 0798

119878+

3= 0 + 0 + 0 = 0341

119878minus

1= 0 + 0 + 0329 = 0329

119878minus

2= 0 + 0178 + 0 = 0178

119878minus

3= 0291 + 0178 + 0329 = 0798

(28)

Table 11 Final rank of criteria and subcriteria using FTOPSIS


119884119894119904(087) prod 119894

119894119905(0963) Spp

119895119901119905(073)

2 119888119894119905(0832) 119888

119895119905(0832) TC

119895119889(066)

3 ℎ119894119905119901(0402) prod

119894119905(075) Sp

119895119901119905(053)

4 SSP119894119901119905(0385) 119888

119903119905(07) SSP

119895119901119905(04)

5 TC119894119904(0155) prod

119895119905(0685)

6 prod119895119895119905(066)

7 prod119903119903119905(0593)

8 ℎ119903119901119905(0402)

9 prod119903119905(034)

10 SSP119903119901119905(0285)

11 ℎ119895119905119901(0244)

Step 5 Compute the relative closeness to ideals

1198621=

119878minus

1

119878+

1+ 119878minus

1

=

0329

0291 + 0329

= 053

1198622=

119878minus

2

119878+

2+ 119878minus

2

=

0178

0798 + 0178

= 0182

1198623=

119878minus

3

119878+

3+ 119878minus

3

=

0798

0341 + 0798

= 07

1198623gt 1198621gt 1198622

(29)

So we can arrange the criteria as followsDistribution (07) gt Supply (053) gt Production (0182)

Table 11 shows the final rank of FTOPSIS Also the resultsfrom different methods were summarized in Table 12

5 Conclusions

This paper applied approaches based on FAHP TOPSISand FTOPSIS methods to evaluate and prioritize the cost-effectiveness criteria in supply chain management FAHPmethod was used to determine the weights of criteria andsubcriteria while TOPSIS method was applied for determi-nation of the final ranking Then fuzzy TOPSIS was per-formed to compare the results with the classic TOPSIS Bothmethods in this research resulted in the same rank At the firstlevel there is a main goal to evaluate the cost-effectivenesscriteria in supply chain any 3 criteria at the second level and20 subcriteria have been located in 3 groups at the third levelThe model presented in this study is expected to enable thecompany to make satisfying and unified decisions in supplychain and also increases its competitive capabilities

Consequently after considering the research process wecan point out the findings from these items

(1) By taking into account the meaning and concept ofeach criterionwhich demonstrates the situation of theorganizational unit (manufacturing or service) themost important weight has been allocated to supply


(TOPSIS 073 FTOPSIS 053) This is followed byproduction (TOPSIS 0269 FTOPSIS 0182) anddistribution (TOPSIS 0159 FTOPSIS 07) In mostof the manufacturing companies suppliers play animportant role The company must ensure about theavailability of the materials and that the materialsare provided in the right time right place and rightamount The only difference that can be observed isthe distribution that has the highest score in FTOPSISbut the lowest score in TOPSIS

(2) In supply groups themost important weight has beenallocated to the total cost of quality (119891coq

119884119894119904) (TOP-

SIS 0209 FTOPSIS 087) and the lowest importantweight is the transportation cost (TC

119894119904) (TOPSIS

0021 FTOPSIS 0155) The company has a specialpoint of view about the quality Most of the workershave the awareness about the cost of quality and theyhave been trying to control the quality of differentparts or products in the factory from the beginningto the end of the process

(3) In production groups the most important weight hasbeen allocated to cost of sales lost for part 119894(Π119894

119894119905)

(TOPSIS 0098 FTOPSIS 0963) and the lowestimportant weight is the holding cost of product119895(ℎ119895119905119901) (TOPSIS 0015 FTOPSIS 0244) Since the

product 119895 is totally dependent on material 119894 and ifthere is shortages of material in production line itdoes not only cause delays in production process butalso imposes loss of costs of sales to the organizationConsequently the company will not be able to satisfyits customersrsquo demands on time and in the long runthe company may lose its reputation

(4) In distribution groups the most important weighthas been allocated to the deficit cost of end periodinventory of product 119895 at warehouse (Spp

119895119901119905) (TOP-

SIS 0253 FTOPSIS 073) and the lowest impor-tant weight is the safety stock cost of product 119895 atwarehouse 119901 in period 119905(SSP

119895119901119905) (TOPSIS 0039

FTOPSIS 04) As the final product of the factorythe safety stock of product 119895 inventory must bedetermined otherwise there would be shortage forthe company

As human decision-making process usually containsfuzziness and vagueness FMCDM was adopted to solvethe problem According to the closeness coefficient we candetermine not only the ranking but also the assessmentstatus of all possible decisionmakers In fact TOPSISmethodis very flexible The method can deal with the ratings ofboth quantitative and qualitative criteria It appears from theforegoing sections that TOPSISmethodmay be a useful addi-tional tool for the problemThe systematic framework for pri-oritizing and evaluating cost-effectiveness criteria in a fuzzyenvironment presented in this paper can be easily extended tothe analysis of other management decision problems Othermultiattribute evaluation methods such as PROMETHEEELECTRE DEA and VIKOR in fuzzy environment canalso be used For future research the authors would like to

Table 12 Comparison table from different methods

Criteria and subcriteria FAHP-TOPSIS FTOPSISSupply (073) (053)

119891coq119884119894119904

(0209) (087)119888119894119905

(0204) (0832)ℎ119894119905119901

(0109) (0402)SSP119894119901119905

(0069) (0385)TC119894119904

(0021) (0155)Production (0269) (0182)

prod119894119894119905

(0098) (0963)119888119895119905

(0095) (0832)prod119894119905

(008) (075)119888119903119905

(0063) (07)prod119895119905

(00618) (0685)prod119895119895119905

(00612) (066)prod119903119903119905

(0037) (0593)prod119903119905

(0035) (0402)ℎ119903119901119905

(0032) (034)SSP119903119901119905

(0032) (0285)ℎ119895119905119901

(0015) (0244)Distribution (0159) (07)

Spp119895119901119905

(0253) (073)TC119895119889

(0215) (066)Sp119895119901119905

(0047) (053)SSP119895119901119905

(0039) (04)

propose an optimizationmodel formaterial routing in supplychain management which integrates decisions of differentfunctions into a single optimization model

Indices

119905 Time period (119905 = 0 1 2 119879)119894 Purchased material (119894 = 0 1 2 119868)119903 Part manufactured in workshops

(119903 = 0 1 2 119877)

119889 Agents for sale (119889 = 0 1 2 119863)119878 Supplier119895 Product manufactured in assembly

workshop119875 Warehouse119890 Work stations

Cost Criteria

119888119895119905 Cost to produce a unit of product 119895 in

period 119905119888119894119905 Cost to purchase a unit of part 119894 in period 119905

119888119903119905 Cost to produce a unit of part 119903 in period

of 119905ℎ119894119905119901 Cost to hold a unit of part 119894 in period 119905

ℎ119895119905119901 Cost to hold a unit of product 119895 in period 119905

ℎ119903119905119901 Cost to hold a unit of part 119903 in period 119905


Π119895119905 Unit cost of deficit for product 119895 in period 119905

Π119895119895119905 Unit cost of sales lost for product 119895 in

period 119905Π119894119905 Unit cost of deficit for part 119894 in period 119905

Π119894119894119905 Unit cost of sales lost for part 119894 in period 119905

Π119903119905 Unit cost of deficit for part 119903 in period 119905


Sp119895119901119905 Storage cost of end of period inventory of

product 119895 at warehouse 119901 in period 119905Spp119895119901119905 Deficit cost of end of period inventory of

product 119895 at warehouse 119901 in period 119905TC119895119889 Transportation cost of one unit of product 119895

to distributor 119889TC119894119904 Transportation cost of one unit of part 119894 from

supplier 119904SSP119895119901119905 Safety stock cost of product 119895 at warehouse 119901

in period 119905SSP119894119901119905 Safety stock cost of part 119894 at warehouse 119901 in

period 119905SSP119903119901119905 Safety stock cost of part 119903 at warehouse 119901 in

period 119905119891coq119884119894119904 Total cost of quality (including preventionand appraisal costs) for supplier 119904 per goodpart 119894 as a function of 119884

119894 the level of

proportion of nonquality components Thisis equivalent to the total cost of quality

Acknowledgment

The author would like to deeply thank the anonymousreferees for their valuable comments

References

[1] M Christopher Logistics and Supply Chain Management Pear-son Education Harlow UK 1998

[2] S Li B Ragu-Nathan S Subba Rao and T S Ragu-NathanldquoThe impact of supply chain management practices on compet-itive advantage and organizational performancerdquo Omega vol34 no 2 pp 107ndash124 2006

[3] W A Jauhari ldquoIntegrated inventory model for three-layersupply chains with stochastic demandrdquo International Journal ofOperational Research vol 13 no 3 pp 295ndash317 2012

[4] H Deng C H Yeh and R J Willis ldquoInter-company compari-son using modified TOPSIS with objective weightsrdquo Computersand Operations Research vol 27 no 10 pp 963ndash973 2000

[5] D L Olson ldquoComparison of weights in TOPSIS modelsrdquoMathematical and ComputerModelling vol 40 no 7-8 pp 721ndash727 2004

[6] E H Sabri and B M Beamon ldquoA multi-objective approach tosimultaneous strategic and operational planning in supply chaindesignrdquo Omega vol 28 no 5 pp 581ndash598 2000

