A Novel Hybrid Evaluation Model for the Performance of ERP Project Based on ANP...
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Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2013, Article ID 913212, 9 pages http://dx.doi.org/10.1155/2013/913212 Research Article A Novel Hybrid Evaluation Model for the Performance of ERP Project Based on ANP and Improved Matter-Element Extension Model Zhao Hui-ru and Li Na-na School of Economics and Management, North China Electric Power University, No. 2 Beinong Road, Zhuxinzhuang Deshengmenwai, Beijing 102206, China Correspondence should be addressed to Li Na-na; [email protected] Received 20 January 2013; Accepted 15 February 2013 Academic Editor: Igor Andrianov Copyright © 2013 Z. Hui-ru and L. Na-na. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Considerable resources are needed when implementing the ERP project, so it is necessary to evaluate its performance. Firstly, the evaluation index system of implementation performance of the ERP project was built, and an Analytic Network Process (ANP) which can fully take the relationship between evaluation indexes into account was employed to determine the index weight. Secondly, an improved matter-element extension model, which can overcome the limitations and inadequacies of traditional matter-element extension model when performing the comprehensive evaluation, was proposed to evaluate the implementation performance of the ERP project. Finally, taking an enterprise’s ERP project as an example, a comprehensive evaluation was done, and the empirical analysis result shows that this proposed hybrid evaluation model is feasible and practical. 1. Introduction e Enterprise Resource Planning (ERP) system which is built on the information technology and systematic manage- ment thoughts can provide a decision-making management platform for enterprise’s management team and staff. e ERP system plays a significant role in improving the business pro- cesses and competitiveness of an enterprise. e implemen- tation of ERP changes the organizational and business mode, which brings a huge impact on each enterprise’s department. Since considerable enterprise resources are needed when implementing ERP project, it is quite necessary to build a reasonable and effective comprehensive evaluation method to evaluate the performance of ERP project. Many evaluation models have been used to evaluate project performance, such as analytic hierarchy process (AHP) [1], fuzzy analytic hierarchy process (FAHP) [2], data envelopment analytic hierarchy process (DEAHP) [3], balanced scorecard (BS) [4], and neural network analysis method [5]. In addition, many studies have also been con- ducted on evaluating ERP project performance. Chen and Lin [6] proposed a fuzzy linguistic performance indicator based on network flow model to assess the performance of ERP sys- tems. Zhan et al. [7] presented an evaluation model based on the Triangle Whiten Function. Xu [8] used an AHP method to evaluate the performance of ERP, considering the feedback and dependence factors. Razmi et al. [9] proposed a fuzzy analytic hierarchy process model (FAHP) which combines fuzzy theory with analytic hierarchy process to evaluate the ERP project. Chang et al. [10] constructed a conceptual model to measure the performance and competitive advantages of ERP from a supply chain management perspective. Hanet al. [11] used ABCD monitoring table and SPA project evaluation method to assess the ERP project. e AHP method does not consider the relationship between different indexes of control level in the index system, which weakens the objectivity of the evaluation result. BP neural network evaluation method does not determine the index weight but it requires a large amount of training samples. Although data envelopment analysis method is relatively objective, it is not suitable for qualitative analysis. ABCD monitoring table and SPA project evaluation method can cover a wide range of indexes, but
Transcript of A Novel Hybrid Evaluation Model for the Performance of ERP Project Based on ANP...
Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2013 Article ID 913212 9 pageshttpdxdoiorg1011552013913212
Research ArticleA Novel Hybrid Evaluation Model for the Performance ofERP Project Based on ANP and Improved Matter-ElementExtension Model
Zhao Hui-ru and Li Na-na
School of Economics and Management North China Electric Power University No 2 Beinong RoadZhuxinzhuang Deshengmenwai Beijing 102206 China
Correspondence should be addressed to Li Na-na nancyli1007163com
Received 20 January 2013 Accepted 15 February 2013
Academic Editor Igor Andrianov
Copyright copy 2013 Z Hui-ru and L Na-na This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
Considerable resources are needed when implementing the ERP project so it is necessary to evaluate its performance Firstly theevaluation index system of implementation performance of the ERP project was built and an Analytic Network Process (ANP)which can fully take the relationship between evaluation indexes into account was employed to determine the index weightSecondly an improved matter-element extension model which can overcome the limitations and inadequacies of traditionalmatter-element extension model when performing the comprehensive evaluation was proposed to evaluate the implementationperformance of the ERP project Finally taking an enterprisersquos ERP project as an example a comprehensive evaluation was doneand the empirical analysis result shows that this proposed hybrid evaluation model is feasible and practical
1 Introduction
The Enterprise Resource Planning (ERP) system which isbuilt on the information technology and systematic manage-ment thoughts can provide a decision-making managementplatform for enterprisersquosmanagement teamand staffTheERPsystem plays a significant role in improving the business pro-cesses and competitiveness of an enterprise The implemen-tation of ERP changes the organizational and business modewhich brings a huge impact on each enterprisersquos departmentSince considerable enterprise resources are needed whenimplementing ERP project it is quite necessary to build areasonable and effective comprehensive evaluationmethod toevaluate the performance of ERP project
Many evaluation models have been used to evaluateproject performance such as analytic hierarchy process(AHP) [1] fuzzy analytic hierarchy process (FAHP) [2]data envelopment analytic hierarchy process (DEAHP) [3]balanced scorecard (BS) [4] and neural network analysismethod [5] In addition many studies have also been con-ducted on evaluating ERPproject performance Chen andLin
[6] proposed a fuzzy linguistic performance indicator basedon network flowmodel to assess the performance of ERP sys-tems Zhan et al [7] presented an evaluation model based onthe Triangle Whiten Function Xu [8] used an AHP methodto evaluate the performance of ERP considering the feedbackand dependence factors Razmi et al [9] proposed a fuzzyanalytic hierarchy process model (FAHP) which combinesfuzzy theory with analytic hierarchy process to evaluate theERPproject Chang et al [10] constructed a conceptualmodelto measure the performance and competitive advantages ofERP from a supply chain management perspective Hanet al[11] used ABCDmonitoring table and SPA project evaluationmethod to assess the ERP projectThe AHPmethod does notconsider the relationship between different indexes of controllevel in the index system which weakens the objectivity ofthe evaluation result BP neural network evaluation methoddoes not determine the index weight but it requires a largeamount of training samples Although data envelopmentanalysis method is relatively objective it is not suitable forqualitative analysis ABCDmonitoring table and SPA projectevaluation method can cover a wide range of indexes but
2 Mathematical Problems in Engineering
the quantification of indexes is very difficult Therefore amore practical and objective evaluation method needs to beproposed
The matter-element extension analysis model transformspractical problem into a formal one using matter-elementand extension theory and presents grade of things throughcalculating the correlation between the matter-element tobe evaluated and each level In addition the matter-elementextension analysis can be also used though there are fewsamples Li and Zhang [12] assessed the performance of theemployees through establishing a qualitative and quantitativeperformance evaluationmethod based on thematter-elementextension theory and results shows that this method is moreobjective Zhou [13] established a performance evaluationmodel based on matter-element and correlation functionQualitative and quantitative evaluations on the performanceof conglomerate merger were done However if index valueexceeds the controlled field correlation function cannot becalculated Therefore the traditional matter-element exten-sion model needs to be improved
In order to evaluate the performance of enterprisersquos ERPproject a hybrid evaluation model combining ANP andimproved matter-element extension model was proposedFirstly the evaluation index system was built secondly anANP was used to determine the weight of each index whichfully took the relationship among various indicators intoaccount and then an improved matter-element extensionmodel which can overcome the limitations and inadequaciesof traditional matter-element extensionmodel was proposedFinally taking an enterprisersquos ERP project as an example thecomprehensive evaluation was done and empirical analysisresults show that this hybrid evaluation model is feasible andpractical
2 Building the Performance Evaluation IndexSystem of ERP Project
21 The Implementation Effect of ERP Project ERP systemrequires a large number of enterprisersquos resources and changesthe organizational and business mode in enterprise Theimplementation of ERP project brings multiple effects onenterprise
ERP project involves many aspects of enterprise man-agement such as production management financial man-agement sales management purchasing management andinventory management [14] Therefore the implementationof ERP project not only relies on IT departments but alsorelies on the collaboration of other departments in enterpriseManagers must be familiar with management and technicalbusiness based on ERP Tasks are completed by professionalstaff so the overall quality of employees production effi-ciency and production capacity will increase correspond-ingly
Based on the financial system financial capital operationreaches a dynamic equilibrium Meanwhile turnover rate ofthe total funds and enterprisersquos return on equity improveaccordingly
The implementation of the procurement and inventorysystem provides many inventory analysis methods for thesupply department This system can not only ensure theprocurement of purchased parts timely but also improveinventory levels which can reduce the backlog of inventoryfunds and accelerate the efficiency timeliness and accuracyof the inventory turnover of delivery The implementation ofprocurement and inventory system will raise overall level ofoperational management market share and new customeracquisition rate
A good operation of ERP system makes data integralaccurate consistent and timely Data sharing becomes accu-rate and timely accordingly ERP project can also supportbusiness decision improve forecasting production plan andensure a stable and efficient operation in an enterprise
22 Building the Evaluation Index System In order to evaluatethe implementation performance of enterprisersquos ERP projectsaccurately it is necessary to establish a reasonable evaluationindex system and grading standard Based on former analysisabout the effect of implementing ERP system we use Delphimethod to build a performance index system of ERP project[5 14] The finance management operations managementand customer management are criterion layer indexes Inaddition 11 extended indexes are concluded in the subcrite-rion layer The index system is shown in Figure 1
3 The Establishment of the HybridEvaluation Model
31 Basic Theory of Extension Analysis Matter-element ex-tension model [13 15 16] is based on matter-element theoryand extension set theory We can determine the level of onething through establishing classical field controlled fieldevaluation level and correlation function However there aresome limitations and deficiencies
(1) When any matter-element index value beyond itscontrolled field the correlation function values areunavailable so thismodel cannot perform evaluation
(2) The level of one thing is obtained by calculating cor-relation function in this model From the perspectiveof algorithm correlation degree can be regarded as anextension of membership degree in fuzzy mathemat-ics so the correlation degree principle is equivalentto the maximummembership principle [15] In somecase however the maximum membership principlecannot reflect the ambiguity of objectrsquos boundary Itwill lose information and lead to the deviation ofresults
Aiming at the limitation of (1) point the classical domainand the matter-element to be evaluated should be normal-ized Aiming at the limitation of (2) point the maximummembership degree criterion should be replaced by thecorrelation degree criterion
32The Establishment of the ImprovedMatter-Element Exten-sion Model The basic idea of matter-element evaluation
Mathematical Problems in Engineering 3
The performance of implementationERP project
Tota
l ass
et tu
rnov
er ra
tio
Retu
rn o
n eq
uity
Inve
ntor
y tu
rnov
er ra
te
Mar
ket s
hare
Rate
of n
ew cu
stom
ers o
btai
nmen
t
Rate
of c
usto
mer
com
plai
nts
Deli
very
accu
racy
Rate
of q
ualifi
ed p
rodu
cts
Rate
of o
rder
fulfi
llmen
t
Dat
a tra
nsfe
r effi
cien
cy
Financial indicators Customer indicators Operating efficiencyindicators11986121198611 1198613
Rate
of a
ccur
ate p
rodu
ctio
npl
anni
ng
119888 1 119888 2 119888 3 119888 4 119888 5 119888 6 119888 7 119888 8 119888 9 119888 10
119888 11
Figure 1 The performance evaluation index system of ERP project
method [13 15] is as follows first of all the object is dividedinto119895 levels and the range of each level is determined bydatabase or experts secondly determine the weight of eachindex Finally calculate the closeness degree and determinethe level of matter-element
Matter element is the logic unit of matter-element exten-sion model it uses an ordered triple 119877 = (119875 119862 119881) to describethings 119875 119862 119881 represent the name the characters and thevalue of one thing respectively The basic steps of improvedmatter-element extension model are as follows
(1) Determine the classical domain controlled field andmatter element of the object to be evaluated
Suppose the classical domainmatter element is as follows
R119895 = (P119895 119888119894 V119894119895) =[[[[
[
119875119895 1198881 V11198951198882 V2119895
119888119899 V119899119895
]]]]
]
=
[[[[[[[
[
119875119895 1198881 ⟨1198861119895 1198871119895⟩
1198882 ⟨1198862119895 1198872119895⟩
119888119899 ⟨119886119899119895 119887119899119895⟩
]]]]]]]
]
(1)
where P119895 represents the 119895th grade 1198881 1198882 119888119899 are 119899 differentcharacteristics of P119895 and V1198951 V1198952 V119895119899 are the value rangesof P119895 about 1198881 1198882 119888119899 respectively namely the classicalfield
Suppose the controlled field matter element is as follows
R119901 = (PC119894V119901119894) =[[[[
[
119875 1198881 V11990111198882 V1199012
119888119899 V119901119899
]]]]
]
=
[[[[[[[
[
119875 1198881 ⟨1198861199011 1198871199011⟩
1198882 ⟨1198861199012 1198871199012⟩
119888119899 ⟨119886119901119899 119887119901119899⟩
]]]]]]]
]
(2)
where119901 represents all grades of the object to be evaluated andV1199011 V1199012 V119901119899 are the value ranges of 119901 about 1198881 1198882 119888119899namely the controlled field of 119901
Suppose the matter element to be evaluated is as follows
R0 = (P0C119894V119894) =[[[[
[
1198750 1198881 V11198882 V2
119888119899 V119899
]]]]
]
(3)
where P0 represents all grades of the object to be evaluatedand V1199011 V1199012 V119901119899 are actual data of P0 about 1198881 1198882 119888119899
(2) Normalization [16]
When an actual value of index exceeds the controlledfield the correlation function cannot be calculated namelythe denominator is zero In this case matter-element andextension model cannot be used to evaluate the performanceof ERP project Therefore the classical domain and matter-element evaluation should be normalized
4 Mathematical Problems in Engineering
Normalize the classical domain R119895 as follows
R1015840119895 = (P119895C119894V1015840119894119895) =
[[[[[[[[[[[[[[
[
119875119895 1198881 ⟨1198861119895
11988711990111198871119895
1198871199011⟩
1198882 ⟨1198862119895
11988711990121198872119895
1198871199012⟩
119888119899 ⟨119886119899119895
119887119901119899119887119899119895
119887119901119899⟩
]]]]]]]]]]]]]]
]
(4)
Normalize the matter-element evaluation R0 as follows
R10158400 =
[[[[[[[[[[
[
1198750 1198881V11198871199011
1198882V21198871199012
119888119899V119899119887119901119899
]]]]]]]]]]
]
(5)
(3) Weight determination
The Weight of the evaluation index directly affects thequality and feasibility of a comprehensive evaluation Sothe determination of index weight is very important to theresult of enterprise performance comprehensive evaluationSince the evaluation index system is complex and related anAnalytic Network Process is used to determine the weight ofeach index which can fully take all characters of indexes intoaccount
(4) Establish and calculate the closeness function
Zhang [17] used closeness degree criteria instead of max-imum degree of membership criteria and made a theoreticalanalysis He put forward an asymmetric closeness formula(119901 = 1) as follows
119873 = 1 minus1
119899 (119899 + 1)
119899
sum119894=1
119863119908119894 (6)
where 119873 represents the value of closeness function 119863represents the distance 119908119894 is the weight
The value of closeness function about each index of thematter element to be evaluated with each level is calculatedas follows
119873119895 (1199010) = 1 minus1
119899 (119899 + 1)
119899
sum119894=1
119863119895 (V1015840119894)119908119894 (119883) (7)
where D119895(V1015840119894 ) = |V
1015840119894 minus ((119886
1015840119894119895 +1198871015840119894119895)2)| minus (12)(119887
1015840119894119895 minus1198861015840119894119895) represents
the distance of matter element to be evaluated related to itscorresponding normalized classical field 119908119894(119883) representsthe weight of evaluation index 119899 represents the number ofevaluation index
Network level
Control level
Goal
Criterion 1198611
Criterion 119861119898
Cluster 1198621
Cluster 1198622
Cluster 1198623
Cluster 119862119894
Cluster 119862119899
Figure 2 The basic structural diagram of ANP
(5) Rating
Suppose 1198731198951015840(1199010) = max119873119895(1199010) the matter element tobe evaluated 1199010 belongs to the 119895
1015840th levelSuppose
119873119895 (1199010) =119873119895 (1199010) minusmin119895119873119895 (1199010)
max119895119873119895 (1199010) minusmin119895119873119895 (1199010)
119895lowast=sum119898119895=1 119895119873119895 (1199010)
sum119898119895=1119873119895 (1199010)
(8)
where 119895lowast represents the level variable eigenvalue of 1199010 Theattributive degree of the evaluated matter-element tending toadjacent levels can be judged from 119895lowast
33 Analytic Network Process Method Analytic NetworkProcess [18ndash20] was developed from analytic hierarchyprocess This method fully considers the interdependencebetween elements mutual influence between elements in thesame level and dominance relation from the lower level Allelements form a network structure of ANP An ANP consistsof two parts The first part is the control layer includinggoal and criterion In this layer each criterion is independentand controlled only by target element The second part isthe network layer it is controlled by control layer and theelements in the network layer influence each other (Figure 2)
331 Basic Operation Process Suppose the elements in thecontrol layer are 1198611 1198612 119861119898 and the elements in the net-work layer are 1198621 1198622 119862119899 119862119894 consisting of 1198901198941 1198901198942 119890119894119899Taking 119861119896 as a principle and 119890119894119896 as a subprinciple we comparethe influence of 119890119894119896 from other elements in the 119862119894 formthe comparison matrix119882119894119895 and calculate the weight matrixrespectively In a similar way we can obtain the influence
