A Study on Evaluation of Modular Suppliers and Discussion of...

Research ArticleA Study on Evaluation of Modular Suppliers andDiscussion of Stability

Wei He

School of Business Administration Jiangxi University of Finance and Economics No 169 East Shuanggang Road ChangbeiNanchang Jiangxi 330013 China

Correspondence should be addressed to Wei He 04hrirene163com

Received 11 January 2018 Revised 24 March 2018 Accepted 3 May 2018 Published 2 July 2018

Academic Editor Manuel De la Sen

Copyright copy 2018 Wei He This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Evaluation of modular suppliers is a crucial step towards building an effective modular production network However few studiesfocus on the salient features of modular production and discuss the selection and evaluation of modular suppliers In this paperthe fuzzy evaluation method is used to make the evaluation Regarding the method this paper applies mathematical analysis tofurther discuss the stability of the method by introducing a dispersion degree and modifying the evaluation vector Then based onmodularization theory this paper adopts a factor analysis to identify the criteria for a modular supplier This paper has two mainfindings constructing an index system to evaluate modular suppliers and providing a way to test the stability of the method usedAs such the results of the paper contribute to helping enterprises involved in modular production to identify qualified modularsuppliers and make reliable decision with regard to modular supplier evaluation

1 Introduction

Since the 1970s and 1980s the global manufacturing sectorhas undergone an extensive and profound change In thepast ten years manufacturing companies tended to take thevertical integration strategy to produce Namely a companyassumes control over several production or distribution stepsinvolved in the creation of its product or service [1] Verticalintegration can help companies reduce costs and improve effi-ciencies by decreasing transportation expenses and reducingturnaround time among other advantages [1ndash5] Neverthe-less with the development of information technology anddiversification of personal needs manufacturing companiesgradually disintegrate many activities and take the focusstrategy Big MNCs such as IBM GM GE Toyota ApplePampG Unilever HP and Philips now focus on a small numberof core businesses (or areas) and outsource the noncorebusinesses through outsourcing and global sourcing andeven sell their productive branches at home or abroad Thepurpose of doing so is to reduce the operation risks respondto the diversified market demands and adapt to the rapiddevelopment of information technology [6ndash9] The verticaldisintegration of industrial organizations does not mean that

they simply return the integrated bureaucracy to the marketIn fact by focusing on its core businesses and connected by thenoncore businesses these firms form network organizationswhich help themember firms to cooperate and obtain benefitthrough win-win activities And it is called the networking ofindustrial organizations production network paradigm [10]

Furthermore with the upsurge ofmodularity namely theuse of exchangeable parts or options in the fabrication ofan object the internal production chain is decomposed andreorganized which leads to the fragmentation of productionprocess and the relocation of these fragments around theglobe Different procedures and processes of production aresplit up and assigned to different countries to produce Thenaround a final product a series of companies are organizedand connected and form the interorganizational networkSuch new industrial organizing mode is called modularproduction network (MPN) Within functionally specializedvalue chain nodes activities tend to remain tightly integratedand based on tacit linkages [10] Between these nodeshowever linkages are formed by the transfer of codified infor-mation From such linkages the network architecture arises

In a modular production network the modular suppliersare always flexible and specialized They can produce ldquothe

HindawiDiscrete Dynamics in Nature and SocietyVolume 2018 Article ID 4950740 25 pageshttpsdoiorg10115520184950740

2 Discrete Dynamics in Nature and Society

capacity pooling effectrdquo That is brand manufacturers caneasily integrate with the necessary modules and service capa-bilities and quickly turn their own ideas and designs into realproducts According to the view of system economics mod-ular production network is actually an organic economic sys-tem which consists of system integrators and generalprivatemodule suppliers Generally modular suppliers have the abil-ity to independently develop and produce modules in accor-dance with system design rules In some cases they can eveninfluence the system integrators who act as system designersin formulating and modifying the system design rules

Therefore in a modular production network themodularsuppliers appear to have strong ability The relationshipbetween modular suppliers and system integrators is nolonger a simple attached and dependent relationship Insteadin order to achieve the optimality of modular productionnetwork they have carried out extensive cooperation So fora modular production network it has dual subjects One isproduction integrator and another is modular supplier Aproduction integrator usually acts as a convener and leader inthemodular production network whereas amodular supplieris also indispensable and to some extent it is even of the sameimportance of production integrator Both production inte-grator andmodular supplier have relatively equal strong abil-ity and this is the distinctive characteristic of modular pro-duction network that differentiates it from other productioncooperation modes Hence for a production integrator tobuild an effective modular production network the selectionand evaluation of modular suppliers are of great importance

However few studies are carried out to discuss theselection of modular suppliers Although there are alreadyabundant researches of supplier evaluation and selectionvery few studies discuss the selection of modular suppliers inthe newmodular production networkThere lacks systematicstudy regarding the construction of the index system of mod-ular supplier selection and the use of evaluation methods

In fact as analyzed above there is a big differencebetween modular suppliers and common suppliers and suchdifference is mainly caused by the characteristics of modularproduction On the premise of modularization modularproduction is a production organizing mode that links mod-ule production enterprises and module assembly enterprisesthrough relationships In the context of such productioncooperation first of all the modular suppliers should possesspowerful module production and RampD capability and canprovide product modules which the production integratorsneed At the same time the compatibility of module supplierswill enable them to better communicate cooperate andinnovate with production integrators under the guidanceof ldquovisible design rulesrdquo Nevertheless these characteristicshave not been fully considered in the evaluation of commonsuppliers

To fill the research gap first in this paper the fuzzyevaluation method is adopted and modified to evaluatethe modular suppliers Based on it the stability of themethod is discussed Then based on the method this paperconducts an empirical study on the index system of modularsupplier selection The index system can provide a com-prehensive lens to study and select the potential modular

suppliers And the method as a whole is supposed to pro-vide references for managers to make better selection deci-sions

This paper is structured as follows the second sectionis a literature review in which relevant studies are reviewedand discussed the third section is an introduction to themethod we propose the fourth section is an empirical studyof the index system By investigation and expert consultationthe questionnaires are designed and an empirical study isconducted the fifth section is a case study Based on the indexsystemwe built and by applying the fuzzy evaluationmethoda modular supplier of JMC company is evaluated and thestability of the result is discussed

2 Literature Review

21 An Overview on Indexes of Supplier Selection The studyon supplier selection can be traced to the 1960s It was firstexamined in the studies about the selection of vendors inthe US [11] And he found that three factors are crucialin the choice of a vendor and they are the ability to meetquality standards the ability to deliver the product on timeand performance history Then many scholars respectivelyconducted studies on selection and evaluation of suppliersfrom different perspectives For example an empirical studywas conducted on US auto industry and 8 indexes out of 26were chosen to evaluate suppliers [12] The indexes includequality delivery reliability relationship flexibility priceand service A study established an objective-orientationdriven supplier customer satisfaction performance ratingsystem [13] In the study the authors found four factorsthat are especially important for supplier selection and theyare incoming inspection line reject performance supplierservice quality and product reliability A study discussed theimportance of suppliersrsquo roles in new product developmentand suggested that supplier selection should be extended toconsider the influence of supplier configuration [14] A studyexamined the extension of the vendor evaluation methodswith environmental green issues [15] By dividing the criteriainto the traditional (managerial) and environmental (green)factors they apply data envelopment analysis (DEA) with thecommon weights analysis (CWA) method to design a weightsystem which helps to determine the environmental factorsas important decision factors Until now the discussion offactors of supplier selection involves a wide range We try tomake a summary of the factorsmentioned in previous studiesand for the summary please see Table 1

From the above research on the index of supplier selectionand evaluation we can see the early research of supplierselection indexmostly focuses on factors such as cost qualityprice delivery and service With the changes of environmentand extension of supplier roles and capability the formerindexes can hardly completely evaluate the capability ofsuppliers In such circumstances some scholars begin topay close attention to other factors such as market agilityinnovation ability information reception and processingability and environmental management ability The supplierselection index is gradually systematized and the evaluationcriteria have been diversified and comprehensive

Discrete Dynamics in Nature and Society 3

Table 1 Indexes of supplier selection

No Criteria References No Criteria References1 On time delivery [16ndash20] 37 Total cost [21]2 Quality [14 16 18 22 23] 38 Material management [24]3 Cost [19ndash21 25 26] 39 Size of enterprise [27]4 After service [27] 40 Procedural compliance [11]5 Product flexibility [24 27] 41 Customer relationship [28]6 Reputation [11 29ndash32] 42 Quality practices [33]7 Technical capability [11 32 34 35] 43 Trust [21]8 Flexibility [21 26 34] 44 Resource utilization [21]9 Capacity and production facility [11 26 30 32 34 35] 45 ISO certification [20]10 Service [21 24 26 27 36] 46 Advanced manufacturing technology [30]11 Financial position [11 20 30 32 35] 47 Product configuration [14]12 Geographical location [11 27 30 35] 48 New technological identification [34]13 Responsiveness [21 37] 49 Support in product development [20]14 Communication [11 19 20 24] 50 Support in value analysis [30]15 Supplierrsquos willingness to cooperate [26] 51 Support in product simplification [30]16 Management and organization [26 30 34 35] 52 Support in modularization activity [30]17 Enterprise environment [24] 53 Manufacturing process [21]18 RampD capability [38 39] 54 Loyalty [40]19 After sales service [11 24 28] 55 Compatibility across levels and functions [34]20 Lead time [19 33] 56 Capability of new product development [34]21 Attitude [11 24 35] 57 Cost saving measure adoption [19]22 Suppliers honesty [24] 58 Process technology [21]23 Innovation [26 39] 59 Process management [21]24 Ability to keep promise [24] 60 Purchasing management [21]25 Managerial capability [26] 61 Factory management [21]26 Percentage defectiveness [25] 62 Quality management [26]27 Design capability [41] 63 Human resource management [26]28 Reliability [20 21 28 36] 64 Potential competence dimension [21]29 Payment terms [40] 65 Testing capability [35]30 Warranties [11] 66 Scope of resources [35]31 Operating controls [11] 67 Industry knowledge [32]32 Product development [20 27] 68 Strategic importance of supplier [30]33 Clustersgrouping of attributes or criteria [11] 69 Employee working conditions [30]34 Customer satisfaction level [34] 70 Supplierrsquos sale and administrative capabilities [30]35 Management system [42] 71 Reciprocal arrangement [11]36 Transportation and storage [27]

22 An Overview on Methodologies of Supplier SelectionRegarding the methodology of supplier selection bothdomestic and foreign scholars apply almost the same meth-ods And the main methods they use are analytic hierar-chy process method (AHP) activity-based costing method(ABC) fuzzy theory linear program method (LP) neuralnetworks and data envelopment analysis method (DEA)

For example a study used Taguchi loss functions tomeasure performance of each supplier candidate with respectto the risks and benefits and adopted AHP method to deter-mine the relative importance of these factors to the decision-maker which provides a comprehensive decision tool forsupplier selection [43] Based on the analysis of the weakness

of the existing ABC method a study established a total costof ownership matrix which defined and classified all kindsof cost by extending the traditional ABCmethod [44] Basedon a case study a study applied the fuzzy theory to design anintegrated fuzzy model to discuss the supplier managementissues [45] By consideringmaterial preparation for outsourc-ing firms technological transition quality lead time andtheir interactions a study adopted a linear programmingmodel with fuzzy multiple goals for analyzing cost effec-tiveness during vendor selection [25] Another study con-structed a supplier quality evaluation index system underSCM environment [46] On the basis of it the BP neuralnetwork is used to conduct an empirical study on the supplier


quality space A study presented a chance-constrained dataenvelopment analysis (CCDEA) approach in the presenceof multiple performance measures that are uncertain andthe effectiveness of application of CCDEA in the area ofpurchasing were demonstrated [28]

Regarding the methodology of supplier selection in earlyresearch some simplemethods such as activity-based costingmethod (ABC) are mainly used With the development oftechnology some more advanced evaluation methods suchas data envelopment analysis method (DEA) and neuralnetworksmethod are applied to evaluate suppliers One trendfor the use of supplier selection method is the combinationand synthesis ofmore than twomethods Another trend is thecontinuous modification of these methods By overcomingthe shortcomings of the methods the essence of todayrsquosmethodologies is to make the evaluation of a supplier havebetter relevance and veracity

23 An Overview on Selection of Modular Supplier Generallyspeaking modular production refers to such network orga-nization that connects the module production enterprisesand module assembly enterprises with the premise of mod-ularization Generally modular production incorporates twoaspects the decomposition of modules namely accordingto certain connection rules to decompose a complex systemor process into self-disciplined subsystems the integrationof modules namely to connect the different independentsubsystems into a complete system or process [47]

The main participants of a modular production networkare system integratorsmodular suppliers and systemdesign-ers Usually the system integrator is the core enterprise inmodular production It has strong comprehensive strengthand can satisfy the customersrsquo needs according to the marketdemands by integrating different modules System designersare responsible for formulating the rulesTheydecompose thecomplicated products determine the configuration interfaceand standard of the product system and guarantee theindependent submodules can be reorganized into an organicsystem In this sense system designers can also serve as thesystem integrators

Modular suppliers are important participants in modu-lar production network According to Masahiko Aoki theeffective operation of a modular system lies in the ldquovisibledesign rulesrdquo and the ldquoimplicit design rulesrdquoThe visible rulesmainly refer to the interfaces and standardswhile the invisiblerules indicate the design and production rules embedded in amoduleThe visible rules enable the producers to decomposethe complicatedmodular products into differentmodules andtherefore design purchase and produce independently Soin a modular production network a modular supplier hashigher discretion than common supplier to produce as longas the module they produce can well connect other modulesbased on the standardized interfaces On the other hand amodule is comprised of many components and is a compli-cated product too According to the invisible rules a modularsupplier should have the capability to do RampD independentlyand decide how to organize these components to produce amodule As such generally modular suppliers have relativelyhigher core competence than common suppliers And such

core competence mainly incorporates the RampD capabilitydesign capability and modularization capability Besides thecapability of a modular supplier to manage a number ofcomponent suppliers also differentiates a modular supplierfrom a common supplier In addition the strong abilityof modular suppliers also alters the relationship betweenmodular suppliers and system integrators It is no longera mere dependent relationship but a mutually beneficialcooperation relationship built based on reciprocity [48] Insome cases the modular suppliers can even influence thesystem integrators by participating in the RampD activities of amodular product and as a result formulating and modifyingthe system design rules [49]

So as an important actor in amodular production systemmodular suppliers are quite different from common suppliersin a number of perspectives At present there are still rarestudies on the selection of modular suppliers A study carriedout a fuzzy collaborative selection of modular suppliersfrom the perspective of the whole process of an enterprise[50] Because the evaluation is built based on the wholeprocess of enterprise production it focuses on the evaluationof production and technical capabilities but fails to takefull account of the modular and production cooperationcapabilities of modular suppliers In fact these capabilitiesare very crucial capabilities for modular suppliers As one ofthe very few studies on the selection of modular suppliersthis study provides a way of thinking about modular supplierselection issues but it lacks to provide a comprehensivepicture of modular suppliers

In summary we can find at present the research onsupplier selection is more systematic and the design ofthe evaluation index is more comprehensive The use ofthe evaluation methods is more inclined to overcome thejudgment errors and other shortcomings as well Under thisresearch backgroundwe reviewed related studies onmodularsupplier selection and found very few studieswere conductedTo fill this research void we endeavor to provide a systematicmethodology from method test to index design to evaluatemodular suppliers To do that first we adopt amodified fuzzyevaluation method and based on mathematical analysis weconduct a stability analysis to further discuss the modularsupplier selection issue Then we adopt a factor analysismethod to identify the criteria for modular suppliers to con-struct an evaluation index system And lastly by a practicalcase the method is applied and tested

3 Fuzzy Evaluation Method andthe Stability Analysis

To select and evaluate modular suppliers we need to considerdifferent factors For the factor system please see Section 4However many of these factors are qualitative and this qual-itative information is in nature ambiguous Based on fuzzysets the fuzzy evaluation method can solve this problemby giving a comprehensive evaluation of the levels of theevaluated [51 52] By dividing the intervals this methodcan deal with the ambiguity of the evaluation standards andconsider the different levels of the objects Besides takingthe advantages of expertsrsquo experiencesmakes the resultsmore


Table 2 The pairwise comparison matrix of an expert

1199061 1199062 1199063 sdot sdot sdot 1199061198981199061 1 0 sdot sdot sdot 01199062 0 1 sdot sdot sdot 11199063 1 0 sdot sdot sdot 0sdot sdot sdot sdot sdot sdot119906119898 1 0 1 sdot sdot sdotobjective and adaptable to the reality So this paper adopts thefuzzy evaluation method to evaluate and select the modularsuppliers

However this method depends much on expertsrsquo subjec-tive judgment If an expert underestimates or overestimatesa factor it may influence the final result So in this paperwe further discuss the stability of the method That is if anexpert underestimates or overestimates a factor whether theresult is stable In the stability analysis a dispersion degreeis introduced which helps to further identify the differencesof expertsrsquo subjective judgment Based on it mathematicalanalysis is adopted to discuss the influence of such differenceon the final results Generally mathematical analysis is alogical demonstration with strictness and continuity andtherefore it can provide reliable argument for the topicdiscussed As such in the stability analysis a mathematicalanalysis is adopted to provide a clear logic to judge the degreeof reliability of the results

31 Determining the Weights Suppose 119876 = (1199021 1199022 119902119905)where 119902119894 denotes an expert consulted 119865 = (1198911 1198912 119891119899)where 119891119894 denotes a factor of modular supplier selection119880 = (1199061 1199062 119906119898) where 119906119894 denotes a criterion of a factorof modular supplier selection 119881 = (V1 V2 V3 V4) whereV1 V2 V3 V4 respectively denote the ldquogoodrdquo ldquogeneralrdquoldquofairly weakrdquo and ldquoweakrdquo comment of each criterion

Each expert makes a series of judgments based onpairwise comparisons of the criteria of a factor For twocriteria of a factor the relative important one is given 1 whilethe less important one is given 0 If the importance is con-sidered as the same then 05 is given to each index So forany expert we can have the following pairwise comparisontable (see Table 2)

Then for each criterion we sum the values of all theexperts (see Table 3)

Then we can calculate the weight of 119906119894119886119906119894= sum119898119896=1sum119905119895=1 119909119894119896119895sum119898119896=1sum119905119895=1 1199091119896119895 + sum119898119896=1sum119905119895=1 1199092119896119895 + sdot sdot sdot + sum119898119896=1sum119905119895=1 119909119898119896119895

(1)

Using the pairwise comparison method we can alsocalculate the weight of each factor

Hence the final weight of each criterion is 119886119880119894 = 119886119891119894 times 11988611990611989432 Establishing Membership and Conducting ComprehensiveEvaluation Although we can get definite comments on eachcriterion the ldquoboundaryrdquo is relatively ambiguous Therefore

Table 3 The pairwise comparison matrix of all experts

1199061 1199062 1199063 sdot sdot sdot 119906119898 sum

1199061 119905sum119895=1

11990912119895 119905sum119895=1

11990913119895 119905sum119895=1

1199091119898119895 119898sum119896=1

119905sum119895=1

11990911198961198951199062 119905sum

119895=1

11990921119895 119905sum119895=1

11990923119895 119905sum119895=1

1199092119898119895 119898sum119896=1

119905sum119895=1

1199092119896119895sdot sdot sdot119906119898 119905sum

119895=1

1199091198981119895 119905sum119895=1

1199091198982119895 119905sum119895=1

1199091198983119895 119898sum119896=1

119905sum119895=1

119909119898119896119895

the membership degree of each criterion to the evaluation setis calculated In doing so we need to grade each criterionbased on specialist consultancy We can get the member-ship vector 119877119895 of criterion 119906119894 to evaluation set 119881 119877119895 =(1199031198951 1199031198952 1199031198953 1199031198954) 119895 = 1 2 119898 times 119899 119903119895119899 (119899 = 1 2 3 4) is theevaluation value of 119906119894 And we have 119903119895119894 = V119895119894sum V119895119899 sum V119895119899 =V1198951 + V1198952 + V1198953 + V1198954 We can get the evaluation membershipmatrix of the criteria of modular supplier selection

Suppose 119860 = (1198861 1198862 119886119898) where 119886119894 is the weight of 119906119894Then we can calculate the comprehensive evaluation vector119875 = 119860 times 119877 = 119906119860∙119877 = sum119898119894=1 119906119860(119906)119906119877(119906)33 Calculating the Dispersion Degree According to theabove method we can get the comprehensive evaluation of asupplier But if there are two suppliers and their comprehen-sive evaluation are similarThat is more than 50 evaluationis general and good But for one supplier the evaluations of allthe criteria are above general while for another supplier somecriteria evaluations are good The evaluations of some othercriteria are below fairly weak So we can easily find the firstsupplier is better than the second one because the second onedoes not develop evenly and therefore its risk is bigger thanthe first one

Considering such circumstance we introduce a disper-sion degree to measure it Based on probability theoryreferring to the definition of variance in statistics we use119871119895 = sum119898119894=1 119886119894(119903119894119895 minus 119887119895)2 to reflect the dispersion degree ofcriterion 119906119895 where 119887119895 = sum119898119894=1 119886119894119903119894119895 If 119871119895 is big then thecomprehensive evaluation should move down We construct119878119895 = 119887119895minus119885119871119895 where119885 denotes the parameter which decision-maker can control It is designed to reflect the adjustment thatthe dispersion causes to the evaluation judgment

We suppose if the accumulative evaluation of level 119873 isbigger than 05 then the comprehensive evaluation of thesupplier is in 119873 level And it should satisfy sum119873minus1119895=1 119901119895 le 05 lesum119873119895=1 119901119895 Based on 119878119895 = 119887119895 minus119885119871119895 we canmodify the judgmentcriterion as follows

119873minus1sum119895=1

119878119895 le 05 minus 119885 (119873 minus 1) 119871 (2)

119873sum119895=1

119878119895 ge 05 minus 119885119873119871 (3)


where 119871 = (1119899)sum119899119895=1 119871119895 By the modification the com-prehensive evaluation of a supplier has both considered themembership matrix and the dispersion degree It is moreobjective and comprehensive