[7] M A Cohen and H L Lee ldquoResource development analysisof global manufacturing and distribution networksrdquo Journal ofManufacturing and Operation Management vol 2 pp 81ndash1041989

[8] D Petrovic R Roy and R Petrovic ldquoModelling and simulationof a supply chain in an uncertain environmentrdquo EuropeanJournal of Operational Research vol 109 no 2 pp 299ndash3091998

[9] H Pirkul and V Jayaraman ldquoA multi-commodity multi-plantcapacitated facility location problem formulation and efficientheuristic solutionrdquo Computers and Operations Research vol 25no 10 pp 869ndash878 1998

[10] C J Vidal and M Goetschalck ldquoModeling the effect of uncer-tainties on global logistics systemsrdquo Journal of Business Logisticsvol 21 no 1 pp 95ndash121 2000

[11] Y H Lee and S H Kim ldquoProduction-distribution planning insupply chain considering capacity constraintsrdquo Computers andIndustrial Engineering vol 43 no 1-2 pp 169ndash190 2002

[12] H Yin J Zheng and XWang ldquoMulti-agent based supply chainmodeling and biddingrdquo in Proceedings of the 5thWorld Congresson Intelligent Control and Automation (WCICA rsquo04) pp 3187ndash3191 Hangzhou China June 2004

[13] F Nonino and R Panizzolo ldquoIntegrated productiondis-tribution planning in the supply chain the Febal case studyrdquoSupply Chain Management vol 12 no 2 pp 150ndash163 2007

[14] A Ross and V Jayaraman ldquoAn evaluation of new heuristics forthe location of cross-docks distribution centers in supply chainnetwork designrdquo Computers and Industrial Engineering vol 55no 1 pp 64ndash79 2008

[15] V Jayaraman andA Ross ldquoA simulated annealingmethodologyto distribution network design and managementrdquo EuropeanJournal of Operational Research vol 144 no 3 pp 629ndash6452003

[16] B J Jeong H S Jung and N K Park ldquoA computerized causalforecasting system using genetic algorithms in supply chainmanagementrdquo Journal of Systems and Software vol 60 no 3pp 223ndash237 2002

[17] Y Yu H Chen and F Chu ldquoA newmodel and hybrid approachfor large scale inventory routing problemsrdquo European Journal ofOperational Research vol 189 no 3 pp 1022ndash1040 2008

[18] M E Seliaman ldquoUsing complete squares method to opti-mize replenishment policies in a four-stage supply chain withplanned backordersrdquo Advances in Decision Sciences vol 2011Article ID 745896 9 pages 2011

[19] A Amirteimoori and L Khoshandam ldquoA data envelopmentanalysis approach to supply chain efficiencyrdquo Advances inDecision Sciences vol 2011 Article ID 608324 8 pages 2011

[20] C L Hwang and K Yoon Multiple Attribute Decision MakingMethods and Application Springer New York NY USA 1981

[21] C T Chen ldquoExtensions of the TOPSIS for group decision-making under fuzzy environmentrdquo Fuzzy Sets and Systems vol114 no 1 pp 1ndash9 2000

[22] YMWang andTM S Elhag ldquoFuzzyTOPSISmethod based onalpha level sets with an application to bridge risk assessmentrdquoExpert Systems with Applications vol 31 no 2 pp 309ndash3192006

[23] T C Wang and T H Chang ldquoApplication of TOPSIS inevaluating initial training aircraft under a fuzzy environmentrdquoExpert Systems with Applications vol 33 no 4 pp 870ndash8802007

[24] T Yang and C C Hung ldquoMultiple-attribute decision mak-ing methods for plant layout design problemrdquo Robotics andComputer-Integrated Manufacturing vol 23 no 1 pp 126ndash1372007

[25] T C Wang and H D Lee ldquoDeveloping a fuzzy TOPSISapproach based on subjective weights and objective weightsrdquoExpert Systems with Applications vol 36 no 5 pp 8980ndash89852009


[26] C Kahraman G Buyukozkan and N Y Ates ldquoA two phasemulti-attribute decision-making approach for new productintroductionrdquo Information Sciences vol 177 no 7 pp 1567ndash15822007

[27] M Dagdeviren S Yavuz and N Kilinc ldquoWeapon selectionusing the AHP and TOPSIS methods under fuzzy environ-mentrdquo Expert Systems with Applications vol 36 no 4 pp 8143ndash8151 2009

[28] A T Gumus ldquoEvaluation of hazardous waste transportationfirms by using a two step fuzzy-AHP and TOPSIS methodol-ogyrdquo Expert Systems with Applications vol 36 no 2 pp 4067ndash4074 2009

[29] C C Sun and G T R Lin ldquoUsing fuzzy TOPSIS method forevaluating the competitive advantages of shopping websitesrdquoExpert Systems with Applications vol 36 no 9 pp 11764ndash117712009

[30] F Torfi and A Rashidi ldquoSelection of project managers inconstruction Firms using analytic hierarchy process (AHP) andfuzzy Topsis a case studyrdquo Journal of Construction in DevelopingCountries vol 16 no 1 pp 69ndash89 2011

[31] E Armero M S Garcıa-Cascales M D Gomez-Lopez andMT Lamata ldquoDecision making in uncertain rural scenarios bymeans of fuzzy TOPSISmethodrdquoAdvances in Decision Sciencesvol 2011 Article ID 937092 15 pages 2011

[32] S J Chen and C L Hwang Fuzzy Multiple Attribute DecisionMaking vol 375 of Lecture Notes in Economics and Mathemati-cal System Series Springer New York NY USA 1992

[33] G Svensson ldquoHolistic and cross-disciplinary deficiencies in thetheory generation of supply chain managementrdquo Supply ChainManagement vol 8 no 4 pp 303ndash316 2003

[34] C Y Wong J S Arlbjoslashrn and J Johansen ldquoSupply chainmanagement practices in toy supply chainsrdquo Supply ChainManagement vol 10 no 5 pp 367ndash378 2005

[35] M E Johnson ldquoLearning from toys lessons in managingsupply chain risk from the toy industryrdquoCaliforniaManagementReview vol 43 no 3 pp 106ndash124 2001

[36] M Christopher R Lowson and H Peck ldquoCreating agile supplychains in the fashion industryrdquo International Journal of Retail ampDistribution Management vol 32 no 8 pp 367ndash376 2004

[37] I Ertugrul and N Karakasoglu ldquoPerformance evaluation ofTurkish cement firms with fuzzy analytic hierarchy process andTOPSISmethodsrdquo Expert Systems with Applications vol 36 no1 pp 702ndash715 2009

Submit your manuscripts athttpwwwhindawicom

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Differential EquationsInternational Journal of

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Applied MathematicsJournal of


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International Journal of


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Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014


Stochastic AnalysisInternational Journal of


The remainder of this paper is organized as followsSection 2 presents the literature review of the supply chainmodelling In Section 3 methodologies of TOPSIS andFTOPSIS are given An application of case study is givenin Section 4 And finally in Section 5 the results of theapplication with two approaches (TOPSIS and FTOPSIS) arepresented and suggestions for the future studies are clarified

2 The Literature Review

An integrated supply chain multi-objective model was devel-oped by Sabri and Beamon [6] and applied in strategicplanning and operational SC The objective of the strategicmodel was to minimize the costs of the chain while theobjective of operational level was to determine the amountof equipment purchased and distribution using the economicorder quantity A deterministic mixed integer nonlinearmathematical programmingmodel based on economic orderquantity (EOQ) technique was offered by Cohen and Lee [7]which extends the overall policy of resource deploymentThetotal profit after tax for manufacturing facilities and distribu-tion centers was maximized in the objective function Alsomanagement constraints logical consistency constraints andmaterial requirements and assignments for all the productswere considered Petrovic et al [8] describe fuzzy modelingand simulation of an SC in an uncertain environment Thegoal was to find the inventory levels and order quantities foreach inventory in an SC to ensure satisfactory performanceat a reasonable total cost for the entire SC Sources ofuncertainty in customerrsquos demand and external supply of rawmaterials have been taken into account and represented byfuzzy sets and then a special SC simulator was developedCurrently it does not consider the real scope of variables andconstraints in a supply chain network (SCN) The PLAN-WAR model developed by Pirkul and Jayaraman [9] is a newformulation of multiproduct multisite problem capacitationlocation of the facility intended to address a number of plantsand distribution centers so that the total operating costs forthe distribution network were minimized In fact they havedeveloped anMIPmodel for the plant and the problem of thewarehouse location In addition Vidal and Goetschalck [10]modeled a Global Logistics System (GLS) By using historicaldata the system approximates the probability that the sup-plier sends shipments on time and the reliability of suppliershas been modeled The effect of exchange rates changes indemand and international transit times were also investi-gated Analytical models have been proposed by Lee and Kim[11] to solve the integrated production-distribution problemsin supply chain management They proposed an integratedmultiperiod multiproduct and multishop production anddistribution model in supply chain to gratify the retailerrsquosdemand in the given time periods For the demand problemthey developed a hybrid method that combined the analysisand simulation model Analytical model minimizes the over-all costs of production distribution inventory holding andshortage costs subjected to various kinds of inventory andoperation time constraints Yin et al [12] proposed a modelfor supply chain by taking into account both multi-input and

multioutput data based on the concept of virtualmarketplacewith multiagents In addition independent production andproduction support were made by the bidding strategies ofdemandsupply officers The simulation experiment showsthe applicability of economic analysis of this framework ina dynamic environment