Mathematical Problems in Engineering 5
matrix of each element influencing 119862119894 under each principleas follows
119882 =1198881119888119899
1198881 sdot sdot sdot 119888119899
[[
[
11988211 sdot sdot sdot 1198821119899 d
1198821198991 sdot sdot sdot 119882119899119899
]]
]
(9)
Taking119861119896 as standardwe compare the influence degree ofeach element to119862119894 and we can get weightedmatrix as follows
119860 = (
1198861 sdot sdot sdot 1198861119899 d
1198861198991 sdot sdot sdot 119886119899119899
) (10)
The matrix 119860 is multiplied by the matrix 119882 then weget the weighted matrix 119882 = 119886119894119895119882119894119895 119894 = 1 2 119899 119895 =
1 2 119899 If the limit of matrix119860 is convergent and only119882infinis the limit relative ranking vector of each element to the 119895element under the 119861119896 principle
34 The Calculation Process of the ANP-Improved Matter-Element Extension Model In summary the steps of compre-hensive evaluation based on the ANP and improved matter-element method are as follows
Step 1 Determine the classical domain controlled field andmatter element to be evaluated
Step 2 Normalize the classical domain controlled field andmatter element to be evaluated when the measure data ofindex exceeds controlled field
Step 3 Calculate the index weight based on the ANP
Step 4 Calculate the value of closeness function of eachgrade
The119873119895lowast(1199010) = max119873119895lowast(1199010) (119895 = 1 2 119898) means thatthe matter element to be evaluated belongs to the 119895lowastth level
4 Case Study
Amanufacturing enterprise began to implement ERP projecttwo years ago In order to figure out the situation of thisproject an evaluation of ERP project performance wasproposed The evaluation process is as follows
41 Determine the Classical Domain Controlled Field MatterElement to Be Evaluated and the Corresponding Normaliza-tion (1) Establish the classical domain The classical fields ofquantitative indicators in evaluation index system were setaccording to related literatures and expert [7 14]The classicaldomain of each level is described as follows 1199011 1199012 1199013 and
1199014 represent high good medium and bad performancerespectively
R1=
[[[[[[[[[[[[[[[[
[
1199011 1198881 (09 1)1198882 (015 25)1198883 (4 5)1198884 (028 035)1198885 (015 02)1198886 (0 004)1198887 (09 1)1198888 (095 1)1198889 (09 1)11988810 (095 1)11988811 (09 1)
]]]]]]]]]]]]]]]]
]
R2=
[[[[[[[[[[[[[[[[
[
1199012 1198881 (08 09)1198882 (008 015)1198883 (3 4)1198884 (02 028)1198885 (01 015)1198886 (004 008)1198887 (08 09)1198888 (09 095)1198889 (08 09)11988810 (09 095)11988811 (08 09)
]]]]]]]]]]]]]]]]
]
R3=
[[[[[[[[[[[[[[[[
[
1199013 1198881 (065 08)1198882 (005 008)1198883 (2 3)1198884 (01 02)1198885 (005 01)1198886 (008 015)1198887 (07 08)1198888 (08 09)1198889 (07 08)11988810 (08 09)11988811 (065 08)
]]]]]]]]]]]]]]]]
]
R4=
[[[[[[[[[[[[[[[[
[
1199014 1198881 (0 065)1198882 (0 005)1198883 (0 2)1198884 (0 01)1198885 (0 005)1198886 (015 025)1198887 (0 07)1198888 (0 08)1198889 (0 07)11988810 (0 08)11988811 (0 065)
]]]]]]]]]]]]]]]]
]
(11)
(2) Establish the controlled fieldThe classical field of eachindex is equal to the sum of all classical field values
(3) Establish the matter element evaluation Accordingto the measured data of enterprise performance evaluationindex thematter element to be evaluated can be builtR119901 andR0 are as follows
R0 =
[[[[[[[[[[[[[[[[
[
1199010 1198881 091198882 0181198883 31198884 021198885 0251198886 0031198887 0851198888 091198889 0911988810 08411988811 083
]]]]]]]]]]]]]]]]
]
R119901 =
[[[[[[[[[[[[[[[[
[
119901p 1198881 (0 1)
1198882 (0 025)1198883 (0 5)1198884 (0 035)1198885 (0 02)1198886 (0 025)1198887 (09 1)1198888 (0 1)1198889 (0 1)11988810 (0 1)11988811 (0 1)
]]]]]]]]]]]]]]]]
]
(12)
We know that the value of index 1198885 has exceeded theclassical domain so the closeness function cannot be cal-culated in traditional matter-element extension model Weshould normalize the classical domain and controlled field
6 Mathematical Problems in Engineering
1198611 1198612 1198613
Figure 3 Inner dependence among criteria
to improve the traditional model The normalized classicaldomain and controlled are below
R10158401=
[[[[[[[[[[[[[[[[
[
1199011 1198881 (09 1)1198882 (06 1)1198883 (08 1)1198884 (08 1)1198885 (075 1)1198886 (0 016)1198887 (09 1)1198888 (095 1)1198889 (09 1)11988810 (095 1)11988811 (09 1)
]]]]]]]]]]]]]]]]
]
R10158402=
[[[[[[[[[[[[[[[[
[
1199012 1198881 (08 09)1198882 (032 06)1198883 (06 08)1198884 (057 08)1198885 (05 075)1198886 (016 032)1198887 (08 09)1198888 (09 095)1198889 (08 09)11988810 (09 095)11988811 (08 09)
]]]]]]]]]]]]]]]]
]
R10158403=
[[[[[[[[[[[[[[[[
[
1199013 1198881 (065 08)1198882 (02 032)1198883 (04 06)1198884 (0286 0571)1198885 (025 05)1198886 (032 06)1198887 (07 08)1198888 (08 09)1198889 (07 08)11988810 (08 09)11988811 (065 08)
]]]]]]]]]]]]]]]]
]
R10158404=
[[[[[[[[[[[[[[[[
[
1199014 1198881 (0 065)1198882 (0 02)1198883 (0 0286)1198884 (0 025)1198885 (06 1)1198886 (0 07)1198887 (0 08)1198888 (0 08)1198889 (0 07)11988810 (0 08)11988811 (0 065)
]]]]]]]]]]]]]]]]
]
R10158400 =
[[[[[[[[[[[[[[[[
[
1199010 1198881 091198882 0721198883 061198884 05711198885 1251198886 0121198887 0851198888 091198889 0911988810 08411988811 083
]]]]]]]]]]]]]]]]
]
(13)
42 Calculate the Index Weight An ANP was used to deter-mine the weight of performance evaluation index whichcan fully take the relationship between various indicatorsinto account Because to the calculation is complicated weemployed ldquoSuper Decisionrdquo software to calculate the weightof each index The steps are as follows
1198881
1198882
1198883
1198884
1198885 1198886
1198887
1198888
1198889
11988810
11988811
Figure 4 Inner dependence among subcriteria
Table 1 The judgment matrix of elements
1198881 1198882 1198883 Local weight1198881 1 05 4 03445441198882 2 1 2 01085251198883 025 05 1 0546931
CR = 000566
(1) Establish ANP networkAccording to the index system diagram in Figure 1the control level and network level are developedbased on the dominance and feedback relationshipThe dependencies among indexes in the controllevel are shown in Figure 3 The relationships amongindexes in network level are depicted in Figure 4 AnANP model is developed on the network structure ofelements
(2) Structure the judgment matrixBased on the clear relationship between elements thejudgmentmatrixes are concluded through comparingelement sets and elements respectively by nine-scalemethod For example the pairwise comparisons ofelements in clutter B1 are conducted and the judgmentmatrix is shown in Table 1 and the local weight can beconcluded by ldquoSuper Decisionrdquo software
(3) Check the consistency of judgment matrixIf CR ratio exceeds 01 we should change the judg-ment matrix until all CR ratios are less than 01
(4) Calculate the weighted supermatrix and the limitmatrixCalculate the weighted supermatrix and the limitmatrix of indicator elements by software The resultsare shown in Figures 5 and 6
Mathematical Problems in Engineering 7
Figure 5 The weighted supermatrix of indicator elements
Figure 6 The limit matrix of indicator elements
Table 2 The global weights of each criterion
Criteria Local weights Subcriteria Local weights Global weights
Financial indicators (1198611) 02969611198881 030034 00780591681198882 037908 00184571071198883 032058 0069383293
Customer indicators (1198612) 0163424
1198884 042456 00326259671198885 0109866169 01125719761198886 011294 00951997571198887 0477648133 0089189267
Operating efficiency indicators (1198613) 0539615
1198888 022703 0027849531198889 005161 033062750711988810 010866 012250879311988811 061271 0058634566
8 Mathematical Problems in Engineering
minus50 minus40 minus30 minus20 minus10 0 5 10
11
12
13
14
15
16
17
18
19
119895lowast
()
1198621
11986271198628
11986291198621011986211
119862211986231198624
11986251198626
Figure 7 Variation of 119895lowast with the index values
1198621
1198623 1198627
1198622
1198628
1198629
1198624
11986210
1198625
1198626
11986211
14
15
16
17
18
19
119895lowast
minus50 minus40 minus30 minus20 minus10 0 10
()20 30 40 50
Figure 8 Variation of 119895lowast with the weight values
Table 3 The119863119895(V1015840119894 ) values
Index High1198631(V1015840119894 ) Good1198632(V
1015840119894 ) Medium1198633(V
1015840119894 ) Bad1198634(V
1015840119894 )
1198881 minus56119864 minus 17 17 155 091198882 minus012 012 04 0521198883 014 minus006 006 0261198884 02286 0 0 028571198885 025 05 075 11198886 minus004 004 02 0481198887 005 minus005 005 0151198888 005 555119864 minus 17 minus56119864 minus 17 011198889 minus56119864 minus 17 minus56119864 minus 17 01 0211988810 011 006 minus004 00411988811 007 minus003 003 018
(5) Calculate the weight of indexes according to theweighted supermatrix and limit matrix The resultsare shown in Table 2
43 Calculate the Value of Closeness Function Calculate thedistance119863119895(V
1015840119894 ) of the evaluatedmatter element related to new
classical domain just as shown in Table 3The value of the closeness degree of each grade is below
1198731 (1199010) = 1 minus11
sum119894=1
1198631 (V1015840119894)119908119894 (119883) = 0999482
1198732 (1199010) = 1 minus11
sum119894=1
1198632 (V1015840119894)119908119894 (119883) = 0998698
1198733 (1199010) = 1 minus11
sum119894=1
1198633 (V1015840119894)119908119894 (119883) = 099829
1198734 (1199010) = 1 minus11
sum119894=1
1198634 (V1015840119894)119908119894 (119883) = 0997647
(14)
44 Determine the Performance Rating Since 1198731(1199010) =maxN119895(1199010) = 0999482 119895 = 1 2 3 4 it is shown that theperformance level of ERP project in this enterprise belongsto ldquohighrdquo
45 Sensitivity Analysis Sensitivity analysis is performedaccording to the performance evaluation index systemof ERPproject When the index value or weight of index changesits level variable characteristic value 119895lowast also changes corre-spondinglyWhen the index value changes by 5 10 minus10minus20 minus30 minus40 minus50 respectively the level variablecharacteristic value 119895lowast changes as shown in Figure 2 Whenthe weight of index changes by plusmn10 plusmn20 plusmn30 plusmn40or plusmn50 the level variable characteristic value 119895lowast changescorrespondingly just as the Figure 3
As we can see from Figure 7 the project performanceindexes 1198881 1198882 1198888 11988811 have large effect on the evaluation resultswhich means that the sensitivity of 1198881 1198882 1198888 11988811 is very strongFor example when the 11988811 index changes the range ofthe 119895lowast value varies from 12 to 18 Although ERP projectperformance level does not change the level gradually tendsto ldquogoodrdquo level from ldquohighrdquo level With the change of index1198883 1198884 1198885 1198886 1198887 1198889 11988810 the 119895
lowast value changes a little from 15 to165 It indicates that the variation of index value will notchange the level which the project performance tends to orbelongs to
In Figure 8 we can know that the change of 1198881 and 11988811indexes affects the 119895lowast value obviously but other indexes haveless effect on the 119895lowast value In a word 1198881 and 11988811 are sensitiveindexes in the ERP project performance evaluation
5 Conclusions
ERP system has been introduced into enterprises for manyyears It is necessary to evaluate the performance of theERP project in enterprise However the factors which affectthe performance of ERP project are complex and relatedSo a hybrid evaluation method of ERP project performancewhich considers these peculiarities was proposed In order
Mathematical Problems in Engineering 9
to analyze the performance of ERP project an index sys-tem of comprehensive benefit evaluation including financecustomer and operation management is established in thispaper An ANP was proposed to determine the weight ofeach index which fully took the relationship between variousindicators into account Due to the limitations and inadequa-cies of traditionalmatter-element extensionmodel when per-forming the comprehensive evaluation an improved matter-element extensionmodel was proposed And then taking oneenterprisersquos ERP project as an example the comprehensiveevaluation was done The empirical analysis results show theperformance of ERPproject in our case belongs to ldquohighrdquo leveland our proposed hybrid evaluation model is feasible andpractical Finally a sensitivity analysis is performed to findsensitive index in the ERP project evaluation The analysisresults show that total asset turnover ratio and data transferefficiency are sensitive indexes so this enterprise should paymore attention to them
Acknowledgments
This study is supported by theNationalNatural Science Foun-dation of China (Grant no 70971038) and the Humanitiesand Social Science project of the Ministry of Education ofChina (Project no 11YJA790217) The authors are grateful tothe editor and anonymous reviewers for their suggestions onimproving the quality of the paper
References
[1] J S Zhang and W Tan ldquoResearch on the performance eval-uation of logistics enterprise based on the analytic hierarchyprocessrdquo Energy Procedia vol 14 pp 1618ndash1623 2012
[2] I Ertugrul and N Karakasoglu ldquoPerformance evaluation ofTurkish cement firms with fuzzy analytic hierarchy process andTOPSISmethodsrdquo Expert Systems with Applications vol 36 no1 pp 702ndash715 2009
[3] H Saranga and R Moser ldquoPerformance evaluation of purchas-ing and supply management using value chain DEA approachrdquoEuropean Journal of Operational Research vol 207 no 1 pp197ndash205 2010
[4] H Y Wu Y K Lin and C H Chang ldquoPerformance evaluationof extension education centers in universities based on thebalanced scorecardrdquo Evaluation and Program Planning vol 34no 1 pp 37ndash50 2011
[5] J Y Li ldquoThe effect evaluation of ERP system based on BP neuralnetworkrdquo Technology Square no 8 pp 25ndash27 2010
[6] S G Chen and Y K Lin ldquoOn performance evaluation ofERP systems with fuzzy mathematicsrdquo Expert Systems WithApplications vol 36 pp 6362ndash6367 2010
[7] X H Zhan X Xu and H Z Liu ldquoERP performance evaluationof power supply engineering Company Based on Gray TriangleWhiten Functionrdquo Systems Engineering Procedia vol 4 pp 116ndash123 2012
[8] L Xu ldquoThe evaluation of ERP sandtable simulation based onAHPrdquo Physics Procedia vol 33 pp 1924ndash1931 2012
[9] J Razmi M S Sangari and R Ghodsi ldquoDeveloping a practicalframework for ERP readiness assessment using fuzzy analyticnetwork processrdquoAdvances in Engineering Software vol 40 no11 pp 1168ndash1178 2009
[10] I C Chang H G Hwang H C Liaw M C Hung S LChen and D C Yen ldquoA neural network evaluation model forERP performance from SCM perspective to enhance enterprisecompetitive advantagerdquo Expert Systems with Applications vol35 no 4 pp 1809ndash1816 2008
[11] T X Han Y F Wang and W M Liu ldquoERP performanceevaluation method study in electric power enterpriserdquo Journalof East China Power vol 35 pp 1064ndash1069 2007
[12] Y Z Li and X Zhang ldquoThe application of principle exten-sion method in evaluating enterprise performancerdquo Journal ofChengdu University (Social Science Edition) vol 17 no 2 pp103ndash107 2010
[13] Y W Zhou ldquoPerformance evaluation based on the entropyweight and matter-element modelrdquo Enterprise Economy no 3pp 76ndash79 2012
[14] L L Yang ldquoThe research on the evaluation index system ofthe ERP system effectrdquo Qingdao University of Science andTechnology 2010
[15] W Cai C Y Yang and W Lin Extension Engineering MethodScience Press Beijing China 1997
[16] Y XHe A YDai J ZhuH YHe and F Li ldquoRisk assessment ofurban network planning in china based on the matter-elementmodel and extension analysisrdquo International Journal of ElectricalPower and Energy Systems vol 33 no 3 pp 775ndash782 2011
[17] X P Zhang ldquoThe fuzzy comprehensive evaluation result setchange based on the close degreerdquo Journal of Shandong Univer-sity vol 39 no 2 pp 25ndash29 2004
[18] C T Lin C B Chen and Y C Ting ldquoAn ERP model forsupplier selection in electronics industryrdquo Expert Systems withApplications vol 38 no 3 pp 1760ndash1765 2011
[19] B Pang and S Bai ldquoAn integrated fuzzy synthetic evaluationapproach for supplier selection based on analytic networkprocessrdquo Journal of Intelligent Manufacturing vol 24 no 1 pp163ndash174 2011
[20] Y C Hu J H Wang and R Y Wang ldquoEvaluating the per-formance of Taiwan homestay using analytic network processrdquoMathematical Problems in Engineering vol 2012 Article ID827193 24 pages 2012
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2 Mathematical Problems in Engineering
the quantification of indexes is very difficult Therefore amore practical and objective evaluation method needs to beproposed
The matter-element extension analysis model transformspractical problem into a formal one using matter-elementand extension theory and presents grade of things throughcalculating the correlation between the matter-element tobe evaluated and each level In addition the matter-elementextension analysis can be also used though there are fewsamples Li and Zhang [12] assessed the performance of theemployees through establishing a qualitative and quantitativeperformance evaluationmethod based on thematter-elementextension theory and results shows that this method is moreobjective Zhou [13] established a performance evaluationmodel based on matter-element and correlation functionQualitative and quantitative evaluations on the performanceof conglomerate merger were done However if index valueexceeds the controlled field correlation function cannot becalculated Therefore the traditional matter-element exten-sion model needs to be improved
In order to evaluate the performance of enterprisersquos ERPproject a hybrid evaluation model combining ANP andimproved matter-element extension model was proposedFirstly the evaluation index system was built secondly anANP was used to determine the weight of each index whichfully took the relationship among various indicators intoaccount and then an improved matter-element extensionmodel which can overcome the limitations and inadequaciesof traditional matter-element extensionmodel was proposedFinally taking an enterprisersquos ERP project as an example thecomprehensive evaluation was done and empirical analysisresults show that this hybrid evaluation model is feasible andpractical
2 Building the Performance Evaluation IndexSystem of ERP Project
21 The Implementation Effect of ERP Project ERP systemrequires a large number of enterprisersquos resources and changesthe organizational and business mode in enterprise Theimplementation of ERP project brings multiple effects onenterprise
ERP project involves many aspects of enterprise man-agement such as production management financial man-agement sales management purchasing management andinventory management [14] Therefore the implementationof ERP project not only relies on IT departments but alsorelies on the collaboration of other departments in enterpriseManagers must be familiar with management and technicalbusiness based on ERP Tasks are completed by professionalstaff so the overall quality of employees production effi-ciency and production capacity will increase correspond-ingly
Based on the financial system financial capital operationreaches a dynamic equilibrium Meanwhile turnover rate ofthe total funds and enterprisersquos return on equity improveaccordingly
The implementation of the procurement and inventorysystem provides many inventory analysis methods for thesupply department This system can not only ensure theprocurement of purchased parts timely but also improveinventory levels which can reduce the backlog of inventoryfunds and accelerate the efficiency timeliness and accuracyof the inventory turnover of delivery The implementation ofprocurement and inventory system will raise overall level ofoperational management market share and new customeracquisition rate
A good operation of ERP system makes data integralaccurate consistent and timely Data sharing becomes accu-rate and timely accordingly ERP project can also supportbusiness decision improve forecasting production plan andensure a stable and efficient operation in an enterprise