34 Stability Analysis Expertsrsquo erroneous judgment mayoccur in adjacent levels or across levels In this paper toinitiate the discussion on these situations and to simplify theproblem we mainly focus on the former circumstance So wesuppose the erroneous judgment of one criterion occurs inadjacent evaluation levels of the criterion That is supposethe positive error Δ119903 occurs in 119903ℎ119896 and the negative errorminusΔ119903 occurs in 119903ℎ1198961015840 Correspondingly there are the followingcircumstances

(1) Both positive and negative errors have impact onformula (2) and formula (3) Namely 119896 le 119873 minus 11198961015840 le 119873 minus 1

(2) The positive error has impact on formula (2) bothpositive and negative errors have impact on formula(3) Namely 119896 le 119873 minus 1 1198961015840 = 119873

(3) The negative error has impact on formula (2) bothpositive and negative error have impact on formula(3) Namely 119896 = 119873 1198961015840 le 119873 minus 1

(4) Both positive and negative errors do not have impacton formula (2) the negative error has impact onformula (3) Namely 119896 gt 119873 1198961015840 = 119873

(5) Both positive and negative errors do not have impacton formula (2) the positive error has impact onformula (3) Namely 119896 = 119873 1198961015840 gt 119873

(6) Both positive and negative errors do not have impacton the two formulas Namely 119896 gt 119873 1198961015840 gt 119873

In this paper 119871 denotes the dispersion degree 119887 denotesthe membership 119903 denotes the initial judgment matrix 119886denotes the weight of a criterion 119896 denotes the evaluationlevel that the accumulative evaluation of a criterion is biggerthan 05 1198961015840 denotes a level lower than 119896

Then we make119860ℎ = (1 minus 119886ℎ) 119886ℎ119861ℎ119896 = 1 minus 2119885 (119903ℎ119896 minus 119887119896)119862ℎ1198961198961015840 = (119903ℎ119896 minus 119887119896) minus (119903ℎ1198961015840 minus 1198871198961015840)119863119873minus1 = 05 minus (119873 minus 1)119885119871 minus 119873minus1sum

119895=1

119878119895 ge 0119864ℎ1198961198961015840(119873minus1) = [119861ℎ119896 minus 119861ℎ1198961015840 + 2 (119873 minus 1)119885119862ℎ1198961198961015840119899 ]119865ℎ1198961198961015840(119873minus1) = 119861ℎ119896 + 2 (119873 minus 1)119885119862ℎ1198961198961015840119899

119866ℎ1198961198961015840 = 119861ℎ1198961015840 minus 2 (119873 minus 1)119885119862ℎ1198961198961015840119899119867119873 = 119873sum

119895=1

119878119895 minus 05 + 119873119885119871 ge 0

(4)

Then we conduct stability analysis as follows(1) Both positive and negative errors have impact on

formula (2) and formula (3) Namely 119896 le 119873 minus 1 1198961015840 le 119873 minus 1Because sum119873minus1119895=1 1198781015840119895 le 05 minus 119885(119873 minus 1)1198711015840 by rearranging the

formula we can get2 (119899 minus 119873 + 1)119885119899 119860ℎΔ1199032minus [119861ℎ119896 minus 119861ℎ1198961015840 + 2 (119873 minus 1)119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119863119873minus1

ge 0(5)

We make 119864ℎ1198961198961015840(119873minus1) = [119861ℎ119896 minus 119861ℎ1198961015840 + 2(119873 minus 1)119885119862ℎ1198961198961015840119899]Then we can get the followingIf (119864ℎ1198961198961015840(119873minus1)119886ℎ)2 minus 4(2(119899 minus119873 + 1)119885119899)119860ℎ119863119873minus1 lt 0 then

the above inequality always holdsIf (119864ℎ1198961198961015840(119873minus1)119886ℎ)2 minus 4(2(119899 minus 119873 + 1)119885119899)119860ℎ119863119873minus1 ge 0

0 le Δ119903 le 119864ℎ1198961198961015840(119873minus1)119886ℎ2 (2119885 (119899 minus 119873 + 1) 119899)119860ℎminus radic(119864ℎ1198961198961015840(119873minus1)119886ℎ)2 minus 4 (2119885 (119899 minus 119873 + 1) 119899) 119860ℎ119863119873minus1(2119885 (119899 minus 119873 + 1) 119899) 119860ℎ

(6)

Because sum119873119895=1 1198781015840119895 le 05 minus 1198851198731198711015840 by rearranging the formulawe can get (2(119899 minus 119873)119885119899)119860ℎΔ1199032

minus[119861ℎ119896 minus 119861ℎ1198961015840 + 2119873119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 minus 119867119873 le 0 (7)

Therefore if

(119864ℎ1198961198961015840119886ℎ)2 minus 42119885 (119899 minus 119873 + 1)119899 119860ℎ119863119873minus1 lt 00 le Δ119903

le 119864ℎ1198961198961015840119873119886ℎ2 (2119885 (119899 minus 119873) 119899)119860ℎ+ radic(119864ℎ1198961198961015840119873119886ℎ)2 + 4 (2119885 (119899 minus 119873) 119899)119860ℎ1198671198732 (2119885 (119899 minus 119873) 119899)119860ℎ

(8)

If (119864ℎ1198961198961015840119886ℎ)2 minus 4(2119885(119899 minus 119873 + 1)119899)119860ℎ119863119873minus1 ge 00 le Δ119903 le min( 119864ℎ1198961198961015840119873119886ℎ2 (2119885 (119899 minus 119873) 119899)119860ℎ

+ radic(119864ℎ1198961198961015840119873119886ℎ)2 + 4 (2119885 (119899 minus 119873) 119899)119860ℎ1198671198732 (2119885 (119899 minus 119873) 119899)119860ℎ 119864ℎ1198961198961015840(119873minus1)119886ℎ2 (2119885 (119899 minus 119873 + 1) 119899) 119860ℎ

minus radic(119864ℎ1198961198961015840(119873minus1)119886ℎ)2 minus 4 (2119885 (119899 minus 119873 + 1) 119899) 119860ℎ119863119873minus12 (2119885 (119899 minus 119873 + 1) 119899) 119860ℎ )

(9)


(2)Thepositive error has impact on formula (2) both positiveand negative errors have impact on formula (3) Namely 119896 le119873 minus 1 1198961015840 = 119873

Because sum119873minus1119895=1 1198781015840119895 le 05 minus 119885(119873 minus 1)1198711015840 by rearranging theformula we can get

119899 minus 2 (119873 minus 1)119885119899 119860ℎΔ1199032minus [119861ℎ119896 + 2 (119873 minus 1)119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119863119873minus1 ge 0 (10)

We make 119865ℎ1198961198961015840(119873minus1) = [119861ℎ119896 + 2(119873 minus 1)119885119862ℎ1198961198961015840119899]Then we can get the followingIf 119899 minus 2(119873 minus 1) ge 0(119865ℎ1198961198961015840(119873minus1)119886ℎ)2 minus 4119899 minus 2 (119873 minus 1)119885119899 119860ℎ119863119873minus1 lt 0 (11)

then the above inequality always holdsIf 119899 minus 2(119873 minus 1) ge 0

(119865ℎ1198961198961015840(119873minus1)119886ℎ)2 minus 4119899 minus 2 (119873 minus 1)119885119899 119860ℎ119863119873minus1 ge 00 le Δ119903 le 119865ℎ1198961198961015840(119873minus1)119886ℎ2 ((119899 minus 2 (119873 minus 1)) 119899) 119885119860ℎ

minus radic(119865ℎ1198961198961015840(119873minus1)119886ℎ)2 minus 4 ((119899 minus 2 (119873 minus 1)) 119899) 119885119860ℎ119863119873minus12 ((119899 minus 2 (119873 minus 1)) 119899) 119885119860ℎ (12)

If 2(119873 minus 1) minus 119899 ge 02 (119873 minus 1) minus 119899119899 119885119860ℎΔ1199032 + 119865ℎ1198961198961015840(119873minus1)119886ℎΔ119903 minus 119863119873minus1 le 00 le Δ119903 le minus119865ℎ1198961198961015840(119873minus1)119886ℎ2 ((2 (119873 minus 1) minus 119899) 119899) 119885119860ℎ

+ radic(119865ℎ1198961198961015840(119873minus1)119886ℎ)2 + 4 ((2 (119873 minus 1) minus 119899) 119899) 119885119860ℎ119863119873minus12 ((2 (119873 minus 1) minus 119899) 119899) 119885119860ℎ (13)

Because both positive and negative errors have impact onformula (3) and according to the deduction of circumstance(1) to satisfy formula (3) it should have

0 le Δ119903le 119864ℎ1198961198961015840119873119886ℎ + radic(119864ℎ1198961198961015840119873119886ℎ)2 + 4 (2119885 (119899 minus 119873) 119899)119860ℎ1198671198732 (2119885 (119899 minus 119873) 119899)119860ℎ (14)

Therefore if 119899 minus 2(119873 minus 1) ge 00 le Δ119903le 119864ℎ1198961198961015840119873119886ℎ + radic(119864ℎ1198961198961015840119873119886ℎ)2 + 4 (2119885 (119899 minus 119873) 119899)119860ℎ1198671198732 (2119885 (119899 minus 119873) 119899)119860ℎ (15)

If 119899 minus 2(119873 minus 1) ge 00 le Δ119903 le min( 119864ℎ1198961198961015840119873119886ℎ2 (2119885 (119899 minus 119873) 119899)119860ℎ

+ radic(119864ℎ1198961198961015840119873119886ℎ)2 + 4 (2119885 (119899 minus 119873) 119899)119860ℎ1198671198732 (2119885 (119899 minus 119873) 119899)119860ℎ 119886ℎ119865ℎ1198961198961015840(119873minus1)2 ((119899 minus 2 (119873 minus 1)) 119899) 119885119860ℎ

minus radic1198862ℎ1198652ℎ1198961198961015840(119873minus1) minus 4 ((119899 minus 2 (119873 minus 1)) 119899) 119885119860ℎ119863119873minus12 ((119899 minus 2 (119873 minus 1)) 119899) 119885119860ℎ )

(16)

If 2(119873 minus 1) minus 119899 ge 00 le Δ119903 le min( 119864ℎ1198961198961015840119873119886ℎ2 (2119885 (119899 minus 119873) 119899)119860ℎ

+ radic(119864ℎ1198961198961015840119873119886ℎ)2 + 4 (2119885 (119899 minus 119873) 119899)119860ℎ1198671198732 (2119885 (119899 minus 119873) 119899)119860ℎ minus119886ℎ119865ℎ1198961198961015840(119873minus1)2 ((2 (119873 minus 1) minus 119899) 119899) 119885119860ℎ

+ radic1198862ℎ1198652ℎ1198961198961015840(119873minus1) + 4 ((2 (119873 minus 1) minus 119899) 119899) 119885119860ℎ119863119873minus12 ((2 (119873 minus 1) minus 119899) 119899) 119885119860ℎ )

(17)

(3) The negative error has impact on formula (2) bothpositive and negative error have impact on formula (3)Namely 119896 = 119873 1198961015840 le 119873 minus 1

Because sum119873minus1119895=1 1198781015840119895 le 05 minus 119885(119873 minus 1)1198711015840 by rearranging theformula we can get119899 minus 2 (119873 minus 1)119885119899 119860ℎΔ1199032

+ [119861ℎ1198961015840 minus 2 (119873 minus 1)119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119863119873minus1 ge 0 (18)

We make 119866ℎ1198961198961015840 = [119861ℎ1198961015840 minus 2(119873 minus 1)119885119862ℎ1198961198961015840119899]Then we can get the following if 119899 minus 2(119873 minus 1) ge 0

(119866ℎ1198961198961015840119886ℎ)2 minus 4119899 minus 2 (119873 minus 1)119885119899 119860ℎ119863119873minus1 lt 0 (19)

then the above inequality always holdsIf 119899 minus 2(119873 minus 1) ge 00 le Δ119903

le minus119866ℎ1198961198961015840119886ℎ minus radic(119866ℎ1198961198961015840119886ℎ)2 minus 4 ((119899 minus 2 (119873 minus 1)) 119899) 119885119860ℎ119863119873minus12 ((119899 minus 2 (119873 minus 1)) 119899) 119885119860ℎ (20)

If 2(119873 minus 1) minus 119899 ge 00 le Δ119903le 119866ℎ1198961198961015840119886ℎ + radic(119866ℎ1198961198961015840119886ℎ)2 + 4 ((2 (119873 minus 1) minus 119899) 119899) 119885119860ℎ119863119873minus12 ((2 (119873 minus 1) minus 119899) 119899) 119885119860ℎ (21)




Therefore if 119899 minus 2(119873 minus 1) ge 00 le Δ119903le (119864ℎ1198961198961015840119873119886ℎ + radic(119864ℎ1198961198961015840119873119886ℎ)2 + 4 (2119885 (119899 minus 119873) 119899)119860ℎ119867119873)2 (2119885 (119899 minus 119873) 119899)119860ℎ (23)


+ radic(119864ℎ1198961198961015840119873119886ℎ)2 + 4 (2119885 (119899 minus 119873) 119899)119860ℎ1198671198732 (2119885 (119899 minus 119873) 119899)119860ℎ minus119886ℎ119866ℎ11989611989610158402 ((119899 minus 2 (119873 minus 1)) 119899) 119885119860ℎ

minus radic1198862ℎ1198662ℎ1198961198961015840

minus 4 ((119899 minus 2 (119873 minus 1)) 119899) 119885119860ℎ119863119873minus12 ((119899 minus 2 (119873 minus 1)) 119899) 119885119860ℎ )

(24)


+ radic(119864ℎ1198961198961015840119873119886ℎ)2 + 4 (2119885 (119899 minus 119873) 119899)119860ℎ1198671198732 (2119885 (119899 minus 119873) 119899)119860ℎ 119886ℎ119866ℎ11989611989610158402 ((2 (119873 minus 1) minus 119899) 119899) 119885119860ℎ

+ radic1198862ℎ1198662ℎ1198961198961015840

+ 4 ((2 (119873 minus 1) minus 119899) 119899) 119885119860ℎ119863119873minus12 ((2 (119873 minus 1) minus 119899) 119899) 119885119860ℎ )

(25)

(4) Both positive and negative errors do not have impact onformula (2) the negative error has impact on formula (3)Namely 119896 gt 119873 1198961015840 = 119873

Because sum119873119895=1 1198781015840119895 ge 05 minus 1198851198731198711015840 by rearranging theformula we can get119899 minus 2119873119899 119885119860ℎΔ1199032 minus [119861ℎ1198961015840 minus 2119873119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119867119873

ge 0 (26)

Then we can get the following if 119899 minus 2119873 ge 0(119866ℎ1198961198961015840119873119886ℎ)2 minus 4119899 minus 2119873119899 119885119860ℎ119863119873minus1 lt 0 (27)

then the above inequality always holdsIf 119899 minus 2119873 ge 00 le Δ119903

le 119866ℎ1198961198961015840119873119886ℎ minus radic(119866ℎ1198961198961015840119873119886ℎ)2 minus 4 ((119899 minus 2119873) 119899) 119885119860ℎ1198671198732 ((119899 minus 2119873) 119899) 119885119860ℎ (28)

If 2119873 minus 119899 ge 00 le Δ119903le minus119866ℎ1198961198961015840119873119886ℎ + radic(119866ℎ1198961198961015840119873119886ℎ)2 + 4 (2119873 minus 119899119899)119885119860ℎ1198671198732 (2119873 minus 119899119899)119885119860ℎ (29)

For formula (2) by rearranging the formula we can get2 (119873 minus 1)119885119899 119860ℎΔ1199032 + 2119886ℎ (119873 minus 1)119885119862ℎ1198961198961015840119899 Δ119903 minus 119863119873minus1 le 00 le Δ119903 le minus2119886ℎ (119873 minus 1)119885119862ℎ11989611989610158401198992 (2 (119873 minus 1) 119899) 119885119860ℎ

+ radic(2119886ℎ (119873 minus 1)119885119862ℎ1198961198961015840119899)2 + 4 (2 (119873 minus 1) 119899) 119885119860ℎ119863119873minus12 (2 (119873 minus 1) 119899) 119885119860ℎ (30)

Therefore if 119899 minus 2119873 ge 00 le Δ119903 le minus2119886ℎ (119873 minus 1)119885119862ℎ11989611989610158401198992 (2 (119873 minus 1) 119899) 119885119860ℎ

+ radic(2119886ℎ (119873 minus 1)119885119862ℎ1198961198961015840119899)2 + 4 (2 (119873 minus 1)119885119860ℎ119863119873minus1119899)2 (2 (119873 minus 1) 119899) 119885119860ℎ (31)

If 119899 minus 2119873 ge 00 le Δ119903 le min(minus2119886ℎ (119873 minus 1)119885119862ℎ11989611989610158401198992 (2 (119873 minus 1) 119899) 119885119860ℎ

+ radic(2119886ℎ (119873 minus 1)119885119862ℎ1198961198961015840119899)2 + 4 (2 (119873 minus 1)119885119860ℎ119863119873minus1119899)2 (2 (119873 minus 1) 119899) 119885119860ℎ 119886ℎ119866ℎ1198961198961015840119873 minus radic1198862

ℎ1198662ℎ1198961198961015840119873

minus 4 ((119899 minus 2119873) 119899) 119885119860ℎ1198671198732 ((119899 minus 2119873) 119899) 119885119860ℎ )(32)


+ radic(2119886ℎ (119873 minus 1)119885119862ℎ1198961198961015840119899)2 + 4 (2 (119873 minus 1)119885119860ℎ119863119873minus1119899)2 (2 (119873 minus 1) 119899) 119885119860ℎ minus119886ℎ119866ℎ1198961198961015840119873 + radic1198862

ℎ1198662ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(33)


(5) Both positive and negative errors do not have impact onformula (2) the positive error has impact on formula (3)Namely 119896 = 119873 1198961015840 gt 119873

Because sum119873119895=1 1198781015840119895 ge 05 minus 1198851198731198711015840 by rearranging the for-mula we can get

119899 minus 2119873119899 119885119860ℎΔ1199032 + [119861ℎ119896 + 2119873119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119867119873ge 0 (34)

Then we can get the following if 119899 minus 2119873 ge 0(119865ℎ1198961198961015840119873119886ℎ)2 minus 4119899 minus 2119873119899 119885119860ℎ119867119873 lt 0 (35)

then the above inequality always holdsIf 119899 minus 2119873 ge 0

0 le Δ119903le minus119865ℎ1198961198961015840119873119886ℎ + radic(119865ℎ1198961198961015840119873119886ℎ)2 minus 4 ((119899 minus 2119873) 119899) 119885119860ℎ1198671198732 ((119899 minus 2119873) 119899) 119885119860ℎ

(36)

If 2119873 minus 119899 ge 00 le Δ119903le 119865ℎ1198961198961015840119873119886ℎ + radic(119865ℎ1198961198961015840119873119886ℎ)2 + 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ

(37)

For formula (2) by rearranging the formula we can get

2 (119873 minus 1)119885119899 119860ℎΔ1199032 + 2119886ℎ (119873 minus 1)119885119862ℎ1198961198961015840119899 Δ119903 minus 119863119873minus1 le 00 le Δ119903 le minus2119886ℎ (119873 minus 1)119885119862ℎ11989611989610158401198992 (2 (119873 minus 1) 119899) 119885119860ℎ






ℎ1198652ℎ1198961198961015840119873

minus 4 ((119899 minus 2119873) 119899) 119885119860ℎ119863119873minus12 ((119899 minus 2119873) 119899) 119885119860ℎ )(40)


+ radic(2119886ℎ (119873 minus 1)119885119862ℎ1198961198961015840119899)2 + 4 (2 (119873 minus 1)119885119860ℎ119863119873minus1119899)2 (2 (119873 minus 1) 119899) 119885119860ℎ 119886ℎ119865ℎ1198961198961015840119873 + radic1198862

ℎ1198652ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(41)

(6) Both positive and negative errors do not have impact onthe two formulas Namely 119896 gt 119873 1198961015840 gt 119873




For formula (3) by rearranging the formula we can get2119873119885119899 119860ℎΔ1199032 + 2119886ℎ119873119885119862ℎ1198961198961015840119899 Δ119903 + 119867119873 ge 0 (43)

If (2119886ℎ119873119885119862ℎ1198961198961015840119899)2 minus 4(2119873119885119899)119860ℎ119867119873 lt 0 then the aboveinequality always holds

If (2119886ℎ119873119885119862ℎ1198961198961015840119899)2 minus 4(2119873119885119899)119860ℎ119867119873 ge 00 le Δ119903le minus2119886ℎ119873119885119862ℎ11989611989610158401198992 (2119873119899)119885119860ℎ

minus radic(2119886ℎ119873119885119862ℎ1198961198961015840119899)2 minus 4 (2119873119885119860ℎ119867119873119899)2 (2119873119899)119885119860ℎ (44)

Therefore if (2119886ℎ119873119885119862ℎ1198961198961015840119899)2 minus 4(2119873119885119860ℎ119867119873119899) lt 00 le Δ119903 le minus2119886ℎ (119873 minus 1)119885119862ℎ11989611989610158401198992 (2 (119873 minus 1) 119899) 119885119860ℎ


If (2119886ℎ119873119885119862ℎ1198961198961015840119899)2 minus 4(2119873119885119860ℎ119867119873119899) ge 00 le Δ119903 le min(minus2119886ℎ (119873 minus 1)119885119862ℎ11989611989610158401198992 (2 (119873 minus 1) 119899) 119885119860ℎ

+ radic(2119886ℎ (119873 minus 1)119885119862ℎ1198961198961015840119899)2 + 4 (2 (119873 minus 1)119885119860ℎ119863119873minus1119899)2 (2 (119873 minus 1) 119899) 119885119860ℎ minus2119886ℎ119873119885119862ℎ1198961198961015840119899 + radic(2119886ℎ119873119885119862ℎ1198961198961015840119899)2 minus 4 (2119873119885119860ℎ119867119873119899)2 (2119873119885119860ℎ119899) )