Nonino and Panizzolo [13] analyzed the problem ofintegrating production and distribution in a single place ofsupply and demand of several places with a focus on improv-ing and streamlining the distribution network and thenoffered effective solutions rather than considering the routingproblem at both strategic and operational perspectives Rossand Jayaraman [14] extended the work by Jayaraman andRoss [15] and provided an assessment of the new heuristicsolution procedures for the location of cross docks anddistribution centers in the network design of SCThe authorsdescribed two heuristic solutions as close to the optimaldesign of distribution systems Jeong et al [16] proposeda mixed model of supply network design and planningof productiondistribution The authors used Lagrangianheuristic for the design of SCN and implemented geneticalgorithm (GA) for the problem of integrated production-distribution planning However their model also ignores thedynamic environment in which demand forecasts changeover time but themodel was not well integrated because theyproposed separate models for the three subnetworks Yu et al[17] examined the inventory period of several deterministicrouting problems with a split delivery (IRPSD) All clientsrsquorequests were identified and met without being backorderedThe model only describes the solution in each period whenthe quantity was delivered to each customer carried by eachdirected arc and the number of times it was visited by vehiclesin the transportation thereof

Seliaman [18] developed a four-stage serial supply chaininventory model with planned backorders This chain con-sists of a supplier a manufacturer a distributor and an endretailer Production and inventory decisions are made at thesuppliermanufacturer anddistributor levelsTheproductionand demand rates were assumed as finite In additionbackorders were permitted for demands that were not met atthe retailer The problem occurs in coordinating productionand inventory decisions across the supply chain so that thetotal cost of the system was minimized Amirteimoori andKhoshandam [19] applied a DEA model for measuring theperformance of suppliers and manufacturers in supply chainoperations Additive efficiency decomposition for suppliersand manufacturers in supply chain operations was proposed

Based on the literature review for the concept of supplychain models there are a few researches on the researchtopic and most of them have been conducted by focusingon production and distribution criteria There is a closeconnection between the design and management of thesupply chain flow (product information and funds) andthe success of a supply chain which can be partly statedthat many of e-businesses failures are due to the weaknessesin their supply chain design and planning Regarding theliterature review this research proposes new cost-orientedcriteria for evaluation in SCM using fuzzy MADM to help anorganization to make unified and satisfactory decisions


3 Methodology




119903119894119895=

119908119894119895

radicsum119869

119895=11199082

119894119895

119895 = 1 2 3 119869 119894 = 1 2 3 119899 (1)


V119894119895= 119908119894lowast 119903119894119895 119895 = 1 2 3 119869 119894 = 1 2 3 119899 (2)


119860+= V+1 V+2 V+3 119899 max values


(3)


119889+

119894= radic

119899

sum

119895=1

(V119894119895minus V+119895)

2

119895 = 1 2 119869

119889minus

119894= radic

119899

sum

119895=1

(V119894119895minus Vminus119895)

2

119895 = 1 2 119869

(4)


CC119894=

119889minus

119894

119889+

119894+ 119889minus

119894

119894 = 1 2 119869 (5)


is determined


1199091

119909119895

119909119899

119863 =

1198601

119860119894

119860119898

(

11990911

1199091119895

1199091119899

1199091198941

119909119894119895

119909119894119899

1199091198981

119909119898119895

119909119898119899

)

(6)





119882 = (1199081 119908

119895 119908

119899) 119908

119895= (120572119895 120573119895 120594119895) (7)



119903119894119895=

119909119894119895 () 119909+

119895= (

119886119894119895

119888+

119895

119887119894119895

119887+

119895

119888119894119895

119886+

119895


119909minus

119895() 119909119894119895 = (

119886minus

119895

119888119894119895

119887minus

119895

119887119894119895

119888minus

119895

119886119894119895


(8)


1199091

119909119895

119909119899

1198631015840=

1198601

119860119894

119860119898

(

11990311

1199031119895

1199031119899

1199031198941

119903119894119895 119903

119894119899

1199031198981

119903119898119895

119903119898119899

)

(9)



V119894119895= 119903119894119895 (sdot) 119908+

119895= (

119886119894119895

119888lowast

119895

120572119895

119887119894119895

119887lowast

119895

120573119895

119888119894119895

119886lowast

119895

120594119895) (10)

V119894119895= 119903119894119895 (sdot) 119908minus

119895= (

119886minus

119895

119888119894119895

120572119895

119887minus

119895

119887119894119895

120573119895

119888minus

119895

119886119894119895

120594119895) (11)


1198831

119883119895

119883119899

V =1198601

119860119894

119860119898

(

V11

V1119895

V1119899

V1198941

V119894119895

V119894119899

V1198981

V119898119895

V119898119899

)

(12)





119895and Vminus

119895are



119872(V119894119895) =

minus1198862

119894119895+ 1198882

119894119895minus 119886119894119895sdot 119887119894119895+ 119888119894119895sdot 119887119894119895

3 (minus119886119894119895+ 119888119894119895)

(13)



119895




119863+

119894119895= 1 minus sup

119909min [propV119894119895

(119909) propV+119895

(119909)]

119863minus

119894119895= 1 minus sup

119909min [propV119894119895


(119909)]

(14)



119863+

119894119895=

1 minus

119888119894119895minus 119886+

119887++ 119888119894119895minus 119886+minus 119887119894119895

for (119887119894119895lt 119887+)

1 minus

119888+minus 119886119894119895

119887119894119895+ 119888+minus 119886119894119895minus 119887+

for (119887+lt 119887119894119895)

119863minus

119894119895=

1 minus

119888minusminus 119886119894119895


for (119887minuslt 119887119894119895)

1 minus

119888119894119895minus 119886minus


for (119887119894119895lt 119887minus)

(15)





119878+


CC119894=

119878minus

119894

119878+

119894+ 119878minus

119894

119894 = 1 2 119868 (16)



119894in

descending order

4 Case Study









cit cjt

hitp hjtp

Πjt

ΠJjt

Πiit

Πit

Πrt

Πrrt

hrpt

crt

Spjpt

Sppjpt

TCjd

SSPjpt

SSPrpt

SSPipt

TCis

fcoqYis


Parts and

materialssuppliers

Sale agencies

W3

W2 W4W1

CKDProduction lines


Pre-montage

Final montage














(119878 119875 119863





119877 =[

[

0672 0703 0329

0523 0502 0768

0523 0502 0548

]

]

(17)


119881 =[

[

0317 0302 0031

0248 0215 0072

0248 0215 0052

]

]

(18)


119860+= 0317 0302 0072

119860minus= 0248 0215 0031

(19)






119894119905(0331) prod 119894

119894119905(0154) Spp

119895119901119905(0409)

2 119891coq119884119894119904(0312) 119888

119895119905(0147) TC

119895119889(0298)

3 ℎ119894119905119901(0173) prod

119894119905(014) Sp

119895119901119905(0231)

4 SSP119894119901119905(0126) 119888

119903119905(011) SSP

119895119901119905(006)

5 TC119894119904(055) prod

119895119905(0098)

6 prod119895119895119905(0087)

7 prod119903119903119905(0074)

8 ℎ119903119901119905(0057)

9 prod119903119905(0046)

10 SSP119903119901119905(0043)

11 ℎ119895119905119901(0035)


119889+

1= 0041 119889

+

2= 0111 119889

+

3= 0112

119889minus

1= 0111 119889

minus

2= 0041 119889

minus

3= 0021

(20)


119862+

1=

119889minus

1

119889+

1+ 119889minus

1

=

0111

0041 + 0111

= 073

119862+

2=

0041

0111 + 0041

= 0269

119862+

3=

0021

0112 + 0021

= 0157

(21)



1198621gt 1198622gt 1198623 (22)








9 7 31198632

7 5 71198633

7 5 5119882 0475 043 0095



119909+

119895(08 1 1) (07 08 09) (06 07 08)

119909minus

119895(07 08 09) (06 07 08) (035 05 065)

11990311= 11990911 (

) 119909+

1= (

07

1

08

1

09

08

) = (07 08 1125)

(23)


1199091

1199092

1199093

1198631015840=

119860111986021198603

(

(07 08 1125) (067 087 114) (075 1 133)

(08 1 125) (078 1 128) (043 071 108)

(07 08 1125) (078 1 128) (075 1 133)

)

(24)


V11= 11990311 (

sdot) 119908+

11= (07 08 1125)

times (08 1 1) = (056 08 1125)

(25)


1199091

1199092

1199093

119881 =

119860111986021198603

(

(056 08 1125) (0469 0696 1026) (045 07 1064)

(064 1 125) (0546 08 115) (0258 0497 0864)

(056 08 1125) (0546 08 115) (045 07 1064)

)

(26)



119884119894119904(0209) prod 119894

119894119905(0098) Spp

119895119901119905(0253)

2 119888119894119905(0204) 119888

119895119905(0095) TC

119895119889(0215)

3 ℎ119894119905119901(0109) prod

119894119905(008) Sp

119895119901119905(0047)

4 SSP119894119901119905(0069) 119888

119903119905(0063) SSP

119895119901119905(0039)

5 TC119894119904(0021) prod

119895119905(00618)

6 prod119895119895119905(00612)

7 prod119903119903119905(0037)

8 prod119903119905(0035)

9 ℎ119903119901119905(0032)

10 SSP119903119901119905(0032)

11 ℎ119895119905119901(0015)







H MH ML1198632

VH H M1198633

H H MH



(07 08 09) (06 07 08) (06 07 08)1198632

(08 1 1) (07 08 09) (035 05 065)1198633





2+ 125

2+ (125 times 08)