22 Building the Evaluation Index System In order to evaluatethe implementation performance of enterprisersquos ERP projectsaccurately it is necessary to establish a reasonable evaluationindex system and grading standard Based on former analysisabout the effect of implementing ERP system we use Delphimethod to build a performance index system of ERP project[5 14] The finance management operations managementand customer management are criterion layer indexes Inaddition 11 extended indexes are concluded in the subcrite-rion layer The index system is shown in Figure 1
3 The Establishment of the HybridEvaluation Model
31 Basic Theory of Extension Analysis Matter-element ex-tension model [13 15 16] is based on matter-element theoryand extension set theory We can determine the level of onething through establishing classical field controlled fieldevaluation level and correlation function However there aresome limitations and deficiencies
(1) When any matter-element index value beyond itscontrolled field the correlation function values areunavailable so thismodel cannot perform evaluation
(2) The level of one thing is obtained by calculating cor-relation function in this model From the perspectiveof algorithm correlation degree can be regarded as anextension of membership degree in fuzzy mathemat-ics so the correlation degree principle is equivalentto the maximummembership principle [15] In somecase however the maximum membership principlecannot reflect the ambiguity of objectrsquos boundary Itwill lose information and lead to the deviation ofresults
Aiming at the limitation of (1) point the classical domainand the matter-element to be evaluated should be normal-ized Aiming at the limitation of (2) point the maximummembership degree criterion should be replaced by thecorrelation degree criterion
32The Establishment of the ImprovedMatter-Element Exten-sion Model The basic idea of matter-element evaluation
Mathematical Problems in Engineering 3
The performance of implementationERP project
Tota
l ass
et tu
rnov
er ra
tio
Retu
rn o
n eq
uity
Inve
ntor
y tu
rnov
er ra
te
Mar
ket s
hare
Rate
of n
ew cu
stom
ers o
btai
nmen
t
Rate
of c
usto
mer
com
plai
nts
Deli
very
accu
racy
Rate
of q
ualifi
ed p
rodu
cts
Rate
of o
rder
fulfi
llmen
t
Dat
a tra
nsfe
r effi
cien
cy
Financial indicators Customer indicators Operating efficiencyindicators11986121198611 1198613
Rate
of a
ccur
ate p
rodu
ctio
npl
anni
ng
119888 1 119888 2 119888 3 119888 4 119888 5 119888 6 119888 7 119888 8 119888 9 119888 10
119888 11
Figure 1 The performance evaluation index system of ERP project
method [13 15] is as follows first of all the object is dividedinto119895 levels and the range of each level is determined bydatabase or experts secondly determine the weight of eachindex Finally calculate the closeness degree and determinethe level of matter-element
Matter element is the logic unit of matter-element exten-sion model it uses an ordered triple 119877 = (119875 119862 119881) to describethings 119875 119862 119881 represent the name the characters and thevalue of one thing respectively The basic steps of improvedmatter-element extension model are as follows
(1) Determine the classical domain controlled field andmatter element of the object to be evaluated
Suppose the classical domainmatter element is as follows
R119895 = (P119895 119888119894 V119894119895) =[[[[
[
119875119895 1198881 V11198951198882 V2119895
119888119899 V119899119895
]]]]
]
=
[[[[[[[
[
119875119895 1198881 ⟨1198861119895 1198871119895⟩
1198882 ⟨1198862119895 1198872119895⟩
119888119899 ⟨119886119899119895 119887119899119895⟩
]]]]]]]
]
(1)
where P119895 represents the 119895th grade 1198881 1198882 119888119899 are 119899 differentcharacteristics of P119895 and V1198951 V1198952 V119895119899 are the value rangesof P119895 about 1198881 1198882 119888119899 respectively namely the classicalfield
Suppose the controlled field matter element is as follows
R119901 = (PC119894V119901119894) =[[[[
[
119875 1198881 V11990111198882 V1199012
119888119899 V119901119899
]]]]
]
=
[[[[[[[
[
119875 1198881 ⟨1198861199011 1198871199011⟩
1198882 ⟨1198861199012 1198871199012⟩
119888119899 ⟨119886119901119899 119887119901119899⟩
]]]]]]]
]
(2)
where119901 represents all grades of the object to be evaluated andV1199011 V1199012 V119901119899 are the value ranges of 119901 about 1198881 1198882 119888119899namely the controlled field of 119901
Suppose the matter element to be evaluated is as follows
R0 = (P0C119894V119894) =[[[[
[
1198750 1198881 V11198882 V2
119888119899 V119899
]]]]
]
(3)
where P0 represents all grades of the object to be evaluatedand V1199011 V1199012 V119901119899 are actual data of P0 about 1198881 1198882 119888119899
(2) Normalization [16]
When an actual value of index exceeds the controlledfield the correlation function cannot be calculated namelythe denominator is zero In this case matter-element andextension model cannot be used to evaluate the performanceof ERP project Therefore the classical domain and matter-element evaluation should be normalized
4 Mathematical Problems in Engineering
Normalize the classical domain R119895 as follows
R1015840119895 = (P119895C119894V1015840119894119895) =
[[[[[[[[[[[[[[
[
119875119895 1198881 ⟨1198861119895
11988711990111198871119895
1198871199011⟩
1198882 ⟨1198862119895
11988711990121198872119895
1198871199012⟩
119888119899 ⟨119886119899119895
119887119901119899119887119899119895
119887119901119899⟩
]]]]]]]]]]]]]]
]
(4)
Normalize the matter-element evaluation R0 as follows
R10158400 =
[[[[[[[[[[
[
1198750 1198881V11198871199011
1198882V21198871199012
119888119899V119899119887119901119899
]]]]]]]]]]
]
(5)
(3) Weight determination
The Weight of the evaluation index directly affects thequality and feasibility of a comprehensive evaluation Sothe determination of index weight is very important to theresult of enterprise performance comprehensive evaluationSince the evaluation index system is complex and related anAnalytic Network Process is used to determine the weight ofeach index which can fully take all characters of indexes intoaccount
(4) Establish and calculate the closeness function
Zhang [17] used closeness degree criteria instead of max-imum degree of membership criteria and made a theoreticalanalysis He put forward an asymmetric closeness formula(119901 = 1) as follows
119873 = 1 minus1
119899 (119899 + 1)
119899
sum119894=1
119863119908119894 (6)
where 119873 represents the value of closeness function 119863represents the distance 119908119894 is the weight
The value of closeness function about each index of thematter element to be evaluated with each level is calculatedas follows
119873119895 (1199010) = 1 minus1
119899 (119899 + 1)
119899
sum119894=1
119863119895 (V1015840119894)119908119894 (119883) (7)
where D119895(V1015840119894 ) = |V
1015840119894 minus ((119886
1015840119894119895 +1198871015840119894119895)2)| minus (12)(119887
1015840119894119895 minus1198861015840119894119895) represents
the distance of matter element to be evaluated related to itscorresponding normalized classical field 119908119894(119883) representsthe weight of evaluation index 119899 represents the number ofevaluation index
Network level
Control level
Goal
Criterion 1198611
Criterion 119861119898
Cluster 1198621
Cluster 1198622
Cluster 1198623
Cluster 119862119894
Cluster 119862119899
Figure 2 The basic structural diagram of ANP
(5) Rating
Suppose 1198731198951015840(1199010) = max119873119895(1199010) the matter element tobe evaluated 1199010 belongs to the 119895
1015840th levelSuppose
119873119895 (1199010) =119873119895 (1199010) minusmin119895119873119895 (1199010)
max119895119873119895 (1199010) minusmin119895119873119895 (1199010)
119895lowast=sum119898119895=1 119895119873119895 (1199010)
sum119898119895=1119873119895 (1199010)
(8)
where 119895lowast represents the level variable eigenvalue of 1199010 Theattributive degree of the evaluated matter-element tending toadjacent levels can be judged from 119895lowast
33 Analytic Network Process Method Analytic NetworkProcess [18ndash20] was developed from analytic hierarchyprocess This method fully considers the interdependencebetween elements mutual influence between elements in thesame level and dominance relation from the lower level Allelements form a network structure of ANP An ANP consistsof two parts The first part is the control layer includinggoal and criterion In this layer each criterion is independentand controlled only by target element The second part isthe network layer it is controlled by control layer and theelements in the network layer influence each other (Figure 2)
331 Basic Operation Process Suppose the elements in thecontrol layer are 1198611 1198612 119861119898 and the elements in the net-work layer are 1198621 1198622 119862119899 119862119894 consisting of 1198901198941 1198901198942 119890119894119899Taking 119861119896 as a principle and 119890119894119896 as a subprinciple we comparethe influence of 119890119894119896 from other elements in the 119862119894 formthe comparison matrix119882119894119895 and calculate the weight matrixrespectively In a similar way we can obtain the influence
Mathematical Problems in Engineering 5
matrix of each element influencing 119862119894 under each principleas follows
119882 =1198881119888119899
1198881 sdot sdot sdot 119888119899
[[
[
11988211 sdot sdot sdot 1198821119899 d
1198821198991 sdot sdot sdot 119882119899119899
]]
]
(9)
Taking119861119896 as standardwe compare the influence degree ofeach element to119862119894 and we can get weightedmatrix as follows
119860 = (
1198861 sdot sdot sdot 1198861119899 d
1198861198991 sdot sdot sdot 119886119899119899
) (10)
The matrix 119860 is multiplied by the matrix 119882 then weget the weighted matrix 119882 = 119886119894119895119882119894119895 119894 = 1 2 119899 119895 =
1 2 119899 If the limit of matrix119860 is convergent and only119882infinis the limit relative ranking vector of each element to the 119895element under the 119861119896 principle
34 The Calculation Process of the ANP-Improved Matter-Element Extension Model In summary the steps of compre-hensive evaluation based on the ANP and improved matter-element method are as follows
Step 1 Determine the classical domain controlled field andmatter element to be evaluated
Step 2 Normalize the classical domain controlled field andmatter element to be evaluated when the measure data ofindex exceeds controlled field
Step 3 Calculate the index weight based on the ANP
Step 4 Calculate the value of closeness function of eachgrade
The119873119895lowast(1199010) = max119873119895lowast(1199010) (119895 = 1 2 119898) means thatthe matter element to be evaluated belongs to the 119895lowastth level
4 Case Study
Amanufacturing enterprise began to implement ERP projecttwo years ago In order to figure out the situation of thisproject an evaluation of ERP project performance wasproposed The evaluation process is as follows
41 Determine the Classical Domain Controlled Field MatterElement to Be Evaluated and the Corresponding Normaliza-tion (1) Establish the classical domain The classical fields ofquantitative indicators in evaluation index system were setaccording to related literatures and expert [7 14]The classicaldomain of each level is described as follows 1199011 1199012 1199013 and
1199014 represent high good medium and bad performancerespectively
R1=
[[[[[[[[[[[[[[[[
[
1199011 1198881 (09 1)1198882 (015 25)1198883 (4 5)1198884 (028 035)1198885 (015 02)1198886 (0 004)1198887 (09 1)1198888 (095 1)1198889 (09 1)11988810 (095 1)11988811 (09 1)
]]]]]]]]]]]]]]]]
]
R2=
[[[[[[[[[[[[[[[[
[
1199012 1198881 (08 09)1198882 (008 015)1198883 (3 4)1198884 (02 028)1198885 (01 015)1198886 (004 008)1198887 (08 09)1198888 (09 095)1198889 (08 09)11988810 (09 095)11988811 (08 09)
]]]]]]]]]]]]]]]]
]
R3=
[[[[[[[[[[[[[[[[
[
1199013 1198881 (065 08)1198882 (005 008)1198883 (2 3)1198884 (01 02)1198885 (005 01)1198886 (008 015)1198887 (07 08)1198888 (08 09)1198889 (07 08)11988810 (08 09)11988811 (065 08)
]]]]]]]]]]]]]]]]
]
R4=
[[[[[[[[[[[[[[[[
[
1199014 1198881 (0 065)1198882 (0 005)1198883 (0 2)1198884 (0 01)1198885 (0 005)1198886 (015 025)1198887 (0 07)1198888 (0 08)1198889 (0 07)11988810 (0 08)11988811 (0 065)
]]]]]]]]]]]]]]]]
]
(11)
(2) Establish the controlled fieldThe classical field of eachindex is equal to the sum of all classical field values
(3) Establish the matter element evaluation Accordingto the measured data of enterprise performance evaluationindex thematter element to be evaluated can be builtR119901 andR0 are as follows
R0 =
[[[[[[[[[[[[[[[[
[
1199010 1198881 091198882 0181198883 31198884 021198885 0251198886 0031198887 0851198888 091198889 0911988810 08411988811 083
]]]]]]]]]]]]]]]]
]
R119901 =
[[[[[[[[[[[[[[[[
[
119901p 1198881 (0 1)
1198882 (0 025)1198883 (0 5)1198884 (0 035)1198885 (0 02)1198886 (0 025)1198887 (09 1)1198888 (0 1)1198889 (0 1)11988810 (0 1)11988811 (0 1)
]]]]]]]]]]]]]]]]
]
(12)
We know that the value of index 1198885 has exceeded theclassical domain so the closeness function cannot be cal-culated in traditional matter-element extension model Weshould normalize the classical domain and controlled field
6 Mathematical Problems in Engineering
1198611 1198612 1198613
Figure 3 Inner dependence among criteria
to improve the traditional model The normalized classicaldomain and controlled are below
R10158401=
[[[[[[[[[[[[[[[[
[
1199011 1198881 (09 1)1198882 (06 1)1198883 (08 1)1198884 (08 1)1198885 (075 1)1198886 (0 016)1198887 (09 1)1198888 (095 1)1198889 (09 1)11988810 (095 1)11988811 (09 1)
]]]]]]]]]]]]]]]]
]
R10158402=
[[[[[[[[[[[[[[[[
[
1199012 1198881 (08 09)1198882 (032 06)1198883 (06 08)1198884 (057 08)1198885 (05 075)1198886 (016 032)1198887 (08 09)1198888 (09 095)1198889 (08 09)11988810 (09 095)11988811 (08 09)
]]]]]]]]]]]]]]]]
]
R10158403=
[[[[[[[[[[[[[[[[
[
1199013 1198881 (065 08)1198882 (02 032)1198883 (04 06)1198884 (0286 0571)1198885 (025 05)1198886 (032 06)1198887 (07 08)1198888 (08 09)1198889 (07 08)11988810 (08 09)11988811 (065 08)
]]]]]]]]]]]]]]]]
]
R10158404=
[[[[[[[[[[[[[[[[
[
1199014 1198881 (0 065)1198882 (0 02)1198883 (0 0286)1198884 (0 025)1198885 (06 1)1198886 (0 07)1198887 (0 08)1198888 (0 08)1198889 (0 07)11988810 (0 08)11988811 (0 065)
]]]]]]]]]]]]]]]]
]
R10158400 =
[[[[[[[[[[[[[[[[
[
1199010 1198881 091198882 0721198883 061198884 05711198885 1251198886 0121198887 0851198888 091198889 0911988810 08411988811 083
]]]]]]]]]]]]]]]]
]
(13)
42 Calculate the Index Weight An ANP was used to deter-mine the weight of performance evaluation index whichcan fully take the relationship between various indicatorsinto account Because to the calculation is complicated weemployed ldquoSuper Decisionrdquo software to calculate the weightof each index The steps are as follows
1198881
1198882
1198883
1198884
1198885 1198886
1198887
1198888
1198889
11988810
11988811
Figure 4 Inner dependence among subcriteria
Table 1 The judgment matrix of elements
1198881 1198882 1198883 Local weight1198881 1 05 4 03445441198882 2 1 2 01085251198883 025 05 1 0546931
CR = 000566
(1) Establish ANP networkAccording to the index system diagram in Figure 1the control level and network level are developedbased on the dominance and feedback relationshipThe dependencies among indexes in the controllevel are shown in Figure 3 The relationships amongindexes in network level are depicted in Figure 4 AnANP model is developed on the network structure ofelements
(2) Structure the judgment matrixBased on the clear relationship between elements thejudgmentmatrixes are concluded through comparingelement sets and elements respectively by nine-scalemethod For example the pairwise comparisons ofelements in clutter B1 are conducted and the judgmentmatrix is shown in Table 1 and the local weight can beconcluded by ldquoSuper Decisionrdquo software
(3) Check the consistency of judgment matrixIf CR ratio exceeds 01 we should change the judg-ment matrix until all CR ratios are less than 01
(4) Calculate the weighted supermatrix and the limitmatrixCalculate the weighted supermatrix and the limitmatrix of indicator elements by software The resultsare shown in Figures 5 and 6
Mathematical Problems in Engineering 7
Figure 5 The weighted supermatrix of indicator elements
Figure 6 The limit matrix of indicator elements
Table 2 The global weights of each criterion
Criteria Local weights Subcriteria Local weights Global weights
Financial indicators (1198611) 02969611198881 030034 00780591681198882 037908 00184571071198883 032058 0069383293
Customer indicators (1198612) 0163424
1198884 042456 00326259671198885 0109866169 01125719761198886 011294 00951997571198887 0477648133 0089189267
Operating efficiency indicators (1198613) 0539615
1198888 022703 0027849531198889 005161 033062750711988810 010866 012250879311988811 061271 0058634566
8 Mathematical Problems in Engineering
minus50 minus40 minus30 minus20 minus10 0 5 10
11
12
13
14
15
16
17
18
19
119895lowast
()
1198621
11986271198628
11986291198621011986211
119862211986231198624
11986251198626
Figure 7 Variation of 119895lowast with the index values
1198621
1198623 1198627
1198622
1198628
1198629
1198624
11986210
1198625
1198626
11986211
14
15
16
17
18
19
119895lowast
minus50 minus40 minus30 minus20 minus10 0 10
()20 30 40 50
Figure 8 Variation of 119895lowast with the weight values
Table 3 The119863119895(V1015840119894 ) values
Index High1198631(V1015840119894 ) Good1198632(V
1015840119894 ) Medium1198633(V
1015840119894 ) Bad1198634(V
1015840119894 )
1198881 minus56119864 minus 17 17 155 091198882 minus012 012 04 0521198883 014 minus006 006 0261198884 02286 0 0 028571198885 025 05 075 11198886 minus004 004 02 0481198887 005 minus005 005 0151198888 005 555119864 minus 17 minus56119864 minus 17 011198889 minus56119864 minus 17 minus56119864 minus 17 01 0211988810 011 006 minus004 00411988811 007 minus003 003 018
(5) Calculate the weight of indexes according to theweighted supermatrix and limit matrix The resultsare shown in Table 2
43 Calculate the Value of Closeness Function Calculate thedistance119863119895(V
1015840119894 ) of the evaluatedmatter element related to new
classical domain just as shown in Table 3The value of the closeness degree of each grade is below
1198731 (1199010) = 1 minus11
sum119894=1
1198631 (V1015840119894)119908119894 (119883) = 0999482
1198732 (1199010) = 1 minus11
sum119894=1
1198632 (V1015840119894)119908119894 (119883) = 0998698
1198733 (1199010) = 1 minus11
sum119894=1
1198633 (V1015840119894)119908119894 (119883) = 099829
1198734 (1199010) = 1 minus11
sum119894=1
1198634 (V1015840119894)119908119894 (119883) = 0997647
(14)
44 Determine the Performance Rating Since 1198731(1199010) =maxN119895(1199010) = 0999482 119895 = 1 2 3 4 it is shown that theperformance level of ERP project in this enterprise belongsto ldquohighrdquo
45 Sensitivity Analysis Sensitivity analysis is performedaccording to the performance evaluation index systemof ERPproject When the index value or weight of index changesits level variable characteristic value 119895lowast also changes corre-spondinglyWhen the index value changes by 5 10 minus10minus20 minus30 minus40 minus50 respectively the level variablecharacteristic value 119895lowast changes as shown in Figure 2 Whenthe weight of index changes by plusmn10 plusmn20 plusmn30 plusmn40or plusmn50 the level variable characteristic value 119895lowast changescorrespondingly just as the Figure 3
As we can see from Figure 7 the project performanceindexes 1198881 1198882 1198888 11988811 have large effect on the evaluation resultswhich means that the sensitivity of 1198881 1198882 1198888 11988811 is very strongFor example when the 11988811 index changes the range ofthe 119895lowast value varies from 12 to 18 Although ERP projectperformance level does not change the level gradually tendsto ldquogoodrdquo level from ldquohighrdquo level With the change of index1198883 1198884 1198885 1198886 1198887 1198889 11988810 the 119895
lowast value changes a little from 15 to165 It indicates that the variation of index value will notchange the level which the project performance tends to orbelongs to
In Figure 8 we can know that the change of 1198881 and 11988811indexes affects the 119895lowast value obviously but other indexes haveless effect on the 119895lowast value In a word 1198881 and 11988811 are sensitiveindexes in the ERP project performance evaluation
5 Conclusions