(46)


4 Empirical Study on Modular SupplierSelection Criteria

In this section we adopt a factor analysis method to build theindex system of modular supplier selection

41 Research Method In this section a factor analysismethod is used to construct the evaluation index systemFrom literature review we find there are a number of criteriawhich are used to selectmodular suppliersHowever whetherall these criteria are important or significantly influence theselection of modular suppliers is questionable Besides thediscussions on the influencing factors of modular supplierselection are mainly qualitative analysis and there lacksquantitative support Factor analysis is a statistical methodwhich uses empirical data to make quantitative analysis Andone advantage of factor analysis is that it can analyze theinterdependence of observed variables and can be used toreduce the set of variables in a dataset Considering this thispaper adopts the factor analysis method to build the indexsystem By using the factor analysis it can quantitatively testthe significance of current criteria and help to cut downthe superfluous and insignificant criteria In doing so theindex system is more accurate to reflect the features ofmodular suppliers and provides reliable index for the nextstep evaluation

Next we follow the procedure of index primary selectionindex optimization and index evaluation to conduct thefactor analysis

42 Index Primary Selection Extensive literature review wasconducted to conceptualize and identify the determinantsof modular supplier selection Based on the representativeresearch of suppliers modular suppliers and strategic sup-pliers the index of modular supplier selection and items ofthe questionnaire were identified (see Table 4)

The university the author affiliates has good alumniresources So we take full advantage of these resourcesHelped by the alumni associations in Shenzhen Guangdongprovince and Jiangsu province we are able to contact relatedenterprises and conduct in-depth investigation of these enter-prises to determine the primary set of the indexWe selected 9enterprises in Shenzhen which make modular production toconduct field interviews telephone or online interviews Forthe basic information of these enterprises please see Table 5

Before the formal interview we confirm the specificinterview schedule with the top management vice presidentof procurement and purchasing supervisorsThenwe carriedout the semistructured interviews and focus group discus-sions All interviews were conducted between 20168 and201611 To avoid the fatigue of interviewees we controlledthe semistructured interviews within 45-60 minutes andfocus group interviews for no more than 90 minutes Withthe consent of the interviewees we recorded the interviewsand sorted out the records after the interviews Around themodular supplier selection criteria and index we designedtwo types of questions (1) the direct questions were such asldquowhat are the requirements for modular supplier selectionrdquoand ldquowhat features do you think a modular vendor should

haverdquo (2) the indirect questions were such as ldquoplease list themain activities a qualified modular suppliers may takerdquo andldquowhat events do you think represent themodular supplier canbe trusted and therefore chosenrdquo

Finally we invited three professors of school of businessadministration of Jiangxi University of Finance and Eco-nomics and two PhD students major in logistics and supplychain management to discuss the clarity and effectiveness ofthe evaluation criteria Taking account of their suggestionsthe indexes obtained through documentation and interviewswere further condensed and were eventually modified from30 to 27

43 Index Optimization First of all we conduct exploratoryfactor analysis based on the survey of 27 items identified bythe initial questionnaire The subjects of the survey are 23enterprises involved in the modular production of electronicmanufacturing computer manufacturing and automotivemanufacturing in Shenzhen and Guangzhou A total of 223questionnaires were sent and 182 valid questionnaires werecollected with an effective rate of 816

Before factor analysis the factor analysis fitness test wasperformed Two judgment indexes namely the KMO valueand Bartlettrsquos test were mainly taken into account [55] IfKMO lt 05 we should not carry out the factor analysis Thedata analysis results show that the KMO value was 0908The statistical significance of Bartlettrsquos test is 0000 whichis smaller than 001 and reach the very significant level Allthese show that it is suitable for conducting a factor analysisIn the exploratory analysis the principal component analysis(PCA) was used with varimax rotation to arrive at the mostinterpretable and significant factor solution

Secondly the item-total correlation is calculated to obtainthe internal consistency coefficient and to determine thequality of each item Combining factor analysis and itemanalysis we find that the initial questionnaire structure is notclearThe initial questionnaire is yet not an effective question-naire and needs to be revised further

The principles for questionnaire revision are as follows[56]

Firstly referring to the results of factor analysis wechoose the items with high communality and high factorloading and delete the items with low communality and lowfactor loading Secondly also referring to the results of factoranalysis we delete items with significant double loadings (thedifference between the two biggest values of the factor loadingis less than 02) and items whose maximum value of thefactor loading is less than 04 Then we adjust and delete theitems with ambiguous meanings Thirdly based on the scoresof items we remove the items with low internal consistencyreliability

After the above modification we identified 25 items fromthe initial questionnaire to form the formal questionnaireThen we conduct a survey by using the formal questionnaireWe sent 472 questionnaires to 45 enterprises in GuangzhouShenzhen Nanchang Shanghai Hangzhou and Suzhou andcollected 230 questionnaires with effective rate of 4873

We conduct an exploratory factor analysis on the 230questionnaires using principal component analysis method


Table 4 Primary indexes of modular supplier selection

No Criteria References No Criteria References1 Quality control [14 16 18 22 23] 16 Support in modularization activity [30]2 Cost control [19ndash21 25 26] 17 Integration capability [36]3 On time delivery [16ndash20] 18 Process management [21]4 Service [21 24 26 27 36] 19 Communication [11 19 20 24]5 Financial situation [11 20 30 32 35] 20 Responsiveness [21 37]6 Reputation [11 29ndash32] 21 Customer satisfaction [34]7 Technical capability [11 32 34 35] 22 Loyalty [40]8 Innovation [26 39] 23 Follow up [28]9 ISO certification [20] 24 Customer relationship [28]10 Product configuration [14] 25 Trust [21]11 New technological identification [34] 26 Customer support [53]12 Industry knowledge [32] 27 Managerial capability [26]13 Commitment to continuous improvement [40] 28 Compatibility across levels and functions [34]14 Support in product development [20] 29 Desire of business [54]15 Support in value analysis [30] 30 Reliability [20 21 28 36]

Table 5 Basic information of enterprises interviewed

No Firm name Industry Interviewees

1 Epson engineering (Shenzhen) Ltd Printer image projector and liquidcrystal display

Purchasing managers businessmanagers

2 BYD Company Limited Automobile new energy and rail transitExecutive director deputy

purchasing director productiondirector

3 Shenzhen Dazhong Science ampTechnology Co Ltd Integrated circuit Purchasing Managers Quality

Directors

4 Shenzhen Huaxun ark Science ampTechnology Co Ltd

Semiconductor devices microwavesystems millimeter wave systems andterahertz micro electronics systems

General manager purchasingdirectors

5 Hasee Computer Co Ltd Laptops desktops LCD computers LCDLCDs and smart TVs

Chairman of the board head ofpurchasing department head of

production department

6 Johnson Electric International Limited Micro motor and parts motormanufacturing machine

General manager purchasingmanagers Division Managers

7 Sunwoda Electronic Co Ltd Lithium ion battery moduleGeneral manager head of

purchasing department head ofquality management department

8 Changan PSA Automobiles Co Ltd AutomobileGeneral manager purchasingdeputy directors supply section

chief

9 Super photoelectric (Shenzhen) Co LtdA-Silicon Poly-Silicon TFT-LCD

display panels for laptops PC monitorsand LCD TVs

Deputy general manager QSEngineers

to extract factors and varimax method to rotate Combin-ing the use of the scree plot we choose the factors whoseeigenvalues are bigger than 1 Besides we discuss the inter-pretability andmeaningfulness of factors within the theoreti-cal framework and finally deleted 4 items and left 21 itemsThen the factors were extracted by principal componentanalysis and rotated by varimax The result shows thatthe index system of modular supplier selection has a clearstructure of four factors whose cumulative contribution of

variance accounted to 73503 For the loadings of itemsplease see Table 6

According to the survey results we can find that theindexes of modular supplier selection include 4 main factorsand the cumulative contribution of variance accounts to73503 The four main factors are shown as follows

Factor 1 is basic capability of modular supplier qualitycontrol cost control on time delivery service financial situ-ation and reputation


Table 6 Loadings of items

No Item FactorF1 F2 F3 F4

Q1 Quality control 821Q2 Cost control 806Q3 On time delivery 753Q4 Service 738Q5 Financial situation 713Q6 Reputation 709Q7 Technical capability 843Q8 Innovation 826Q10 New technological identification 742Q9 ISO certification 703Q11 Industry knowledge 664Q12 Support in product development 763Q15 Integration capability 747Q14 Support in modularization activity 741Q13 Support in value analysis 738Q16 Communication 762Q18 Customer satisfaction 757Q20 Trust 751Q19 Loyalty 748Q17 Responsiveness 733Q21 Customer support 707

Eigenvalue 3935 1591 1287 1116Variance contribution rate (73503) 34621 17193 11727 9962

Factor 2 is technological capability of modular suppliertechnical capability innovation new technological identifi-cation ISO certification and industry knowledge

Factor 3 is modular capability of modular suppliersupport in product development support in value analysissupport inmodularization activity and integration capability

Factor 4 is cooperation capability of modular suppliercommunication responsiveness customer satisfaction loy-alty trust and customer support

44 Index Evaluation

441 Conceptual Model Based on literature review inter-views and expert consultation through item analysis andexploratory factor analysis we can obtain a four-factormodelfor modular supplier selection This four-factor model mod-ifies the preliminary index list of modular supplier selectionand uncovers the underlying structure of these indexes Thusit constructs the conceptualmodel for the confirmatory factoranalysis Please see Figure 1Next confirmatory factor analysisis conducted to test the four-factor model

442 Confirmatory Factor Analysis In the confirmatoryfactor analysis we sent 500 questionnaires to 41 enterprises

in Guangzhou Foshan Shenzhen Suzhou Wuxi and Nan-chang We received 278 questionnaires back and the effectiverate is 556

Our conceptual model is a four-factor model while itscompetitivemodel can be the single-factor model two-factormodel and three-factor model There are 21 items in thequestionnairesTherefore there is only one possibility for thesingle-factor model there are 210 possibilities for the two-factor model there are 1330 possibilities for the three-factormodel It is not possible for us to compare all of them So thestrategy we take is to find out the most reasonable model foreach factor model and compare them

As for the two-factormodel based on the exploratory fac-tor analysis we adopt varimax orthogonal rotation methodto extract 2 factors from 21 items with compulsion anddiscuss whether the two-factor model is better than the four-factor model In the two-factor model Q1 Q2 Q5 Q7 Q8Q10 Q11 Q12 Q13 and Q21 form the first factor while Q3Q4 Q6 Q9 Q14 Q15 Q16 Q17 Q18 Q19 and Q20 formthe second factor The variance contribution rates of thetwo factors are respectively 28458 and 9902 And thevariance cumulative contribution rate is 38361

As for the three-factor model because the technologicalcapability and modular capability of modular supplier to


Modular supplier selection

Cooperationcapability

Modular capability

Technological capability

Basic capability

Quality control

Cost controlOn time delivery

Service

Financial situationReputation

Technical capabilityInnovation

New technological identificationISO certification

Industry knowledgeSupport in product development

Support in value analysisSupport in modularization activity

Integration capabilityCommunicationResponsiveness

Customer satisfactionLoyalty

TrustCustomer support

Figure 1 Conceptual model

some extent incorporate the content of technology andinnovation the two concepts are relatively close to each otherIn investigation we also notice it Therefore in the three-factor model we suppose the technological capability andmodular capability are in the same factor

From Table 7 we can find the index such as RMSEA GFICFI NNFI and PNFI of the single model the two-factormodel and the three-factor model have not reached an ideallevel Nevertheless the indexes of the four-factor model allreach a relatively ideal level Hence the four-factor modelis a better model for the index system of modular supplierselection

443 Validity and Reliability Analysis The reliability of thescale was checked by calculating the internal consistencycoefficients (Cronbach Alpha Coefficients) From Table 8 wecan see that apart from the fourth factor it is 0693 theinternal consistency coefficients of the other three factors areall above 0700 and the total internal consistency coefficientsare 0833 Scholars posit that if the internal consistency coef-ficients are above 070 it shows the results are acceptable [57]Therefore the reliability of the questionnaire is acceptableand it indicates the results are reliable

Validity refers to the effectiveness and correctness ofquestionnaires that is the degree of the questionnaires tomeasure what it wants tomeasure It is an important criterionto evaluate the quality of the questionnaire Generally itincludes the content validity and construct validity In thedesign of the questionnaire of modular supplier selectionwe respectively ask the advices of the professors of business

administration faculty and doctoral students in logistics andsupply chain management and invite them to evaluate thequestionnaire At the same time we choose the managementof related enterprises to conduct a pretest The data of theuniversity circle and industry aids to improve the question-naire According to the results we can see the questionnairecan basically reflect the content ofmodular supplier selectionHence the questionnaire has good content validity As for theconstruct validity firstly the results of both exploratory factoranalysis and confirmatory factor analysis confirmed thevalidity of the structure of the questionnaireThe result showsthat the factor structure is clear and each criterion matchesthe requirement of psychometrics The results of confirma-tory factor analysis are consistent with the theoretical modelSecondly the item scores of each dimension are correlatedwith the total scores of the dimension It also can verifythe structure validity of the questionnaire For the resultsplease see Table 9 From the table we can see the correlationcoefficients of each item and its dimension is between 0669and 0766 and all reach the significant level It indicates theitems have good homogeneity which from another perspec-tive shows the questionnaire has good construct validity

5 Case Analysis

In this section we use the information of a modular supplierof JianglingMotors Co Ltd (JMC) as an example to conducta case analysis By using fuzzy evaluation method andconducting the stability analysis we discuss the evaluation ofthe supplier as well as the stability of the method


Table 7 Comparison of fit indexes of models

1205942119889119891 RMSEA CFI GFI NNFI PNFINull model 23081Single model 4877 0103 0717 0852 0673 0579Two factor model 4131 0093 0753 0873 0712 0602Three factor model 3879 0089 0807 0881 0771 0633Four factor model 2281 0059 0901 0929 0881 0685

Table 8 120572 coefficients of factors

Factor F1 F2 F3 F4 Total120572 coefficient 0757 0716 0702 0693 0833

51 Case Description Jiangling Motors Co Ltd (JMC inabbreviation hereinafter) is a key player in China automotiveindustry with commercial vehicle as its core competitivenessIt was established in 1968 and went public in 1993 It hasbeen ranked as one of China Top 100 Listed Companiesfor consecutive years Currently there are 14036 people inthe company In the year 2014 JMC hit a high record inits business indexes with sales revenue reaching 255 billionRMB and volume over 276000 units

As we know automobile is a typical modular productAround the production of an automobile an automobilemanufacturer needs to build a modular production net-work and cooperate with various modular suppliers Inthe modular production network JMC company works asproduction integrator and it has built relationships withdifferentmodular suppliers Each year it is amajor task for thedirector of procurement department of JMC to select someof its modular suppliers So we take JMC company as anexample to discuss its selection of modular suppliers In thiscompany we take pick-up truck as study object and discussthe evaluation of one of the suppliers

52 Calculating the Weights Based on the analysis of Sec-tion 3 the index system of modular supplier selection canbe divided into 2 levels the first level is the four factors ofmodular supplier selection and the second level is the itemsof each factor For the index system please Table 10

We employ pairwise comparison method to calculate theweights 15 specialists are invited to make the pairwise com-parison Among them 2 persons are professors 4 personsare associate professors and 9 persons are PhD studentsAll of them are from the school of business administrationof Jiangxi University of Finance and Economics

For the pairwise comparison matrixes please see Tables11ndash15

53 Establishing Membership and Conducting ComprehensiveEvaluation Based on the above analysis we select a groupof 10 experts They mainly come from two sources 5 of themaremanagers of production and procurement departments ofenterprises 5 of them are college professors in logistics andsupply chain management The alternative answers includeldquogoodrdquo ldquogeneralrdquo ldquofairly weakrdquo and ldquoweakrdquo and we give

Table 9 Correlations between criteria and factors

Item F1 F2 F3 F4Q1 0756lowastlowast

Q2 0741lowastlowast

Q3 0766lowastlowast

Q4 0712lowastlowast

Q5 0728lowastlowast

Q6 0734lowastlowast

Q7 0729lowastlowast

Q8 0712lowastlowast

Q9 0745lowastlowast

Q10 0708lowastlowast












each of them from 1 to 4 respectively We send themthe questionnaires and related information of the modularsupplier by email and make sure they do not know eachotherrsquos answer Then we can get the fuzzy evaluation matrixof the modular supplier (see Table 16)

Then we can evaluate the supplier

1198751198611 = 11986011986111minus11986116 times 11987711986111minus11986116= (0178 0178 0193 0129 0162 016)

times[[[[[[[[[[[[

02 05 03 004 04 02 002 03 03 0202 03 04 0103 04 03 001 03 03 03

]]]]]]]]]]]]= (02358 03696 02951 00995)


Table 10 Hierarchical structure of the index system of modular supplier selection

The target layer The first layer The second layer

The index system of modularsupplier selection 119860

Basic capability requirement for modular supplier 1198611Quality control 11986111Cost control 11986112

On time delivery 11986113Service 11986114

Financial situation 11986115Reputation 11986116

Technological capability requirement for modularsupplier 1198612

Technical capability 11986121Innovation 11986122

New technological identification 11986123ISO certification 11986124

Industry knowledge 11986125Modular capability requirement for modular

supplier 1198613Support in product development 11986131

Integration capability 11986132Support in modularization activity 11986133

Support in value analysis 11986134Cooperation capability requirement for modular

supplier 1198614Communication 11986141

Customer satisfaction 11986142Trust 11986143Loyalty 11986144

Responsiveness 11986145Customer support 11986146

Table 11 Judgment matrix of 1198611 minus 11986111198961198611 11986111 11986112 11986113 11986114 11986115 11986116 Total Weight11986111 6 65 10 75 10 40 017811986112 9 7 9 7 8 40 017811986113 85 8 9 9 9 435 019311986114 5 6 6 6 6 29 012911986115 75 8 6 9 6 365 016211986116 5 7 6 9 9 36 016

Table 12 Judgment matrix of 1198612 minus 11986121198961198612 11986121 11986122 11986123 11986124 11986125 Total Weight11986121 75 10 11 9 375 02511986122 75 8 10 7 325 021711986123 5 7 95 6 275 018311986124 4 5 55 9 235 015711986125 6 8 9 6 29 0193

1198751198612 = 11986011986121minus11986125 times 11987711986121minus11986125= (025 0217 0183 0157 0193)times

[[[[[[[[[

04 03 02 0102 03 04 0102 05 01 0204 05 01 003 03 02 02

]]]]]]]]]

= (03007 0368 02094 01219)1198751198613 = 11986011986131minus11986134 times 11987711986131minus11986134= (0233 0294 0261 0212)

times [[[[[[[

02 04 03 0102 03 03 0203 02 03 0201 04 05 0]]]]]]]= (02049 03184 03424 01343)


times[[[[[[[[[[[[[

03 04 02 0104 04 02 002 03 03 0203 03 03 0103 04 03 002 03 03 02

]]]]]]]]]]]]]= (02768 03506 02687 01039)119875119860 = 1198601198611minus1198614 times 1198771198611minus1198614


Table 13 Judgment matrix of 1198613 minus 11986131198961198613 11986131 11986132 11986133 11986134 Total Weight11986131 5 7 9 21 023311986132 10 75 9 265 029411986133 8 75 8 235 026111986134 6 6 7 19 0212


= (025 0278 0289 0183)times [[[[[[

02358 03696 02951 0099503007 0368 02094 0121902049 03184 03424 0134302768 03506 02687 01039]]]]]]= (02524 03509 02801 01166)

(47)

So 1198871 = 025241198872 = 035091198873 = 028011198874 = 01166(48)

And we can calculate the dispersion degree

1198711 = 00080211198712 = 00178911198713 = 00089591198714 = 0026638(49)

119871 = 0015377 and we make 119885 = 05 According to 119878119895 = 119887119895 minus119885119871119895 we can get that the adjusted evaluation judgment vectoris

(02484 03420 02756 01033) (50)

54 Stability Analysis According to the calculation of Sec-tion 53 we can know119873 = 2 From the calculation of weightswe can know integration capability (11986132) has the highestweight among all the indexesThere are diverse circumstancesof experts making erroneous judgments In this case study


we choose one of them as an example to illustrate how themethod discussed in the previous sections can be adoptedto select the potential modular suppliers Therefore wesuppose some experts overestimate the integration capabilityof the supplier Then we discuss whether their judgment mayinfluence the final results

According to the analysis of Section 4 in the circum-stance that experts overestimate the integration capability(11986132) we know 119896 = 1 1198961015840 = 2 There are four levels ofevaluation So 119899 = 4 And we make 119885 = 05

So 119896 le 119873 minus 1 1198961015840 = 119873 It is circumstance (2)

119860ℎ = (1 minus 119886ℎ) 119886ℎ = (1 minus 0294) times 0294 = 02076119861ℎ119896 = 1 minus 2119885 (119903ℎ119896 minus 119887119896) = 1 minus 2 times 05 times (02 minus 02524)

= 10524119862ℎ1198961198961015840 = (119903ℎ119896 minus 119887119896) minus (119903ℎ1198961015840 minus 1198871198961015840)= (02 minus 02524) minus (03 minus 03509) = minus00015119863119873minus1 = 05 minus (119873 minus 1)119885119871 minus 119873minus1sum

119895=1

119878119895= 05 minus (2 minus 1) times 05 times 001538 minus 0248389= 024392

119864ℎ1198961198961015840(119873minus1) = [119861ℎ119896 minus 119861ℎ1198961015840 + 2 (119873 minus 1)119885119862ℎ1198961198961015840119899 ]= (10524 minus 10509)

+ 2 times (2 minus 1) times 05 times (minus00015)4 = minus000225119865ℎ1198961198961015840(119873minus1) = 119861ℎ119896 + 2 (119873 minus 1)119885119862ℎ1198961198961015840119899