3 (125 minus 056)

= 0828

119872 =

1003816100381610038161003816100381610038161003816100381610038161003816

0828 073 073

0963 0832 0539

0828 0832 073

1003816100381610038161003816100381610038161003816100381610038161003816

V+1

V+2

V+3

119860+= (064 1 125) (0546 08 115) (045 07 1064)

Vminus1

Vminus2

Vminus3

119860minus= (056 08 1125) (0469 0696 1026) (0258 0497 0864)

(27)


and 119860minus

119863+

11= 1 minus

1125 minus 064

1 + 1125 minus 064 minus 08

= 0291

119863+= (

0291 0 0

0291 0178 0329

0 0 0

)

119863minus

33= 1 minus

0864 minus 045

07 + 0864 minus 045 minus 0497

= 0329

119863minus= (

0 0 0329

0 0178 0

0291 0178 0329

)

119878+

1= 0291 + 0 + 0 = 0291

119878+

2= 0291 + 0178 + 0329 = 0798

119878+

3= 0 + 0 + 0 = 0341

119878minus

1= 0 + 0 + 0329 = 0329

119878minus

2= 0 + 0178 + 0 = 0178

119878minus

3= 0291 + 0178 + 0329 = 0798

(28)



119884119894119904(087) prod 119894

119894119905(0963) Spp

119895119901119905(073)

2 119888119894119905(0832) 119888

119895119905(0832) TC

119895119889(066)

3 ℎ119894119905119901(0402) prod

119894119905(075) Sp

119895119901119905(053)

4 SSP119894119901119905(0385) 119888

119903119905(07) SSP

119895119901119905(04)

5 TC119894119904(0155) prod

119895119905(0685)

6 prod119895119895119905(066)

7 prod119903119903119905(0593)

8 ℎ119903119901119905(0402)

9 prod119903119905(034)

10 SSP119903119901119905(0285)

11 ℎ119895119905119901(0244)


1198621=

119878minus

1

119878+

1+ 119878minus

1

=

0329

0291 + 0329

= 053

1198622=

119878minus

2

119878+

2+ 119878minus

2

=

0178

0798 + 0178

= 0182

1198623=

119878minus

3

119878+

3+ 119878minus

3

=

0798

0341 + 0798

= 07

1198623gt 1198621gt 1198622

(29)



5 Conclusions







119884119894119904) (TOP-


119894119904) (TOPSIS



119894119905)




119895119901119905) (TOP-


119895119901119905) (TOPSIS 0039





119891coq119884119894119904

(0209) (087)119888119894119905

(0204) (0832)ℎ119894119905119901

(0109) (0402)SSP119894119901119905

(0069) (0385)TC119894119904

(0021) (0155)Production (0269) (0182)

prod119894119894119905

(0098) (0963)119888119895119905

(0095) (0832)prod119894119905

(008) (075)119888119903119905

(0063) (07)prod119895119905

(00618) (0685)prod119895119895119905

(00612) (066)prod119903119903119905

(0037) (0593)prod119903119905

(0035) (0402)ℎ119903119901119905

(0032) (034)SSP119903119901119905

(0032) (0285)ℎ119895119905119901

(0015) (0244)Distribution (0159) (07)

Spp119895119901119905

(0253) (073)TC119895119889

(0215) (066)Sp119895119901119905

(0047) (053)SSP119895119901119905

(0039) (04)


Indices


(119903 = 0 1 2 119877)



Cost Criteria






















119894 the level of


Acknowledgment


References














































Volume 2014




Journal of











Journal of


Function Spaces






Algebra







Volume 2014




3 Methodology




119903119894119895=

119908119894119895

radicsum119869

119895=11199082

119894119895

119895 = 1 2 3 119869 119894 = 1 2 3 119899 (1)


V119894119895= 119908119894lowast 119903119894119895 119895 = 1 2 3 119869 119894 = 1 2 3 119899 (2)


119860+= V+1 V+2 V+3 119899 max values


(3)


119889+

119894= radic

119899

sum

119895=1

(V119894119895minus V+119895)

2

119895 = 1 2 119869

119889minus

119894= radic

119899

sum

119895=1

(V119894119895minus Vminus119895)

2

119895 = 1 2 119869

(4)


CC119894=

119889minus

119894

119889+

119894+ 119889minus

119894

119894 = 1 2 119869 (5)


is determined


1199091

119909119895

119909119899

119863 =

1198601

119860119894

119860119898

(

11990911

1199091119895

1199091119899

1199091198941

119909119894119895

119909119894119899

1199091198981

119909119898119895

119909119898119899

)

(6)





119882 = (1199081 119908

119895 119908

119899) 119908

119895= (120572119895 120573119895 120594119895) (7)



119903119894119895=

119909119894119895 () 119909+

119895= (

119886119894119895

119888+

119895

119887119894119895

119887+

119895

119888119894119895

119886+

119895


119909minus

119895() 119909119894119895 = (

119886minus

119895

119888119894119895

119887minus

119895

119887119894119895

119888minus

119895

119886119894119895


(8)


1199091

119909119895

119909119899

1198631015840=

1198601

119860119894

119860119898

(

11990311

1199031119895

1199031119899

1199031198941

119903119894119895 119903

119894119899

1199031198981

119903119898119895

119903119898119899

)

(9)



V119894119895= 119903119894119895 (sdot) 119908+

119895= (

119886119894119895

119888lowast

119895

120572119895

119887119894119895

119887lowast

119895

120573119895

119888119894119895

119886lowast

119895

120594119895) (10)

V119894119895= 119903119894119895 (sdot) 119908minus

119895= (

119886minus

119895

119888119894119895

120572119895

119887minus

119895

119887119894119895

120573119895

119888minus

119895

119886119894119895

120594119895) (11)


1198831

119883119895

119883119899

V =1198601

119860119894

119860119898

(

V11

V1119895

V1119899

V1198941

V119894119895

V119894119899

V1198981

V119898119895

V119898119899

)

(12)





119895and Vminus

119895are



119872(V119894119895) =

minus1198862

119894119895+ 1198882

119894119895minus 119886119894119895sdot 119887119894119895+ 119888119894119895sdot 119887119894119895

3 (minus119886119894119895+ 119888119894119895)

(13)



119895




119863+

119894119895= 1 minus sup

119909min [propV119894119895

(119909) propV+119895

(119909)]

119863minus

119894119895= 1 minus sup

119909min [propV119894119895


(119909)]

(14)



119863+

119894119895=

1 minus

119888119894119895minus 119886+

119887++ 119888119894119895minus 119886+minus 119887119894119895

for (119887119894119895lt 119887+)

1 minus

119888+minus 119886119894119895

119887119894119895+ 119888+minus 119886119894119895minus 119887+

for (119887+lt 119887119894119895)

119863minus

119894119895=

1 minus

119888minusminus 119886119894119895


for (119887minuslt 119887119894119895)

1 minus

119888119894119895minus 119886minus


for (119887119894119895lt 119887minus)

(15)





119878+


CC119894=

119878minus

119894

119878+

119894+ 119878minus

119894

119894 = 1 2 119868 (16)



119894in

descending order

4 Case Study









cit cjt

hitp hjtp

Πjt

ΠJjt

Πiit

Πit

Πrt

Πrrt

hrpt

crt

Spjpt

Sppjpt

TCjd

SSPjpt

SSPrpt

SSPipt

TCis

fcoqYis


Parts and

materialssuppliers

Sale agencies

W3

W2 W4W1

CKDProduction lines


Pre-montage

Final montage














(119878 119875 119863





119877 =[

[

0672 0703 0329

0523 0502 0768

0523 0502 0548

]

]

(17)


119881 =[

[

0317 0302 0031

0248 0215 0072

0248 0215 0052

]

]

(18)


119860+= 0317 0302 0072

119860minus= 0248 0215 0031

(19)






119894119905(0331) prod 119894

119894119905(0154) Spp

119895119901119905(0409)

2 119891coq119884119894119904(0312) 119888

119895119905(0147) TC

119895119889(0298)

3 ℎ119894119905119901(0173) prod

119894119905(014) Sp

119895119901119905(0231)

4 SSP119894119901119905(0126) 119888

119903119905(011) SSP

119895119901119905(006)

5 TC119894119904(055) prod

119895119905(0098)

6 prod119895119895119905(0087)

7 prod119903119903119905(0074)

8 ℎ119903119901119905(0057)

9 prod119903119905(0046)

10 SSP119903119901119905(0043)

11 ℎ119895119905119901(0035)


119889+

1= 0041 119889

+

2= 0111 119889

+

3= 0112

119889minus

1= 0111 119889

minus

2= 0041 119889

minus

3= 0021

(20)


119862+

1=

119889minus

1

119889+

1+ 119889minus

1

=

0111

0041 + 0111

= 073

119862+

2=

0041

0111 + 0041

= 0269

119862+

3=

0021

0112 + 0021

= 0157

(21)



1198621gt 1198622gt 1198623 (22)








9 7 31198632

7 5 71198633

7 5 5119882 0475 043 0095



119909+

119895(08 1 1) (07 08 09) (06 07 08)

119909minus

119895(07 08 09) (06 07 08) (035 05 065)

11990311= 11990911 (

) 119909+

1= (

07

1

08

1

09

08

) = (07 08 1125)

(23)


1199091

1199092

1199093

1198631015840=

119860111986021198603

(

(07 08 1125) (067 087 114) (075 1 133)

(08 1 125) (078 1 128) (043 071 108)

(07 08 1125) (078 1 128) (075 1 133)