ERP system has been introduced into enterprises for manyyears It is necessary to evaluate the performance of theERP project in enterprise However the factors which affectthe performance of ERP project are complex and relatedSo a hybrid evaluation method of ERP project performancewhich considers these peculiarities was proposed In order
Mathematical Problems in Engineering 9
to analyze the performance of ERP project an index sys-tem of comprehensive benefit evaluation including financecustomer and operation management is established in thispaper An ANP was proposed to determine the weight ofeach index which fully took the relationship between variousindicators into account Due to the limitations and inadequa-cies of traditionalmatter-element extensionmodel when per-forming the comprehensive evaluation an improved matter-element extensionmodel was proposed And then taking oneenterprisersquos ERP project as an example the comprehensiveevaluation was done The empirical analysis results show theperformance of ERPproject in our case belongs to ldquohighrdquo leveland our proposed hybrid evaluation model is feasible andpractical Finally a sensitivity analysis is performed to findsensitive index in the ERP project evaluation The analysisresults show that total asset turnover ratio and data transferefficiency are sensitive indexes so this enterprise should paymore attention to them
Acknowledgments
This study is supported by theNationalNatural Science Foun-dation of China (Grant no 70971038) and the Humanitiesand Social Science project of the Ministry of Education ofChina (Project no 11YJA790217) The authors are grateful tothe editor and anonymous reviewers for their suggestions onimproving the quality of the paper
References
[1] J S Zhang and W Tan ldquoResearch on the performance eval-uation of logistics enterprise based on the analytic hierarchyprocessrdquo Energy Procedia vol 14 pp 1618ndash1623 2012
[2] I Ertugrul and N Karakasoglu ldquoPerformance evaluation ofTurkish cement firms with fuzzy analytic hierarchy process andTOPSISmethodsrdquo Expert Systems with Applications vol 36 no1 pp 702ndash715 2009
[3] H Saranga and R Moser ldquoPerformance evaluation of purchas-ing and supply management using value chain DEA approachrdquoEuropean Journal of Operational Research vol 207 no 1 pp197ndash205 2010
[4] H Y Wu Y K Lin and C H Chang ldquoPerformance evaluationof extension education centers in universities based on thebalanced scorecardrdquo Evaluation and Program Planning vol 34no 1 pp 37ndash50 2011
[5] J Y Li ldquoThe effect evaluation of ERP system based on BP neuralnetworkrdquo Technology Square no 8 pp 25ndash27 2010
[6] S G Chen and Y K Lin ldquoOn performance evaluation ofERP systems with fuzzy mathematicsrdquo Expert Systems WithApplications vol 36 pp 6362ndash6367 2010
[7] X H Zhan X Xu and H Z Liu ldquoERP performance evaluationof power supply engineering Company Based on Gray TriangleWhiten Functionrdquo Systems Engineering Procedia vol 4 pp 116ndash123 2012
[8] L Xu ldquoThe evaluation of ERP sandtable simulation based onAHPrdquo Physics Procedia vol 33 pp 1924ndash1931 2012
[9] J Razmi M S Sangari and R Ghodsi ldquoDeveloping a practicalframework for ERP readiness assessment using fuzzy analyticnetwork processrdquoAdvances in Engineering Software vol 40 no11 pp 1168ndash1178 2009
[10] I C Chang H G Hwang H C Liaw M C Hung S LChen and D C Yen ldquoA neural network evaluation model forERP performance from SCM perspective to enhance enterprisecompetitive advantagerdquo Expert Systems with Applications vol35 no 4 pp 1809ndash1816 2008
[11] T X Han Y F Wang and W M Liu ldquoERP performanceevaluation method study in electric power enterpriserdquo Journalof East China Power vol 35 pp 1064ndash1069 2007
[12] Y Z Li and X Zhang ldquoThe application of principle exten-sion method in evaluating enterprise performancerdquo Journal ofChengdu University (Social Science Edition) vol 17 no 2 pp103ndash107 2010
[13] Y W Zhou ldquoPerformance evaluation based on the entropyweight and matter-element modelrdquo Enterprise Economy no 3pp 76ndash79 2012
[14] L L Yang ldquoThe research on the evaluation index system ofthe ERP system effectrdquo Qingdao University of Science andTechnology 2010
[15] W Cai C Y Yang and W Lin Extension Engineering MethodScience Press Beijing China 1997
[16] Y XHe A YDai J ZhuH YHe and F Li ldquoRisk assessment ofurban network planning in china based on the matter-elementmodel and extension analysisrdquo International Journal of ElectricalPower and Energy Systems vol 33 no 3 pp 775ndash782 2011
[17] X P Zhang ldquoThe fuzzy comprehensive evaluation result setchange based on the close degreerdquo Journal of Shandong Univer-sity vol 39 no 2 pp 25ndash29 2004
[18] C T Lin C B Chen and Y C Ting ldquoAn ERP model forsupplier selection in electronics industryrdquo Expert Systems withApplications vol 38 no 3 pp 1760ndash1765 2011
[19] B Pang and S Bai ldquoAn integrated fuzzy synthetic evaluationapproach for supplier selection based on analytic networkprocessrdquo Journal of Intelligent Manufacturing vol 24 no 1 pp163ndash174 2011
[20] Y C Hu J H Wang and R Y Wang ldquoEvaluating the per-formance of Taiwan homestay using analytic network processrdquoMathematical Problems in Engineering vol 2012 Article ID827193 24 pages 2012
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Mathematical Problems in Engineering
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International Journal of
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Discrete Dynamicsin Nature and Society
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Volume 2013
Advances in
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ProbabilityandStatistics
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Advances in
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Stochastic AnalysisInternational Journal of
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DifferentialEquations
International Journal of
Volume 2013
Mathematical Problems in Engineering 3
The performance of implementationERP project
Tota
l ass
et tu
rnov
er ra
tio
Retu
rn o
n eq
uity
Inve
ntor
y tu
rnov
er ra
te
Mar
ket s
hare
Rate
of n
ew cu
stom
ers o
btai
nmen
t
Rate
of c
usto
mer
com
plai
nts
Deli
very
accu
racy
Rate
of q
ualifi
ed p
rodu
cts
Rate
of o
rder
fulfi
llmen
t
Dat
a tra
nsfe
r effi
cien
cy
Financial indicators Customer indicators Operating efficiencyindicators11986121198611 1198613
Rate
of a
ccur
ate p
rodu
ctio
npl
anni
ng
119888 1 119888 2 119888 3 119888 4 119888 5 119888 6 119888 7 119888 8 119888 9 119888 10
119888 11
Figure 1 The performance evaluation index system of ERP project
method [13 15] is as follows first of all the object is dividedinto119895 levels and the range of each level is determined bydatabase or experts secondly determine the weight of eachindex Finally calculate the closeness degree and determinethe level of matter-element
Matter element is the logic unit of matter-element exten-sion model it uses an ordered triple 119877 = (119875 119862 119881) to describethings 119875 119862 119881 represent the name the characters and thevalue of one thing respectively The basic steps of improvedmatter-element extension model are as follows
(1) Determine the classical domain controlled field andmatter element of the object to be evaluated
Suppose the classical domainmatter element is as follows
R119895 = (P119895 119888119894 V119894119895) =[[[[
[
119875119895 1198881 V11198951198882 V2119895
119888119899 V119899119895
]]]]
]
=
[[[[[[[
[
119875119895 1198881 ⟨1198861119895 1198871119895⟩
1198882 ⟨1198862119895 1198872119895⟩
119888119899 ⟨119886119899119895 119887119899119895⟩
]]]]]]]
]
(1)
where P119895 represents the 119895th grade 1198881 1198882 119888119899 are 119899 differentcharacteristics of P119895 and V1198951 V1198952 V119895119899 are the value rangesof P119895 about 1198881 1198882 119888119899 respectively namely the classicalfield
Suppose the controlled field matter element is as follows
R119901 = (PC119894V119901119894) =[[[[
[
119875 1198881 V11990111198882 V1199012
119888119899 V119901119899
]]]]
]
=
[[[[[[[
[
119875 1198881 ⟨1198861199011 1198871199011⟩
1198882 ⟨1198861199012 1198871199012⟩
119888119899 ⟨119886119901119899 119887119901119899⟩
]]]]]]]
]
(2)
where119901 represents all grades of the object to be evaluated andV1199011 V1199012 V119901119899 are the value ranges of 119901 about 1198881 1198882 119888119899namely the controlled field of 119901
Suppose the matter element to be evaluated is as follows
R0 = (P0C119894V119894) =[[[[
[
1198750 1198881 V11198882 V2
119888119899 V119899
]]]]
]
(3)
where P0 represents all grades of the object to be evaluatedand V1199011 V1199012 V119901119899 are actual data of P0 about 1198881 1198882 119888119899
(2) Normalization [16]
When an actual value of index exceeds the controlledfield the correlation function cannot be calculated namelythe denominator is zero In this case matter-element andextension model cannot be used to evaluate the performanceof ERP project Therefore the classical domain and matter-element evaluation should be normalized
4 Mathematical Problems in Engineering
Normalize the classical domain R119895 as follows
R1015840119895 = (P119895C119894V1015840119894119895) =
[[[[[[[[[[[[[[
[
119875119895 1198881 ⟨1198861119895
11988711990111198871119895
1198871199011⟩
1198882 ⟨1198862119895
11988711990121198872119895
1198871199012⟩
119888119899 ⟨119886119899119895
119887119901119899119887119899119895
119887119901119899⟩
]]]]]]]]]]]]]]
]
(4)
Normalize the matter-element evaluation R0 as follows
R10158400 =
[[[[[[[[[[
[
1198750 1198881V11198871199011
1198882V21198871199012
119888119899V119899119887119901119899
]]]]]]]]]]
]
(5)
(3) Weight determination
The Weight of the evaluation index directly affects thequality and feasibility of a comprehensive evaluation Sothe determination of index weight is very important to theresult of enterprise performance comprehensive evaluationSince the evaluation index system is complex and related anAnalytic Network Process is used to determine the weight ofeach index which can fully take all characters of indexes intoaccount
(4) Establish and calculate the closeness function
Zhang [17] used closeness degree criteria instead of max-imum degree of membership criteria and made a theoreticalanalysis He put forward an asymmetric closeness formula(119901 = 1) as follows
119873 = 1 minus1
119899 (119899 + 1)
119899
sum119894=1
119863119908119894 (6)
where 119873 represents the value of closeness function 119863represents the distance 119908119894 is the weight
The value of closeness function about each index of thematter element to be evaluated with each level is calculatedas follows
119873119895 (1199010) = 1 minus1
119899 (119899 + 1)
119899
sum119894=1
119863119895 (V1015840119894)119908119894 (119883) (7)
where D119895(V1015840119894 ) = |V
1015840119894 minus ((119886
1015840119894119895 +1198871015840119894119895)2)| minus (12)(119887
1015840119894119895 minus1198861015840119894119895) represents
the distance of matter element to be evaluated related to itscorresponding normalized classical field 119908119894(119883) representsthe weight of evaluation index 119899 represents the number ofevaluation index
Network level
Control level
Goal
Criterion 1198611
Criterion 119861119898
Cluster 1198621
Cluster 1198622
Cluster 1198623
Cluster 119862119894
Cluster 119862119899
Figure 2 The basic structural diagram of ANP
(5) Rating
Suppose 1198731198951015840(1199010) = max119873119895(1199010) the matter element tobe evaluated 1199010 belongs to the 119895
1015840th levelSuppose
119873119895 (1199010) =119873119895 (1199010) minusmin119895119873119895 (1199010)
max119895119873119895 (1199010) minusmin119895119873119895 (1199010)
119895lowast=sum119898119895=1 119895119873119895 (1199010)
sum119898119895=1119873119895 (1199010)
(8)
where 119895lowast represents the level variable eigenvalue of 1199010 Theattributive degree of the evaluated matter-element tending toadjacent levels can be judged from 119895lowast
33 Analytic Network Process Method Analytic NetworkProcess [18ndash20] was developed from analytic hierarchyprocess This method fully considers the interdependencebetween elements mutual influence between elements in thesame level and dominance relation from the lower level Allelements form a network structure of ANP An ANP consistsof two parts The first part is the control layer includinggoal and criterion In this layer each criterion is independentand controlled only by target element The second part isthe network layer it is controlled by control layer and theelements in the network layer influence each other (Figure 2)
331 Basic Operation Process Suppose the elements in thecontrol layer are 1198611 1198612 119861119898 and the elements in the net-work layer are 1198621 1198622 119862119899 119862119894 consisting of 1198901198941 1198901198942 119890119894119899Taking 119861119896 as a principle and 119890119894119896 as a subprinciple we comparethe influence of 119890119894119896 from other elements in the 119862119894 formthe comparison matrix119882119894119895 and calculate the weight matrixrespectively In a similar way we can obtain the influence
Mathematical Problems in Engineering 5
matrix of each element influencing 119862119894 under each principleas follows
119882 =1198881119888119899
1198881 sdot sdot sdot 119888119899
[[
[
11988211 sdot sdot sdot 1198821119899 d
1198821198991 sdot sdot sdot 119882119899119899
]]
]
(9)
Taking119861119896 as standardwe compare the influence degree ofeach element to119862119894 and we can get weightedmatrix as follows
119860 = (
1198861 sdot sdot sdot 1198861119899 d
1198861198991 sdot sdot sdot 119886119899119899
) (10)
The matrix 119860 is multiplied by the matrix 119882 then weget the weighted matrix 119882 = 119886119894119895119882119894119895 119894 = 1 2 119899 119895 =
1 2 119899 If the limit of matrix119860 is convergent and only119882infinis the limit relative ranking vector of each element to the 119895element under the 119861119896 principle
34 The Calculation Process of the ANP-Improved Matter-Element Extension Model In summary the steps of compre-hensive evaluation based on the ANP and improved matter-element method are as follows
Step 1 Determine the classical domain controlled field andmatter element to be evaluated
Step 2 Normalize the classical domain controlled field andmatter element to be evaluated when the measure data ofindex exceeds controlled field
Step 3 Calculate the index weight based on the ANP
Step 4 Calculate the value of closeness function of eachgrade
The119873119895lowast(1199010) = max119873119895lowast(1199010) (119895 = 1 2 119898) means thatthe matter element to be evaluated belongs to the 119895lowastth level
4 Case Study
Amanufacturing enterprise began to implement ERP projecttwo years ago In order to figure out the situation of thisproject an evaluation of ERP project performance wasproposed The evaluation process is as follows
41 Determine the Classical Domain Controlled Field MatterElement to Be Evaluated and the Corresponding Normaliza-tion (1) Establish the classical domain The classical fields ofquantitative indicators in evaluation index system were setaccording to related literatures and expert [7 14]The classicaldomain of each level is described as follows 1199011 1199012 1199013 and
1199014 represent high good medium and bad performancerespectively
R1=
[[[[[[[[[[[[[[[[
[
1199011 1198881 (09 1)1198882 (015 25)1198883 (4 5)1198884 (028 035)1198885 (015 02)1198886 (0 004)1198887 (09 1)1198888 (095 1)1198889 (09 1)11988810 (095 1)11988811 (09 1)
]]]]]]]]]]]]]]]]
]
R2=
[[[[[[[[[[[[[[[[
[
1199012 1198881 (08 09)1198882 (008 015)1198883 (3 4)1198884 (02 028)1198885 (01 015)1198886 (004 008)1198887 (08 09)1198888 (09 095)1198889 (08 09)11988810 (09 095)11988811 (08 09)
]]]]]]]]]]]]]]]]
]
R3=
[[[[[[[[[[[[[[[[
[
1199013 1198881 (065 08)1198882 (005 008)1198883 (2 3)1198884 (01 02)1198885 (005 01)1198886 (008 015)1198887 (07 08)1198888 (08 09)1198889 (07 08)11988810 (08 09)11988811 (065 08)
]]]]]]]]]]]]]]]]
]
R4=
[[[[[[[[[[[[[[[[
[
1199014 1198881 (0 065)1198882 (0 005)1198883 (0 2)1198884 (0 01)1198885 (0 005)1198886 (015 025)1198887 (0 07)1198888 (0 08)1198889 (0 07)11988810 (0 08)11988811 (0 065)
]]]]]]]]]]]]]]]]
]
(11)
(2) Establish the controlled fieldThe classical field of eachindex is equal to the sum of all classical field values
(3) Establish the matter element evaluation Accordingto the measured data of enterprise performance evaluationindex thematter element to be evaluated can be builtR119901 andR0 are as follows
R0 =
[[[[[[[[[[[[[[[[
[
1199010 1198881 091198882 0181198883 31198884 021198885 0251198886 0031198887 0851198888 091198889 0911988810 08411988811 083
]]]]]]]]]]]]]]]]
]
R119901 =
[[[[[[[[[[[[[[[[
[
119901p 1198881 (0 1)
1198882 (0 025)1198883 (0 5)1198884 (0 035)1198885 (0 02)1198886 (0 025)1198887 (09 1)1198888 (0 1)1198889 (0 1)11988810 (0 1)11988811 (0 1)
]]]]]]]]]]]]]]]]
]
(12)
We know that the value of index 1198885 has exceeded theclassical domain so the closeness function cannot be cal-culated in traditional matter-element extension model Weshould normalize the classical domain and controlled field
6 Mathematical Problems in Engineering
1198611 1198612 1198613
Figure 3 Inner dependence among criteria
to improve the traditional model The normalized classicaldomain and controlled are below
R10158401=
[[[[[[[[[[[[[[[[
[
1199011 1198881 (09 1)1198882 (06 1)1198883 (08 1)1198884 (08 1)1198885 (075 1)1198886 (0 016)1198887 (09 1)1198888 (095 1)1198889 (09 1)11988810 (095 1)11988811 (09 1)
]]]]]]]]]]]]]]]]
]
R10158402=
[[[[[[[[[[[[[[[[
[
1199012 1198881 (08 09)1198882 (032 06)1198883 (06 08)1198884 (057 08)1198885 (05 075)1198886 (016 032)1198887 (08 09)1198888 (09 095)1198889 (08 09)11988810 (09 095)11988811 (08 09)
]]]]]]]]]]]]]]]]
]
R10158403=
[[[[[[[[[[[[[[[[
[
1199013 1198881 (065 08)1198882 (02 032)1198883 (04 06)1198884 (0286 0571)1198885 (025 05)1198886 (032 06)1198887 (07 08)1198888 (08 09)1198889 (07 08)11988810 (08 09)11988811 (065 08)
]]]]]]]]]]]]]]]]
]
R10158404=
[[[[[[[[[[[[[[[[
[
1199014 1198881 (0 065)1198882 (0 02)1198883 (0 0286)1198884 (0 025)1198885 (06 1)1198886 (0 07)1198887 (0 08)1198888 (0 08)1198889 (0 07)11988810 (0 08)11988811 (0 065)
]]]]]]]]]]]]]]]]
]
R10158400 =
[[[[[[[[[[[[[[[[
[
1199010 1198881 091198882 0721198883 061198884 05711198885 1251198886 0121198887 0851198888 091198889 0911988810 08411988811 083
]]]]]]]]]]]]]]]]
]
(13)
42 Calculate the Index Weight An ANP was used to deter-mine the weight of performance evaluation index whichcan fully take the relationship between various indicatorsinto account Because to the calculation is complicated weemployed ldquoSuper Decisionrdquo software to calculate the weightof each index The steps are as follows
1198881
1198882
1198883
1198884
1198885 1198886
1198887
1198888
1198889
11988810
11988811
Figure 4 Inner dependence among subcriteria
Table 1 The judgment matrix of elements
1198881 1198882 1198883 Local weight1198881 1 05 4 03445441198882 2 1 2 01085251198883 025 05 1 0546931
CR = 000566
(1) Establish ANP networkAccording to the index system diagram in Figure 1the control level and network level are developedbased on the dominance and feedback relationshipThe dependencies among indexes in the controllevel are shown in Figure 3 The relationships amongindexes in network level are depicted in Figure 4 AnANP model is developed on the network structure ofelements
(2) Structure the judgment matrixBased on the clear relationship between elements thejudgmentmatrixes are concluded through comparingelement sets and elements respectively by nine-scalemethod For example the pairwise comparisons ofelements in clutter B1 are conducted and the judgmentmatrix is shown in Table 1 and the local weight can beconcluded by ldquoSuper Decisionrdquo software
(3) Check the consistency of judgment matrixIf CR ratio exceeds 01 we should change the judg-ment matrix until all CR ratios are less than 01
(4) Calculate the weighted supermatrix and the limitmatrixCalculate the weighted supermatrix and the limitmatrix of indicator elements by software The resultsare shown in Figures 5 and 6
Mathematical Problems in Engineering 7
Figure 5 The weighted supermatrix of indicator elements
Figure 6 The limit matrix of indicator elements
Table 2 The global weights of each criterion
Criteria Local weights Subcriteria Local weights Global weights
Financial indicators (1198611) 02969611198881 030034 00780591681198882 037908 00184571071198883 032058 0069383293