= 10524 + 2 times (2 minus 1) times 05 times (minus00015)4= 1052025119866ℎ1198961198961015840 = 119861ℎ1198961015840 minus 2 (119873 minus 1)119885119862ℎ1198961198961015840119899

= 10509 minus 2 times (2 minus 1) times 05 times (minus00015)4= 1051275


Table 16 Fuzzy evaluation matrix of the supplier

11986111 11986112 11986113 11986114 11986115 11986116 11986121 11986122 11986123 11986124 11986125 11986131 11986132 11986133 11986134 11986141 11986142 11986143 11986144 11986145 119861461198811 02 04 02 02 03 01 04 02 02 04 03 02 02 03 01 03 04 02 03 03 021198812 05 04 03 03 04 03 03 03 05 05 03 04 03 02 04 04 04 03 03 04 031198813 03 02 03 04 03 03 02 04 01 01 02 03 03 03 05 02 02 03 03 03 031198814 0 0 02 01 0 03 01 01 02 0 02 01 02 02 0 01 0 02 01 0 02

119867119873 = 119873sum119895=1

119878119895 minus 05 + 119873119885119871= (0248389 + 0341954) minus 05 + 2 times 05

times 00153773 = 010572119899 minus 2 (119873 minus 1) = 4 minus 2 times (2 minus 1) = 2 gt 01198862ℎ1198652ℎ1198961198961015840(119873minus1) minus 4119899 minus 2 (119873 minus 1)119899 119885119860ℎ119863119873minus1

= 02942 times 10520252 minus 4 times 4 minus 2 (2 minus 1)4 times 05times 02076 times 024392 = 0045022 gt 0

(51)

So

0 le Δ119903le min(119864ℎ1198961198961015840119873119886ℎ + radic(119864ℎ1198961198961015840119873119886ℎ)2 + 4 (2119885 (119899 minus 119873) 119899)119860ℎ1198671198732 (2119885 (119899 minus 119873) 119899)119860ℎ

119886ℎ119865ℎ1198961198961015840(119873minus1)2 ((119899 minus 2 (119873 minus 1)) 119899) 119885119860ℎminus radic1198862ℎ1198652ℎ1198961198961015840(119873minus1) minus 4 ((119899 minus 2 (119873 minus 1)) 119899) 119885119860ℎ119863119873minus12 ((119899 minus 2 (119873 minus 1)) 119899) 119885119860ℎ )

(52)

By calculation we can get 0 le Δ119903 le 100602555 Discussion Based on the adjusted evaluation judgmentvector we calculated in Section 53 we can know the resultssatisfy these two formulas sum119873minus1119895=1 119878119895 le 05 minus 119885(119873 minus 1)119871 andsum119873119895=1 119878119895 ge 05minus119885119873119871 So we can conclude that the supplier is ageneral modular supplier In other words the supplier has thebasic characteristics of a modular supplier and can be takeninto consideration to participate in the modular production

But another important issue we need to consider is towhich extent we can trust the result So we refer to thestability analysisThere are 10 experts tomake evaluations andhence1006025 times 10 = 1006025 The result of the stabilityanalysis indicates that even if all the 10 experts overestimatethe integration capability it would not influence the finalresults So it is safe to say the comprehensive evaluation isstable And we can trust the result

As such our method is divided into two parts The firstpart is calculating the adjusted evaluation judgment vector

According to it we can know whether the supplier is agood modular supplier or a general modular supplier or afairly weak modular supplier or a weak modular supplierThis part gives us a basic evaluation of the supplier andhelps us make a basic judgment on the supplier whether itis a modular supplier or not The second part is about thestability analysis Based on the first evaluation if the supplieris a modular supplier then we need to further to considerwhether the result is stable or not So the stability analysiscan help us to estimate the maximum tolerant number ofexpertsrsquo erroneous judgments on a single index In doing soit helps us to estimate to which degree we can trust the resultsIf the tolerant number of expertsrsquo erroneous judgments istoo small say less than 3 which indicates that if three orless than three experts make erroneous judgments the resultwill be greatly influenced Then it shows the results are verysensitive to expertsrsquo judgment and they are not stable Andweperhaps need to reconsider the result or even to reconductthe evaluation In doing so the method discussed in thispaper provides a relatively reliable way to evaluate whethera supplier is a modular supplier and supplements the currentstudies

6 Conclusions

Based on an empirical study this paper explores and furtherconfirms the factor structure of modular supplier selectionOn the basis of it it applies the fuzzy evaluation methodto evaluate the suppliers and the stability of the method isdiscussedThemain findings and contributions are as follows

(1) Based on literature review interviews and openquestionnaire by adopting exploratory factor analysis andconfirmatory factor analysis this paper discusses the factorstructure of the index system of modular supplier selectionThe results show that the index system of modular supplierselection mainly includes four factors that is the basiccapability requirement technological capability requirementmodular capability requirement and cooperation capabilityrequirement This finding contributes to building a compre-hensive evaluation criteria system for modular suppliers anddeepening the research on modular production

From the results we can have the implication thatdifferent from general supplier evaluation modular supplierevaluation needs to place particular emphasis on themodularcapability of the suppliers Modular suppliersrsquo capability inproduct development integration and so on are importantperspectives of a modular supplier and according to theempirical study they are emphasized by the manufacturersBesides the cooperation capability is also important criterionfor evaluating whether the suppliers are competent and


suitable to take on modular production Thus the index sys-tem provides comprehensive criteria and therefore can helpmanagers to better identify the possible modular supplier

(2) Based on it this paper adopts the fuzzy evaluationmethod to evaluate and select themodular suppliers Consid-ering this method depending much on an expertrsquos subjectivejudgment the stability of the method is discussed By intro-ducing the dispersion degree we modify the comprehensiveevaluation vector which considers the influence of bothmembership and dispersion Lastly we apply this method toa practical case

Based on the stability analysis we discuss the range ofsubjective judgment errors in different circumstances Suchstability analysis can help managers to understand to whichdegree they can trust the results and therefore provides moreprecise and trustworthy evaluationThus by using the stabilityanalysis the managers is able to makemore reliable decisionsconcerning modular supplier selection

In a whole this paper contributes to providing a system-atic view to study the evaluation and selection of modularsupplier by constructing an index system and proposing anevaluation method with stability analysis

However this paper also has some limitations In thestability analysis to simplify the problem we mainly discussthe expertsrsquo erroneous judgment in adjacent levels and weonly discuss the influence of erroneous judgment on onesingle index In fact the purpose of this paper is to initiatethe discussion on the reliability of the fuzzy mathematicalmethod In further studies more sophisticated mathematicalmodels can be built to take more circumstances into accountand then make the discussion more conducive

Appendix

The followings are the detailedmathematical induction of thestability analysis

(1) Both positive and negative errors have impact onformula (2) and formula (3) Namely 119896 le 119873 minus 1 1198961015840 le 119873 minus 1119873minus1sum119895=1

1198781015840119895 = sum119895 =1198961198961015840

119878119895 + 1198781015840119896 + 11987810158401198961015840= sum119895 =1198961198961015840

119878119895 + 119878119896 minus 119885119860ℎΔ1199032 + 119861ℎ119896119886ℎΔ119903 + 1198781198961015840minus 119885119860ℎΔ1199032 minus 119861ℎ1198961015840119886ℎΔ119903

= 119873minus1sum119895=1

119878119895 minus 2119885119860ℎΔ1199032 + 119886ℎ (119861ℎ119896 minus 119861ℎ1198961015840) Δ11990305 minus (119873 minus 1)1198851198711015840

= 05 minus (119873 minus 1)119885(119871 + 2119899119860ℎΔ1199032 + 2119886ℎ119862ℎ1198961198961015840119899 Δ119903)= 05 minus (119873 minus 1)119885119871 minus 2 (119873 minus 1)119885119899 119860ℎΔ1199032

minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A1)


2 (119899 minus 119873 + 1)119885119899 119860ℎΔ1199032minus [119861ℎ119896 minus 119861ℎ1198961015840 + 2 (119873 minus 1)119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903+ 119863119873minus1 ge 0

(A2)

We make

119864ℎ1198961198961015840(119873minus1) = [119861ℎ119896 minus 119861ℎ1198961015840 + 2 (119873 minus 1)119885119862ℎ1198961198961015840119899 ] (A3)

Then

2 (119899 minus 119873 + 1)119885119899 119860ℎΔ1199032 minus 119864ℎ1198961198961015840(119873minus1)119886ℎΔ119903 + 119863119873minus1ge 0 (A4)

Because 119899 minus 119873 + 1 ge 0 if(119864ℎ1198961198961015840(119873minus1)119886ℎ)2 minus 42 (119899 minus 119873 + 1)119885119899 119860ℎ119863119873minus1 lt 0 (A5)

then the above inequality always holdsIf (119864ℎ1198961198961015840(119873minus1)119886ℎ)2 minus 4(2(119899 minus 119873 + 1)119885119899)119860ℎ119863119873minus1 ge 0

0 le Δ119903 le 119864ℎ1198961198961015840(119873minus1)119886ℎ2 (2119885 (119899 minus 119873 + 1) 119899) 119860ℎminus radic(119864ℎ1198961198961015840(119873minus1)119886ℎ)2 minus 4 (2119885 (119899 minus 119873 + 1) 119899)119860ℎ119863119873minus1(2119885 (119899 minus 119873 + 1) 119899) 119860ℎ119873sum119895=1

1198781015840119895 = sum119895 =1198961198961015840

119878119895 + 1198781015840119896 + 11987810158401198961015840= sum119895 =1198961198961015840

119878119895 + 119878119896 minus 119885119860ℎΔ1199032 + 119861ℎ119896119886ℎΔ119903 + 1198781198961015840 minus 119885119860ℎΔ1199032minus 119861ℎ1198961015840119886ℎΔ119903 = 119873sum

119895=1

119878119895 minus 2119885119860ℎΔ1199032 + 119886ℎ (119861ℎ119896 minus 119861ℎ1198961015840) Δ11990305 minus 1198731198851198711015840 = 05 minus 119873119885(119871 + 2119899119860ℎΔ1199032 + 2119886ℎ119862ℎ1198961198961015840119899 Δ119903)

= 05 minus 119873119885119871 minus 2119873119885119899 119860ℎΔ1199032 minus 2119873119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A6)

Because sum119873119895=1 1198781015840119895 le 05 minus 1198851198731198711015840 by rearranging the formulawe can get

2 (119899 minus 119873)119885119899 119860ℎΔ1199032minus [119861ℎ119896 minus 119861ℎ1198961015840 + 2119873119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 minus 119867119873 le 0 (A7)


That is (2(119899 minus 119873)119885119899)119860ℎΔ1199032 minus 119864ℎ1198961198961015840119873119886ℎΔ119903 minus 119867119873 le 00 le Δ119903le 119864ℎ1198961198961015840119873119886ℎ2 (2119885 (119899 minus 119873) 119899)119860ℎ

+ radic(119864ℎ1198961198961015840119873119886ℎ)2 + 4 (2119885 (119899 minus 119873) 119899)119860ℎ1198671198732 (2119885 (119899 minus 119873) 119899)119860ℎ (A8)

Therefore if



(A9)


+ radic(119864ℎ1198961198961015840119873119886ℎ)2 + 4 (2119885 (119899 minus 119873) 119899)119860ℎ1198671198732 (2119885 (119899 minus 119873) 119899)119860ℎ 119864ℎ1198961198961015840(119873minus1)119886ℎ2 (2119885 (119899 minus 119873 + 1) 119899)119860ℎ

minus radic(119864ℎ1198961198961015840(119873minus1)119886ℎ)2 minus 4 (2119885 (119899 minus 119873 + 1) 119899) 119860ℎ119863119873minus12 (2119885 (119899 minus 119873 + 1) 119899)119860ℎ )

(A10)

(2)Thepositive error has impact on formula (2) both positiveand negative errors have impact on formula (3) Namely 119896 le119873 minus 1 1198961015840 = 119873119873minus1sum119895=1

1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896

119878119895 + 119878119896 minus 119885119860ℎΔ1199032 + 119861ℎ119896119886ℎΔ119903= 119873minus1sum119895=1

119878119895 minus 119885119860ℎΔ1199032 + 119861ℎ119896119886ℎΔ11990305 minus (119873 minus 1)1198851198711015840


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A11)


minus [119861ℎ119896 + 2 (119873 minus 1)119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119863119873minus1ge 0

(A12)

We make

119865ℎ1198961198961015840(119873minus1) = [119861ℎ119896 + 2 (119873 minus 1)119885119862ℎ1198961198961015840119899 ] (A13)

Then119899 minus 2 (119873 minus 1)119885119899 119860ℎΔ1199032 minus 119865ℎ1198961198961015840(119873minus1)119886ℎΔ119903 + 119863119873minus1ge 0 (A14)

If 119899 minus 2(119873 minus 1) ge 0(119865ℎ1198961198961015840(119873minus1)119886ℎ)2 minus 4119899 minus 2 (119873 minus 1)119885119899 119860ℎ119863119873minus1 lt 0 (A15)

then the above inequality always holdsIf 119899 minus 2(119873 minus 1) ge 0(119865ℎ1198961198961015840(119873minus1)119886ℎ)2 minus 4119899 minus 2 (119873 minus 1)119885119899 119860ℎ119863119873minus1 ge 00 le Δ119903 le 119865ℎ1198961198961015840(119873minus1)119886ℎ2 ((119899 minus 2 (119873 minus 1)) 119899) 119885119860ℎ

minus radic(119865ℎ1198961198961015840(119873minus1)119886ℎ)2 minus 4 ((119899 minus 2 (119873 minus 1)) 119899) 119885119860ℎ119863119873minus12 ((119899 minus 2 (119873 minus 1)) 119899) 119885119860ℎ (A16)


+ radic(119865ℎ1198961198961015840(119873minus1)119886ℎ)2 + 4 ((2 (119873 minus 1) minus 119899) 119899) 119885119860ℎ119863119873minus12 ((2 (119873 minus 1) minus 119899) 119899) 119885119860ℎ (A17)

Because both positive and negative errors have impact onformula (3) according to the deduction of circumstance (1)to satisfy formula (3) it should have0 le Δ119903

le 119864ℎ1198961198961015840119873119886ℎ + radic(119864ℎ1198961198961015840119873119886ℎ)2 + 4 (2119885 (119899 minus 119873) 119899)119860ℎ1198671198732 (2119885 (119899 minus 119873) 119899)119860ℎ(A18)

Therefore if 119899 minus 2(119873 minus 1) ge 0 1198862ℎ1198652ℎ1198961198961015840(119873minus1) minus 4((119899 minus 2(119873 minus1))119899)119885119860ℎ119863119873minus1 lt 00 le Δ119903le 119864ℎ1198961198961015840119873119886ℎ + radic(119864ℎ1198961198961015840119873119886ℎ)2 + 4 (2119885 (119899 minus 119873) 119899)119860ℎ1198671198732 (2119885 (119899 minus 119873) 119899)119860ℎ (A19)


If 119899minus2(119873minus1) ge 0 1198862ℎ1198652ℎ1198961198961015840(119873minus1)minus4((119899minus2(119873minus1))119899)119885119860ℎ119863119873minus1 ge00 le Δ119903 le min( 119864ℎ1198961198961015840119873119886ℎ2 (2119885 (119899 minus 119873) 119899)119860ℎ



(A20)




(A21)

(3) The negative error has impact on formula (2) bothpositive and negative error have impact on formula (3)Namely 119896 = 119873 1198961015840 le 119873 minus 1119873minus1sum119895=1

1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840

119878119895 + 1198781198961015840 minus 119885119860ℎΔ1199032 minus 119861ℎ1198961015840119886ℎΔ119903= 119873minus1sum119895=1

119878119895 minus 119885119860ℎΔ1199032 minus 119861ℎ1198961015840119886ℎΔ11990305 minus (119873 minus 1)1198851198711015840

= 05minus (119873 minus 1)119885(119871 + 2119899119860ℎΔ1199032 + 2119886ℎ119862ℎ1198961198961015840119899 Δ119903)

= 05 minus (119873 minus 1)119885119871 minus 2 (119873 minus 1)119885119899 119860ℎΔ1199032minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A22)


+ [119861ℎ1198961015840 minus 2 (119873 minus 1)119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119863119873minus1ge 0

(A23)

We make 119866ℎ1198961198961015840 = [119861ℎ1198961015840 minus (2(119873 minus 1)119885119862ℎ1198961198961015840119899)]Then ((119899 minus 2(119873minus 1)119885)119899)119860ℎΔ1199032 +119866ℎ1198961198961015840119886ℎΔ119903+119863119873minus1 ge 0If 119899 minus 2(119873 minus 1) ge 0(119866ℎ1198961198961015840119886ℎ)2 minus 4119899 minus 2 (119873 minus 1)119885119899 119860ℎ119863119873minus1 lt 0 (A24)


(119866ℎ1198961198961015840119886ℎ)2 minus 4119899 minus 2 (119873 minus 1)119885119899 119860ℎ119863119873minus1 ge 00 le Δ119903le minus119866ℎ1198961198961015840119886ℎ minus radic(119866ℎ1198961198961015840119886ℎ)2 minus 4 ((119899 minus 2 (119873 minus 1)) 119899) 119885119860ℎ119863119873minus12 ((119899 minus 2 (119873 minus 1)) 119899) 119885119860ℎ

(A25)

If 2(119873 minus 1) minus 119899 ge 02 (119873 minus 1) minus 119899119899 119885119860ℎΔ1199032 minus 119866ℎ1198961198961015840119886ℎΔ119903 minus 119863119873minus1 le 00 le Δ119903le 119866ℎ1198961198961015840119886ℎ + radic(119866ℎ1198961198961015840119886ℎ)2 + 4 ((2 (119873 minus 1) minus 119899) 119899) 119885119860ℎ119863119873minus12 ((2 (119873 minus 1) minus 119899) 119899) 119885119860ℎ

(A26)

Because both positive and negative errors have impact onformula (3) according to the deduction of circumstance (1)to satisfy formula (3) it should have

0 le Δ119903le 119864ℎ1198961198961015840119873119886ℎ + radic(119864ℎ1198961198961015840119873119886ℎ)2 + 4 (2119885 (119899 minus 119873) 119899)119860ℎ1198671198732 (2119885 (119899 minus 119873) 119899)119860ℎ (A27)Therefore if 119899 minus 2(119873 minus 1) ge 0 1198862ℎ1198662ℎ1198961198961015840 minus 4((119899 minus 2(119873 minus1))119899)119885119860ℎ119863119873minus1 lt 00 le Δ119903le 119864ℎ1198961198961015840119873119886ℎ + radic(119864ℎ1198961198961015840119873119886ℎ)2 + 4 (2119885 (119899 minus 119873) 119899)119860ℎ1198671198732 (2119885 (119899 minus 119873) 119899)119860ℎ (A28)

If 119899minus2(119873minus1) ge 0 1198862ℎ1198662ℎ1198961198961015840 minus4((119899minus2(119873minus1))119899)119885119860ℎ119863119873minus1 ge 00 le Δ119903 le min( 119864ℎ1198961198961015840119873119886ℎ2 (2119885 (119899 minus 119873) 119899)119860ℎ

+ radic(119864ℎ1198961198961015840119873119886ℎ)2 + 4 (2119885 (119899 minus 119873) 119899)119860ℎ1198671198732 (2119885 (119899 minus 119873) 119899)119860ℎ


minus119886ℎ119866ℎ11989611989610158402 ((119899 minus 2 (119873 minus 1)) 119899) 119885119860ℎminus radic1198862ℎ1198662ℎ1198961198961015840

minus 4 ((119899 minus 2 (119873 minus 1)) 119899) 119885119860ℎ119863119873minus12 ((119899 minus 2 (119873 minus 1)) 119899) 119885119860ℎ )(A29)



+ radic1198862ℎ1198662ℎ1198961198961015840


(A30)


119873sum119895=1

1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840

119878119895 + 1198781198961015840 minus 119885119860ℎΔ1199032 minus 119861ℎ1198961015840119886ℎΔ119903= 119873sum119895=1

119878119895 minus 119885119860ℎΔ1199032 minus 119861ℎ1198961015840119886ℎΔ11990305 minus 1198731198851198711015840

= 05 minus 119873119885(119871 + 2119899119860ℎΔ1199032 + 2119886ℎ119862ℎ1198961198961015840119899 Δ119903)= 05 minus 119873119885119871 minus 2119873119885119899 119860ℎΔ1199032 minus 2119873119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A31)

Because sum119873119895=1 1198781015840119895 ge 05 minus 1198851198731198711015840 by rearranging the formulawe can get

119899 minus 2119873119899 119885119860ℎΔ1199032 minus [119861ℎ1198961015840 minus 2119873119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119867119873ge 0 (A32)

That is ((119899 minus 2119873)119899)119885119860ℎΔ1199032 minus 119866ℎ1198961198961015840119873119886ℎΔ119903 + 119867119873 ge 0If 119899 minus 2119873 ge 0

(119866ℎ1198961198961015840119873119886ℎ)2 minus 4119899 minus 2119873119899 119885119860ℎ119863119873minus1 lt 0 (A33)

then the above inequality always holds

If 119899 minus 2119873 ge 0(119866ℎ1198961198961015840119873119886ℎ)2 minus 4119899 minus 2119873119899 119885119860ℎ119867119873 ge 00 le Δ119903le 119866ℎ1198961198961015840119873119886ℎ minus radic(119866ℎ1198961198961015840119873119886ℎ)2 minus 4 ((119899 minus 2119873) 119899) 119885119860ℎ1198671198732 ((119899 minus 2119873) 119899) 119885119860ℎ

(A34)

If 2119873 minus 119899 ge 02119873 minus 119899119899 119885119860ℎΔ1199032 + 119866ℎ1198961198961015840119873119886ℎΔ119903 minus 119867119873 le 00 le Δ119903le minus119866ℎ1198961198961015840119873119886ℎ + radic(119866ℎ1198961198961015840119873119886ℎ)2 + 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ

(A35)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05

minus (119873 minus 1)119885(119871 + 2119899119860ℎΔ1199032 + 2119886ℎ119862ℎ1198961198961015840119899 Δ119903)= 05 minus (119873 minus 1)119885119871 minus 2 (119873 minus 1)119885119899 119860ℎΔ1199032

minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A36)