)

(24)


V11= 11990311 (

sdot) 119908+

11= (07 08 1125)

times (08 1 1) = (056 08 1125)

(25)


1199091

1199092

1199093

119881 =

119860111986021198603

(

(056 08 1125) (0469 0696 1026) (045 07 1064)

(064 1 125) (0546 08 115) (0258 0497 0864)

(056 08 1125) (0546 08 115) (045 07 1064)

)

(26)



119884119894119904(0209) prod 119894

119894119905(0098) Spp

119895119901119905(0253)

2 119888119894119905(0204) 119888

119895119905(0095) TC

119895119889(0215)

3 ℎ119894119905119901(0109) prod

119894119905(008) Sp

119895119901119905(0047)

4 SSP119894119901119905(0069) 119888

119903119905(0063) SSP

119895119901119905(0039)

5 TC119894119904(0021) prod

119895119905(00618)

6 prod119895119895119905(00612)

7 prod119903119903119905(0037)

8 prod119903119905(0035)

9 ℎ119903119901119905(0032)

10 SSP119903119901119905(0032)

11 ℎ119895119905119901(0015)







H MH ML1198632

VH H M1198633

H H MH



(07 08 09) (06 07 08) (06 07 08)1198632

(08 1 1) (07 08 09) (035 05 065)1198633





2+ 125

2+ (125 times 08)

3 (125 minus 056)

= 0828

119872 =

1003816100381610038161003816100381610038161003816100381610038161003816

0828 073 073

0963 0832 0539

0828 0832 073

1003816100381610038161003816100381610038161003816100381610038161003816

V+1

V+2

V+3

119860+= (064 1 125) (0546 08 115) (045 07 1064)

Vminus1

Vminus2

Vminus3

119860minus= (056 08 1125) (0469 0696 1026) (0258 0497 0864)

(27)


and 119860minus

119863+

11= 1 minus

1125 minus 064

1 + 1125 minus 064 minus 08

= 0291

119863+= (

0291 0 0

0291 0178 0329

0 0 0

)

119863minus

33= 1 minus

0864 minus 045

07 + 0864 minus 045 minus 0497

= 0329

119863minus= (

0 0 0329

0 0178 0

0291 0178 0329

)

119878+

1= 0291 + 0 + 0 = 0291

119878+

2= 0291 + 0178 + 0329 = 0798

119878+

3= 0 + 0 + 0 = 0341

119878minus

1= 0 + 0 + 0329 = 0329

119878minus

2= 0 + 0178 + 0 = 0178

119878minus

3= 0291 + 0178 + 0329 = 0798

(28)



119884119894119904(087) prod 119894

119894119905(0963) Spp

119895119901119905(073)

2 119888119894119905(0832) 119888

119895119905(0832) TC

119895119889(066)

3 ℎ119894119905119901(0402) prod

119894119905(075) Sp

119895119901119905(053)

4 SSP119894119901119905(0385) 119888

119903119905(07) SSP

119895119901119905(04)

5 TC119894119904(0155) prod

119895119905(0685)

6 prod119895119895119905(066)

7 prod119903119903119905(0593)

8 ℎ119903119901119905(0402)

9 prod119903119905(034)

10 SSP119903119901119905(0285)

11 ℎ119895119905119901(0244)


1198621=

119878minus

1

119878+

1+ 119878minus

1

=

0329

0291 + 0329

= 053

1198622=

119878minus

2

119878+

2+ 119878minus

2

=

0178

0798 + 0178

= 0182

1198623=

119878minus

3

119878+

3+ 119878minus

3

=

0798

0341 + 0798

= 07

1198623gt 1198621gt 1198622

(29)



5 Conclusions







119884119894119904) (TOP-


119894119904) (TOPSIS



119894119905)




119895119901119905) (TOP-


119895119901119905) (TOPSIS 0039





119891coq119884119894119904

(0209) (087)119888119894119905

(0204) (0832)ℎ119894119905119901

(0109) (0402)SSP119894119901119905

(0069) (0385)TC119894119904

(0021) (0155)Production (0269) (0182)

prod119894119894119905

(0098) (0963)119888119895119905

(0095) (0832)prod119894119905

(008) (075)119888119903119905

(0063) (07)prod119895119905

(00618) (0685)prod119895119895119905

(00612) (066)prod119903119903119905

(0037) (0593)prod119903119905

(0035) (0402)ℎ119903119901119905

(0032) (034)SSP119903119901119905

(0032) (0285)ℎ119895119905119901

(0015) (0244)Distribution (0159) (07)

Spp119895119901119905

(0253) (073)TC119895119889

(0215) (066)Sp119895119901119905

(0047) (053)SSP119895119901119905

(0039) (04)


Indices


(119903 = 0 1 2 119877)



Cost Criteria






















119894 the level of


Acknowledgment


References














































Volume 2014




Journal of











Journal of


Function Spaces






Algebra







Volume 2014







119895and Vminus

119895are



119872(V119894119895) =

minus1198862

119894119895+ 1198882

119894119895minus 119886119894119895sdot 119887119894119895+ 119888119894119895sdot 119887119894119895

3 (minus119886119894119895+ 119888119894119895)

(13)



119895




119863+

119894119895= 1 minus sup

119909min [propV119894119895

(119909) propV+119895

(119909)]

119863minus

119894119895= 1 minus sup

119909min [propV119894119895


(119909)]

(14)



119863+

119894119895=

1 minus

119888119894119895minus 119886+

119887++ 119888119894119895minus 119886+minus 119887119894119895

for (119887119894119895lt 119887+)

1 minus

119888+minus 119886119894119895

119887119894119895+ 119888+minus 119886119894119895minus 119887+

for (119887+lt 119887119894119895)

119863minus

119894119895=

1 minus

119888minusminus 119886119894119895


for (119887minuslt 119887119894119895)

1 minus

119888119894119895minus 119886minus


for (119887119894119895lt 119887minus)

(15)





119878+


CC119894=

119878minus

119894

119878+

119894+ 119878minus

119894

119894 = 1 2 119868 (16)



119894in

descending order

4 Case Study









cit cjt

hitp hjtp

Πjt

ΠJjt

Πiit

Πit

Πrt

Πrrt

hrpt

crt

Spjpt

Sppjpt

TCjd

SSPjpt

SSPrpt

SSPipt

TCis

fcoqYis


Parts and

materialssuppliers

Sale agencies

W3

W2 W4W1

CKDProduction lines


Pre-montage

Final montage














(119878 119875 119863





119877 =[

[

0672 0703 0329

0523 0502 0768

0523 0502 0548

]

]

(17)


119881 =[

[

0317 0302 0031

0248 0215 0072

0248 0215 0052

]

]

(18)


119860+= 0317 0302 0072

119860minus= 0248 0215 0031

(19)






119894119905(0331) prod 119894

119894119905(0154) Spp

119895119901119905(0409)

2 119891coq119884119894119904(0312) 119888

119895119905(0147) TC

119895119889(0298)

3 ℎ119894119905119901(0173) prod

119894119905(014) Sp

119895119901119905(0231)

4 SSP119894119901119905(0126) 119888

119903119905(011) SSP

119895119901119905(006)

5 TC119894119904(055) prod

119895119905(0098)

6 prod119895119895119905(0087)

7 prod119903119903119905(0074)

8 ℎ119903119901119905(0057)

9 prod119903119905(0046)

10 SSP119903119901119905(0043)

11 ℎ119895119905119901(0035)


119889+

1= 0041 119889

+

2= 0111 119889

+

3= 0112

119889minus

1= 0111 119889

minus

2= 0041 119889

minus

3= 0021

(20)


119862+

1=

119889minus

1

119889+

1+ 119889minus

1

=

0111

0041 + 0111

= 073

119862+

2=

0041

0111 + 0041

= 0269

119862+

3=

0021

0112 + 0021

= 0157

(21)



1198621gt 1198622gt 1198623 (22)








9 7 31198632

7 5 71198633

7 5 5119882 0475 043 0095



119909+

119895(08 1 1) (07 08 09) (06 07 08)

119909minus

119895(07 08 09) (06 07 08) (035 05 065)

11990311= 11990911 (

) 119909+

1= (

07

1

08

1

09

08

) = (07 08 1125)

(23)


1199091

1199092

1199093

1198631015840=

119860111986021198603

(

(07 08 1125) (067 087 114) (075 1 133)

(08 1 125) (078 1 128) (043 071 108)

(07 08 1125) (078 1 128) (075 1 133)

)

(24)


V11= 11990311 (

sdot) 119908+

11= (07 08 1125)

times (08 1 1) = (056 08 1125)

(25)


1199091

1199092

1199093

119881 =

119860111986021198603

(

(056 08 1125) (0469 0696 1026) (045 07 1064)

(064 1 125) (0546 08 115) (0258 0497 0864)

(056 08 1125) (0546 08 115) (045 07 1064)

)

(26)



119884119894119904(0209) prod 119894

119894119905(0098) Spp

119895119901119905(0253)

2 119888119894119905(0204) 119888

119895119905(0095) TC

119895119889(0215)

3 ℎ119894119905119901(0109) prod

119894119905(008) Sp

119895119901119905(0047)

4 SSP119894119901119905(0069) 119888

119903119905(0063) SSP

119895119901119905(0039)

5 TC119894119904(0021) prod

119895119905(00618)

6 prod119895119895119905(00612)

7 prod119903119903119905(0037)

8 prod119903119905(0035)

9 ℎ119903119901119905(0032)