Customer indicators (1198612) 0163424
1198884 042456 00326259671198885 0109866169 01125719761198886 011294 00951997571198887 0477648133 0089189267
Operating efficiency indicators (1198613) 0539615
1198888 022703 0027849531198889 005161 033062750711988810 010866 012250879311988811 061271 0058634566
8 Mathematical Problems in Engineering
minus50 minus40 minus30 minus20 minus10 0 5 10
11
12
13
14
15
16
17
18
19
119895lowast
()
1198621
11986271198628
11986291198621011986211
119862211986231198624
11986251198626
Figure 7 Variation of 119895lowast with the index values
1198621
1198623 1198627
1198622
1198628
1198629
1198624
11986210
1198625
1198626
11986211
14
15
16
17
18
19
119895lowast
minus50 minus40 minus30 minus20 minus10 0 10
()20 30 40 50
Figure 8 Variation of 119895lowast with the weight values
Table 3 The119863119895(V1015840119894 ) values
Index High1198631(V1015840119894 ) Good1198632(V
1015840119894 ) Medium1198633(V
1015840119894 ) Bad1198634(V
1015840119894 )
1198881 minus56119864 minus 17 17 155 091198882 minus012 012 04 0521198883 014 minus006 006 0261198884 02286 0 0 028571198885 025 05 075 11198886 minus004 004 02 0481198887 005 minus005 005 0151198888 005 555119864 minus 17 minus56119864 minus 17 011198889 minus56119864 minus 17 minus56119864 minus 17 01 0211988810 011 006 minus004 00411988811 007 minus003 003 018
(5) Calculate the weight of indexes according to theweighted supermatrix and limit matrix The resultsare shown in Table 2
43 Calculate the Value of Closeness Function Calculate thedistance119863119895(V
1015840119894 ) of the evaluatedmatter element related to new
classical domain just as shown in Table 3The value of the closeness degree of each grade is below
1198731 (1199010) = 1 minus11
sum119894=1
1198631 (V1015840119894)119908119894 (119883) = 0999482
1198732 (1199010) = 1 minus11
sum119894=1
1198632 (V1015840119894)119908119894 (119883) = 0998698
1198733 (1199010) = 1 minus11
sum119894=1
1198633 (V1015840119894)119908119894 (119883) = 099829
1198734 (1199010) = 1 minus11
sum119894=1
1198634 (V1015840119894)119908119894 (119883) = 0997647
(14)
44 Determine the Performance Rating Since 1198731(1199010) =maxN119895(1199010) = 0999482 119895 = 1 2 3 4 it is shown that theperformance level of ERP project in this enterprise belongsto ldquohighrdquo
45 Sensitivity Analysis Sensitivity analysis is performedaccording to the performance evaluation index systemof ERPproject When the index value or weight of index changesits level variable characteristic value 119895lowast also changes corre-spondinglyWhen the index value changes by 5 10 minus10minus20 minus30 minus40 minus50 respectively the level variablecharacteristic value 119895lowast changes as shown in Figure 2 Whenthe weight of index changes by plusmn10 plusmn20 plusmn30 plusmn40or plusmn50 the level variable characteristic value 119895lowast changescorrespondingly just as the Figure 3
As we can see from Figure 7 the project performanceindexes 1198881 1198882 1198888 11988811 have large effect on the evaluation resultswhich means that the sensitivity of 1198881 1198882 1198888 11988811 is very strongFor example when the 11988811 index changes the range ofthe 119895lowast value varies from 12 to 18 Although ERP projectperformance level does not change the level gradually tendsto ldquogoodrdquo level from ldquohighrdquo level With the change of index1198883 1198884 1198885 1198886 1198887 1198889 11988810 the 119895
lowast value changes a little from 15 to165 It indicates that the variation of index value will notchange the level which the project performance tends to orbelongs to
In Figure 8 we can know that the change of 1198881 and 11988811indexes affects the 119895lowast value obviously but other indexes haveless effect on the 119895lowast value In a word 1198881 and 11988811 are sensitiveindexes in the ERP project performance evaluation
5 Conclusions
ERP system has been introduced into enterprises for manyyears It is necessary to evaluate the performance of theERP project in enterprise However the factors which affectthe performance of ERP project are complex and relatedSo a hybrid evaluation method of ERP project performancewhich considers these peculiarities was proposed In order
Mathematical Problems in Engineering 9
to analyze the performance of ERP project an index sys-tem of comprehensive benefit evaluation including financecustomer and operation management is established in thispaper An ANP was proposed to determine the weight ofeach index which fully took the relationship between variousindicators into account Due to the limitations and inadequa-cies of traditionalmatter-element extensionmodel when per-forming the comprehensive evaluation an improved matter-element extensionmodel was proposed And then taking oneenterprisersquos ERP project as an example the comprehensiveevaluation was done The empirical analysis results show theperformance of ERPproject in our case belongs to ldquohighrdquo leveland our proposed hybrid evaluation model is feasible andpractical Finally a sensitivity analysis is performed to findsensitive index in the ERP project evaluation The analysisresults show that total asset turnover ratio and data transferefficiency are sensitive indexes so this enterprise should paymore attention to them
Acknowledgments
This study is supported by theNationalNatural Science Foun-dation of China (Grant no 70971038) and the Humanitiesand Social Science project of the Ministry of Education ofChina (Project no 11YJA790217) The authors are grateful tothe editor and anonymous reviewers for their suggestions onimproving the quality of the paper
References
[1] J S Zhang and W Tan ldquoResearch on the performance eval-uation of logistics enterprise based on the analytic hierarchyprocessrdquo Energy Procedia vol 14 pp 1618ndash1623 2012
[2] I Ertugrul and N Karakasoglu ldquoPerformance evaluation ofTurkish cement firms with fuzzy analytic hierarchy process andTOPSISmethodsrdquo Expert Systems with Applications vol 36 no1 pp 702ndash715 2009
[3] H Saranga and R Moser ldquoPerformance evaluation of purchas-ing and supply management using value chain DEA approachrdquoEuropean Journal of Operational Research vol 207 no 1 pp197ndash205 2010
[4] H Y Wu Y K Lin and C H Chang ldquoPerformance evaluationof extension education centers in universities based on thebalanced scorecardrdquo Evaluation and Program Planning vol 34no 1 pp 37ndash50 2011
[5] J Y Li ldquoThe effect evaluation of ERP system based on BP neuralnetworkrdquo Technology Square no 8 pp 25ndash27 2010
[6] S G Chen and Y K Lin ldquoOn performance evaluation ofERP systems with fuzzy mathematicsrdquo Expert Systems WithApplications vol 36 pp 6362ndash6367 2010
[7] X H Zhan X Xu and H Z Liu ldquoERP performance evaluationof power supply engineering Company Based on Gray TriangleWhiten Functionrdquo Systems Engineering Procedia vol 4 pp 116ndash123 2012
[8] L Xu ldquoThe evaluation of ERP sandtable simulation based onAHPrdquo Physics Procedia vol 33 pp 1924ndash1931 2012
[9] J Razmi M S Sangari and R Ghodsi ldquoDeveloping a practicalframework for ERP readiness assessment using fuzzy analyticnetwork processrdquoAdvances in Engineering Software vol 40 no11 pp 1168ndash1178 2009
[10] I C Chang H G Hwang H C Liaw M C Hung S LChen and D C Yen ldquoA neural network evaluation model forERP performance from SCM perspective to enhance enterprisecompetitive advantagerdquo Expert Systems with Applications vol35 no 4 pp 1809ndash1816 2008
[11] T X Han Y F Wang and W M Liu ldquoERP performanceevaluation method study in electric power enterpriserdquo Journalof East China Power vol 35 pp 1064ndash1069 2007
[12] Y Z Li and X Zhang ldquoThe application of principle exten-sion method in evaluating enterprise performancerdquo Journal ofChengdu University (Social Science Edition) vol 17 no 2 pp103ndash107 2010
[13] Y W Zhou ldquoPerformance evaluation based on the entropyweight and matter-element modelrdquo Enterprise Economy no 3pp 76ndash79 2012
[14] L L Yang ldquoThe research on the evaluation index system ofthe ERP system effectrdquo Qingdao University of Science andTechnology 2010
[15] W Cai C Y Yang and W Lin Extension Engineering MethodScience Press Beijing China 1997
[16] Y XHe A YDai J ZhuH YHe and F Li ldquoRisk assessment ofurban network planning in china based on the matter-elementmodel and extension analysisrdquo International Journal of ElectricalPower and Energy Systems vol 33 no 3 pp 775ndash782 2011
[17] X P Zhang ldquoThe fuzzy comprehensive evaluation result setchange based on the close degreerdquo Journal of Shandong Univer-sity vol 39 no 2 pp 25ndash29 2004
[18] C T Lin C B Chen and Y C Ting ldquoAn ERP model forsupplier selection in electronics industryrdquo Expert Systems withApplications vol 38 no 3 pp 1760ndash1765 2011
[19] B Pang and S Bai ldquoAn integrated fuzzy synthetic evaluationapproach for supplier selection based on analytic networkprocessrdquo Journal of Intelligent Manufacturing vol 24 no 1 pp163ndash174 2011
[20] Y C Hu J H Wang and R Y Wang ldquoEvaluating the per-formance of Taiwan homestay using analytic network processrdquoMathematical Problems in Engineering vol 2012 Article ID827193 24 pages 2012
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Mathematical Problems in Engineering
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Abstract and Applied Analysis
ISRN Applied Mathematics
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Volume 2013
International Journal of
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Discrete Dynamicsin Nature and Society
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Volume 2013
Advances in
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ISRN Algebra
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ProbabilityandStatistics
Journal of
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Advances in
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Stochastic AnalysisInternational Journal of
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DifferentialEquations
International Journal of
Volume 2013
4 Mathematical Problems in Engineering
Normalize the classical domain R119895 as follows
R1015840119895 = (P119895C119894V1015840119894119895) =
[[[[[[[[[[[[[[
[
119875119895 1198881 ⟨1198861119895
11988711990111198871119895
1198871199011⟩
1198882 ⟨1198862119895
11988711990121198872119895
1198871199012⟩
119888119899 ⟨119886119899119895
119887119901119899119887119899119895
119887119901119899⟩
]]]]]]]]]]]]]]
]
(4)
Normalize the matter-element evaluation R0 as follows
R10158400 =
[[[[[[[[[[
[
1198750 1198881V11198871199011
1198882V21198871199012
119888119899V119899119887119901119899
]]]]]]]]]]
]
(5)
(3) Weight determination
The Weight of the evaluation index directly affects thequality and feasibility of a comprehensive evaluation Sothe determination of index weight is very important to theresult of enterprise performance comprehensive evaluationSince the evaluation index system is complex and related anAnalytic Network Process is used to determine the weight ofeach index which can fully take all characters of indexes intoaccount
(4) Establish and calculate the closeness function
Zhang [17] used closeness degree criteria instead of max-imum degree of membership criteria and made a theoreticalanalysis He put forward an asymmetric closeness formula(119901 = 1) as follows
119873 = 1 minus1
119899 (119899 + 1)
119899
sum119894=1
119863119908119894 (6)
where 119873 represents the value of closeness function 119863represents the distance 119908119894 is the weight
The value of closeness function about each index of thematter element to be evaluated with each level is calculatedas follows
119873119895 (1199010) = 1 minus1
119899 (119899 + 1)
119899
sum119894=1
119863119895 (V1015840119894)119908119894 (119883) (7)
where D119895(V1015840119894 ) = |V
1015840119894 minus ((119886
1015840119894119895 +1198871015840119894119895)2)| minus (12)(119887
1015840119894119895 minus1198861015840119894119895) represents
the distance of matter element to be evaluated related to itscorresponding normalized classical field 119908119894(119883) representsthe weight of evaluation index 119899 represents the number ofevaluation index
Network level
Control level
Goal
Criterion 1198611
Criterion 119861119898
Cluster 1198621
Cluster 1198622
Cluster 1198623
Cluster 119862119894
Cluster 119862119899
Figure 2 The basic structural diagram of ANP
(5) Rating
Suppose 1198731198951015840(1199010) = max119873119895(1199010) the matter element tobe evaluated 1199010 belongs to the 119895
1015840th levelSuppose
119873119895 (1199010) =119873119895 (1199010) minusmin119895119873119895 (1199010)
max119895119873119895 (1199010) minusmin119895119873119895 (1199010)
119895lowast=sum119898119895=1 119895119873119895 (1199010)
sum119898119895=1119873119895 (1199010)
(8)
where 119895lowast represents the level variable eigenvalue of 1199010 Theattributive degree of the evaluated matter-element tending toadjacent levels can be judged from 119895lowast
33 Analytic Network Process Method Analytic NetworkProcess [18ndash20] was developed from analytic hierarchyprocess This method fully considers the interdependencebetween elements mutual influence between elements in thesame level and dominance relation from the lower level Allelements form a network structure of ANP An ANP consistsof two parts The first part is the control layer includinggoal and criterion In this layer each criterion is independentand controlled only by target element The second part isthe network layer it is controlled by control layer and theelements in the network layer influence each other (Figure 2)
331 Basic Operation Process Suppose the elements in thecontrol layer are 1198611 1198612 119861119898 and the elements in the net-work layer are 1198621 1198622 119862119899 119862119894 consisting of 1198901198941 1198901198942 119890119894119899Taking 119861119896 as a principle and 119890119894119896 as a subprinciple we comparethe influence of 119890119894119896 from other elements in the 119862119894 formthe comparison matrix119882119894119895 and calculate the weight matrixrespectively In a similar way we can obtain the influence
Mathematical Problems in Engineering 5
matrix of each element influencing 119862119894 under each principleas follows
119882 =1198881119888119899
1198881 sdot sdot sdot 119888119899
[[
[
11988211 sdot sdot sdot 1198821119899 d
1198821198991 sdot sdot sdot 119882119899119899
]]
]
(9)
Taking119861119896 as standardwe compare the influence degree ofeach element to119862119894 and we can get weightedmatrix as follows
119860 = (
1198861 sdot sdot sdot 1198861119899 d
1198861198991 sdot sdot sdot 119886119899119899
) (10)
The matrix 119860 is multiplied by the matrix 119882 then weget the weighted matrix 119882 = 119886119894119895119882119894119895 119894 = 1 2 119899 119895 =
1 2 119899 If the limit of matrix119860 is convergent and only119882infinis the limit relative ranking vector of each element to the 119895element under the 119861119896 principle
34 The Calculation Process of the ANP-Improved Matter-Element Extension Model In summary the steps of compre-hensive evaluation based on the ANP and improved matter-element method are as follows
Step 1 Determine the classical domain controlled field andmatter element to be evaluated
Step 2 Normalize the classical domain controlled field andmatter element to be evaluated when the measure data ofindex exceeds controlled field
Step 3 Calculate the index weight based on the ANP
Step 4 Calculate the value of closeness function of eachgrade
The119873119895lowast(1199010) = max119873119895lowast(1199010) (119895 = 1 2 119898) means thatthe matter element to be evaluated belongs to the 119895lowastth level
4 Case Study
Amanufacturing enterprise began to implement ERP projecttwo years ago In order to figure out the situation of thisproject an evaluation of ERP project performance wasproposed The evaluation process is as follows
41 Determine the Classical Domain Controlled Field MatterElement to Be Evaluated and the Corresponding Normaliza-tion (1) Establish the classical domain The classical fields ofquantitative indicators in evaluation index system were setaccording to related literatures and expert [7 14]The classicaldomain of each level is described as follows 1199011 1199012 1199013 and
1199014 represent high good medium and bad performancerespectively
R1=
[[[[[[[[[[[[[[[[
[
1199011 1198881 (09 1)1198882 (015 25)1198883 (4 5)1198884 (028 035)1198885 (015 02)1198886 (0 004)1198887 (09 1)1198888 (095 1)1198889 (09 1)11988810 (095 1)11988811 (09 1)
]]]]]]]]]]]]]]]]
]
R2=
[[[[[[[[[[[[[[[[
[
1199012 1198881 (08 09)1198882 (008 015)1198883 (3 4)1198884 (02 028)1198885 (01 015)1198886 (004 008)1198887 (08 09)1198888 (09 095)1198889 (08 09)11988810 (09 095)11988811 (08 09)
]]]]]]]]]]]]]]]]
]
R3=
[[[[[[[[[[[[[[[[
[
1199013 1198881 (065 08)1198882 (005 008)1198883 (2 3)1198884 (01 02)1198885 (005 01)1198886 (008 015)1198887 (07 08)1198888 (08 09)1198889 (07 08)11988810 (08 09)11988811 (065 08)
]]]]]]]]]]]]]]]]
]
R4=
[[[[[[[[[[[[[[[[
[
1199014 1198881 (0 065)1198882 (0 005)1198883 (0 2)1198884 (0 01)1198885 (0 005)1198886 (015 025)1198887 (0 07)1198888 (0 08)1198889 (0 07)11988810 (0 08)11988811 (0 065)
]]]]]]]]]]]]]]]]
]
(11)
(2) Establish the controlled fieldThe classical field of eachindex is equal to the sum of all classical field values
(3) Establish the matter element evaluation Accordingto the measured data of enterprise performance evaluationindex thematter element to be evaluated can be builtR119901 andR0 are as follows
R0 =
[[[[[[[[[[[[[[[[
[
1199010 1198881 091198882 0181198883 31198884 021198885 0251198886 0031198887 0851198888 091198889 0911988810 08411988811 083
]]]]]]]]]]]]]]]]
]
R119901 =
[[[[[[[[[[[[[[[[
[
119901p 1198881 (0 1)
1198882 (0 025)1198883 (0 5)1198884 (0 035)1198885 (0 02)1198886 (0 025)1198887 (09 1)1198888 (0 1)1198889 (0 1)11988810 (0 1)11988811 (0 1)
]]]]]]]]]]]]]]]]
]
(12)
We know that the value of index 1198885 has exceeded theclassical domain so the closeness function cannot be cal-culated in traditional matter-element extension model Weshould normalize the classical domain and controlled field
6 Mathematical Problems in Engineering
1198611 1198612 1198613
Figure 3 Inner dependence among criteria
to improve the traditional model The normalized classicaldomain and controlled are below
R10158401=
[[[[[[[[[[[[[[[[
[
1199011 1198881 (09 1)1198882 (06 1)1198883 (08 1)1198884 (08 1)1198885 (075 1)1198886 (0 016)1198887 (09 1)1198888 (095 1)1198889 (09 1)11988810 (095 1)11988811 (09 1)
]]]]]]]]]]]]]]]]
]
R10158402=
[[[[[[[[[[[[[[[[
[
1199012 1198881 (08 09)1198882 (032 06)1198883 (06 08)1198884 (057 08)1198885 (05 075)1198886 (016 032)1198887 (08 09)1198888 (09 095)1198889 (08 09)11988810 (09 095)11988811 (08 09)
]]]]]]]]]]]]]]]]
]
R10158403=
[[[[[[[[[[[[[[[[
[
1199013 1198881 (065 08)1198882 (02 032)1198883 (04 06)1198884 (0286 0571)1198885 (025 05)1198886 (032 06)1198887 (07 08)1198888 (08 09)1198889 (07 08)11988810 (08 09)11988811 (065 08)
]]]]]]]]]]]]]]]]
]
R10158404=
[[[[[[[[[[[[[[[[
[
1199014 1198881 (0 065)1198882 (0 02)1198883 (0 0286)1198884 (0 025)1198885 (06 1)1198886 (0 07)1198887 (0 08)1198888 (0 08)1198889 (0 07)11988810 (0 08)11988811 (0 065)
]]]]]]]]]]]]]]]]
]
R10158400 =
[[[[[[[[[[[[[[[[
[
1199010 1198881 091198882 0721198883 061198884 05711198885 1251198886 0121198887 0851198888 091198889 0911988810 08411988811 083
]]]]]]]]]]]]]]]]
]
(13)
42 Calculate the Index Weight An ANP was used to deter-mine the weight of performance evaluation index whichcan fully take the relationship between various indicatorsinto account Because to the calculation is complicated weemployed ldquoSuper Decisionrdquo software to calculate the weightof each index The steps are as follows
1198881
1198882
1198883
1198884
1198885 1198886
1198887
1198888
1198889
11988810
11988811
Figure 4 Inner dependence among subcriteria
Table 1 The judgment matrix of elements
1198881 1198882 1198883 Local weight1198881 1 05 4 03445441198882 2 1 2 01085251198883 025 05 1 0546931
CR = 000566
(1) Establish ANP networkAccording to the index system diagram in Figure 1the control level and network level are developedbased on the dominance and feedback relationshipThe dependencies among indexes in the controllevel are shown in Figure 3 The relationships amongindexes in network level are depicted in Figure 4 AnANP model is developed on the network structure ofelements