By rearranging the formula we can get


+ radic(2119886ℎ (119873 minus 1)119885119862ℎ1198961198961015840119899)2 + 4 (2 (119873 minus 1) 119899) 119885119860ℎ119863119873minus12 (2 (119873 minus 1) 119899) 119885119860ℎ (A37)

Therefore if 119899 minus 2119873 ge 01198862ℎ1198662ℎ1198961198961015840119873 minus 4119899 minus 2119873119899 119885119860ℎ119867119873 lt 00 le Δ119903 le minus2119886ℎ (119873 minus 1)119885119862ℎ11989611989610158401198992 (2 (119873 minus 1) 119899) 119885119860ℎ

+ radic(2119886ℎ (119873 minus 1)119885119862ℎ1198961198961015840119899)2 + 4 (2 (119873 minus 1)119885119860ℎ119863119873minus1119899)2 (2 (119873 minus 1) 119899) 119885119860ℎ (A38)

If 119899 minus 2119873 ge 01198862ℎ1198662ℎ1198961198961015840119873 minus 4119899 minus 2119873119899 119885119860ℎ119867119873 ge 00 le Δ119903 le min(minus2119886ℎ (119873 minus 1)119885119862ℎ11989611989610158401198992 (2 (119873 minus 1) 119899) 119885119860ℎ



ℎ1198662ℎ1198961198961015840119873

minus 4 ((119899 minus 2119873) 119899) 119885119860ℎ1198671198732 ((119899 minus 2119873) 119899) 119885119860ℎ )(A39)



ℎ1198662ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A40)


119873sum119895=1

1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896

119878119895 + 119878119896 minus 119885119860ℎΔ1199032 + 119861ℎ119896119886ℎΔ119903= 119873sum119895=1

119878119895 minus 119885119860ℎΔ1199032 + 119861ℎ119896119886ℎΔ11990305 minus 1198731198851198711015840


(A41)


119899 minus 2119873119899 119885119860ℎΔ1199032 + [119861ℎ119896 + 2119873119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119867119873ge 0 (A42)

Then ((119899 minus 2119873)119899)119885119860ℎΔ1199032 + 119865ℎ1198961198961015840119873119886ℎΔ119903 + 119867119873 ge 0If 119899 minus 2119873 ge 0

(119865ℎ1198961198961015840119873119886ℎ)2 minus 4119899 minus 2119873119899 119885119860ℎ119867119873 lt 0 (A43)


If 119899 minus 2119873 ge 0(119865ℎ1198961198961015840119873119886ℎ)2 minus 4119899 minus 2119873119899 119885119860ℎ119867119873 ge 00 le Δ119903le minus119865ℎ1198961198961015840119873119886ℎ + radic(119865ℎ1198961198961015840119873119886ℎ)2 minus 4 ((119899 minus 2119873) 119899) 119885119860ℎ1198671198732 ((119899 minus 2119873) 119899) 119885119860ℎ

(A44)

If 2119873 minus 119899 ge 02119873 minus 119899119899 119885119860ℎΔ1199032 minus 119865ℎ1198961198961015840119873119886ℎΔ119903 minus 119867119873 le 00 le Δ119903le 119865ℎ1198961198961015840119873119886ℎ + radic(119865ℎ1198961198961015840119873119886ℎ)2 + 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ

(A45)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A46)









ℎ1198652ℎ1198961198961015840119873

minus 4 ((119899 minus 2119873) 119899) 119885119860ℎ119863119873minus12 ((119899 minus 2119873) 119899) 119885119860ℎ )

(A49)



ℎ1198652ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A50)

(6) Both positive and negative errors do not have impact onthe two formulad Namely 119896 gt 119873 1198961015840 gt 119873

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A51)




For formula (3)

119873sum119895=1

1198781015840119895 = 119873sum119895=1

119878119895 ge 05 minus 1198731198851198711015840= 05 minus 119873119885(119871 + 2119899119860ℎΔ1199032 + 2119886ℎ119862ℎ1198961198961015840119899 Δ119903)= 05 minus 119873119885119871 minus 2119873119885119899 119860ℎΔ1199032

minus 2119873119885119886ℎ119862ℎ1198961198961015840119899 Δ119903(A53)


2119873119885119899 119860ℎΔ1199032 + 2119886ℎ119873119885119862ℎ1198961198961015840119899 Δ119903 + 119867119873 ge 0 (A54)



minus radic(2119886ℎ119873119885119862ℎ1198961198961015840119899)2 minus 4 (2119873119885119860ℎ119867119873119899)2 (2119873119899)119885119860ℎ (A55)



If (2119886ℎ119873119885119862ℎ1198961198961015840119899)2 minus 4(2119873119885119860ℎ119867119873119899) ge 0

0 le Δ119903 le min[[[minus2119886ℎ (119873 minus 1)119885119862ℎ11989611989610158401198992 (2 (119873 minus 1) 119899) 119885119860ℎ + radic(2119886ℎ (119873 minus 1)119885119862ℎ1198961198961015840119899)2 + 4 (2 (119873 minus 1)119885119860ℎ119863119873minus1119899)2 (2 (119873 minus 1) 119899) 119885119860ℎ

minus2119886ℎ119873119885119862ℎ1198961198961015840119899 + radic(2119886ℎ119873119885119862ℎ1198961198961015840119899)2 minus 4 (2119873119885119860ℎ119867119873119899)2 (2119873119885119860ℎ119899) ]]](A57)


Data Availability

The data underlying the findings of the study were mainlycollected via questionnaires Readers wishing to access thesedata can do so by contacting the corresponding author

Conflicts of Interest

The author declares no conflicts of interest The author hasno financial and personal relationships with other people ororganizations that can inappropriately influence the work

Acknowledgments

This work was supported by the China Scholarship Councilthe National Natural Science Foundations of China (Grantsnos 71462009 and 71361013) the Natural Science Founda-tions of Jiangxi Province (Grants nos 20171BAA208013) andthe Science and Technology Project of Jiangxi ProvincialDepartment of Education (Grant no GJJ160440)

References

[1] G Ursino ldquoSupply Chain Control ATheory of Vertical Integra-tionrdquo BE Journal of Economic Analysis and Policy vol 15 no 4pp 1831ndash1866 2015

[2] W He ldquoA Dynamic Evolutionary Game Model of ModularProduction NetworkrdquoDiscrete Dynamics in Nature and Societyvol 2016 Article ID 6425158 2016

[3] W He and S-H Chen ldquoGame analysis of determinants ofstability of semiconductor modular production networksrdquo Sus-tainability vol 6 no 8 pp 4772ndash4794 2014

[4] S-h Chen ldquoAn evolutionary game model of knowledge work-ersrsquo counterproductive work behaviors based on preferencesrdquoComplexity Art ID 3295436 11 pages 2017

[5] S-H Chen ldquoThe influencing factors of enterprise sustainableinnovation an empirical studyrdquo Sustainability vol 8 no 5article 425 17 pages 2016

[6] L Jabbour and P Zuniga ldquoThe Outsourcing of Research andDevelopment in Global Markets Evidence from FrancerdquoWorldEconomy vol 39 no 3 pp 339ndash368 2016

[7] H Wei ldquoAn inventory controlled supply chain model based onimproved BP neural networkrdquoDiscrete Dynamics in Nature andSociety vol 2013 Article ID 537675 7 pages 2013

[8] S-H Chen and W He ldquoStudy on knowledge propagationin complex networks based on preferences taking wechat asexamplerdquo Abstract and Applied Analysis vol 2014 Article ID543734 11 pages 2014

[9] I-H Chen ldquoAn evolutionary game study of an ecologicalindustry chain based on multi-agent simulation A case studyof the Poyang Lake Eco-Economic zonerdquo Sustainability vol 9no 7 article 1165 2017

[10] T J Sturgeon ldquoModular production networks a new Americanmodel of industrial organizationrdquo Industrial and CorporateChange vol 11 no 3 pp 451ndash496 2002

[11] G W Dickson ldquoAn Analysis Of Vendor Selection Systems AndDecisionsrdquo Journal of Purchasing vol 2 no 1 pp 5ndash17 1966

[12] T Y Choi and J L Hartley ldquoAn exploration of supplier selectionpractices across the supply chainrdquo Journal of Operations Man-agement vol 14 no 4 pp 333ndash343 1996

[13] C-C Chen T-M Yeh and C-C Yang ldquoCustomer-focused rat-ing system of supplier quality performancerdquo Journal of Manu-facturing Technology Management vol 15 no 7 pp 599ndash6062004

[14] D Y Kim and S M Wagner ldquoSupplier selection problem revis-ited from the perspective of product configurationrdquo Interna-tional Journal of Production Research vol 50 no 11 pp 2864ndash2876 2012

[15] I Dobos and G Vorosmarty ldquoGreen supplier selection andevaluation using DEA-type composite indicatorsrdquo InternationalJournal of Production Economics vol 157 no 1 pp 273ndash2782014

[16] S I Omurca ldquoAn intelligent supplier evaluation selection anddevelopment systemrdquo Applied Soft Computing vol 13 no 1 pp690ndash697 2013

[17] P K Hayes B Buchholz and A E Walsby ldquoGas vesicles arestrengthened by the outer-surface protein GvpCrdquo Archives ofMicrobiology vol 157 no 3 pp 229ndash234 1992

[18] M A M A Kermani H Navidi and F Alborzi ldquoA novelmethod for supplier selection by two competitors includingmultiple criteriardquo International Journal of Computer IntegratedManufacturing vol 25 no 6 pp 527ndash535 2012

[19] M E Bilisik N Caglar and O N Bilisik ldquoA Comparative Per-formance Analyze Model and Supplier Positioning in Perfor-mance Maps for Supplier Selection and Evaluationrdquo Procedia -Social and Behavioral Sciences vol 58 pp 1434ndash1442 2012

[20] S S Reddy R P RamN T V Sastry and B I DeviAgriculturalEconomics Oxford and IBHPublishingCo Pvt Ltd NewDelhi2010

[21] D A Sarode K V Sunnapwar and M P Khodke ldquoA literaturereview for identification of performancemeasures for establish-ing a frame work for performance measurement in supplychainsrdquo International Journal of Applied Management and Tech-nology vol 6 no 3 pp 241ndash287 2008

[22] J Rezaei and R Ortt ldquoSupplier segmentation using fuzzy logicrdquoIndustrial Marketing Management vol 42 no 4 pp 507ndash5172013

[23] A Sarkar and P K J Mohapatra ldquoEvaluation of supplier capa-bility and performance a method for supply base reductionrdquoJournal of Purchasing and Supply Management vol 12 no 3 pp148ndash163 2006

[24] F T S Chan N Kumar M K Tiwari H C W Lau and K LChoy ldquoGlobal supplier selection a fuzzy-AHP approachrdquo Inter-national Journal of ProductionResearch vol 46 no 14 pp 3825ndash3857 2008

[25] E JWang Y C ChenW SWang andT S Su ldquoAnalysis of out-sourcing cost-effectiveness using a linear programming modelwith fuzzy multiple goalsrdquo International Journal of Produc-tion Research vol 48 no 2 pp 501ndash523 2010

[26] DWu and D L Olson ldquoA comparison of stochastic dominanceand stochastic DEA for vendor evaluationrdquo International Jour-nal of Production Research vol 46 no 8 pp 2313ndash2327 2008

[27] W Li P KHumphreys A C L Yeung and T C E Cheng ldquoTheimpact of supplier development on buyer competitive advan-tage A path analyticmodelrdquo International Journal of ProductionEconomics vol 135 no 1 pp 353ndash366 2012

[28] S Talluri R Narasimhan and A Nair ldquoVendor performancewith supply risk A chance-constrained DEA approachrdquo Inter-national Journal of Production Economics vol 100 no 2 pp212ndash222 2006

[29] Q Li ldquoAn ANN pruning algorithm based approach to vendorselectionrdquo Kybernetes vol 38 no 3-4 pp 314ndash320 2009


[30] R M Monczka and R J Trent ldquoEvolving Sourcing Strategiesfor the 1990srdquo International Journal of Physical Distribution ampLogistics Management vol 21 no 5 pp 4ndash12 1991

[31] F P Buffa and W M Jackson ldquoA Goal Programming Modelfor Purchase Planningrdquo Journal of Purchasing ampMaterials Man-agement vol 19 no 3 pp 27ndash34 1983

[32] L R Lamberson D Diederich and J Wuori ldquoQuantitativeVendor Evaluationrdquo Journal of Purchasing ampMaterials Manage-ment vol 12 no 1 pp 19ndash28 1976

[33] E M Guller ldquoIncorporating multi-criteria considerations intosupplier selection problem using analytical hierarchy process acase studyrdquo Journal of Yasar University vol 3 no 12 pp 1787ndash1810 2008

[34] M D Sezhiyan and T Nambirajan ldquoAn empirical investigationon relationships between critical supply chain managementactivities and supplier selection on the business performanceusing structural equation modelrdquo Journal of International Busi-ness and Economics vol 10 no 1 pp 121ndash133 2010

[35] W R Soukup ldquoSupplier Selection Strategiesrdquo Journal of Pur-chasing amp Materials Management vol 23 no 2 pp 7ndash12 1987

[36] V R Kannan and K C Tan ldquoBuyer-supplier relationships Theimpact of supplier selection and buyer-supplier engagementon relationship and firm performancerdquo International Journal ofPhysical Distribution and Logistics Management vol 36 no 10pp 755ndash775 2006

[37] M A Youssef M Zairi and B Mohanty ldquoSupplier selection inan advanced manufacturing technology environment an opti-mization modelrdquo Benchmarking for Quality Management ampTechnology vol 3 no 4 pp 60ndash72 1996

[38] PHumphreys GHuang andT Cadden ldquoAweb-based supplierevaluation tool for the product development processrdquo IndustrialManagement amp Data Systems vol 105 no 2 pp 147ndash163 2005

[39] D R Krause T V Scannell and R J Calantone ldquoA structuralanalysis of the effectiveness of buying firmsrsquo strategies to im-prove supplier performancerdquoDecision Sciences vol 31 no 1 pp33ndash54 2000

[40] H Min ldquoInternational Supplier Selection A Multi-attributeUtility Approachrdquo International Journal of Physical Distributionamp Logistics Management vol 24 no 5 pp 24ndash33 1994

[41] N J Pearson and M L Ellram ldquoSupplier selection and evalu-ation in small versus large electronics firmsrdquo Journal of SmallBusiness Management vol 33 no 4 pp 53ndash61 1995

[42] S Vachon ldquoGreen supply chain practices and the selection ofenvironmental technologiesrdquo International Journal of Produc-tion Research vol 45 no 18-19 pp 4357ndash4379 2007

[43] S M Ordoobadi ldquoApplication of AHP and Taguchi loss func-tions in supply chainrdquo Industrial Management amp Data Systemsvol 110 no 8 pp 1251ndash1269 2010

[44] P Y Ou Y L Wang and P X Wang ldquoThe study of supplierselection and evaluation based onABC approachrdquoManagementReview vol 19 no 2 pp 46ndash51 2007

[45] S H Amin and J Razmi ldquoAn integrated fuzzy model for sup-pliermanagement A case study of ISP selection and evaluationrdquoExpert Systems with Applications vol 36 no 4 pp 8639ndash86482009

[46] Y N Jia and P Sun ldquoAlgorithm for the evaluation of supplierquality based on BP neural networkrdquo Statistics amp Decisions volno 4 pp 172ndash174 2015

[47] M R Hoogeweegen W J M Teunissen P H M Vervest andR W Wagenaar ldquoModular network design Using informationand communication technology to allocate production tasks in

a virtual organizationrdquoDecision Sciences vol 30 no 4 pp 1073ndash1094 1999

[48] R Lema R Quadros and H Schmitz ldquoReorganising globalvalue chains and building innovation capabilities in Brazil andIndiardquo Research Policy vol 44 no 7 pp 1376ndash1386 2015

[49] G Hoetker A Swaminathan andWMitchell ldquoModularity andthe impact of buyer-supplier relationships on the survival ofsuppliersrdquoManagement Science vol 53 no 2 pp 178ndash191 2007

[50] H J Wang J Z Feng and H Zou ldquoA research on the evalua-tion of strategic module suppliers and management mecha-nism from the perspective of collaborative innovationrdquo ScienceResearch Management vol 37 no 3 pp 1ndash12 2016

[51] S H Chen ldquoConstruction of an Early Risk Warning Modelof Organizational Resilience An Empirical Study Based onSamples of RampD Teamsrdquo Discrete Dynamics in Nature andSociety vol 2016 9 pages 2016

[52] S-H Chen ldquoThe game analysis of negative externality of envi-ronmental logistics and governmental regulationrdquo InternationalJournal of Environment and Pollution vol 51 no 3-4 pp 143ndash155 2013

[53] A Panwar B Nepal R Jain and O P Yadav ldquoImplementationof benchmarking concepts in Indian automobile industry - anempirical studyrdquoBenchmarking vol 20 no 6 pp 777ndash804 2013

[54] M Safa A Shahi C T Haas and K W Hipel ldquoSupplier selec-tion process in an integrated construction materials manage-ment modelrdquo Automation in Construction vol 48 pp 64ndash732014

[55] J D Bartholomew F Steele J Galbraith and I MoustakiAnalysis of Multivariate Social Science Data Statistics in theSocial and Behavioral Sciences Series Taylor amp Francis FL USA2nd edition 2008

[56] D Child The Essentials of Factor Analysis Bloomsbury Aca-demic Press London UK 3rd edition 2006

[57] C J Nunnally Psychrometric Methods McGrawHill New YorkNY USA 1978

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of


Mathematical Problems in Engineering

Applied MathematicsJournal of


Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of



Engineering Mathematics

International Journal of


Operations ResearchAdvances in

Journal of


Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences


Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018


Decision SciencesAdvances in


AnalysisInternational Journal of


Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom


capacity pooling effectrdquo That is brand manufacturers caneasily integrate with the necessary modules and service capa-bilities and quickly turn their own ideas and designs into realproducts According to the view of system economics mod-ular production network is actually an organic economic sys-tem which consists of system integrators and generalprivatemodule suppliers Generally modular suppliers have the abil-ity to independently develop and produce modules in accor-dance with system design rules In some cases they can eveninfluence the system integrators who act as system designersin formulating and modifying the system design rules

Therefore in a modular production network themodularsuppliers appear to have strong ability The relationshipbetween modular suppliers and system integrators is nolonger a simple attached and dependent relationship Insteadin order to achieve the optimality of modular productionnetwork they have carried out extensive cooperation So fora modular production network it has dual subjects One isproduction integrator and another is modular supplier Aproduction integrator usually acts as a convener and leader inthemodular production network whereas amodular supplieris also indispensable and to some extent it is even of the sameimportance of production integrator Both production inte-grator andmodular supplier have relatively equal strong abil-ity and this is the distinctive characteristic of modular pro-duction network that differentiates it from other productioncooperation modes Hence for a production integrator tobuild an effective modular production network the selectionand evaluation of modular suppliers are of great importance

However few studies are carried out to discuss theselection of modular suppliers Although there are alreadyabundant researches of supplier evaluation and selectionvery few studies discuss the selection of modular suppliers inthe newmodular production networkThere lacks systematicstudy regarding the construction of the index system of mod-ular supplier selection and the use of evaluation methods

In fact as analyzed above there is a big differencebetween modular suppliers and common suppliers and suchdifference is mainly caused by the characteristics of modularproduction On the premise of modularization modularproduction is a production organizing mode that links mod-ule production enterprises and module assembly enterprisesthrough relationships In the context of such productioncooperation first of all the modular suppliers should possesspowerful module production and RampD capability and canprovide product modules which the production integratorsneed At the same time the compatibility of module supplierswill enable them to better communicate cooperate andinnovate with production integrators under the guidanceof ldquovisible design rulesrdquo Nevertheless these characteristicshave not been fully considered in the evaluation of commonsuppliers

To fill the research gap first in this paper the fuzzyevaluation method is adopted and modified to evaluatethe modular suppliers Based on it the stability of themethod is discussed Then based on the method this paperconducts an empirical study on the index system of modularsupplier selection The index system can provide a com-prehensive lens to study and select the potential modular

suppliers And the method as a whole is supposed to pro-vide references for managers to make better selection deci-sions

This paper is structured as follows the second sectionis a literature review in which relevant studies are reviewedand discussed the third section is an introduction to themethod we propose the fourth section is an empirical studyof the index system By investigation and expert consultationthe questionnaires are designed and an empirical study isconducted the fifth section is a case study Based on the indexsystemwe built and by applying the fuzzy evaluationmethoda modular supplier of JMC company is evaluated and thestability of the result is discussed

2 Literature Review

21 An Overview on Indexes of Supplier Selection The studyon supplier selection can be traced to the 1960s It was firstexamined in the studies about the selection of vendors inthe US [11] And he found that three factors are crucialin the choice of a vendor and they are the ability to meetquality standards the ability to deliver the product on timeand performance history Then many scholars respectivelyconducted studies on selection and evaluation of suppliersfrom different perspectives For example an empirical studywas conducted on US auto industry and 8 indexes out of 26were chosen to evaluate suppliers [12] The indexes includequality delivery reliability relationship flexibility priceand service A study established an objective-orientationdriven supplier customer satisfaction performance ratingsystem [13] In the study the authors found four factorsthat are especially important for supplier selection and theyare incoming inspection line reject performance supplierservice quality and product reliability A study discussed theimportance of suppliersrsquo roles in new product developmentand suggested that supplier selection should be extended toconsider the influence of supplier configuration [14] A studyexamined the extension of the vendor evaluation methodswith environmental green issues [15] By dividing the criteriainto the traditional (managerial) and environmental (green)factors they apply data envelopment analysis (DEA) with thecommon weights analysis (CWA) method to design a weightsystem which helps to determine the environmental factorsas important decision factors Until now the discussion offactors of supplier selection involves a wide range We try tomake a summary of the factorsmentioned in previous studiesand for the summary please see Table 1