10 SSP119903119901119905(0032)

11 ℎ119895119905119901(0015)







H MH ML1198632

VH H M1198633

H H MH



(07 08 09) (06 07 08) (06 07 08)1198632

(08 1 1) (07 08 09) (035 05 065)1198633





2+ 125

2+ (125 times 08)

3 (125 minus 056)

= 0828

119872 =

1003816100381610038161003816100381610038161003816100381610038161003816

0828 073 073

0963 0832 0539

0828 0832 073

1003816100381610038161003816100381610038161003816100381610038161003816

V+1

V+2

V+3

119860+= (064 1 125) (0546 08 115) (045 07 1064)

Vminus1

Vminus2

Vminus3

119860minus= (056 08 1125) (0469 0696 1026) (0258 0497 0864)

(27)


and 119860minus

119863+

11= 1 minus

1125 minus 064

1 + 1125 minus 064 minus 08

= 0291

119863+= (

0291 0 0

0291 0178 0329

0 0 0

)

119863minus

33= 1 minus

0864 minus 045

07 + 0864 minus 045 minus 0497

= 0329

119863minus= (

0 0 0329

0 0178 0

0291 0178 0329

)

119878+

1= 0291 + 0 + 0 = 0291

119878+

2= 0291 + 0178 + 0329 = 0798

119878+

3= 0 + 0 + 0 = 0341

119878minus

1= 0 + 0 + 0329 = 0329

119878minus

2= 0 + 0178 + 0 = 0178

119878minus

3= 0291 + 0178 + 0329 = 0798

(28)



119884119894119904(087) prod 119894

119894119905(0963) Spp

119895119901119905(073)

2 119888119894119905(0832) 119888

119895119905(0832) TC

119895119889(066)

3 ℎ119894119905119901(0402) prod

119894119905(075) Sp

119895119901119905(053)

4 SSP119894119901119905(0385) 119888

119903119905(07) SSP

119895119901119905(04)

5 TC119894119904(0155) prod

119895119905(0685)

6 prod119895119895119905(066)

7 prod119903119903119905(0593)

8 ℎ119903119901119905(0402)

9 prod119903119905(034)

10 SSP119903119901119905(0285)

11 ℎ119895119905119901(0244)


1198621=

119878minus

1

119878+

1+ 119878minus

1

=

0329

0291 + 0329

= 053

1198622=

119878minus

2

119878+

2+ 119878minus

2

=

0178

0798 + 0178

= 0182

1198623=

119878minus

3

119878+

3+ 119878minus

3

=

0798

0341 + 0798

= 07

1198623gt 1198621gt 1198622

(29)



5 Conclusions







119884119894119904) (TOP-


119894119904) (TOPSIS



119894119905)




119895119901119905) (TOP-


119895119901119905) (TOPSIS 0039





119891coq119884119894119904

(0209) (087)119888119894119905

(0204) (0832)ℎ119894119905119901

(0109) (0402)SSP119894119901119905

(0069) (0385)TC119894119904

(0021) (0155)Production (0269) (0182)

prod119894119894119905

(0098) (0963)119888119895119905

(0095) (0832)prod119894119905

(008) (075)119888119903119905

(0063) (07)prod119895119905

(00618) (0685)prod119895119895119905

(00612) (066)prod119903119903119905

(0037) (0593)prod119903119905

(0035) (0402)ℎ119903119901119905

(0032) (034)SSP119903119901119905

(0032) (0285)ℎ119895119905119901

(0015) (0244)Distribution (0159) (07)

Spp119895119901119905

(0253) (073)TC119895119889

(0215) (066)Sp119895119901119905

(0047) (053)SSP119895119901119905

(0039) (04)


Indices


(119903 = 0 1 2 119877)



Cost Criteria






















119894 the level of


Acknowledgment


References














































Volume 2014




Journal of











Journal of


Function Spaces






Algebra







Volume 2014






cit cjt

hitp hjtp

Πjt

ΠJjt

Πiit

Πit

Πrt

Πrrt

hrpt

crt

Spjpt

Sppjpt

TCjd

SSPjpt

SSPrpt

SSPipt

TCis

fcoqYis


Parts and

materialssuppliers

Sale agencies

W3

W2 W4W1

CKDProduction lines


Pre-montage

Final montage














(119878 119875 119863





119877 =[

[

0672 0703 0329

0523 0502 0768

0523 0502 0548

]

]

(17)


119881 =[

[

0317 0302 0031

0248 0215 0072

0248 0215 0052

]

]

(18)


119860+= 0317 0302 0072

119860minus= 0248 0215 0031

(19)






119894119905(0331) prod 119894

119894119905(0154) Spp

119895119901119905(0409)

2 119891coq119884119894119904(0312) 119888

119895119905(0147) TC

119895119889(0298)

3 ℎ119894119905119901(0173) prod

119894119905(014) Sp

119895119901119905(0231)

4 SSP119894119901119905(0126) 119888

119903119905(011) SSP

119895119901119905(006)

5 TC119894119904(055) prod

119895119905(0098)

6 prod119895119895119905(0087)

7 prod119903119903119905(0074)

8 ℎ119903119901119905(0057)

9 prod119903119905(0046)

10 SSP119903119901119905(0043)

11 ℎ119895119905119901(0035)


119889+

1= 0041 119889

+

2= 0111 119889

+

3= 0112

119889minus

1= 0111 119889

minus

2= 0041 119889

minus

3= 0021

(20)


119862+

1=

119889minus

1

119889+

1+ 119889minus

1

=

0111

0041 + 0111

= 073

119862+

2=

0041

0111 + 0041

= 0269

119862+

3=

0021

0112 + 0021

= 0157

(21)



1198621gt 1198622gt 1198623 (22)








9 7 31198632

7 5 71198633

7 5 5119882 0475 043 0095



119909+

119895(08 1 1) (07 08 09) (06 07 08)

119909minus

119895(07 08 09) (06 07 08) (035 05 065)

11990311= 11990911 (

) 119909+

1= (

07

1

08

1

09

08

) = (07 08 1125)

(23)


1199091

1199092

1199093

1198631015840=

119860111986021198603

(

(07 08 1125) (067 087 114) (075 1 133)

(08 1 125) (078 1 128) (043 071 108)

(07 08 1125) (078 1 128) (075 1 133)

)

(24)


V11= 11990311 (

sdot) 119908+

11= (07 08 1125)

times (08 1 1) = (056 08 1125)

(25)


1199091

1199092

1199093

119881 =

119860111986021198603

(

(056 08 1125) (0469 0696 1026) (045 07 1064)

(064 1 125) (0546 08 115) (0258 0497 0864)

(056 08 1125) (0546 08 115) (045 07 1064)

)

(26)



119884119894119904(0209) prod 119894

119894119905(0098) Spp

119895119901119905(0253)

2 119888119894119905(0204) 119888

119895119905(0095) TC

119895119889(0215)

3 ℎ119894119905119901(0109) prod

119894119905(008) Sp

119895119901119905(0047)

4 SSP119894119901119905(0069) 119888

119903119905(0063) SSP

119895119901119905(0039)

5 TC119894119904(0021) prod

119895119905(00618)

6 prod119895119895119905(00612)

7 prod119903119903119905(0037)

8 prod119903119905(0035)

9 ℎ119903119901119905(0032)

10 SSP119903119901119905(0032)

11 ℎ119895119905119901(0015)







H MH ML1198632

VH H M1198633

H H MH



(07 08 09) (06 07 08) (06 07 08)1198632

(08 1 1) (07 08 09) (035 05 065)1198633





2+ 125

2+ (125 times 08)

3 (125 minus 056)

= 0828

119872 =

1003816100381610038161003816100381610038161003816100381610038161003816

0828 073 073

0963 0832 0539

0828 0832 073

1003816100381610038161003816100381610038161003816100381610038161003816

V+1

V+2

V+3

119860+= (064 1 125) (0546 08 115) (045 07 1064)

Vminus1

Vminus2

Vminus3

119860minus= (056 08 1125) (0469 0696 1026) (0258 0497 0864)

(27)


and 119860minus

119863+

11= 1 minus

1125 minus 064

1 + 1125 minus 064 minus 08

= 0291

119863+= (

0291 0 0

0291 0178 0329

0 0 0

)

119863minus

33= 1 minus

0864 minus 045

07 + 0864 minus 045 minus 0497

= 0329

119863minus= (

0 0 0329

0 0178 0

0291 0178 0329

)

119878+

1= 0291 + 0 + 0 = 0291

119878+

2= 0291 + 0178 + 0329 = 0798

119878+

3= 0 + 0 + 0 = 0341

119878minus

1= 0 + 0 + 0329 = 0329

119878minus

2= 0 + 0178 + 0 = 0178

119878minus

3= 0291 + 0178 + 0329 = 0798

(28)



119884119894119904(087) prod 119894

119894119905(0963) Spp

119895119901119905(073)

2 119888119894119905(0832) 119888

119895119905(0832) TC

119895119889(066)

3 ℎ119894119905119901(0402) prod

119894119905(075) Sp

119895119901119905(053)

4 SSP119894119901119905(0385) 119888

119903119905(07) SSP

119895119901119905(04)

5 TC119894119904(0155) prod

119895119905(0685)

6 prod119895119895119905(066)

7 prod119903119903119905(0593)

8 ℎ119903119901119905(0402)

9 prod119903119905(034)

10 SSP119903119901119905(0285)

11 ℎ119895119905119901(0244)