(2) Structure the judgment matrixBased on the clear relationship between elements thejudgmentmatrixes are concluded through comparingelement sets and elements respectively by nine-scalemethod For example the pairwise comparisons ofelements in clutter B1 are conducted and the judgmentmatrix is shown in Table 1 and the local weight can beconcluded by ldquoSuper Decisionrdquo software
(3) Check the consistency of judgment matrixIf CR ratio exceeds 01 we should change the judg-ment matrix until all CR ratios are less than 01
(4) Calculate the weighted supermatrix and the limitmatrixCalculate the weighted supermatrix and the limitmatrix of indicator elements by software The resultsare shown in Figures 5 and 6
Mathematical Problems in Engineering 7
Figure 5 The weighted supermatrix of indicator elements
Figure 6 The limit matrix of indicator elements
Table 2 The global weights of each criterion
Criteria Local weights Subcriteria Local weights Global weights
Financial indicators (1198611) 02969611198881 030034 00780591681198882 037908 00184571071198883 032058 0069383293
Customer indicators (1198612) 0163424
1198884 042456 00326259671198885 0109866169 01125719761198886 011294 00951997571198887 0477648133 0089189267
Operating efficiency indicators (1198613) 0539615
1198888 022703 0027849531198889 005161 033062750711988810 010866 012250879311988811 061271 0058634566
8 Mathematical Problems in Engineering
minus50 minus40 minus30 minus20 minus10 0 5 10
11
12
13
14
15
16
17
18
19
119895lowast
()
1198621
11986271198628
11986291198621011986211
119862211986231198624
11986251198626
Figure 7 Variation of 119895lowast with the index values
1198621
1198623 1198627
1198622
1198628
1198629
1198624
11986210
1198625
1198626
11986211
14
15
16
17
18
19
119895lowast
minus50 minus40 minus30 minus20 minus10 0 10
()20 30 40 50
Figure 8 Variation of 119895lowast with the weight values
Table 3 The119863119895(V1015840119894 ) values
Index High1198631(V1015840119894 ) Good1198632(V
1015840119894 ) Medium1198633(V
1015840119894 ) Bad1198634(V
1015840119894 )
1198881 minus56119864 minus 17 17 155 091198882 minus012 012 04 0521198883 014 minus006 006 0261198884 02286 0 0 028571198885 025 05 075 11198886 minus004 004 02 0481198887 005 minus005 005 0151198888 005 555119864 minus 17 minus56119864 minus 17 011198889 minus56119864 minus 17 minus56119864 minus 17 01 0211988810 011 006 minus004 00411988811 007 minus003 003 018
(5) Calculate the weight of indexes according to theweighted supermatrix and limit matrix The resultsare shown in Table 2
43 Calculate the Value of Closeness Function Calculate thedistance119863119895(V
1015840119894 ) of the evaluatedmatter element related to new
classical domain just as shown in Table 3The value of the closeness degree of each grade is below
1198731 (1199010) = 1 minus11
sum119894=1
1198631 (V1015840119894)119908119894 (119883) = 0999482
1198732 (1199010) = 1 minus11
sum119894=1
1198632 (V1015840119894)119908119894 (119883) = 0998698
1198733 (1199010) = 1 minus11
sum119894=1
1198633 (V1015840119894)119908119894 (119883) = 099829
1198734 (1199010) = 1 minus11
sum119894=1
1198634 (V1015840119894)119908119894 (119883) = 0997647
(14)
44 Determine the Performance Rating Since 1198731(1199010) =maxN119895(1199010) = 0999482 119895 = 1 2 3 4 it is shown that theperformance level of ERP project in this enterprise belongsto ldquohighrdquo
45 Sensitivity Analysis Sensitivity analysis is performedaccording to the performance evaluation index systemof ERPproject When the index value or weight of index changesits level variable characteristic value 119895lowast also changes corre-spondinglyWhen the index value changes by 5 10 minus10minus20 minus30 minus40 minus50 respectively the level variablecharacteristic value 119895lowast changes as shown in Figure 2 Whenthe weight of index changes by plusmn10 plusmn20 plusmn30 plusmn40or plusmn50 the level variable characteristic value 119895lowast changescorrespondingly just as the Figure 3
As we can see from Figure 7 the project performanceindexes 1198881 1198882 1198888 11988811 have large effect on the evaluation resultswhich means that the sensitivity of 1198881 1198882 1198888 11988811 is very strongFor example when the 11988811 index changes the range ofthe 119895lowast value varies from 12 to 18 Although ERP projectperformance level does not change the level gradually tendsto ldquogoodrdquo level from ldquohighrdquo level With the change of index1198883 1198884 1198885 1198886 1198887 1198889 11988810 the 119895
lowast value changes a little from 15 to165 It indicates that the variation of index value will notchange the level which the project performance tends to orbelongs to
In Figure 8 we can know that the change of 1198881 and 11988811indexes affects the 119895lowast value obviously but other indexes haveless effect on the 119895lowast value In a word 1198881 and 11988811 are sensitiveindexes in the ERP project performance evaluation
5 Conclusions
ERP system has been introduced into enterprises for manyyears It is necessary to evaluate the performance of theERP project in enterprise However the factors which affectthe performance of ERP project are complex and relatedSo a hybrid evaluation method of ERP project performancewhich considers these peculiarities was proposed In order
Mathematical Problems in Engineering 9
to analyze the performance of ERP project an index sys-tem of comprehensive benefit evaluation including financecustomer and operation management is established in thispaper An ANP was proposed to determine the weight ofeach index which fully took the relationship between variousindicators into account Due to the limitations and inadequa-cies of traditionalmatter-element extensionmodel when per-forming the comprehensive evaluation an improved matter-element extensionmodel was proposed And then taking oneenterprisersquos ERP project as an example the comprehensiveevaluation was done The empirical analysis results show theperformance of ERPproject in our case belongs to ldquohighrdquo leveland our proposed hybrid evaluation model is feasible andpractical Finally a sensitivity analysis is performed to findsensitive index in the ERP project evaluation The analysisresults show that total asset turnover ratio and data transferefficiency are sensitive indexes so this enterprise should paymore attention to them
Acknowledgments
This study is supported by theNationalNatural Science Foun-dation of China (Grant no 70971038) and the Humanitiesand Social Science project of the Ministry of Education ofChina (Project no 11YJA790217) The authors are grateful tothe editor and anonymous reviewers for their suggestions onimproving the quality of the paper
References
[1] J S Zhang and W Tan ldquoResearch on the performance eval-uation of logistics enterprise based on the analytic hierarchyprocessrdquo Energy Procedia vol 14 pp 1618ndash1623 2012
[2] I Ertugrul and N Karakasoglu ldquoPerformance evaluation ofTurkish cement firms with fuzzy analytic hierarchy process andTOPSISmethodsrdquo Expert Systems with Applications vol 36 no1 pp 702ndash715 2009
[3] H Saranga and R Moser ldquoPerformance evaluation of purchas-ing and supply management using value chain DEA approachrdquoEuropean Journal of Operational Research vol 207 no 1 pp197ndash205 2010
[4] H Y Wu Y K Lin and C H Chang ldquoPerformance evaluationof extension education centers in universities based on thebalanced scorecardrdquo Evaluation and Program Planning vol 34no 1 pp 37ndash50 2011
[5] J Y Li ldquoThe effect evaluation of ERP system based on BP neuralnetworkrdquo Technology Square no 8 pp 25ndash27 2010
[6] S G Chen and Y K Lin ldquoOn performance evaluation ofERP systems with fuzzy mathematicsrdquo Expert Systems WithApplications vol 36 pp 6362ndash6367 2010
[7] X H Zhan X Xu and H Z Liu ldquoERP performance evaluationof power supply engineering Company Based on Gray TriangleWhiten Functionrdquo Systems Engineering Procedia vol 4 pp 116ndash123 2012
[8] L Xu ldquoThe evaluation of ERP sandtable simulation based onAHPrdquo Physics Procedia vol 33 pp 1924ndash1931 2012
[9] J Razmi M S Sangari and R Ghodsi ldquoDeveloping a practicalframework for ERP readiness assessment using fuzzy analyticnetwork processrdquoAdvances in Engineering Software vol 40 no11 pp 1168ndash1178 2009
[10] I C Chang H G Hwang H C Liaw M C Hung S LChen and D C Yen ldquoA neural network evaluation model forERP performance from SCM perspective to enhance enterprisecompetitive advantagerdquo Expert Systems with Applications vol35 no 4 pp 1809ndash1816 2008
[11] T X Han Y F Wang and W M Liu ldquoERP performanceevaluation method study in electric power enterpriserdquo Journalof East China Power vol 35 pp 1064ndash1069 2007
[12] Y Z Li and X Zhang ldquoThe application of principle exten-sion method in evaluating enterprise performancerdquo Journal ofChengdu University (Social Science Edition) vol 17 no 2 pp103ndash107 2010
[13] Y W Zhou ldquoPerformance evaluation based on the entropyweight and matter-element modelrdquo Enterprise Economy no 3pp 76ndash79 2012
[14] L L Yang ldquoThe research on the evaluation index system ofthe ERP system effectrdquo Qingdao University of Science andTechnology 2010
[15] W Cai C Y Yang and W Lin Extension Engineering MethodScience Press Beijing China 1997
[16] Y XHe A YDai J ZhuH YHe and F Li ldquoRisk assessment ofurban network planning in china based on the matter-elementmodel and extension analysisrdquo International Journal of ElectricalPower and Energy Systems vol 33 no 3 pp 775ndash782 2011
[17] X P Zhang ldquoThe fuzzy comprehensive evaluation result setchange based on the close degreerdquo Journal of Shandong Univer-sity vol 39 no 2 pp 25ndash29 2004
[18] C T Lin C B Chen and Y C Ting ldquoAn ERP model forsupplier selection in electronics industryrdquo Expert Systems withApplications vol 38 no 3 pp 1760ndash1765 2011
[19] B Pang and S Bai ldquoAn integrated fuzzy synthetic evaluationapproach for supplier selection based on analytic networkprocessrdquo Journal of Intelligent Manufacturing vol 24 no 1 pp163ndash174 2011
[20] Y C Hu J H Wang and R Y Wang ldquoEvaluating the per-formance of Taiwan homestay using analytic network processrdquoMathematical Problems in Engineering vol 2012 Article ID827193 24 pages 2012
Submit your manuscripts athttpwwwhindawicom
OperationsResearch
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Abstract and Applied Analysis
ISRN Applied Mathematics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2013
International Journal of
Combinatorics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Journal of Function Spaces and Applications
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
ISRN Geometry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Discrete Dynamicsin Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2013
Advances in
Mathematical Physics
ISRN Algebra
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
ProbabilityandStatistics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
ISRN Mathematical Analysis
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Journal ofApplied Mathematics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Advances in
DecisionSciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Stochastic AnalysisInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawi Publishing Corporation httpwwwhindawicom Volume 2013
The Scientific World Journal
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
ISRN Discrete Mathematics
Hindawi Publishing Corporationhttpwwwhindawicom
DifferentialEquations
International Journal of
Volume 2013
Mathematical Problems in Engineering 5
matrix of each element influencing 119862119894 under each principleas follows
119882 =1198881119888119899
1198881 sdot sdot sdot 119888119899
[[
[
11988211 sdot sdot sdot 1198821119899 d
1198821198991 sdot sdot sdot 119882119899119899
]]
]
(9)
Taking119861119896 as standardwe compare the influence degree ofeach element to119862119894 and we can get weightedmatrix as follows
119860 = (
1198861 sdot sdot sdot 1198861119899 d
1198861198991 sdot sdot sdot 119886119899119899
) (10)
The matrix 119860 is multiplied by the matrix 119882 then weget the weighted matrix 119882 = 119886119894119895119882119894119895 119894 = 1 2 119899 119895 =
1 2 119899 If the limit of matrix119860 is convergent and only119882infinis the limit relative ranking vector of each element to the 119895element under the 119861119896 principle
34 The Calculation Process of the ANP-Improved Matter-Element Extension Model In summary the steps of compre-hensive evaluation based on the ANP and improved matter-element method are as follows
Step 1 Determine the classical domain controlled field andmatter element to be evaluated
Step 2 Normalize the classical domain controlled field andmatter element to be evaluated when the measure data ofindex exceeds controlled field
Step 3 Calculate the index weight based on the ANP
Step 4 Calculate the value of closeness function of eachgrade
The119873119895lowast(1199010) = max119873119895lowast(1199010) (119895 = 1 2 119898) means thatthe matter element to be evaluated belongs to the 119895lowastth level
4 Case Study
Amanufacturing enterprise began to implement ERP projecttwo years ago In order to figure out the situation of thisproject an evaluation of ERP project performance wasproposed The evaluation process is as follows
41 Determine the Classical Domain Controlled Field MatterElement to Be Evaluated and the Corresponding Normaliza-tion (1) Establish the classical domain The classical fields ofquantitative indicators in evaluation index system were setaccording to related literatures and expert [7 14]The classicaldomain of each level is described as follows 1199011 1199012 1199013 and
1199014 represent high good medium and bad performancerespectively
R1=
[[[[[[[[[[[[[[[[
[
1199011 1198881 (09 1)1198882 (015 25)1198883 (4 5)1198884 (028 035)1198885 (015 02)1198886 (0 004)1198887 (09 1)1198888 (095 1)1198889 (09 1)11988810 (095 1)11988811 (09 1)
]]]]]]]]]]]]]]]]
]
R2=
[[[[[[[[[[[[[[[[
[
1199012 1198881 (08 09)1198882 (008 015)1198883 (3 4)1198884 (02 028)1198885 (01 015)1198886 (004 008)1198887 (08 09)1198888 (09 095)1198889 (08 09)11988810 (09 095)11988811 (08 09)
]]]]]]]]]]]]]]]]
]
R3=
[[[[[[[[[[[[[[[[
[
1199013 1198881 (065 08)1198882 (005 008)1198883 (2 3)1198884 (01 02)1198885 (005 01)1198886 (008 015)1198887 (07 08)1198888 (08 09)1198889 (07 08)11988810 (08 09)11988811 (065 08)
]]]]]]]]]]]]]]]]
]
R4=
[[[[[[[[[[[[[[[[
[
1199014 1198881 (0 065)1198882 (0 005)1198883 (0 2)1198884 (0 01)1198885 (0 005)1198886 (015 025)1198887 (0 07)1198888 (0 08)1198889 (0 07)11988810 (0 08)11988811 (0 065)
]]]]]]]]]]]]]]]]
]
(11)
(2) Establish the controlled fieldThe classical field of eachindex is equal to the sum of all classical field values
(3) Establish the matter element evaluation Accordingto the measured data of enterprise performance evaluationindex thematter element to be evaluated can be builtR119901 andR0 are as follows
R0 =
[[[[[[[[[[[[[[[[
[
1199010 1198881 091198882 0181198883 31198884 021198885 0251198886 0031198887 0851198888 091198889 0911988810 08411988811 083
]]]]]]]]]]]]]]]]
]
R119901 =
[[[[[[[[[[[[[[[[
[
119901p 1198881 (0 1)
1198882 (0 025)1198883 (0 5)1198884 (0 035)1198885 (0 02)1198886 (0 025)1198887 (09 1)1198888 (0 1)1198889 (0 1)11988810 (0 1)11988811 (0 1)
]]]]]]]]]]]]]]]]
]
(12)
We know that the value of index 1198885 has exceeded theclassical domain so the closeness function cannot be cal-culated in traditional matter-element extension model Weshould normalize the classical domain and controlled field
6 Mathematical Problems in Engineering
1198611 1198612 1198613
Figure 3 Inner dependence among criteria
to improve the traditional model The normalized classicaldomain and controlled are below
R10158401=
[[[[[[[[[[[[[[[[
[
1199011 1198881 (09 1)1198882 (06 1)1198883 (08 1)1198884 (08 1)1198885 (075 1)1198886 (0 016)1198887 (09 1)1198888 (095 1)1198889 (09 1)11988810 (095 1)11988811 (09 1)
]]]]]]]]]]]]]]]]
]
R10158402=
[[[[[[[[[[[[[[[[
[
1199012 1198881 (08 09)1198882 (032 06)1198883 (06 08)1198884 (057 08)1198885 (05 075)1198886 (016 032)1198887 (08 09)1198888 (09 095)1198889 (08 09)11988810 (09 095)11988811 (08 09)
]]]]]]]]]]]]]]]]
]
R10158403=
[[[[[[[[[[[[[[[[
[
1199013 1198881 (065 08)1198882 (02 032)1198883 (04 06)1198884 (0286 0571)1198885 (025 05)1198886 (032 06)1198887 (07 08)1198888 (08 09)1198889 (07 08)11988810 (08 09)11988811 (065 08)
]]]]]]]]]]]]]]]]
]
R10158404=
[[[[[[[[[[[[[[[[
[
1199014 1198881 (0 065)1198882 (0 02)1198883 (0 0286)1198884 (0 025)1198885 (06 1)1198886 (0 07)1198887 (0 08)1198888 (0 08)1198889 (0 07)11988810 (0 08)11988811 (0 065)
]]]]]]]]]]]]]]]]
]
R10158400 =
[[[[[[[[[[[[[[[[
[
1199010 1198881 091198882 0721198883 061198884 05711198885 1251198886 0121198887 0851198888 091198889 0911988810 08411988811 083
]]]]]]]]]]]]]]]]
]
(13)
42 Calculate the Index Weight An ANP was used to deter-mine the weight of performance evaluation index whichcan fully take the relationship between various indicatorsinto account Because to the calculation is complicated weemployed ldquoSuper Decisionrdquo software to calculate the weightof each index The steps are as follows
1198881
1198882
1198883
1198884
1198885 1198886
1198887
1198888
1198889
11988810
11988811
Figure 4 Inner dependence among subcriteria
Table 1 The judgment matrix of elements
1198881 1198882 1198883 Local weight1198881 1 05 4 03445441198882 2 1 2 01085251198883 025 05 1 0546931
CR = 000566
(1) Establish ANP networkAccording to the index system diagram in Figure 1the control level and network level are developedbased on the dominance and feedback relationshipThe dependencies among indexes in the controllevel are shown in Figure 3 The relationships amongindexes in network level are depicted in Figure 4 AnANP model is developed on the network structure ofelements
(2) Structure the judgment matrixBased on the clear relationship between elements thejudgmentmatrixes are concluded through comparingelement sets and elements respectively by nine-scalemethod For example the pairwise comparisons ofelements in clutter B1 are conducted and the judgmentmatrix is shown in Table 1 and the local weight can beconcluded by ldquoSuper Decisionrdquo software
(3) Check the consistency of judgment matrixIf CR ratio exceeds 01 we should change the judg-ment matrix until all CR ratios are less than 01
(4) Calculate the weighted supermatrix and the limitmatrixCalculate the weighted supermatrix and the limitmatrix of indicator elements by software The resultsare shown in Figures 5 and 6
Mathematical Problems in Engineering 7
Figure 5 The weighted supermatrix of indicator elements
Figure 6 The limit matrix of indicator elements
Table 2 The global weights of each criterion
Criteria Local weights Subcriteria Local weights Global weights
Financial indicators (1198611) 02969611198881 030034 00780591681198882 037908 00184571071198883 032058 0069383293
Customer indicators (1198612) 0163424
1198884 042456 00326259671198885 0109866169 01125719761198886 011294 00951997571198887 0477648133 0089189267
Operating efficiency indicators (1198613) 0539615
1198888 022703 0027849531198889 005161 033062750711988810 010866 012250879311988811 061271 0058634566
8 Mathematical Problems in Engineering
minus50 minus40 minus30 minus20 minus10 0 5 10
11
12
13
14
15
16
17
18
19
119895lowast
()
1198621
11986271198628
11986291198621011986211
119862211986231198624
11986251198626
Figure 7 Variation of 119895lowast with the index values
1198621
1198623 1198627
1198622
1198628
1198629
1198624
11986210
1198625
1198626
11986211
14
15
16
17
18
19
119895lowast
minus50 minus40 minus30 minus20 minus10 0 10
()20 30 40 50
Figure 8 Variation of 119895lowast with the weight values
Table 3 The119863119895(V1015840119894 ) values
Index High1198631(V1015840119894 ) Good1198632(V
1015840119894 ) Medium1198633(V
1015840119894 ) Bad1198634(V
1015840119894 )
1198881 minus56119864 minus 17 17 155 091198882 minus012 012 04 0521198883 014 minus006 006 0261198884 02286 0 0 028571198885 025 05 075 11198886 minus004 004 02 0481198887 005 minus005 005 0151198888 005 555119864 minus 17 minus56119864 minus 17 011198889 minus56119864 minus 17 minus56119864 minus 17 01 0211988810 011 006 minus004 00411988811 007 minus003 003 018
(5) Calculate the weight of indexes according to theweighted supermatrix and limit matrix The resultsare shown in Table 2