From the above research on the index of supplier selectionand evaluation we can see the early research of supplierselection indexmostly focuses on factors such as cost qualityprice delivery and service With the changes of environmentand extension of supplier roles and capability the formerindexes can hardly completely evaluate the capability ofsuppliers In such circumstances some scholars begin topay close attention to other factors such as market agilityinnovation ability information reception and processingability and environmental management ability The supplierselection index is gradually systematized and the evaluationcriteria have been diversified and comprehensive


























(1)





1199061 119905sum119895=1

11990912119895 119905sum119895=1

11990913119895 119905sum119895=1

1199091119898119895 119898sum119896=1

119905sum119895=1

11990911198961198951199062 119905sum

119895=1

11990921119895 119905sum119895=1

11990923119895 119905sum119895=1

1199092119898119895 119898sum119896=1

119905sum119895=1


119895=1

1199091198981119895 119905sum119895=1

1199091198982119895 119905sum119895=1

1199091198983119895 119898sum119896=1

119905sum119895=1

119909119898119896119895





119873minus1sum119895=1

119878119895 le 05 minus 119885 (119873 minus 1) 119871 (2)

119873sum119895=1

119878119895 ge 05 minus 119885119873119871 (3)












119895=1



119895=1

119878119895 minus 05 + 119873119885119871 ge 0

(4)




ge 0(5)




(6)



Therefore if



(8)




(9)

















(16)




(17)















minus radic1198862ℎ1198662ℎ1198961198961015840


(24)



+ radic1198862ℎ1198662ℎ1198961198961015840


(25)



ge 0 (26)











ℎ1198662ℎ1198961198961015840119873




ℎ1198662ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(33)




119899 minus 2119873119899 119885119860ℎΔ1199032 + [119861ℎ119896 + 2119873119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119867119873ge 0 (34)




(36)


(37)








ℎ1198652ℎ1198961198961015840119873




ℎ1198652ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(41)













(46)




























Directors












chief
















44 Index Evaluation










Modular capability


Basic capability

Quality control


Service















5 Case Analysis















Q2 0741lowastlowast

Q3 0766lowastlowast

Q4 0712lowastlowast

Q5 0728lowastlowast

Q6 0734lowastlowast

Q7 0729lowastlowast

Q8 0712lowastlowast

Q9 0745lowastlowast
















times[[[[[[[[[[[[

02 05 03 004 04 02 002 03 03 0202 03 04 0103 04 03 001 03 03 03

]]]]]]]]]]]]= (02358 03696 02951 00995)





















[[[[[[[[[

04 03 02 0102 03 04 0102 05 01 0204 05 01 003 03 02 02

]]]]]]]]]


times [[[[[[[

02 04 03 0102 03 03 0203 02 03 0201 04 05 0]]]]]]]= (02049 03184 03424 01343)


times[[[[[[[[[[[[[

03 04 02 0104 04 02 002 03 03 0203 03 03 0103 04 03 002 03 03 02





= (025 0278 0289 0183)times [[[[[[

02358 03696 02951 0099503007 0368 02094 0121902049 03184 03424 0134302768 03506 02687 01039]]]]]]= (02524 03509 02801 01166)

(47)

So 1198871 = 025241198872 = 035091198873 = 028011198874 = 01166(48)


1198711 = 00080211198712 = 00178911198713 = 00089591198714 = 0026638(49)


(02484 03420 02756 01033) (50)








119895=1








11986111 11986112 11986113 11986114 11986115 11986116 11986121 11986122 11986123 11986124 11986125 11986131 11986132 11986133 11986134 11986141 11986142 11986143 11986144 11986145 119861461198811 02 04 02 02 03 01 04 02 02 04 03 02 02 03 01 03 04 02 03 03 021198812 05 04 03 03 04 03 03 03 05 05 03 04 03 02 04 04 04 03 03 04 031198813 03 02 03 04 03 03 02 04 01 01 02 03 03 03 05 02 02 03 03 03 031198814 0 0 02 01 0 03 01 01 02 0 02 01 02 02 0 01 0 02 01 0 02

119867119873 = 119873sum119895=1




(51)

So



(52)





6 Conclusions










Appendix



1198781015840119895 = sum119895 =1198961198961015840

119878119895 + 1198781015840119896 + 11987810158401198961015840= sum119895 =1198961198961015840


= 119873minus1sum119895=1



minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A1)



(A2)

We make


Then





1198781015840119895 = sum119895 =1198961198961015840

119878119895 + 1198781015840119896 + 11987810158401198961015840= sum119895 =1198961198961015840


119895=1



(A6)






Therefore if



(A9)




(A10)


1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896




minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A11)



(A12)

We make

119865ℎ1198961198961015840(119873minus1) = [119861ℎ119896 + 2 (119873 minus 1)119885119862ℎ1198961198961015840119899 ] (A13)














(A20)




(A21)


1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840





(A22)



(A23)




(A25)


(A26)










+ radic1198862ℎ1198662ℎ1198961198961015840


(A30)


119873sum119895=1

1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840




(A31)







(A34)


(A35)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A36)









ℎ1198662ℎ1198961198961015840119873




ℎ1198662ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A40)


119873sum119895=1

1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896

119878119895 + 119878119896 minus 119885119860ℎΔ1199032 + 119861ℎ119896119886ℎΔ119903= 119873sum119895=1



(A41)


119899 minus 2119873119899 119885119860ℎΔ1199032 + [119861ℎ119896 + 2119873119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119867119873ge 0 (A42)





(A44)


(A45)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A46)









ℎ1198652ℎ1198961198961015840119873


(A49)



ℎ1198652ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A50)


For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A51)




For formula (3)

119873sum119895=1

1198781015840119895 = 119873sum119895=1


minus 2119873119885119886ℎ119862ℎ1198961198961015840119899 Δ119903(A53)


2119873119885119899 119860ℎΔ1199032 + 2119886ℎ119873119885119862ℎ1198961198961015840119899 Δ119903 + 119867119873 ge 0 (A54)






If (2119886ℎ119873119885119862ℎ1198961198961015840119899)2 minus 4(2119873119885119860ℎ119867119873119899) ge 0




Data Availability




Acknowledgments


References



































































Journal of












Journal of







Volume 2018






Volume 2018

































(1)





1199061 119905sum119895=1

11990912119895 119905sum119895=1

11990913119895 119905sum119895=1

1199091119898119895 119898sum119896=1

119905sum119895=1

11990911198961198951199062 119905sum

119895=1

11990921119895 119905sum119895=1

11990923119895 119905sum119895=1

1199092119898119895 119898sum119896=1

119905sum119895=1


119895=1

1199091198981119895 119905sum119895=1

1199091198982119895 119905sum119895=1

1199091198983119895 119898sum119896=1

119905sum119895=1

119909119898119896119895





119873minus1sum119895=1

119878119895 le 05 minus 119885 (119873 minus 1) 119871 (2)

119873sum119895=1

119878119895 ge 05 minus 119885119873119871 (3)












119895=1



119895=1

119878119895 minus 05 + 119873119885119871 ge 0

(4)




ge 0(5)




(6)



Therefore if



(8)




(9)

















(16)




(17)















minus radic1198862ℎ1198662ℎ1198961198961015840


(24)



+ radic1198862ℎ1198662ℎ1198961198961015840


(25)



ge 0 (26)











ℎ1198662ℎ1198961198961015840119873




ℎ1198662ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(33)




119899 minus 2119873119899 119885119860ℎΔ1199032 + [119861ℎ119896 + 2119873119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119867119873ge 0 (34)




(36)


(37)








ℎ1198652ℎ1198961198961015840119873




ℎ1198652ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(41)













(46)




























Directors












chief
















44 Index Evaluation










Modular capability


Basic capability

Quality control


Service















5 Case Analysis















Q2 0741lowastlowast

Q3 0766lowastlowast

Q4 0712lowastlowast

Q5 0728lowastlowast

Q6 0734lowastlowast

Q7 0729lowastlowast

Q8 0712lowastlowast

Q9 0745lowastlowast
















times[[[[[[[[[[[[

02 05 03 004 04 02 002 03 03 0202 03 04 0103 04 03 001 03 03 03

]]]]]]]]]]]]= (02358 03696 02951 00995)





















[[[[[[[[[

04 03 02 0102 03 04 0102 05 01 0204 05 01 003 03 02 02

]]]]]]]]]


times [[[[[[[

02 04 03 0102 03 03 0203 02 03 0201 04 05 0]]]]]]]= (02049 03184 03424 01343)


times[[[[[[[[[[[[[

03 04 02 0104 04 02 002 03 03 0203 03 03 0103 04 03 002 03 03 02





= (025 0278 0289 0183)times [[[[[[

02358 03696 02951 0099503007 0368 02094 0121902049 03184 03424 0134302768 03506 02687 01039]]]]]]= (02524 03509 02801 01166)

(47)

So 1198871 = 025241198872 = 035091198873 = 028011198874 = 01166(48)


1198711 = 00080211198712 = 00178911198713 = 00089591198714 = 0026638(49)


(02484 03420 02756 01033) (50)








119895=1








11986111 11986112 11986113 11986114 11986115 11986116 11986121 11986122 11986123 11986124 11986125 11986131 11986132 11986133 11986134 11986141 11986142 11986143 11986144 11986145 119861461198811 02 04 02 02 03 01 04 02 02 04 03 02 02 03 01 03 04 02 03 03 021198812 05 04 03 03 04 03 03 03 05 05 03 04 03 02 04 04 04 03 03 04 031198813 03 02 03 04 03 03 02 04 01 01 02 03 03 03 05 02 02 03 03 03 031198814 0 0 02 01 0 03 01 01 02 0 02 01 02 02 0 01 0 02 01 0 02

119867119873 = 119873sum119895=1




(51)

So



(52)





6 Conclusions










Appendix



1198781015840119895 = sum119895 =1198961198961015840

119878119895 + 1198781015840119896 + 11987810158401198961015840= sum119895 =1198961198961015840


= 119873minus1sum119895=1



minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A1)



(A2)

We make


Then





1198781015840119895 = sum119895 =1198961198961015840

119878119895 + 1198781015840119896 + 11987810158401198961015840= sum119895 =1198961198961015840


119895=1



(A6)






Therefore if



(A9)




(A10)


1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896




minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A11)



(A12)

We make

119865ℎ1198961198961015840(119873minus1) = [119861ℎ119896 + 2 (119873 minus 1)119885119862ℎ1198961198961015840119899 ] (A13)














(A20)




(A21)


1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840





(A22)



(A23)




(A25)


(A26)










+ radic1198862ℎ1198662ℎ1198961198961015840


(A30)


119873sum119895=1

1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840




(A31)







(A34)


(A35)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A36)









ℎ1198662ℎ1198961198961015840119873




ℎ1198662ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A40)


119873sum119895=1

1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896

119878119895 + 119878119896 minus 119885119860ℎΔ1199032 + 119861ℎ119896119886ℎΔ119903= 119873sum119895=1



(A41)


119899 minus 2119873119899 119885119860ℎΔ1199032 + [119861ℎ119896 + 2119873119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119867119873ge 0 (A42)





(A44)


(A45)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A46)









ℎ1198652ℎ1198961198961015840119873


(A49)



ℎ1198652ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A50)


For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A51)




For formula (3)

119873sum119895=1

1198781015840119895 = 119873sum119895=1


minus 2119873119885119886ℎ119862ℎ1198961198961015840119899 Δ119903(A53)


2119873119885119899 119860ℎΔ1199032 + 2119886ℎ119873119885119862ℎ1198961198961015840119899 Δ119903 + 119867119873 ge 0 (A54)






If (2119886ℎ119873119885119862ℎ1198961198961015840119899)2 minus 4(2119873119885119860ℎ119867119873119899) ge 0




Data Availability




Acknowledgments


References



































































Journal of












Journal of







Volume 2018






Volume 2018



















119895=1



119895=1

119878119895 minus 05 + 119873119885119871 ge 0

(4)




ge 0(5)




(6)



Therefore if



(8)




(9)

















(16)




(17)















minus radic1198862ℎ1198662ℎ1198961198961015840


(24)



+ radic1198862ℎ1198662ℎ1198961198961015840


(25)



ge 0 (26)











ℎ1198662ℎ1198961198961015840119873




ℎ1198662ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(33)




119899 minus 2119873119899 119885119860ℎΔ1199032 + [119861ℎ119896 + 2119873119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119867119873ge 0 (34)




(36)


(37)








ℎ1198652ℎ1198961198961015840119873




ℎ1198652ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(41)













(46)




























Directors












chief
















44 Index Evaluation










Modular capability


Basic capability

Quality control


Service















5 Case Analysis















Q2 0741lowastlowast

Q3 0766lowastlowast

Q4 0712lowastlowast

Q5 0728lowastlowast

Q6 0734lowastlowast

Q7 0729lowastlowast

Q8 0712lowastlowast

Q9 0745lowastlowast
















times[[[[[[[[[[[[

02 05 03 004 04 02 002 03 03 0202 03 04 0103 04 03 001 03 03 03

]]]]]]]]]]]]= (02358 03696 02951 00995)





















[[[[[[[[[

04 03 02 0102 03 04 0102 05 01 0204 05 01 003 03 02 02

]]]]]]]]]


times [[[[[[[

02 04 03 0102 03 03 0203 02 03 0201 04 05 0]]]]]]]= (02049 03184 03424 01343)


times[[[[[[[[[[[[[

03 04 02 0104 04 02 002 03 03 0203 03 03 0103 04 03 002 03 03 02





= (025 0278 0289 0183)times [[[[[[

02358 03696 02951 0099503007 0368 02094 0121902049 03184 03424 0134302768 03506 02687 01039]]]]]]= (02524 03509 02801 01166)

(47)

So 1198871 = 025241198872 = 035091198873 = 028011198874 = 01166(48)


1198711 = 00080211198712 = 00178911198713 = 00089591198714 = 0026638(49)


(02484 03420 02756 01033) (50)








119895=1








11986111 11986112 11986113 11986114 11986115 11986116 11986121 11986122 11986123 11986124 11986125 11986131 11986132 11986133 11986134 11986141 11986142 11986143 11986144 11986145 119861461198811 02 04 02 02 03 01 04 02 02 04 03 02 02 03 01 03 04 02 03 03 021198812 05 04 03 03 04 03 03 03 05 05 03 04 03 02 04 04 04 03 03 04 031198813 03 02 03 04 03 03 02 04 01 01 02 03 03 03 05 02 02 03 03 03 031198814 0 0 02 01 0 03 01 01 02 0 02 01 02 02 0 01 0 02 01 0 02

119867119873 = 119873sum119895=1




(51)

So



(52)





6 Conclusions










Appendix



1198781015840119895 = sum119895 =1198961198961015840

119878119895 + 1198781015840119896 + 11987810158401198961015840= sum119895 =1198961198961015840


= 119873minus1sum119895=1



minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A1)



(A2)

We make


Then





1198781015840119895 = sum119895 =1198961198961015840

119878119895 + 1198781015840119896 + 11987810158401198961015840= sum119895 =1198961198961015840


119895=1



(A6)






Therefore if



(A9)




(A10)


1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896




minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A11)



(A12)

We make

119865ℎ1198961198961015840(119873minus1) = [119861ℎ119896 + 2 (119873 minus 1)119885119862ℎ1198961198961015840119899 ] (A13)














(A20)




(A21)


1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840





(A22)



(A23)




(A25)


(A26)










+ radic1198862ℎ1198662ℎ1198961198961015840


(A30)


119873sum119895=1

1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840




(A31)







(A34)


(A35)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A36)









ℎ1198662ℎ1198961198961015840119873




ℎ1198662ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A40)


119873sum119895=1

1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896

119878119895 + 119878119896 minus 119885119860ℎΔ1199032 + 119861ℎ119896119886ℎΔ119903= 119873sum119895=1



(A41)


119899 minus 2119873119899 119885119860ℎΔ1199032 + [119861ℎ119896 + 2119873119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119867119873ge 0 (A42)





(A44)


(A45)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A46)









ℎ1198652ℎ1198961198961015840119873


(A49)



ℎ1198652ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A50)


For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A51)




For formula (3)

119873sum119895=1

1198781015840119895 = 119873sum119895=1


minus 2119873119885119886ℎ119862ℎ1198961198961015840119899 Δ119903(A53)


2119873119885119899 119860ℎΔ1199032 + 2119886ℎ119873119885119862ℎ1198961198961015840119899 Δ119903 + 119867119873 ge 0 (A54)






If (2119886ℎ119873119885119862ℎ1198961198961015840119899)2 minus 4(2119873119885119860ℎ119867119873119899) ge 0




Data Availability




Acknowledgments


References



































































Journal of












Journal of







Volume 2018






Volume 2018
























(16)




(17)















minus radic1198862ℎ1198662ℎ1198961198961015840


(24)



+ radic1198862ℎ1198662ℎ1198961198961015840


(25)



ge 0 (26)











ℎ1198662ℎ1198961198961015840119873




ℎ1198662ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(33)




119899 minus 2119873119899 119885119860ℎΔ1199032 + [119861ℎ119896 + 2119873119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119867119873ge 0 (34)




(36)


(37)








ℎ1198652ℎ1198961198961015840119873




ℎ1198652ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(41)













(46)




























Directors












chief
















44 Index Evaluation










Modular capability


Basic capability

Quality control


Service















5 Case Analysis















Q2 0741lowastlowast

Q3 0766lowastlowast

Q4 0712lowastlowast

Q5 0728lowastlowast

Q6 0734lowastlowast

Q7 0729lowastlowast

Q8 0712lowastlowast

Q9 0745lowastlowast
















times[[[[[[[[[[[[

02 05 03 004 04 02 002 03 03 0202 03 04 0103 04 03 001 03 03 03

]]]]]]]]]]]]= (02358 03696 02951 00995)





















[[[[[[[[[

04 03 02 0102 03 04 0102 05 01 0204 05 01 003 03 02 02

]]]]]]]]]


times [[[[[[[

02 04 03 0102 03 03 0203 02 03 0201 04 05 0]]]]]]]= (02049 03184 03424 01343)


times[[[[[[[[[[[[[

03 04 02 0104 04 02 002 03 03 0203 03 03 0103 04 03 002 03 03 02





= (025 0278 0289 0183)times [[[[[[

02358 03696 02951 0099503007 0368 02094 0121902049 03184 03424 0134302768 03506 02687 01039]]]]]]= (02524 03509 02801 01166)

(47)

So 1198871 = 025241198872 = 035091198873 = 028011198874 = 01166(48)


1198711 = 00080211198712 = 00178911198713 = 00089591198714 = 0026638(49)


(02484 03420 02756 01033) (50)








119895=1








11986111 11986112 11986113 11986114 11986115 11986116 11986121 11986122 11986123 11986124 11986125 11986131 11986132 11986133 11986134 11986141 11986142 11986143 11986144 11986145 119861461198811 02 04 02 02 03 01 04 02 02 04 03 02 02 03 01 03 04 02 03 03 021198812 05 04 03 03 04 03 03 03 05 05 03 04 03 02 04 04 04 03 03 04 031198813 03 02 03 04 03 03 02 04 01 01 02 03 03 03 05 02 02 03 03 03 031198814 0 0 02 01 0 03 01 01 02 0 02 01 02 02 0 01 0 02 01 0 02

119867119873 = 119873sum119895=1




(51)

So



(52)





6 Conclusions










Appendix



1198781015840119895 = sum119895 =1198961198961015840

119878119895 + 1198781015840119896 + 11987810158401198961015840= sum119895 =1198961198961015840


= 119873minus1sum119895=1



minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A1)



(A2)

We make


Then





1198781015840119895 = sum119895 =1198961198961015840

119878119895 + 1198781015840119896 + 11987810158401198961015840= sum119895 =1198961198961015840


119895=1



(A6)






Therefore if



(A9)




(A10)


1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896




minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A11)



(A12)

We make

119865ℎ1198961198961015840(119873minus1) = [119861ℎ119896 + 2 (119873 minus 1)119885119862ℎ1198961198961015840119899 ] (A13)














(A20)




(A21)


1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840





(A22)



(A23)




(A25)


(A26)










+ radic1198862ℎ1198662ℎ1198961198961015840


(A30)


119873sum119895=1

1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840




(A31)







(A34)


(A35)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A36)









ℎ1198662ℎ1198961198961015840119873




ℎ1198662ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A40)


119873sum119895=1

1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896

119878119895 + 119878119896 minus 119885119860ℎΔ1199032 + 119861ℎ119896119886ℎΔ119903= 119873sum119895=1



(A41)


119899 minus 2119873119899 119885119860ℎΔ1199032 + [119861ℎ119896 + 2119873119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119867119873ge 0 (A42)





(A44)


(A45)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A46)









ℎ1198652ℎ1198961198961015840119873


(A49)



ℎ1198652ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A50)


For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A51)




For formula (3)

119873sum119895=1

1198781015840119895 = 119873sum119895=1


minus 2119873119885119886ℎ119862ℎ1198961198961015840119899 Δ119903(A53)


2119873119885119899 119860ℎΔ1199032 + 2119886ℎ119873119885119862ℎ1198961198961015840119899 Δ119903 + 119867119873 ge 0 (A54)






If (2119886ℎ119873119885119862ℎ1198961198961015840119899)2 minus 4(2119873119885119860ℎ119867119873119899) ge 0




Data Availability




Acknowledgments


References



































































Journal of












Journal of







Volume 2018






Volume 2018














minus radic1198862ℎ1198662ℎ1198961198961015840


(24)



+ radic1198862ℎ1198662ℎ1198961198961015840


(25)



ge 0 (26)











ℎ1198662ℎ1198961198961015840119873




ℎ1198662ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(33)




119899 minus 2119873119899 119885119860ℎΔ1199032 + [119861ℎ119896 + 2119873119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119867119873ge 0 (34)




(36)


(37)








ℎ1198652ℎ1198961198961015840119873




ℎ1198652ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(41)













(46)




