1198621=

119878minus

1

119878+

1+ 119878minus

1

=

0329

0291 + 0329

= 053

1198622=

119878minus

2

119878+

2+ 119878minus

2

=

0178

0798 + 0178

= 0182

1198623=

119878minus

3

119878+

3+ 119878minus

3

=

0798

0341 + 0798

= 07

1198623gt 1198621gt 1198622

(29)



5 Conclusions







119884119894119904) (TOP-


119894119904) (TOPSIS



119894119905)




119895119901119905) (TOP-


119895119901119905) (TOPSIS 0039





119891coq119884119894119904

(0209) (087)119888119894119905

(0204) (0832)ℎ119894119905119901

(0109) (0402)SSP119894119901119905

(0069) (0385)TC119894119904

(0021) (0155)Production (0269) (0182)

prod119894119894119905

(0098) (0963)119888119895119905

(0095) (0832)prod119894119905

(008) (075)119888119903119905

(0063) (07)prod119895119905

(00618) (0685)prod119895119895119905

(00612) (066)prod119903119903119905

(0037) (0593)prod119903119905

(0035) (0402)ℎ119903119901119905

(0032) (034)SSP119903119901119905

(0032) (0285)ℎ119895119905119901

(0015) (0244)Distribution (0159) (07)

Spp119895119901119905

(0253) (073)TC119895119889

(0215) (066)Sp119895119901119905

(0047) (053)SSP119895119901119905

(0039) (04)


Indices


(119903 = 0 1 2 119877)



Cost Criteria






















119894 the level of


Acknowledgment


References














































Volume 2014




Journal of











Journal of


Function Spaces






Algebra







Volume 2014











(119878 119875 119863





119877 =[

[

0672 0703 0329

0523 0502 0768

0523 0502 0548

]

]

(17)


119881 =[

[

0317 0302 0031

0248 0215 0072

0248 0215 0052

]

]

(18)


119860+= 0317 0302 0072

119860minus= 0248 0215 0031

(19)






119894119905(0331) prod 119894

119894119905(0154) Spp

119895119901119905(0409)

2 119891coq119884119894119904(0312) 119888

119895119905(0147) TC

119895119889(0298)

3 ℎ119894119905119901(0173) prod

119894119905(014) Sp

119895119901119905(0231)

4 SSP119894119901119905(0126) 119888

119903119905(011) SSP

119895119901119905(006)

5 TC119894119904(055) prod

119895119905(0098)

6 prod119895119895119905(0087)

7 prod119903119903119905(0074)

8 ℎ119903119901119905(0057)

9 prod119903119905(0046)

10 SSP119903119901119905(0043)

11 ℎ119895119905119901(0035)


119889+

1= 0041 119889

+

2= 0111 119889

+

3= 0112

119889minus

1= 0111 119889

minus

2= 0041 119889

minus

3= 0021

(20)


119862+

1=

119889minus

1

119889+

1+ 119889minus

1

=

0111

0041 + 0111

= 073

119862+

2=

0041

0111 + 0041

= 0269

119862+

3=

0021

0112 + 0021

= 0157

(21)



1198621gt 1198622gt 1198623 (22)








9 7 31198632

7 5 71198633

7 5 5119882 0475 043 0095



119909+

119895(08 1 1) (07 08 09) (06 07 08)

119909minus

119895(07 08 09) (06 07 08) (035 05 065)

11990311= 11990911 (

) 119909+

1= (

07

1

08

1

09

08

) = (07 08 1125)

(23)


1199091

1199092

1199093

1198631015840=

119860111986021198603

(

(07 08 1125) (067 087 114) (075 1 133)

(08 1 125) (078 1 128) (043 071 108)

(07 08 1125) (078 1 128) (075 1 133)

)

(24)


V11= 11990311 (

sdot) 119908+

11= (07 08 1125)

times (08 1 1) = (056 08 1125)

(25)


1199091

1199092

1199093

119881 =

119860111986021198603

(

(056 08 1125) (0469 0696 1026) (045 07 1064)

(064 1 125) (0546 08 115) (0258 0497 0864)

(056 08 1125) (0546 08 115) (045 07 1064)

)

(26)



119884119894119904(0209) prod 119894

119894119905(0098) Spp

119895119901119905(0253)

2 119888119894119905(0204) 119888

119895119905(0095) TC

119895119889(0215)

3 ℎ119894119905119901(0109) prod

119894119905(008) Sp

119895119901119905(0047)

4 SSP119894119901119905(0069) 119888

119903119905(0063) SSP

119895119901119905(0039)

5 TC119894119904(0021) prod

119895119905(00618)

6 prod119895119895119905(00612)

7 prod119903119903119905(0037)

8 prod119903119905(0035)

9 ℎ119903119901119905(0032)

10 SSP119903119901119905(0032)

11 ℎ119895119905119901(0015)







H MH ML1198632

VH H M1198633

H H MH



(07 08 09) (06 07 08) (06 07 08)1198632

(08 1 1) (07 08 09) (035 05 065)1198633





2+ 125

2+ (125 times 08)

3 (125 minus 056)

= 0828

119872 =

1003816100381610038161003816100381610038161003816100381610038161003816

0828 073 073

0963 0832 0539

0828 0832 073

1003816100381610038161003816100381610038161003816100381610038161003816

V+1

V+2

V+3

119860+= (064 1 125) (0546 08 115) (045 07 1064)

Vminus1

Vminus2

Vminus3

119860minus= (056 08 1125) (0469 0696 1026) (0258 0497 0864)

(27)


and 119860minus

119863+

11= 1 minus

1125 minus 064

1 + 1125 minus 064 minus 08

= 0291

119863+= (

0291 0 0

0291 0178 0329

0 0 0

)

119863minus

33= 1 minus

0864 minus 045

07 + 0864 minus 045 minus 0497

= 0329

119863minus= (

0 0 0329

0 0178 0

0291 0178 0329

)

119878+

1= 0291 + 0 + 0 = 0291

119878+

2= 0291 + 0178 + 0329 = 0798

119878+

3= 0 + 0 + 0 = 0341

119878minus

1= 0 + 0 + 0329 = 0329

119878minus

2= 0 + 0178 + 0 = 0178

119878minus

3= 0291 + 0178 + 0329 = 0798

(28)



119884119894119904(087) prod 119894

119894119905(0963) Spp

119895119901119905(073)

2 119888119894119905(0832) 119888

119895119905(0832) TC

119895119889(066)

3 ℎ119894119905119901(0402) prod

119894119905(075) Sp

119895119901119905(053)

4 SSP119894119901119905(0385) 119888

119903119905(07) SSP

119895119901119905(04)

5 TC119894119904(0155) prod

119895119905(0685)

6 prod119895119895119905(066)

7 prod119903119903119905(0593)

8 ℎ119903119901119905(0402)

9 prod119903119905(034)

10 SSP119903119901119905(0285)

11 ℎ119895119905119901(0244)


1198621=

119878minus

1

119878+

1+ 119878minus

1

=

0329

0291 + 0329

= 053

1198622=

119878minus

2

119878+

2+ 119878minus

2

=

0178

0798 + 0178

= 0182

1198623=

119878minus

3

119878+

3+ 119878minus

3

=

0798

0341 + 0798

= 07

1198623gt 1198621gt 1198622

(29)



5 Conclusions







119884119894119904) (TOP-


119894119904) (TOPSIS



119894119905)




119895119901119905) (TOP-


119895119901119905) (TOPSIS 0039





119891coq119884119894119904

(0209) (087)119888119894119905

(0204) (0832)ℎ119894119905119901

(0109) (0402)SSP119894119901119905

(0069) (0385)TC119894119904

(0021) (0155)Production (0269) (0182)

prod119894119894119905

(0098) (0963)119888119895119905

(0095) (0832)prod119894119905

(008) (075)119888119903119905

(0063) (07)prod119895119905

(00618) (0685)prod119895119895119905

(00612) (066)prod119903119903119905

(0037) (0593)prod119903119905

(0035) (0402)ℎ119903119901119905

(0032) (034)SSP119903119901119905

(0032) (0285)ℎ119895119905119901

(0015) (0244)Distribution (0159) (07)

Spp119895119901119905

(0253) (073)TC119895119889

(0215) (066)Sp119895119901119905

(0047) (053)SSP119895119901119905

(0039) (04)


Indices


(119903 = 0 1 2 119877)



Cost Criteria






















119894 the level of


Acknowledgment


References














































Volume 2014




Journal of











Journal of


Function Spaces






Algebra







Volume 2014








9 7 31198632

7 5 71198633

7 5 5119882 0475 043 0095



119909+

119895(08 1 1) (07 08 09) (06 07 08)

119909minus

119895(07 08 09) (06 07 08) (035 05 065)

11990311= 11990911 (

) 119909+

1= (

07

1

08

1

09

08

) = (07 08 1125)

(23)


1199091

1199092

1199093

1198631015840=

119860111986021198603

(

(07 08 1125) (067 087 114) (075 1 133)

(08 1 125) (078 1 128) (043 071 108)

(07 08 1125) (078 1 128) (075 1 133)

)

(24)


V11= 11990311 (

sdot) 119908+

11= (07 08 1125)

times (08 1 1) = (056 08 1125)

(25)


1199091

1199092

1199093

119881 =

119860111986021198603

(

(056 08 1125) (0469 0696 1026) (045 07 1064)

(064 1 125) (0546 08 115) (0258 0497 0864)

(056 08 1125) (0546 08 115) (045 07 1064)

)

(26)



119884119894119904(0209) prod 119894

119894119905(0098) Spp

119895119901119905(0253)