43 Calculate the Value of Closeness Function Calculate thedistance119863119895(V
1015840119894 ) of the evaluatedmatter element related to new
classical domain just as shown in Table 3The value of the closeness degree of each grade is below
1198731 (1199010) = 1 minus11
sum119894=1
1198631 (V1015840119894)119908119894 (119883) = 0999482
1198732 (1199010) = 1 minus11
sum119894=1
1198632 (V1015840119894)119908119894 (119883) = 0998698
1198733 (1199010) = 1 minus11
sum119894=1
1198633 (V1015840119894)119908119894 (119883) = 099829
1198734 (1199010) = 1 minus11
sum119894=1
1198634 (V1015840119894)119908119894 (119883) = 0997647
(14)
44 Determine the Performance Rating Since 1198731(1199010) =maxN119895(1199010) = 0999482 119895 = 1 2 3 4 it is shown that theperformance level of ERP project in this enterprise belongsto ldquohighrdquo
45 Sensitivity Analysis Sensitivity analysis is performedaccording to the performance evaluation index systemof ERPproject When the index value or weight of index changesits level variable characteristic value 119895lowast also changes corre-spondinglyWhen the index value changes by 5 10 minus10minus20 minus30 minus40 minus50 respectively the level variablecharacteristic value 119895lowast changes as shown in Figure 2 Whenthe weight of index changes by plusmn10 plusmn20 plusmn30 plusmn40or plusmn50 the level variable characteristic value 119895lowast changescorrespondingly just as the Figure 3
As we can see from Figure 7 the project performanceindexes 1198881 1198882 1198888 11988811 have large effect on the evaluation resultswhich means that the sensitivity of 1198881 1198882 1198888 11988811 is very strongFor example when the 11988811 index changes the range ofthe 119895lowast value varies from 12 to 18 Although ERP projectperformance level does not change the level gradually tendsto ldquogoodrdquo level from ldquohighrdquo level With the change of index1198883 1198884 1198885 1198886 1198887 1198889 11988810 the 119895
lowast value changes a little from 15 to165 It indicates that the variation of index value will notchange the level which the project performance tends to orbelongs to
In Figure 8 we can know that the change of 1198881 and 11988811indexes affects the 119895lowast value obviously but other indexes haveless effect on the 119895lowast value In a word 1198881 and 11988811 are sensitiveindexes in the ERP project performance evaluation
5 Conclusions
ERP system has been introduced into enterprises for manyyears It is necessary to evaluate the performance of theERP project in enterprise However the factors which affectthe performance of ERP project are complex and relatedSo a hybrid evaluation method of ERP project performancewhich considers these peculiarities was proposed In order
Mathematical Problems in Engineering 9
to analyze the performance of ERP project an index sys-tem of comprehensive benefit evaluation including financecustomer and operation management is established in thispaper An ANP was proposed to determine the weight ofeach index which fully took the relationship between variousindicators into account Due to the limitations and inadequa-cies of traditionalmatter-element extensionmodel when per-forming the comprehensive evaluation an improved matter-element extensionmodel was proposed And then taking oneenterprisersquos ERP project as an example the comprehensiveevaluation was done The empirical analysis results show theperformance of ERPproject in our case belongs to ldquohighrdquo leveland our proposed hybrid evaluation model is feasible andpractical Finally a sensitivity analysis is performed to findsensitive index in the ERP project evaluation The analysisresults show that total asset turnover ratio and data transferefficiency are sensitive indexes so this enterprise should paymore attention to them
Acknowledgments
This study is supported by theNationalNatural Science Foun-dation of China (Grant no 70971038) and the Humanitiesand Social Science project of the Ministry of Education ofChina (Project no 11YJA790217) The authors are grateful tothe editor and anonymous reviewers for their suggestions onimproving the quality of the paper
References
[1] J S Zhang and W Tan ldquoResearch on the performance eval-uation of logistics enterprise based on the analytic hierarchyprocessrdquo Energy Procedia vol 14 pp 1618ndash1623 2012
[2] I Ertugrul and N Karakasoglu ldquoPerformance evaluation ofTurkish cement firms with fuzzy analytic hierarchy process andTOPSISmethodsrdquo Expert Systems with Applications vol 36 no1 pp 702ndash715 2009
[3] H Saranga and R Moser ldquoPerformance evaluation of purchas-ing and supply management using value chain DEA approachrdquoEuropean Journal of Operational Research vol 207 no 1 pp197ndash205 2010
[4] H Y Wu Y K Lin and C H Chang ldquoPerformance evaluationof extension education centers in universities based on thebalanced scorecardrdquo Evaluation and Program Planning vol 34no 1 pp 37ndash50 2011
[5] J Y Li ldquoThe effect evaluation of ERP system based on BP neuralnetworkrdquo Technology Square no 8 pp 25ndash27 2010
[6] S G Chen and Y K Lin ldquoOn performance evaluation ofERP systems with fuzzy mathematicsrdquo Expert Systems WithApplications vol 36 pp 6362ndash6367 2010
[7] X H Zhan X Xu and H Z Liu ldquoERP performance evaluationof power supply engineering Company Based on Gray TriangleWhiten Functionrdquo Systems Engineering Procedia vol 4 pp 116ndash123 2012
[8] L Xu ldquoThe evaluation of ERP sandtable simulation based onAHPrdquo Physics Procedia vol 33 pp 1924ndash1931 2012
[9] J Razmi M S Sangari and R Ghodsi ldquoDeveloping a practicalframework for ERP readiness assessment using fuzzy analyticnetwork processrdquoAdvances in Engineering Software vol 40 no11 pp 1168ndash1178 2009
[10] I C Chang H G Hwang H C Liaw M C Hung S LChen and D C Yen ldquoA neural network evaluation model forERP performance from SCM perspective to enhance enterprisecompetitive advantagerdquo Expert Systems with Applications vol35 no 4 pp 1809ndash1816 2008
[11] T X Han Y F Wang and W M Liu ldquoERP performanceevaluation method study in electric power enterpriserdquo Journalof East China Power vol 35 pp 1064ndash1069 2007
[12] Y Z Li and X Zhang ldquoThe application of principle exten-sion method in evaluating enterprise performancerdquo Journal ofChengdu University (Social Science Edition) vol 17 no 2 pp103ndash107 2010
[13] Y W Zhou ldquoPerformance evaluation based on the entropyweight and matter-element modelrdquo Enterprise Economy no 3pp 76ndash79 2012
[14] L L Yang ldquoThe research on the evaluation index system ofthe ERP system effectrdquo Qingdao University of Science andTechnology 2010
[15] W Cai C Y Yang and W Lin Extension Engineering MethodScience Press Beijing China 1997
[16] Y XHe A YDai J ZhuH YHe and F Li ldquoRisk assessment ofurban network planning in china based on the matter-elementmodel and extension analysisrdquo International Journal of ElectricalPower and Energy Systems vol 33 no 3 pp 775ndash782 2011
[17] X P Zhang ldquoThe fuzzy comprehensive evaluation result setchange based on the close degreerdquo Journal of Shandong Univer-sity vol 39 no 2 pp 25ndash29 2004
[18] C T Lin C B Chen and Y C Ting ldquoAn ERP model forsupplier selection in electronics industryrdquo Expert Systems withApplications vol 38 no 3 pp 1760ndash1765 2011
[19] B Pang and S Bai ldquoAn integrated fuzzy synthetic evaluationapproach for supplier selection based on analytic networkprocessrdquo Journal of Intelligent Manufacturing vol 24 no 1 pp163ndash174 2011
[20] Y C Hu J H Wang and R Y Wang ldquoEvaluating the per-formance of Taiwan homestay using analytic network processrdquoMathematical Problems in Engineering vol 2012 Article ID827193 24 pages 2012
Submit your manuscripts athttpwwwhindawicom
OperationsResearch
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Abstract and Applied Analysis
ISRN Applied Mathematics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2013
International Journal of
Combinatorics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Journal of Function Spaces and Applications
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
ISRN Geometry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Discrete Dynamicsin Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2013
Advances in
Mathematical Physics
ISRN Algebra
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
ProbabilityandStatistics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
ISRN Mathematical Analysis
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Journal ofApplied Mathematics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Advances in
DecisionSciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Stochastic AnalysisInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawi Publishing Corporation httpwwwhindawicom Volume 2013
The Scientific World Journal
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
ISRN Discrete Mathematics
Hindawi Publishing Corporationhttpwwwhindawicom
DifferentialEquations
International Journal of
Volume 2013
6 Mathematical Problems in Engineering
1198611 1198612 1198613
Figure 3 Inner dependence among criteria
to improve the traditional model The normalized classicaldomain and controlled are below
R10158401=
[[[[[[[[[[[[[[[[
[
1199011 1198881 (09 1)1198882 (06 1)1198883 (08 1)1198884 (08 1)1198885 (075 1)1198886 (0 016)1198887 (09 1)1198888 (095 1)1198889 (09 1)11988810 (095 1)11988811 (09 1)
]]]]]]]]]]]]]]]]
]
R10158402=
[[[[[[[[[[[[[[[[
[
1199012 1198881 (08 09)1198882 (032 06)1198883 (06 08)1198884 (057 08)1198885 (05 075)1198886 (016 032)1198887 (08 09)1198888 (09 095)1198889 (08 09)11988810 (09 095)11988811 (08 09)
]]]]]]]]]]]]]]]]
]
R10158403=
[[[[[[[[[[[[[[[[
[
1199013 1198881 (065 08)1198882 (02 032)1198883 (04 06)1198884 (0286 0571)1198885 (025 05)1198886 (032 06)1198887 (07 08)1198888 (08 09)1198889 (07 08)11988810 (08 09)11988811 (065 08)
]]]]]]]]]]]]]]]]
]
R10158404=
[[[[[[[[[[[[[[[[
[
1199014 1198881 (0 065)1198882 (0 02)1198883 (0 0286)1198884 (0 025)1198885 (06 1)1198886 (0 07)1198887 (0 08)1198888 (0 08)1198889 (0 07)11988810 (0 08)11988811 (0 065)
]]]]]]]]]]]]]]]]
]
R10158400 =
[[[[[[[[[[[[[[[[
[
1199010 1198881 091198882 0721198883 061198884 05711198885 1251198886 0121198887 0851198888 091198889 0911988810 08411988811 083
]]]]]]]]]]]]]]]]
]
(13)
42 Calculate the Index Weight An ANP was used to deter-mine the weight of performance evaluation index whichcan fully take the relationship between various indicatorsinto account Because to the calculation is complicated weemployed ldquoSuper Decisionrdquo software to calculate the weightof each index The steps are as follows
1198881
1198882
1198883
1198884
1198885 1198886
1198887
1198888
1198889
11988810
11988811
Figure 4 Inner dependence among subcriteria
Table 1 The judgment matrix of elements
1198881 1198882 1198883 Local weight1198881 1 05 4 03445441198882 2 1 2 01085251198883 025 05 1 0546931
CR = 000566
(1) Establish ANP networkAccording to the index system diagram in Figure 1the control level and network level are developedbased on the dominance and feedback relationshipThe dependencies among indexes in the controllevel are shown in Figure 3 The relationships amongindexes in network level are depicted in Figure 4 AnANP model is developed on the network structure ofelements
(2) Structure the judgment matrixBased on the clear relationship between elements thejudgmentmatrixes are concluded through comparingelement sets and elements respectively by nine-scalemethod For example the pairwise comparisons ofelements in clutter B1 are conducted and the judgmentmatrix is shown in Table 1 and the local weight can beconcluded by ldquoSuper Decisionrdquo software
(3) Check the consistency of judgment matrixIf CR ratio exceeds 01 we should change the judg-ment matrix until all CR ratios are less than 01
(4) Calculate the weighted supermatrix and the limitmatrixCalculate the weighted supermatrix and the limitmatrix of indicator elements by software The resultsare shown in Figures 5 and 6
Mathematical Problems in Engineering 7
Figure 5 The weighted supermatrix of indicator elements
Figure 6 The limit matrix of indicator elements
Table 2 The global weights of each criterion
Criteria Local weights Subcriteria Local weights Global weights
Financial indicators (1198611) 02969611198881 030034 00780591681198882 037908 00184571071198883 032058 0069383293
Customer indicators (1198612) 0163424
1198884 042456 00326259671198885 0109866169 01125719761198886 011294 00951997571198887 0477648133 0089189267
Operating efficiency indicators (1198613) 0539615
1198888 022703 0027849531198889 005161 033062750711988810 010866 012250879311988811 061271 0058634566
8 Mathematical Problems in Engineering
minus50 minus40 minus30 minus20 minus10 0 5 10
11
12
13
14
15
16
17
18
19
119895lowast
()
1198621
11986271198628
11986291198621011986211
119862211986231198624
11986251198626
Figure 7 Variation of 119895lowast with the index values
1198621
1198623 1198627
1198622
1198628
1198629
1198624
11986210
1198625
1198626
11986211
14
15
16
17
18
19
119895lowast
minus50 minus40 minus30 minus20 minus10 0 10
()20 30 40 50
Figure 8 Variation of 119895lowast with the weight values
Table 3 The119863119895(V1015840119894 ) values
Index High1198631(V1015840119894 ) Good1198632(V
1015840119894 ) Medium1198633(V
1015840119894 ) Bad1198634(V
1015840119894 )
1198881 minus56119864 minus 17 17 155 091198882 minus012 012 04 0521198883 014 minus006 006 0261198884 02286 0 0 028571198885 025 05 075 11198886 minus004 004 02 0481198887 005 minus005 005 0151198888 005 555119864 minus 17 minus56119864 minus 17 011198889 minus56119864 minus 17 minus56119864 minus 17 01 0211988810 011 006 minus004 00411988811 007 minus003 003 018
(5) Calculate the weight of indexes according to theweighted supermatrix and limit matrix The resultsare shown in Table 2
43 Calculate the Value of Closeness Function Calculate thedistance119863119895(V
1015840119894 ) of the evaluatedmatter element related to new
classical domain just as shown in Table 3The value of the closeness degree of each grade is below
1198731 (1199010) = 1 minus11
sum119894=1
1198631 (V1015840119894)119908119894 (119883) = 0999482
1198732 (1199010) = 1 minus11
sum119894=1
1198632 (V1015840119894)119908119894 (119883) = 0998698
1198733 (1199010) = 1 minus11
sum119894=1
1198633 (V1015840119894)119908119894 (119883) = 099829
1198734 (1199010) = 1 minus11
sum119894=1
1198634 (V1015840119894)119908119894 (119883) = 0997647
(14)
44 Determine the Performance Rating Since 1198731(1199010) =maxN119895(1199010) = 0999482 119895 = 1 2 3 4 it is shown that theperformance level of ERP project in this enterprise belongsto ldquohighrdquo
45 Sensitivity Analysis Sensitivity analysis is performedaccording to the performance evaluation index systemof ERPproject When the index value or weight of index changesits level variable characteristic value 119895lowast also changes corre-spondinglyWhen the index value changes by 5 10 minus10minus20 minus30 minus40 minus50 respectively the level variablecharacteristic value 119895lowast changes as shown in Figure 2 Whenthe weight of index changes by plusmn10 plusmn20 plusmn30 plusmn40or plusmn50 the level variable characteristic value 119895lowast changescorrespondingly just as the Figure 3
As we can see from Figure 7 the project performanceindexes 1198881 1198882 1198888 11988811 have large effect on the evaluation resultswhich means that the sensitivity of 1198881 1198882 1198888 11988811 is very strongFor example when the 11988811 index changes the range ofthe 119895lowast value varies from 12 to 18 Although ERP projectperformance level does not change the level gradually tendsto ldquogoodrdquo level from ldquohighrdquo level With the change of index1198883 1198884 1198885 1198886 1198887 1198889 11988810 the 119895
lowast value changes a little from 15 to165 It indicates that the variation of index value will notchange the level which the project performance tends to orbelongs to
In Figure 8 we can know that the change of 1198881 and 11988811indexes affects the 119895lowast value obviously but other indexes haveless effect on the 119895lowast value In a word 1198881 and 11988811 are sensitiveindexes in the ERP project performance evaluation
5 Conclusions
ERP system has been introduced into enterprises for manyyears It is necessary to evaluate the performance of theERP project in enterprise However the factors which affectthe performance of ERP project are complex and relatedSo a hybrid evaluation method of ERP project performancewhich considers these peculiarities was proposed In order
Mathematical Problems in Engineering 9
to analyze the performance of ERP project an index sys-tem of comprehensive benefit evaluation including financecustomer and operation management is established in thispaper An ANP was proposed to determine the weight ofeach index which fully took the relationship between variousindicators into account Due to the limitations and inadequa-cies of traditionalmatter-element extensionmodel when per-forming the comprehensive evaluation an improved matter-element extensionmodel was proposed And then taking oneenterprisersquos ERP project as an example the comprehensiveevaluation was done The empirical analysis results show theperformance of ERPproject in our case belongs to ldquohighrdquo leveland our proposed hybrid evaluation model is feasible andpractical Finally a sensitivity analysis is performed to findsensitive index in the ERP project evaluation The analysisresults show that total asset turnover ratio and data transferefficiency are sensitive indexes so this enterprise should paymore attention to them
Acknowledgments
This study is supported by theNationalNatural Science Foun-dation of China (Grant no 70971038) and the Humanitiesand Social Science project of the Ministry of Education ofChina (Project no 11YJA790217) The authors are grateful tothe editor and anonymous reviewers for their suggestions onimproving the quality of the paper
References
[1] J S Zhang and W Tan ldquoResearch on the performance eval-uation of logistics enterprise based on the analytic hierarchyprocessrdquo Energy Procedia vol 14 pp 1618ndash1623 2012
[2] I Ertugrul and N Karakasoglu ldquoPerformance evaluation ofTurkish cement firms with fuzzy analytic hierarchy process andTOPSISmethodsrdquo Expert Systems with Applications vol 36 no1 pp 702ndash715 2009
[3] H Saranga and R Moser ldquoPerformance evaluation of purchas-ing and supply management using value chain DEA approachrdquoEuropean Journal of Operational Research vol 207 no 1 pp197ndash205 2010
[4] H Y Wu Y K Lin and C H Chang ldquoPerformance evaluationof extension education centers in universities based on thebalanced scorecardrdquo Evaluation and Program Planning vol 34no 1 pp 37ndash50 2011
[5] J Y Li ldquoThe effect evaluation of ERP system based on BP neuralnetworkrdquo Technology Square no 8 pp 25ndash27 2010
[6] S G Chen and Y K Lin ldquoOn performance evaluation ofERP systems with fuzzy mathematicsrdquo Expert Systems WithApplications vol 36 pp 6362ndash6367 2010
[7] X H Zhan X Xu and H Z Liu ldquoERP performance evaluationof power supply engineering Company Based on Gray TriangleWhiten Functionrdquo Systems Engineering Procedia vol 4 pp 116ndash123 2012
[8] L Xu ldquoThe evaluation of ERP sandtable simulation based onAHPrdquo Physics Procedia vol 33 pp 1924ndash1931 2012
[9] J Razmi M S Sangari and R Ghodsi ldquoDeveloping a practicalframework for ERP readiness assessment using fuzzy analyticnetwork processrdquoAdvances in Engineering Software vol 40 no11 pp 1168ndash1178 2009
[10] I C Chang H G Hwang H C Liaw M C Hung S LChen and D C Yen ldquoA neural network evaluation model forERP performance from SCM perspective to enhance enterprisecompetitive advantagerdquo Expert Systems with Applications vol35 no 4 pp 1809ndash1816 2008
[11] T X Han Y F Wang and W M Liu ldquoERP performanceevaluation method study in electric power enterpriserdquo Journalof East China Power vol 35 pp 1064ndash1069 2007
[12] Y Z Li and X Zhang ldquoThe application of principle exten-sion method in evaluating enterprise performancerdquo Journal ofChengdu University (Social Science Edition) vol 17 no 2 pp103ndash107 2010
[13] Y W Zhou ldquoPerformance evaluation based on the entropyweight and matter-element modelrdquo Enterprise Economy no 3pp 76ndash79 2012
[14] L L Yang ldquoThe research on the evaluation index system ofthe ERP system effectrdquo Qingdao University of Science andTechnology 2010