Directors












chief
















44 Index Evaluation










Modular capability


Basic capability

Quality control


Service















5 Case Analysis















Q2 0741lowastlowast

Q3 0766lowastlowast

Q4 0712lowastlowast

Q5 0728lowastlowast

Q6 0734lowastlowast

Q7 0729lowastlowast

Q8 0712lowastlowast

Q9 0745lowastlowast
















times[[[[[[[[[[[[

02 05 03 004 04 02 002 03 03 0202 03 04 0103 04 03 001 03 03 03

]]]]]]]]]]]]= (02358 03696 02951 00995)





















[[[[[[[[[

04 03 02 0102 03 04 0102 05 01 0204 05 01 003 03 02 02

]]]]]]]]]


times [[[[[[[

02 04 03 0102 03 03 0203 02 03 0201 04 05 0]]]]]]]= (02049 03184 03424 01343)


times[[[[[[[[[[[[[

03 04 02 0104 04 02 002 03 03 0203 03 03 0103 04 03 002 03 03 02





= (025 0278 0289 0183)times [[[[[[

02358 03696 02951 0099503007 0368 02094 0121902049 03184 03424 0134302768 03506 02687 01039]]]]]]= (02524 03509 02801 01166)

(47)

So 1198871 = 025241198872 = 035091198873 = 028011198874 = 01166(48)


1198711 = 00080211198712 = 00178911198713 = 00089591198714 = 0026638(49)


(02484 03420 02756 01033) (50)








119895=1








11986111 11986112 11986113 11986114 11986115 11986116 11986121 11986122 11986123 11986124 11986125 11986131 11986132 11986133 11986134 11986141 11986142 11986143 11986144 11986145 119861461198811 02 04 02 02 03 01 04 02 02 04 03 02 02 03 01 03 04 02 03 03 021198812 05 04 03 03 04 03 03 03 05 05 03 04 03 02 04 04 04 03 03 04 031198813 03 02 03 04 03 03 02 04 01 01 02 03 03 03 05 02 02 03 03 03 031198814 0 0 02 01 0 03 01 01 02 0 02 01 02 02 0 01 0 02 01 0 02

119867119873 = 119873sum119895=1




(51)

So



(52)





6 Conclusions










Appendix



1198781015840119895 = sum119895 =1198961198961015840

119878119895 + 1198781015840119896 + 11987810158401198961015840= sum119895 =1198961198961015840


= 119873minus1sum119895=1



minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A1)



(A2)

We make


Then





1198781015840119895 = sum119895 =1198961198961015840

119878119895 + 1198781015840119896 + 11987810158401198961015840= sum119895 =1198961198961015840


119895=1



(A6)






Therefore if



(A9)




(A10)


1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896




minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A11)



(A12)

We make

119865ℎ1198961198961015840(119873minus1) = [119861ℎ119896 + 2 (119873 minus 1)119885119862ℎ1198961198961015840119899 ] (A13)














(A20)




(A21)


1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840





(A22)



(A23)




(A25)


(A26)










+ radic1198862ℎ1198662ℎ1198961198961015840


(A30)


119873sum119895=1

1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840




(A31)







(A34)


(A35)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A36)









ℎ1198662ℎ1198961198961015840119873




ℎ1198662ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A40)


119873sum119895=1

1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896

119878119895 + 119878119896 minus 119885119860ℎΔ1199032 + 119861ℎ119896119886ℎΔ119903= 119873sum119895=1



(A41)


119899 minus 2119873119899 119885119860ℎΔ1199032 + [119861ℎ119896 + 2119873119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119867119873ge 0 (A42)





(A44)


(A45)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A46)









ℎ1198652ℎ1198961198961015840119873


(A49)



ℎ1198652ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A50)


For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A51)




For formula (3)

119873sum119895=1

1198781015840119895 = 119873sum119895=1


minus 2119873119885119886ℎ119862ℎ1198961198961015840119899 Δ119903(A53)


2119873119885119899 119860ℎΔ1199032 + 2119886ℎ119873119885119862ℎ1198961198961015840119899 Δ119903 + 119867119873 ge 0 (A54)






If (2119886ℎ119873119885119862ℎ1198961198961015840119899)2 minus 4(2119873119885119860ℎ119867119873119899) ge 0




Data Availability




Acknowledgments


References



































































Journal of












Journal of







Volume 2018






Volume 2018











119899 minus 2119873119899 119885119860ℎΔ1199032 + [119861ℎ119896 + 2119873119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119867119873ge 0 (34)




(36)


(37)








ℎ1198652ℎ1198961198961015840119873




ℎ1198652ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(41)













(46)




























Directors












chief
















44 Index Evaluation










Modular capability


Basic capability

Quality control


Service















5 Case Analysis















Q2 0741lowastlowast

Q3 0766lowastlowast

Q4 0712lowastlowast

Q5 0728lowastlowast

Q6 0734lowastlowast

Q7 0729lowastlowast

Q8 0712lowastlowast

Q9 0745lowastlowast
















times[[[[[[[[[[[[

02 05 03 004 04 02 002 03 03 0202 03 04 0103 04 03 001 03 03 03

]]]]]]]]]]]]= (02358 03696 02951 00995)





















[[[[[[[[[

04 03 02 0102 03 04 0102 05 01 0204 05 01 003 03 02 02

]]]]]]]]]


times [[[[[[[

02 04 03 0102 03 03 0203 02 03 0201 04 05 0]]]]]]]= (02049 03184 03424 01343)


times[[[[[[[[[[[[[

03 04 02 0104 04 02 002 03 03 0203 03 03 0103 04 03 002 03 03 02





= (025 0278 0289 0183)times [[[[[[

02358 03696 02951 0099503007 0368 02094 0121902049 03184 03424 0134302768 03506 02687 01039]]]]]]= (02524 03509 02801 01166)

(47)

So 1198871 = 025241198872 = 035091198873 = 028011198874 = 01166(48)


1198711 = 00080211198712 = 00178911198713 = 00089591198714 = 0026638(49)


(02484 03420 02756 01033) (50)








119895=1








11986111 11986112 11986113 11986114 11986115 11986116 11986121 11986122 11986123 11986124 11986125 11986131 11986132 11986133 11986134 11986141 11986142 11986143 11986144 11986145 119861461198811 02 04 02 02 03 01 04 02 02 04 03 02 02 03 01 03 04 02 03 03 021198812 05 04 03 03 04 03 03 03 05 05 03 04 03 02 04 04 04 03 03 04 031198813 03 02 03 04 03 03 02 04 01 01 02 03 03 03 05 02 02 03 03 03 031198814 0 0 02 01 0 03 01 01 02 0 02 01 02 02 0 01 0 02 01 0 02

119867119873 = 119873sum119895=1




(51)

So



(52)





6 Conclusions










Appendix



1198781015840119895 = sum119895 =1198961198961015840

119878119895 + 1198781015840119896 + 11987810158401198961015840= sum119895 =1198961198961015840


= 119873minus1sum119895=1



minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A1)



(A2)

We make


Then





1198781015840119895 = sum119895 =1198961198961015840

119878119895 + 1198781015840119896 + 11987810158401198961015840= sum119895 =1198961198961015840


119895=1



(A6)






Therefore if



(A9)




(A10)


1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896




minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A11)



(A12)

We make

119865ℎ1198961198961015840(119873minus1) = [119861ℎ119896 + 2 (119873 minus 1)119885119862ℎ1198961198961015840119899 ] (A13)














(A20)




(A21)


1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840





(A22)



(A23)




(A25)


(A26)










+ radic1198862ℎ1198662ℎ1198961198961015840


(A30)


119873sum119895=1

1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840




(A31)







(A34)


(A35)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A36)









ℎ1198662ℎ1198961198961015840119873




ℎ1198662ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A40)


119873sum119895=1

1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896

119878119895 + 119878119896 minus 119885119860ℎΔ1199032 + 119861ℎ119896119886ℎΔ119903= 119873sum119895=1



(A41)


119899 minus 2119873119899 119885119860ℎΔ1199032 + [119861ℎ119896 + 2119873119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119867119873ge 0 (A42)





(A44)


(A45)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A46)









ℎ1198652ℎ1198961198961015840119873


(A49)



ℎ1198652ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A50)


For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A51)




For formula (3)

119873sum119895=1

1198781015840119895 = 119873sum119895=1


minus 2119873119885119886ℎ119862ℎ1198961198961015840119899 Δ119903(A53)


2119873119885119899 119860ℎΔ1199032 + 2119886ℎ119873119885119862ℎ1198961198961015840119899 Δ119903 + 119867119873 ge 0 (A54)






If (2119886ℎ119873119885119862ℎ1198961198961015840119899)2 minus 4(2119873119885119860ℎ119867119873119899) ge 0




Data Availability




Acknowledgments


References



































































Journal of












Journal of







Volume 2018






Volume 2018



































Directors












chief
















44 Index Evaluation










Modular capability


Basic capability

Quality control


Service















5 Case Analysis















Q2 0741lowastlowast

Q3 0766lowastlowast

Q4 0712lowastlowast

Q5 0728lowastlowast

Q6 0734lowastlowast

Q7 0729lowastlowast

Q8 0712lowastlowast

Q9 0745lowastlowast
















times[[[[[[[[[[[[

02 05 03 004 04 02 002 03 03 0202 03 04 0103 04 03 001 03 03 03

]]]]]]]]]]]]= (02358 03696 02951 00995)





















[[[[[[[[[

04 03 02 0102 03 04 0102 05 01 0204 05 01 003 03 02 02

]]]]]]]]]


times [[[[[[[

02 04 03 0102 03 03 0203 02 03 0201 04 05 0]]]]]]]= (02049 03184 03424 01343)


times[[[[[[[[[[[[[

03 04 02 0104 04 02 002 03 03 0203 03 03 0103 04 03 002 03 03 02





= (025 0278 0289 0183)times [[[[[[

02358 03696 02951 0099503007 0368 02094 0121902049 03184 03424 0134302768 03506 02687 01039]]]]]]= (02524 03509 02801 01166)

(47)

So 1198871 = 025241198872 = 035091198873 = 028011198874 = 01166(48)


1198711 = 00080211198712 = 00178911198713 = 00089591198714 = 0026638(49)


(02484 03420 02756 01033) (50)








119895=1








11986111 11986112 11986113 11986114 11986115 11986116 11986121 11986122 11986123 11986124 11986125 11986131 11986132 11986133 11986134 11986141 11986142 11986143 11986144 11986145 119861461198811 02 04 02 02 03 01 04 02 02 04 03 02 02 03 01 03 04 02 03 03 021198812 05 04 03 03 04 03 03 03 05 05 03 04 03 02 04 04 04 03 03 04 031198813 03 02 03 04 03 03 02 04 01 01 02 03 03 03 05 02 02 03 03 03 031198814 0 0 02 01 0 03 01 01 02 0 02 01 02 02 0 01 0 02 01 0 02

119867119873 = 119873sum119895=1




(51)

So



(52)





6 Conclusions










Appendix



1198781015840119895 = sum119895 =1198961198961015840

119878119895 + 1198781015840119896 + 11987810158401198961015840= sum119895 =1198961198961015840


= 119873minus1sum119895=1



minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A1)



(A2)

We make


Then





1198781015840119895 = sum119895 =1198961198961015840

119878119895 + 1198781015840119896 + 11987810158401198961015840= sum119895 =1198961198961015840


119895=1



(A6)






Therefore if



(A9)




(A10)


1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896




minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A11)



(A12)

We make

119865ℎ1198961198961015840(119873minus1) = [119861ℎ119896 + 2 (119873 minus 1)119885119862ℎ1198961198961015840119899 ] (A13)














(A20)




(A21)


1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840





(A22)



(A23)




(A25)


(A26)










+ radic1198862ℎ1198662ℎ1198961198961015840


(A30)


119873sum119895=1

1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840




(A31)







(A34)


(A35)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A36)









ℎ1198662ℎ1198961198961015840119873




ℎ1198662ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A40)


119873sum119895=1

1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896

119878119895 + 119878119896 minus 119885119860ℎΔ1199032 + 119861ℎ119896119886ℎΔ119903= 119873sum119895=1



(A41)


119899 minus 2119873119899 119885119860ℎΔ1199032 + [119861ℎ119896 + 2119873119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119867119873ge 0 (A42)





(A44)


(A45)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A46)









ℎ1198652ℎ1198961198961015840119873


(A49)



ℎ1198652ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A50)


For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A51)




For formula (3)

119873sum119895=1

1198781015840119895 = 119873sum119895=1


minus 2119873119885119886ℎ119862ℎ1198961198961015840119899 Δ119903(A53)


2119873119885119899 119860ℎΔ1199032 + 2119886ℎ119873119885119862ℎ1198961198961015840119899 Δ119903 + 119867119873 ge 0 (A54)






If (2119886ℎ119873119885119862ℎ1198961198961015840119899)2 minus 4(2119873119885119860ℎ119867119873119899) ge 0




Data Availability




Acknowledgments


References



































































Journal of












Journal of







Volume 2018






Volume 2018
















44 Index Evaluation










Modular capability


Basic capability

Quality control


Service















5 Case Analysis















Q2 0741lowastlowast

Q3 0766lowastlowast

Q4 0712lowastlowast

Q5 0728lowastlowast

Q6 0734lowastlowast

Q7 0729lowastlowast

Q8 0712lowastlowast

Q9 0745lowastlowast
















times[[[[[[[[[[[[

02 05 03 004 04 02 002 03 03 0202 03 04 0103 04 03 001 03 03 03

]]]]]]]]]]]]= (02358 03696 02951 00995)





















[[[[[[[[[

04 03 02 0102 03 04 0102 05 01 0204 05 01 003 03 02 02

]]]]]]]]]


times [[[[[[[

02 04 03 0102 03 03 0203 02 03 0201 04 05 0]]]]]]]= (02049 03184 03424 01343)


times[[[[[[[[[[[[[

03 04 02 0104 04 02 002 03 03 0203 03 03 0103 04 03 002 03 03 02





= (025 0278 0289 0183)times [[[[[[

02358 03696 02951 0099503007 0368 02094 0121902049 03184 03424 0134302768 03506 02687 01039]]]]]]= (02524 03509 02801 01166)

(47)

So 1198871 = 025241198872 = 035091198873 = 028011198874 = 01166(48)


1198711 = 00080211198712 = 00178911198713 = 00089591198714 = 0026638(49)


(02484 03420 02756 01033) (50)








119895=1








11986111 11986112 11986113 11986114 11986115 11986116 11986121 11986122 11986123 11986124 11986125 11986131 11986132 11986133 11986134 11986141 11986142 11986143 11986144 11986145 119861461198811 02 04 02 02 03 01 04 02 02 04 03 02 02 03 01 03 04 02 03 03 021198812 05 04 03 03 04 03 03 03 05 05 03 04 03 02 04 04 04 03 03 04 031198813 03 02 03 04 03 03 02 04 01 01 02 03 03 03 05 02 02 03 03 03 031198814 0 0 02 01 0 03 01 01 02 0 02 01 02 02 0 01 0 02 01 0 02

119867119873 = 119873sum119895=1




(51)

So



(52)





6 Conclusions










Appendix



1198781015840119895 = sum119895 =1198961198961015840

119878119895 + 1198781015840119896 + 11987810158401198961015840= sum119895 =1198961198961015840


= 119873minus1sum119895=1



minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A1)



(A2)

We make


Then





1198781015840119895 = sum119895 =1198961198961015840

119878119895 + 1198781015840119896 + 11987810158401198961015840= sum119895 =1198961198961015840


119895=1



(A6)






Therefore if



(A9)




(A10)


1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896




minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A11)



(A12)

We make

119865ℎ1198961198961015840(119873minus1) = [119861ℎ119896 + 2 (119873 minus 1)119885119862ℎ1198961198961015840119899 ] (A13)














(A20)




(A21)


1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840





(A22)



(A23)




(A25)


(A26)










+ radic1198862ℎ1198662ℎ1198961198961015840


(A30)


119873sum119895=1

1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840




(A31)







(A34)


(A35)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A36)









ℎ1198662ℎ1198961198961015840119873




ℎ1198662ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A40)


119873sum119895=1

1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896

119878119895 + 119878119896 minus 119885119860ℎΔ1199032 + 119861ℎ119896119886ℎΔ119903= 119873sum119895=1



(A41)


119899 minus 2119873119899 119885119860ℎΔ1199032 + [119861ℎ119896 + 2119873119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119867119873ge 0 (A42)





(A44)


(A45)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A46)









ℎ1198652ℎ1198961198961015840119873


(A49)



ℎ1198652ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A50)


For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A51)




For formula (3)

119873sum119895=1

1198781015840119895 = 119873sum119895=1


minus 2119873119885119886ℎ119862ℎ1198961198961015840119899 Δ119903(A53)


2119873119885119899 119860ℎΔ1199032 + 2119886ℎ119873119885119862ℎ1198961198961015840119899 Δ119903 + 119867119873 ge 0 (A54)






If (2119886ℎ119873119885119862ℎ1198961198961015840119899)2 minus 4(2119873119885119860ℎ119867119873119899) ge 0




Data Availability




Acknowledgments


References



































































Journal of












Journal of







Volume 2018






Volume 2018











Modular capability


Basic capability

Quality control


Service















5 Case Analysis















Q2 0741lowastlowast

Q3 0766lowastlowast

Q4 0712lowastlowast

Q5 0728lowastlowast

Q6 0734lowastlowast

Q7 0729lowastlowast

Q8 0712lowastlowast

Q9 0745lowastlowast
















times[[[[[[[[[[[[

02 05 03 004 04 02 002 03 03 0202 03 04 0103 04 03 001 03 03 03

]]]]]]]]]]]]= (02358 03696 02951 00995)





















[[[[[[[[[

04 03 02 0102 03 04 0102 05 01 0204 05 01 003 03 02 02

]]]]]]]]]


times [[[[[[[

02 04 03 0102 03 03 0203 02 03 0201 04 05 0]]]]]]]= (02049 03184 03424 01343)


times[[[[[[[[[[[[[

03 04 02 0104 04 02 002 03 03 0203 03 03 0103 04 03 002 03 03 02





= (025 0278 0289 0183)times [[[[[[

02358 03696 02951 0099503007 0368 02094 0121902049 03184 03424 0134302768 03506 02687 01039]]]]]]= (02524 03509 02801 01166)

(47)

So 1198871 = 025241198872 = 035091198873 = 028011198874 = 01166(48)


1198711 = 00080211198712 = 00178911198713 = 00089591198714 = 0026638(49)


(02484 03420 02756 01033) (50)








119895=1








11986111 11986112 11986113 11986114 11986115 11986116 11986121 11986122 11986123 11986124 11986125 11986131 11986132 11986133 11986134 11986141 11986142 11986143 11986144 11986145 119861461198811 02 04 02 02 03 01 04 02 02 04 03 02 02 03 01 03 04 02 03 03 021198812 05 04 03 03 04 03 03 03 05 05 03 04 03 02 04 04 04 03 03 04 031198813 03 02 03 04 03 03 02 04 01 01 02 03 03 03 05 02 02 03 03 03 031198814 0 0 02 01 0 03 01 01 02 0 02 01 02 02 0 01 0 02 01 0 02

119867119873 = 119873sum119895=1




(51)

So



(52)





6 Conclusions










Appendix



1198781015840119895 = sum119895 =1198961198961015840

119878119895 + 1198781015840119896 + 11987810158401198961015840= sum119895 =1198961198961015840


= 119873minus1sum119895=1



minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A1)



(A2)

We make


Then





1198781015840119895 = sum119895 =1198961198961015840

119878119895 + 1198781015840119896 + 11987810158401198961015840= sum119895 =1198961198961015840


119895=1



(A6)






Therefore if



(A9)




(A10)


1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896




minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A11)



(A12)

We make

119865ℎ1198961198961015840(119873minus1) = [119861ℎ119896 + 2 (119873 minus 1)119885119862ℎ1198961198961015840119899 ] (A13)














(A20)




(A21)


1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840





(A22)



(A23)




(A25)


(A26)










+ radic1198862ℎ1198662ℎ1198961198961015840


(A30)


119873sum119895=1

1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840




(A31)







(A34)


(A35)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A36)









ℎ1198662ℎ1198961198961015840119873




ℎ1198662ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A40)


119873sum119895=1

1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896

119878119895 + 119878119896 minus 119885119860ℎΔ1199032 + 119861ℎ119896119886ℎΔ119903= 119873sum119895=1



(A41)


119899 minus 2119873119899 119885119860ℎΔ1199032 + [119861ℎ119896 + 2119873119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119867119873ge 0 (A42)





(A44)


(A45)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A46)









ℎ1198652ℎ1198961198961015840119873


(A49)



ℎ1198652ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A50)


For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A51)




For formula (3)

119873sum119895=1

1198781015840119895 = 119873sum119895=1


minus 2119873119885119886ℎ119862ℎ1198961198961015840119899 Δ119903(A53)


2119873119885119899 119860ℎΔ1199032 + 2119886ℎ119873119885119862ℎ1198961198961015840119899 Δ119903 + 119867119873 ge 0 (A54)






If (2119886ℎ119873119885119862ℎ1198961198961015840119899)2 minus 4(2119873119885119860ℎ119867119873119899) ge 0




Data Availability




Acknowledgments


References



































































Journal of












Journal of







Volume 2018






Volume 2018





















Q2 0741lowastlowast

Q3 0766lowastlowast

Q4 0712lowastlowast

Q5 0728lowastlowast

Q6 0734lowastlowast

Q7 0729lowastlowast

Q8 0712lowastlowast

Q9 0745lowastlowast
















times[[[[[[[[[[[[

02 05 03 004 04 02 002 03 03 0202 03 04 0103 04 03 001 03 03 03

]]]]]]]]]]]]= (02358 03696 02951 00995)





















[[[[[[[[[

04 03 02 0102 03 04 0102 05 01 0204 05 01 003 03 02 02

]]]]]]]]]


times [[[[[[[

02 04 03 0102 03 03 0203 02 03 0201 04 05 0]]]]]]]= (02049 03184 03424 01343)


times[[[[[[[[[[[[[

03 04 02 0104 04 02 002 03 03 0203 03 03 0103 04 03 002 03 03 02





= (025 0278 0289 0183)times [[[[[[

02358 03696 02951 0099503007 0368 02094 0121902049 03184 03424 0134302768 03506 02687 01039]]]]]]= (02524 03509 02801 01166)