2 119888119894119905(0204) 119888

119895119905(0095) TC

119895119889(0215)

3 ℎ119894119905119901(0109) prod

119894119905(008) Sp

119895119901119905(0047)

4 SSP119894119901119905(0069) 119888

119903119905(0063) SSP

119895119901119905(0039)

5 TC119894119904(0021) prod

119895119905(00618)

6 prod119895119895119905(00612)

7 prod119903119903119905(0037)

8 prod119903119905(0035)

9 ℎ119903119901119905(0032)

10 SSP119903119901119905(0032)

11 ℎ119895119905119901(0015)







H MH ML1198632

VH H M1198633

H H MH



(07 08 09) (06 07 08) (06 07 08)1198632

(08 1 1) (07 08 09) (035 05 065)1198633





2+ 125

2+ (125 times 08)

3 (125 minus 056)

= 0828

119872 =

1003816100381610038161003816100381610038161003816100381610038161003816

0828 073 073

0963 0832 0539

0828 0832 073

1003816100381610038161003816100381610038161003816100381610038161003816

V+1

V+2

V+3

119860+= (064 1 125) (0546 08 115) (045 07 1064)

Vminus1

Vminus2

Vminus3

119860minus= (056 08 1125) (0469 0696 1026) (0258 0497 0864)

(27)


and 119860minus

119863+

11= 1 minus

1125 minus 064

1 + 1125 minus 064 minus 08

= 0291

119863+= (

0291 0 0

0291 0178 0329

0 0 0

)

119863minus

33= 1 minus

0864 minus 045

07 + 0864 minus 045 minus 0497

= 0329

119863minus= (

0 0 0329

0 0178 0

0291 0178 0329

)

119878+

1= 0291 + 0 + 0 = 0291

119878+

2= 0291 + 0178 + 0329 = 0798

119878+

3= 0 + 0 + 0 = 0341

119878minus

1= 0 + 0 + 0329 = 0329

119878minus

2= 0 + 0178 + 0 = 0178

119878minus

3= 0291 + 0178 + 0329 = 0798

(28)



119884119894119904(087) prod 119894

119894119905(0963) Spp

119895119901119905(073)

2 119888119894119905(0832) 119888

119895119905(0832) TC

119895119889(066)

3 ℎ119894119905119901(0402) prod

119894119905(075) Sp

119895119901119905(053)

4 SSP119894119901119905(0385) 119888

119903119905(07) SSP

119895119901119905(04)

5 TC119894119904(0155) prod

119895119905(0685)

6 prod119895119895119905(066)

7 prod119903119903119905(0593)

8 ℎ119903119901119905(0402)

9 prod119903119905(034)

10 SSP119903119901119905(0285)

11 ℎ119895119905119901(0244)


1198621=

119878minus

1

119878+

1+ 119878minus

1

=

0329

0291 + 0329

= 053

1198622=

119878minus

2

119878+

2+ 119878minus

2

=

0178

0798 + 0178

= 0182

1198623=

119878minus

3

119878+

3+ 119878minus

3

=

0798

0341 + 0798

= 07

1198623gt 1198621gt 1198622

(29)



5 Conclusions







119884119894119904) (TOP-


119894119904) (TOPSIS



119894119905)




119895119901119905) (TOP-


119895119901119905) (TOPSIS 0039





119891coq119884119894119904

(0209) (087)119888119894119905

(0204) (0832)ℎ119894119905119901

(0109) (0402)SSP119894119901119905

(0069) (0385)TC119894119904

(0021) (0155)Production (0269) (0182)

prod119894119894119905

(0098) (0963)119888119895119905

(0095) (0832)prod119894119905

(008) (075)119888119903119905

(0063) (07)prod119895119905

(00618) (0685)prod119895119895119905

(00612) (066)prod119903119903119905

(0037) (0593)prod119903119905

(0035) (0402)ℎ119903119901119905

(0032) (034)SSP119903119901119905

(0032) (0285)ℎ119895119905119901

(0015) (0244)Distribution (0159) (07)

Spp119895119901119905

(0253) (073)TC119895119889

(0215) (066)Sp119895119901119905

(0047) (053)SSP119895119901119905

(0039) (04)


Indices


(119903 = 0 1 2 119877)



Cost Criteria






















119894 the level of


Acknowledgment


References














































Volume 2014




Journal of











Journal of


Function Spaces






Algebra







Volume 2014






2+ 125

2+ (125 times 08)

3 (125 minus 056)

= 0828

119872 =

1003816100381610038161003816100381610038161003816100381610038161003816

0828 073 073

0963 0832 0539

0828 0832 073

1003816100381610038161003816100381610038161003816100381610038161003816

V+1

V+2

V+3

119860+= (064 1 125) (0546 08 115) (045 07 1064)

Vminus1

Vminus2

Vminus3

119860minus= (056 08 1125) (0469 0696 1026) (0258 0497 0864)

(27)


and 119860minus

119863+

11= 1 minus

1125 minus 064

1 + 1125 minus 064 minus 08

= 0291

119863+= (

0291 0 0

0291 0178 0329

0 0 0

)

119863minus

33= 1 minus

0864 minus 045

07 + 0864 minus 045 minus 0497

= 0329

119863minus= (

0 0 0329

0 0178 0

0291 0178 0329

)

119878+

1= 0291 + 0 + 0 = 0291

119878+

2= 0291 + 0178 + 0329 = 0798

119878+

3= 0 + 0 + 0 = 0341

119878minus

1= 0 + 0 + 0329 = 0329

119878minus

2= 0 + 0178 + 0 = 0178

119878minus

3= 0291 + 0178 + 0329 = 0798

(28)



119884119894119904(087) prod 119894

119894119905(0963) Spp

119895119901119905(073)

2 119888119894119905(0832) 119888

119895119905(0832) TC

119895119889(066)

3 ℎ119894119905119901(0402) prod

119894119905(075) Sp

119895119901119905(053)

4 SSP119894119901119905(0385) 119888

119903119905(07) SSP

119895119901119905(04)

5 TC119894119904(0155) prod

119895119905(0685)

6 prod119895119895119905(066)

7 prod119903119903119905(0593)

8 ℎ119903119901119905(0402)

9 prod119903119905(034)

10 SSP119903119901119905(0285)

11 ℎ119895119905119901(0244)


1198621=

119878minus

1

119878+

1+ 119878minus

1

=

0329

0291 + 0329

= 053

1198622=

119878minus

2

119878+

2+ 119878minus

2

=

0178

0798 + 0178

= 0182

1198623=

119878minus

3

119878+

3+ 119878minus

3

=

0798

0341 + 0798

= 07

1198623gt 1198621gt 1198622

(29)



5 Conclusions







119884119894119904) (TOP-


119894119904) (TOPSIS



119894119905)




119895119901119905) (TOP-


119895119901119905) (TOPSIS 0039





119891coq119884119894119904

(0209) (087)119888119894119905

(0204) (0832)ℎ119894119905119901

(0109) (0402)SSP119894119901119905

(0069) (0385)TC119894119904

(0021) (0155)Production (0269) (0182)

prod119894119894119905

(0098) (0963)119888119895119905

(0095) (0832)prod119894119905

(008) (075)119888119903119905

(0063) (07)prod119895119905

(00618) (0685)prod119895119895119905

(00612) (066)prod119903119903119905

(0037) (0593)prod119903119905

(0035) (0402)ℎ119903119901119905

(0032) (034)SSP119903119901119905

(0032) (0285)ℎ119895119905119901

(0015) (0244)Distribution (0159) (07)

Spp119895119901119905

(0253) (073)TC119895119889

(0215) (066)Sp119895119901119905

(0047) (053)SSP119895119901119905

(0039) (04)


Indices


(119903 = 0 1 2 119877)



Cost Criteria






















119894 the level of


Acknowledgment


References














































Volume 2014




Journal of











Journal of


Function Spaces






Algebra







Volume 2014






119884119894119904) (TOP-


119894119904) (TOPSIS



119894119905)




119895119901119905) (TOP-


119895119901119905) (TOPSIS 0039





119891coq119884119894119904

(0209) (087)119888119894119905

(0204) (0832)ℎ119894119905119901

(0109) (0402)SSP119894119901119905

(0069) (0385)TC119894119904

(0021) (0155)Production (0269) (0182)

prod119894119894119905

(0098) (0963)119888119895119905

(0095) (0832)prod119894119905

(008) (075)119888119903119905

(0063) (07)prod119895119905

(00618) (0685)prod119895119895119905

(00612) (066)prod119903119903119905

(0037) (0593)prod119903119905

(0035) (0402)ℎ119903119901119905

(0032) (034)SSP119903119901119905

(0032) (0285)ℎ119895119905119901

(0015) (0244)Distribution (0159) (07)

Spp119895119901119905

(0253) (073)TC119895119889

(0215) (066)Sp119895119901119905

(0047) (053)SSP119895119901119905

(0039) (04)


Indices


(119903 = 0 1 2 119877)



Cost Criteria






















119894 the level of


Acknowledgment


References














































Volume 2014




Journal of











Journal of


Function Spaces






Algebra







Volume 2014


















119894 the level of


Acknowledgment


References














































Volume 2014




Journal of











Journal of


Function Spaces






Algebra







Volume 2014























Volume 2014




Journal of











Journal of


Function Spaces






Algebra







Volume 2014



Evaluation of Cost-Effectiveness Criteria in Supply Chain Management: Case Study

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Transcript of Evaluation of Cost-Effectiveness Criteria in Supply Chain Management: Case Study