(47)

So 1198871 = 025241198872 = 035091198873 = 028011198874 = 01166(48)


1198711 = 00080211198712 = 00178911198713 = 00089591198714 = 0026638(49)


(02484 03420 02756 01033) (50)








119895=1








11986111 11986112 11986113 11986114 11986115 11986116 11986121 11986122 11986123 11986124 11986125 11986131 11986132 11986133 11986134 11986141 11986142 11986143 11986144 11986145 119861461198811 02 04 02 02 03 01 04 02 02 04 03 02 02 03 01 03 04 02 03 03 021198812 05 04 03 03 04 03 03 03 05 05 03 04 03 02 04 04 04 03 03 04 031198813 03 02 03 04 03 03 02 04 01 01 02 03 03 03 05 02 02 03 03 03 031198814 0 0 02 01 0 03 01 01 02 0 02 01 02 02 0 01 0 02 01 0 02

119867119873 = 119873sum119895=1




(51)

So



(52)





6 Conclusions










Appendix



1198781015840119895 = sum119895 =1198961198961015840

119878119895 + 1198781015840119896 + 11987810158401198961015840= sum119895 =1198961198961015840


= 119873minus1sum119895=1



minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A1)



(A2)

We make


Then





1198781015840119895 = sum119895 =1198961198961015840

119878119895 + 1198781015840119896 + 11987810158401198961015840= sum119895 =1198961198961015840


119895=1



(A6)






Therefore if



(A9)




(A10)


1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896




minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A11)



(A12)

We make

119865ℎ1198961198961015840(119873minus1) = [119861ℎ119896 + 2 (119873 minus 1)119885119862ℎ1198961198961015840119899 ] (A13)














(A20)




(A21)


1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840





(A22)



(A23)




(A25)


(A26)










+ radic1198862ℎ1198662ℎ1198961198961015840


(A30)


119873sum119895=1

1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840




(A31)







(A34)


(A35)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A36)









ℎ1198662ℎ1198961198961015840119873




ℎ1198662ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A40)


119873sum119895=1

1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896

119878119895 + 119878119896 minus 119885119860ℎΔ1199032 + 119861ℎ119896119886ℎΔ119903= 119873sum119895=1



(A41)


119899 minus 2119873119899 119885119860ℎΔ1199032 + [119861ℎ119896 + 2119873119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119867119873ge 0 (A42)





(A44)


(A45)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A46)









ℎ1198652ℎ1198961198961015840119873


(A49)



ℎ1198652ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A50)


For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A51)




For formula (3)

119873sum119895=1

1198781015840119895 = 119873sum119895=1


minus 2119873119885119886ℎ119862ℎ1198961198961015840119899 Δ119903(A53)


2119873119885119899 119860ℎΔ1199032 + 2119886ℎ119873119885119862ℎ1198961198961015840119899 Δ119903 + 119867119873 ge 0 (A54)






If (2119886ℎ119873119885119862ℎ1198961198961015840119899)2 minus 4(2119873119885119860ℎ119867119873119899) ge 0




Data Availability




Acknowledgments


References



































































Journal of












Journal of







Volume 2018






Volume 2018




























[[[[[[[[[

04 03 02 0102 03 04 0102 05 01 0204 05 01 003 03 02 02

]]]]]]]]]


times [[[[[[[

02 04 03 0102 03 03 0203 02 03 0201 04 05 0]]]]]]]= (02049 03184 03424 01343)


times[[[[[[[[[[[[[

03 04 02 0104 04 02 002 03 03 0203 03 03 0103 04 03 002 03 03 02





= (025 0278 0289 0183)times [[[[[[

02358 03696 02951 0099503007 0368 02094 0121902049 03184 03424 0134302768 03506 02687 01039]]]]]]= (02524 03509 02801 01166)

(47)

So 1198871 = 025241198872 = 035091198873 = 028011198874 = 01166(48)


1198711 = 00080211198712 = 00178911198713 = 00089591198714 = 0026638(49)


(02484 03420 02756 01033) (50)








119895=1








11986111 11986112 11986113 11986114 11986115 11986116 11986121 11986122 11986123 11986124 11986125 11986131 11986132 11986133 11986134 11986141 11986142 11986143 11986144 11986145 119861461198811 02 04 02 02 03 01 04 02 02 04 03 02 02 03 01 03 04 02 03 03 021198812 05 04 03 03 04 03 03 03 05 05 03 04 03 02 04 04 04 03 03 04 031198813 03 02 03 04 03 03 02 04 01 01 02 03 03 03 05 02 02 03 03 03 031198814 0 0 02 01 0 03 01 01 02 0 02 01 02 02 0 01 0 02 01 0 02

119867119873 = 119873sum119895=1




(51)

So



(52)





6 Conclusions










Appendix



1198781015840119895 = sum119895 =1198961198961015840

119878119895 + 1198781015840119896 + 11987810158401198961015840= sum119895 =1198961198961015840


= 119873minus1sum119895=1



minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A1)



(A2)

We make


Then





1198781015840119895 = sum119895 =1198961198961015840

119878119895 + 1198781015840119896 + 11987810158401198961015840= sum119895 =1198961198961015840


119895=1



(A6)






Therefore if



(A9)




(A10)


1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896




minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A11)



(A12)

We make

119865ℎ1198961198961015840(119873minus1) = [119861ℎ119896 + 2 (119873 minus 1)119885119862ℎ1198961198961015840119899 ] (A13)














(A20)




(A21)


1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840





(A22)



(A23)




(A25)


(A26)










+ radic1198862ℎ1198662ℎ1198961198961015840


(A30)


119873sum119895=1

1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840




(A31)







(A34)


(A35)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A36)









ℎ1198662ℎ1198961198961015840119873




ℎ1198662ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A40)


119873sum119895=1

1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896

119878119895 + 119878119896 minus 119885119860ℎΔ1199032 + 119861ℎ119896119886ℎΔ119903= 119873sum119895=1



(A41)


119899 minus 2119873119899 119885119860ℎΔ1199032 + [119861ℎ119896 + 2119873119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119867119873ge 0 (A42)





(A44)


(A45)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A46)









ℎ1198652ℎ1198961198961015840119873


(A49)



ℎ1198652ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A50)


For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A51)




For formula (3)

119873sum119895=1

1198781015840119895 = 119873sum119895=1


minus 2119873119885119886ℎ119862ℎ1198961198961015840119899 Δ119903(A53)


2119873119885119899 119860ℎΔ1199032 + 2119886ℎ119873119885119862ℎ1198961198961015840119899 Δ119903 + 119867119873 ge 0 (A54)






If (2119886ℎ119873119885119862ℎ1198961198961015840119899)2 minus 4(2119873119885119860ℎ119867119873119899) ge 0




Data Availability




Acknowledgments


References



































































Journal of












Journal of







Volume 2018






Volume 2018











= (025 0278 0289 0183)times [[[[[[

02358 03696 02951 0099503007 0368 02094 0121902049 03184 03424 0134302768 03506 02687 01039]]]]]]= (02524 03509 02801 01166)

(47)

So 1198871 = 025241198872 = 035091198873 = 028011198874 = 01166(48)


1198711 = 00080211198712 = 00178911198713 = 00089591198714 = 0026638(49)


(02484 03420 02756 01033) (50)








119895=1








11986111 11986112 11986113 11986114 11986115 11986116 11986121 11986122 11986123 11986124 11986125 11986131 11986132 11986133 11986134 11986141 11986142 11986143 11986144 11986145 119861461198811 02 04 02 02 03 01 04 02 02 04 03 02 02 03 01 03 04 02 03 03 021198812 05 04 03 03 04 03 03 03 05 05 03 04 03 02 04 04 04 03 03 04 031198813 03 02 03 04 03 03 02 04 01 01 02 03 03 03 05 02 02 03 03 03 031198814 0 0 02 01 0 03 01 01 02 0 02 01 02 02 0 01 0 02 01 0 02

119867119873 = 119873sum119895=1




(51)

So



(52)





6 Conclusions










Appendix



1198781015840119895 = sum119895 =1198961198961015840

119878119895 + 1198781015840119896 + 11987810158401198961015840= sum119895 =1198961198961015840


= 119873minus1sum119895=1



minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A1)



(A2)

We make


Then





1198781015840119895 = sum119895 =1198961198961015840

119878119895 + 1198781015840119896 + 11987810158401198961015840= sum119895 =1198961198961015840


119895=1



(A6)






Therefore if



(A9)




(A10)


1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896




minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A11)



(A12)

We make

119865ℎ1198961198961015840(119873minus1) = [119861ℎ119896 + 2 (119873 minus 1)119885119862ℎ1198961198961015840119899 ] (A13)














(A20)




(A21)


1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840





(A22)



(A23)




(A25)


(A26)










+ radic1198862ℎ1198662ℎ1198961198961015840


(A30)


119873sum119895=1

1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840




(A31)







(A34)


(A35)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A36)









ℎ1198662ℎ1198961198961015840119873




ℎ1198662ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A40)


119873sum119895=1

1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896

119878119895 + 119878119896 minus 119885119860ℎΔ1199032 + 119861ℎ119896119886ℎΔ119903= 119873sum119895=1



(A41)


119899 minus 2119873119899 119885119860ℎΔ1199032 + [119861ℎ119896 + 2119873119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119867119873ge 0 (A42)





(A44)


(A45)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A46)









ℎ1198652ℎ1198961198961015840119873


(A49)



ℎ1198652ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A50)


For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A51)




For formula (3)

119873sum119895=1

1198781015840119895 = 119873sum119895=1


minus 2119873119885119886ℎ119862ℎ1198961198961015840119899 Δ119903(A53)


2119873119885119899 119860ℎΔ1199032 + 2119886ℎ119873119885119862ℎ1198961198961015840119899 Δ119903 + 119867119873 ge 0 (A54)






If (2119886ℎ119873119885119862ℎ1198961198961015840119899)2 minus 4(2119873119885119860ℎ119867119873119899) ge 0




Data Availability




Acknowledgments


References



































































Journal of












Journal of







Volume 2018






Volume 2018










11986111 11986112 11986113 11986114 11986115 11986116 11986121 11986122 11986123 11986124 11986125 11986131 11986132 11986133 11986134 11986141 11986142 11986143 11986144 11986145 119861461198811 02 04 02 02 03 01 04 02 02 04 03 02 02 03 01 03 04 02 03 03 021198812 05 04 03 03 04 03 03 03 05 05 03 04 03 02 04 04 04 03 03 04 031198813 03 02 03 04 03 03 02 04 01 01 02 03 03 03 05 02 02 03 03 03 031198814 0 0 02 01 0 03 01 01 02 0 02 01 02 02 0 01 0 02 01 0 02

119867119873 = 119873sum119895=1




(51)

So



(52)





6 Conclusions










Appendix



1198781015840119895 = sum119895 =1198961198961015840

119878119895 + 1198781015840119896 + 11987810158401198961015840= sum119895 =1198961198961015840


= 119873minus1sum119895=1



minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A1)



(A2)

We make


Then





1198781015840119895 = sum119895 =1198961198961015840

119878119895 + 1198781015840119896 + 11987810158401198961015840= sum119895 =1198961198961015840


119895=1



(A6)






Therefore if



(A9)




(A10)


1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896




minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A11)



(A12)

We make

119865ℎ1198961198961015840(119873minus1) = [119861ℎ119896 + 2 (119873 minus 1)119885119862ℎ1198961198961015840119899 ] (A13)














(A20)




(A21)


1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840





(A22)



(A23)




(A25)


(A26)










+ radic1198862ℎ1198662ℎ1198961198961015840


(A30)


119873sum119895=1

1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840




(A31)







(A34)


(A35)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A36)









ℎ1198662ℎ1198961198961015840119873




ℎ1198662ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A40)


119873sum119895=1

1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896

119878119895 + 119878119896 minus 119885119860ℎΔ1199032 + 119861ℎ119896119886ℎΔ119903= 119873sum119895=1



(A41)


119899 minus 2119873119899 119885119860ℎΔ1199032 + [119861ℎ119896 + 2119873119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119867119873ge 0 (A42)





(A44)


(A45)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A46)









ℎ1198652ℎ1198961198961015840119873


(A49)



ℎ1198652ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A50)


For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A51)




For formula (3)

119873sum119895=1

1198781015840119895 = 119873sum119895=1


minus 2119873119885119886ℎ119862ℎ1198961198961015840119899 Δ119903(A53)


2119873119885119899 119860ℎΔ1199032 + 2119886ℎ119873119885119862ℎ1198961198961015840119899 Δ119903 + 119867119873 ge 0 (A54)






If (2119886ℎ119873119885119862ℎ1198961198961015840119899)2 minus 4(2119873119885119860ℎ119867119873119899) ge 0




Data Availability




Acknowledgments


References



































































Journal of












Journal of







Volume 2018






Volume 2018














Appendix



1198781015840119895 = sum119895 =1198961198961015840

119878119895 + 1198781015840119896 + 11987810158401198961015840= sum119895 =1198961198961015840


= 119873minus1sum119895=1



minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A1)



(A2)

We make


Then





1198781015840119895 = sum119895 =1198961198961015840

119878119895 + 1198781015840119896 + 11987810158401198961015840= sum119895 =1198961198961015840


119895=1



(A6)






Therefore if



(A9)




(A10)


1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896




minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A11)



(A12)

We make

119865ℎ1198961198961015840(119873minus1) = [119861ℎ119896 + 2 (119873 minus 1)119885119862ℎ1198961198961015840119899 ] (A13)














(A20)




(A21)


1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840





(A22)



(A23)




(A25)


(A26)










+ radic1198862ℎ1198662ℎ1198961198961015840


(A30)


119873sum119895=1

1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840




(A31)







(A34)


(A35)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A36)









ℎ1198662ℎ1198961198961015840119873




ℎ1198662ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A40)


119873sum119895=1

1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896

119878119895 + 119878119896 minus 119885119860ℎΔ1199032 + 119861ℎ119896119886ℎΔ119903= 119873sum119895=1



(A41)


119899 minus 2119873119899 119885119860ℎΔ1199032 + [119861ℎ119896 + 2119873119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119867119873ge 0 (A42)





(A44)


(A45)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A46)









ℎ1198652ℎ1198961198961015840119873


(A49)



ℎ1198652ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A50)


For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A51)




For formula (3)

119873sum119895=1

1198781015840119895 = 119873sum119895=1


minus 2119873119885119886ℎ119862ℎ1198961198961015840119899 Δ119903(A53)


2119873119885119899 119860ℎΔ1199032 + 2119886ℎ119873119885119862ℎ1198961198961015840119899 Δ119903 + 119867119873 ge 0 (A54)






If (2119886ℎ119873119885119862ℎ1198961198961015840119899)2 minus 4(2119873119885119860ℎ119867119873119899) ge 0




Data Availability




Acknowledgments


References



































































Journal of












Journal of







Volume 2018






Volume 2018











Therefore if



(A9)




(A10)


1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896




minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A11)



(A12)

We make

119865ℎ1198961198961015840(119873minus1) = [119861ℎ119896 + 2 (119873 minus 1)119885119862ℎ1198961198961015840119899 ] (A13)














(A20)




(A21)


1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840





(A22)



(A23)




(A25)


(A26)










+ radic1198862ℎ1198662ℎ1198961198961015840


(A30)


119873sum119895=1

1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840




(A31)







(A34)


(A35)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A36)









ℎ1198662ℎ1198961198961015840119873




ℎ1198662ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A40)


119873sum119895=1

1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896

119878119895 + 119878119896 minus 119885119860ℎΔ1199032 + 119861ℎ119896119886ℎΔ119903= 119873sum119895=1



(A41)


119899 minus 2119873119899 119885119860ℎΔ1199032 + [119861ℎ119896 + 2119873119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119867119873ge 0 (A42)





(A44)


(A45)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A46)









ℎ1198652ℎ1198961198961015840119873


(A49)



ℎ1198652ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A50)


For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A51)




For formula (3)

119873sum119895=1

1198781015840119895 = 119873sum119895=1


minus 2119873119885119886ℎ119862ℎ1198961198961015840119899 Δ119903(A53)


2119873119885119899 119860ℎΔ1199032 + 2119886ℎ119873119885119862ℎ1198961198961015840119899 Δ119903 + 119867119873 ge 0 (A54)






If (2119886ℎ119873119885119862ℎ1198961198961015840119899)2 minus 4(2119873119885119860ℎ119867119873119899) ge 0




Data Availability




Acknowledgments


References



































































Journal of












Journal of







Volume 2018






Volume 2018












(A20)




(A21)


1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840





(A22)



(A23)




(A25)


(A26)










+ radic1198862ℎ1198662ℎ1198961198961015840


(A30)


119873sum119895=1

1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840




(A31)







(A34)


(A35)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A36)









ℎ1198662ℎ1198961198961015840119873




ℎ1198662ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A40)


119873sum119895=1

1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896

119878119895 + 119878119896 minus 119885119860ℎΔ1199032 + 119861ℎ119896119886ℎΔ119903= 119873sum119895=1



(A41)


119899 minus 2119873119899 119885119860ℎΔ1199032 + [119861ℎ119896 + 2119873119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119867119873ge 0 (A42)





(A44)


(A45)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A46)









ℎ1198652ℎ1198961198961015840119873


(A49)



ℎ1198652ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A50)


For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A51)




For formula (3)

119873sum119895=1

1198781015840119895 = 119873sum119895=1


minus 2119873119885119886ℎ119862ℎ1198961198961015840119899 Δ119903(A53)


2119873119885119899 119860ℎΔ1199032 + 2119886ℎ119873119885119862ℎ1198961198961015840119899 Δ119903 + 119867119873 ge 0 (A54)






If (2119886ℎ119873119885119862ℎ1198961198961015840119899)2 minus 4(2119873119885119860ℎ119867119873119899) ge 0




Data Availability




Acknowledgments


References



































































Journal of












Journal of







Volume 2018






Volume 2018













+ radic1198862ℎ1198662ℎ1198961198961015840


(A30)


119873sum119895=1

1198781015840119895 = sum119895 =1198961015840

119878119895 + 11987810158401198961015840= sum119895 =1198961015840




(A31)







(A34)


(A35)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A36)









ℎ1198662ℎ1198961198961015840119873




ℎ1198662ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A40)


119873sum119895=1

1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896

119878119895 + 119878119896 minus 119885119860ℎΔ1199032 + 119861ℎ119896119886ℎΔ119903= 119873sum119895=1



(A41)


119899 minus 2119873119899 119885119860ℎΔ1199032 + [119861ℎ119896 + 2119873119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119867119873ge 0 (A42)





(A44)


(A45)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A46)









ℎ1198652ℎ1198961198961015840119873


(A49)



ℎ1198652ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A50)


For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A51)




For formula (3)

119873sum119895=1

1198781015840119895 = 119873sum119895=1


minus 2119873119885119886ℎ119862ℎ1198961198961015840119899 Δ119903(A53)


2119873119885119899 119860ℎΔ1199032 + 2119886ℎ119873119885119862ℎ1198961198961015840119899 Δ119903 + 119867119873 ge 0 (A54)






If (2119886ℎ119873119885119862ℎ1198961198961015840119899)2 minus 4(2119873119885119860ℎ119867119873119899) ge 0




Data Availability




Acknowledgments


References



































































Journal of












Journal of







Volume 2018






Volume 2018










ℎ1198662ℎ1198961198961015840119873




ℎ1198662ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A40)


119873sum119895=1

1198781015840119895 = sum119895 =119896

119878119895 + 1198781015840119896= sum119895 =119896

119878119895 + 119878119896 minus 119885119860ℎΔ1199032 + 119861ℎ119896119886ℎΔ119903= 119873sum119895=1



(A41)


119899 minus 2119873119899 119885119860ℎΔ1199032 + [119861ℎ119896 + 2119873119885119862ℎ1198961198961015840119899 ] 119886ℎΔ119903 + 119867119873ge 0 (A42)





(A44)


(A45)

For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A46)









ℎ1198652ℎ1198961198961015840119873


(A49)



ℎ1198652ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A50)


For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A51)




For formula (3)

119873sum119895=1

1198781015840119895 = 119873sum119895=1


minus 2119873119885119886ℎ119862ℎ1198961198961015840119899 Δ119903(A53)


2119873119885119899 119860ℎΔ1199032 + 2119886ℎ119873119885119862ℎ1198961198961015840119899 Δ119903 + 119867119873 ge 0 (A54)






If (2119886ℎ119873119885119862ℎ1198961198961015840119899)2 minus 4(2119873119885119860ℎ119867119873119899) ge 0




Data Availability




Acknowledgments


References



































































Journal of












Journal of







Volume 2018






Volume 2018











ℎ1198652ℎ1198961198961015840119873


(A49)



ℎ1198652ℎ1198961198961015840119873

+ 4 ((2119873 minus 119899) 119899) 119885119860ℎ1198671198732 ((2119873 minus 119899) 119899) 119885119860ℎ )(A50)


For formula (2)

119873minus1sum119895=1

1198781015840119895 = 119873minus1sum119895=1

119878119895 le 05 minus (119873 minus 1)1198851198711015840= 05


minus 2 (119873 minus 1)119885119886ℎ119862ℎ1198961198961015840119899 Δ119903

(A51)




For formula (3)

119873sum119895=1

1198781015840119895 = 119873sum119895=1


minus 2119873119885119886ℎ119862ℎ1198961198961015840119899 Δ119903(A53)


2119873119885119899 119860ℎΔ1199032 + 2119886ℎ119873119885119862ℎ1198961198961015840119899 Δ119903 + 119867119873 ge 0 (A54)






If (2119886ℎ119873119885119862ℎ1198961198961015840119899)2 minus 4(2119873119885119860ℎ119867119873119899) ge 0




Data Availability




Acknowledgments


References



































































Journal of












Journal of







Volume 2018






Volume 2018









Data Availability




Acknowledgments


References



































































Journal of












Journal of







Volume 2018






Volume 2018













































Journal of












Journal of







Volume 2018






Volume 2018








A Study on Evaluation of Modular Suppliers and Discussion of...

Documents

Transcript of A Study on Evaluation of Modular Suppliers and Discussion of...