[15] W Cai C Y Yang and W Lin Extension Engineering MethodScience Press Beijing China 1997
[16] Y XHe A YDai J ZhuH YHe and F Li ldquoRisk assessment ofurban network planning in china based on the matter-elementmodel and extension analysisrdquo International Journal of ElectricalPower and Energy Systems vol 33 no 3 pp 775ndash782 2011
[17] X P Zhang ldquoThe fuzzy comprehensive evaluation result setchange based on the close degreerdquo Journal of Shandong Univer-sity vol 39 no 2 pp 25ndash29 2004
[18] C T Lin C B Chen and Y C Ting ldquoAn ERP model forsupplier selection in electronics industryrdquo Expert Systems withApplications vol 38 no 3 pp 1760ndash1765 2011
[19] B Pang and S Bai ldquoAn integrated fuzzy synthetic evaluationapproach for supplier selection based on analytic networkprocessrdquo Journal of Intelligent Manufacturing vol 24 no 1 pp163ndash174 2011
[20] Y C Hu J H Wang and R Y Wang ldquoEvaluating the per-formance of Taiwan homestay using analytic network processrdquoMathematical Problems in Engineering vol 2012 Article ID827193 24 pages 2012
Submit your manuscripts athttpwwwhindawicom
OperationsResearch
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Abstract and Applied Analysis
ISRN Applied Mathematics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2013
International Journal of
Combinatorics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Journal of Function Spaces and Applications
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
ISRN Geometry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Discrete Dynamicsin Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2013
Advances in
Mathematical Physics
ISRN Algebra
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
ProbabilityandStatistics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
ISRN Mathematical Analysis
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Journal ofApplied Mathematics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Advances in
DecisionSciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Stochastic AnalysisInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawi Publishing Corporation httpwwwhindawicom Volume 2013
The Scientific World Journal
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
ISRN Discrete Mathematics
Hindawi Publishing Corporationhttpwwwhindawicom
DifferentialEquations
International Journal of
Volume 2013
Mathematical Problems in Engineering 7
Figure 5 The weighted supermatrix of indicator elements
Figure 6 The limit matrix of indicator elements
Table 2 The global weights of each criterion
Criteria Local weights Subcriteria Local weights Global weights
Financial indicators (1198611) 02969611198881 030034 00780591681198882 037908 00184571071198883 032058 0069383293
Customer indicators (1198612) 0163424
1198884 042456 00326259671198885 0109866169 01125719761198886 011294 00951997571198887 0477648133 0089189267
Operating efficiency indicators (1198613) 0539615
1198888 022703 0027849531198889 005161 033062750711988810 010866 012250879311988811 061271 0058634566
8 Mathematical Problems in Engineering
minus50 minus40 minus30 minus20 minus10 0 5 10
11
12
13
14
15
16
17
18
19
119895lowast
()
1198621
11986271198628
11986291198621011986211
119862211986231198624
11986251198626
Figure 7 Variation of 119895lowast with the index values
1198621
1198623 1198627
1198622
1198628
1198629
1198624
11986210
1198625
1198626
11986211
14
15
16
17
18
19
119895lowast
minus50 minus40 minus30 minus20 minus10 0 10
()20 30 40 50
Figure 8 Variation of 119895lowast with the weight values
Table 3 The119863119895(V1015840119894 ) values
Index High1198631(V1015840119894 ) Good1198632(V
1015840119894 ) Medium1198633(V
1015840119894 ) Bad1198634(V
1015840119894 )
1198881 minus56119864 minus 17 17 155 091198882 minus012 012 04 0521198883 014 minus006 006 0261198884 02286 0 0 028571198885 025 05 075 11198886 minus004 004 02 0481198887 005 minus005 005 0151198888 005 555119864 minus 17 minus56119864 minus 17 011198889 minus56119864 minus 17 minus56119864 minus 17 01 0211988810 011 006 minus004 00411988811 007 minus003 003 018
(5) Calculate the weight of indexes according to theweighted supermatrix and limit matrix The resultsare shown in Table 2
43 Calculate the Value of Closeness Function Calculate thedistance119863119895(V
1015840119894 ) of the evaluatedmatter element related to new
classical domain just as shown in Table 3The value of the closeness degree of each grade is below
1198731 (1199010) = 1 minus11
sum119894=1
1198631 (V1015840119894)119908119894 (119883) = 0999482
1198732 (1199010) = 1 minus11
sum119894=1
1198632 (V1015840119894)119908119894 (119883) = 0998698
1198733 (1199010) = 1 minus11
sum119894=1
1198633 (V1015840119894)119908119894 (119883) = 099829
1198734 (1199010) = 1 minus11
sum119894=1
1198634 (V1015840119894)119908119894 (119883) = 0997647
(14)
44 Determine the Performance Rating Since 1198731(1199010) =maxN119895(1199010) = 0999482 119895 = 1 2 3 4 it is shown that theperformance level of ERP project in this enterprise belongsto ldquohighrdquo
45 Sensitivity Analysis Sensitivity analysis is performedaccording to the performance evaluation index systemof ERPproject When the index value or weight of index changesits level variable characteristic value 119895lowast also changes corre-spondinglyWhen the index value changes by 5 10 minus10minus20 minus30 minus40 minus50 respectively the level variablecharacteristic value 119895lowast changes as shown in Figure 2 Whenthe weight of index changes by plusmn10 plusmn20 plusmn30 plusmn40or plusmn50 the level variable characteristic value 119895lowast changescorrespondingly just as the Figure 3
As we can see from Figure 7 the project performanceindexes 1198881 1198882 1198888 11988811 have large effect on the evaluation resultswhich means that the sensitivity of 1198881 1198882 1198888 11988811 is very strongFor example when the 11988811 index changes the range ofthe 119895lowast value varies from 12 to 18 Although ERP projectperformance level does not change the level gradually tendsto ldquogoodrdquo level from ldquohighrdquo level With the change of index1198883 1198884 1198885 1198886 1198887 1198889 11988810 the 119895
lowast value changes a little from 15 to165 It indicates that the variation of index value will notchange the level which the project performance tends to orbelongs to
In Figure 8 we can know that the change of 1198881 and 11988811indexes affects the 119895lowast value obviously but other indexes haveless effect on the 119895lowast value In a word 1198881 and 11988811 are sensitiveindexes in the ERP project performance evaluation
5 Conclusions
ERP system has been introduced into enterprises for manyyears It is necessary to evaluate the performance of theERP project in enterprise However the factors which affectthe performance of ERP project are complex and relatedSo a hybrid evaluation method of ERP project performancewhich considers these peculiarities was proposed In order
Mathematical Problems in Engineering 9
to analyze the performance of ERP project an index sys-tem of comprehensive benefit evaluation including financecustomer and operation management is established in thispaper An ANP was proposed to determine the weight ofeach index which fully took the relationship between variousindicators into account Due to the limitations and inadequa-cies of traditionalmatter-element extensionmodel when per-forming the comprehensive evaluation an improved matter-element extensionmodel was proposed And then taking oneenterprisersquos ERP project as an example the comprehensiveevaluation was done The empirical analysis results show theperformance of ERPproject in our case belongs to ldquohighrdquo leveland our proposed hybrid evaluation model is feasible andpractical Finally a sensitivity analysis is performed to findsensitive index in the ERP project evaluation The analysisresults show that total asset turnover ratio and data transferefficiency are sensitive indexes so this enterprise should paymore attention to them
Acknowledgments
This study is supported by theNationalNatural Science Foun-dation of China (Grant no 70971038) and the Humanitiesand Social Science project of the Ministry of Education ofChina (Project no 11YJA790217) The authors are grateful tothe editor and anonymous reviewers for their suggestions onimproving the quality of the paper
References
[1] J S Zhang and W Tan ldquoResearch on the performance eval-uation of logistics enterprise based on the analytic hierarchyprocessrdquo Energy Procedia vol 14 pp 1618ndash1623 2012
[2] I Ertugrul and N Karakasoglu ldquoPerformance evaluation ofTurkish cement firms with fuzzy analytic hierarchy process andTOPSISmethodsrdquo Expert Systems with Applications vol 36 no1 pp 702ndash715 2009
[3] H Saranga and R Moser ldquoPerformance evaluation of purchas-ing and supply management using value chain DEA approachrdquoEuropean Journal of Operational Research vol 207 no 1 pp197ndash205 2010
[4] H Y Wu Y K Lin and C H Chang ldquoPerformance evaluationof extension education centers in universities based on thebalanced scorecardrdquo Evaluation and Program Planning vol 34no 1 pp 37ndash50 2011
[5] J Y Li ldquoThe effect evaluation of ERP system based on BP neuralnetworkrdquo Technology Square no 8 pp 25ndash27 2010
[6] S G Chen and Y K Lin ldquoOn performance evaluation ofERP systems with fuzzy mathematicsrdquo Expert Systems WithApplications vol 36 pp 6362ndash6367 2010
[7] X H Zhan X Xu and H Z Liu ldquoERP performance evaluationof power supply engineering Company Based on Gray TriangleWhiten Functionrdquo Systems Engineering Procedia vol 4 pp 116ndash123 2012
[8] L Xu ldquoThe evaluation of ERP sandtable simulation based onAHPrdquo Physics Procedia vol 33 pp 1924ndash1931 2012
[9] J Razmi M S Sangari and R Ghodsi ldquoDeveloping a practicalframework for ERP readiness assessment using fuzzy analyticnetwork processrdquoAdvances in Engineering Software vol 40 no11 pp 1168ndash1178 2009
[10] I C Chang H G Hwang H C Liaw M C Hung S LChen and D C Yen ldquoA neural network evaluation model forERP performance from SCM perspective to enhance enterprisecompetitive advantagerdquo Expert Systems with Applications vol35 no 4 pp 1809ndash1816 2008
[11] T X Han Y F Wang and W M Liu ldquoERP performanceevaluation method study in electric power enterpriserdquo Journalof East China Power vol 35 pp 1064ndash1069 2007
[12] Y Z Li and X Zhang ldquoThe application of principle exten-sion method in evaluating enterprise performancerdquo Journal ofChengdu University (Social Science Edition) vol 17 no 2 pp103ndash107 2010
[13] Y W Zhou ldquoPerformance evaluation based on the entropyweight and matter-element modelrdquo Enterprise Economy no 3pp 76ndash79 2012
[14] L L Yang ldquoThe research on the evaluation index system ofthe ERP system effectrdquo Qingdao University of Science andTechnology 2010
[15] W Cai C Y Yang and W Lin Extension Engineering MethodScience Press Beijing China 1997
[16] Y XHe A YDai J ZhuH YHe and F Li ldquoRisk assessment ofurban network planning in china based on the matter-elementmodel and extension analysisrdquo International Journal of ElectricalPower and Energy Systems vol 33 no 3 pp 775ndash782 2011
[17] X P Zhang ldquoThe fuzzy comprehensive evaluation result setchange based on the close degreerdquo Journal of Shandong Univer-sity vol 39 no 2 pp 25ndash29 2004
[18] C T Lin C B Chen and Y C Ting ldquoAn ERP model forsupplier selection in electronics industryrdquo Expert Systems withApplications vol 38 no 3 pp 1760ndash1765 2011
[19] B Pang and S Bai ldquoAn integrated fuzzy synthetic evaluationapproach for supplier selection based on analytic networkprocessrdquo Journal of Intelligent Manufacturing vol 24 no 1 pp163ndash174 2011
[20] Y C Hu J H Wang and R Y Wang ldquoEvaluating the per-formance of Taiwan homestay using analytic network processrdquoMathematical Problems in Engineering vol 2012 Article ID827193 24 pages 2012
Submit your manuscripts athttpwwwhindawicom
OperationsResearch
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Abstract and Applied Analysis
ISRN Applied Mathematics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2013
International Journal of
Combinatorics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Journal of Function Spaces and Applications
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
ISRN Geometry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Discrete Dynamicsin Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2013
Advances in
Mathematical Physics
ISRN Algebra
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
ProbabilityandStatistics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
ISRN Mathematical Analysis
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Journal ofApplied Mathematics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Advances in
DecisionSciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Stochastic AnalysisInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawi Publishing Corporation httpwwwhindawicom Volume 2013
The Scientific World Journal
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
ISRN Discrete Mathematics
Hindawi Publishing Corporationhttpwwwhindawicom
DifferentialEquations
International Journal of
Volume 2013
8 Mathematical Problems in Engineering
minus50 minus40 minus30 minus20 minus10 0 5 10
11
12
13
14
15
16
17
18
19
119895lowast
()
1198621
11986271198628
11986291198621011986211
119862211986231198624
11986251198626
Figure 7 Variation of 119895lowast with the index values
1198621
1198623 1198627
1198622
1198628
1198629
1198624
11986210
1198625
1198626
11986211
14
15
16
17
18
19
119895lowast
minus50 minus40 minus30 minus20 minus10 0 10
()20 30 40 50
Figure 8 Variation of 119895lowast with the weight values
Table 3 The119863119895(V1015840119894 ) values
Index High1198631(V1015840119894 ) Good1198632(V
1015840119894 ) Medium1198633(V
1015840119894 ) Bad1198634(V
1015840119894 )
1198881 minus56119864 minus 17 17 155 091198882 minus012 012 04 0521198883 014 minus006 006 0261198884 02286 0 0 028571198885 025 05 075 11198886 minus004 004 02 0481198887 005 minus005 005 0151198888 005 555119864 minus 17 minus56119864 minus 17 011198889 minus56119864 minus 17 minus56119864 minus 17 01 0211988810 011 006 minus004 00411988811 007 minus003 003 018
(5) Calculate the weight of indexes according to theweighted supermatrix and limit matrix The resultsare shown in Table 2
43 Calculate the Value of Closeness Function Calculate thedistance119863119895(V
1015840119894 ) of the evaluatedmatter element related to new
classical domain just as shown in Table 3The value of the closeness degree of each grade is below
1198731 (1199010) = 1 minus11
sum119894=1
1198631 (V1015840119894)119908119894 (119883) = 0999482
1198732 (1199010) = 1 minus11
sum119894=1
1198632 (V1015840119894)119908119894 (119883) = 0998698
1198733 (1199010) = 1 minus11
sum119894=1
1198633 (V1015840119894)119908119894 (119883) = 099829
1198734 (1199010) = 1 minus11
sum119894=1
1198634 (V1015840119894)119908119894 (119883) = 0997647
(14)
44 Determine the Performance Rating Since 1198731(1199010) =maxN119895(1199010) = 0999482 119895 = 1 2 3 4 it is shown that theperformance level of ERP project in this enterprise belongsto ldquohighrdquo
45 Sensitivity Analysis Sensitivity analysis is performedaccording to the performance evaluation index systemof ERPproject When the index value or weight of index changesits level variable characteristic value 119895lowast also changes corre-spondinglyWhen the index value changes by 5 10 minus10minus20 minus30 minus40 minus50 respectively the level variablecharacteristic value 119895lowast changes as shown in Figure 2 Whenthe weight of index changes by plusmn10 plusmn20 plusmn30 plusmn40or plusmn50 the level variable characteristic value 119895lowast changescorrespondingly just as the Figure 3
As we can see from Figure 7 the project performanceindexes 1198881 1198882 1198888 11988811 have large effect on the evaluation resultswhich means that the sensitivity of 1198881 1198882 1198888 11988811 is very strongFor example when the 11988811 index changes the range ofthe 119895lowast value varies from 12 to 18 Although ERP projectperformance level does not change the level gradually tendsto ldquogoodrdquo level from ldquohighrdquo level With the change of index1198883 1198884 1198885 1198886 1198887 1198889 11988810 the 119895
lowast value changes a little from 15 to165 It indicates that the variation of index value will notchange the level which the project performance tends to orbelongs to
In Figure 8 we can know that the change of 1198881 and 11988811indexes affects the 119895lowast value obviously but other indexes haveless effect on the 119895lowast value In a word 1198881 and 11988811 are sensitiveindexes in the ERP project performance evaluation
5 Conclusions
ERP system has been introduced into enterprises for manyyears It is necessary to evaluate the performance of theERP project in enterprise However the factors which affectthe performance of ERP project are complex and relatedSo a hybrid evaluation method of ERP project performancewhich considers these peculiarities was proposed In order
Mathematical Problems in Engineering 9
to analyze the performance of ERP project an index sys-tem of comprehensive benefit evaluation including financecustomer and operation management is established in thispaper An ANP was proposed to determine the weight ofeach index which fully took the relationship between variousindicators into account Due to the limitations and inadequa-cies of traditionalmatter-element extensionmodel when per-forming the comprehensive evaluation an improved matter-element extensionmodel was proposed And then taking oneenterprisersquos ERP project as an example the comprehensiveevaluation was done The empirical analysis results show theperformance of ERPproject in our case belongs to ldquohighrdquo leveland our proposed hybrid evaluation model is feasible andpractical Finally a sensitivity analysis is performed to findsensitive index in the ERP project evaluation The analysisresults show that total asset turnover ratio and data transferefficiency are sensitive indexes so this enterprise should paymore attention to them
Acknowledgments
This study is supported by theNationalNatural Science Foun-dation of China (Grant no 70971038) and the Humanitiesand Social Science project of the Ministry of Education ofChina (Project no 11YJA790217) The authors are grateful tothe editor and anonymous reviewers for their suggestions onimproving the quality of the paper
References
[1] J S Zhang and W Tan ldquoResearch on the performance eval-uation of logistics enterprise based on the analytic hierarchyprocessrdquo Energy Procedia vol 14 pp 1618ndash1623 2012
[2] I Ertugrul and N Karakasoglu ldquoPerformance evaluation ofTurkish cement firms with fuzzy analytic hierarchy process andTOPSISmethodsrdquo Expert Systems with Applications vol 36 no1 pp 702ndash715 2009
[3] H Saranga and R Moser ldquoPerformance evaluation of purchas-ing and supply management using value chain DEA approachrdquoEuropean Journal of Operational Research vol 207 no 1 pp197ndash205 2010
[4] H Y Wu Y K Lin and C H Chang ldquoPerformance evaluationof extension education centers in universities based on thebalanced scorecardrdquo Evaluation and Program Planning vol 34no 1 pp 37ndash50 2011
[5] J Y Li ldquoThe effect evaluation of ERP system based on BP neuralnetworkrdquo Technology Square no 8 pp 25ndash27 2010
[6] S G Chen and Y K Lin ldquoOn performance evaluation ofERP systems with fuzzy mathematicsrdquo Expert Systems WithApplications vol 36 pp 6362ndash6367 2010
[7] X H Zhan X Xu and H Z Liu ldquoERP performance evaluationof power supply engineering Company Based on Gray TriangleWhiten Functionrdquo Systems Engineering Procedia vol 4 pp 116ndash123 2012
[8] L Xu ldquoThe evaluation of ERP sandtable simulation based onAHPrdquo Physics Procedia vol 33 pp 1924ndash1931 2012
[9] J Razmi M S Sangari and R Ghodsi ldquoDeveloping a practicalframework for ERP readiness assessment using fuzzy analyticnetwork processrdquoAdvances in Engineering Software vol 40 no11 pp 1168ndash1178 2009
[10] I C Chang H G Hwang H C Liaw M C Hung S LChen and D C Yen ldquoA neural network evaluation model forERP performance from SCM perspective to enhance enterprisecompetitive advantagerdquo Expert Systems with Applications vol35 no 4 pp 1809ndash1816 2008
[11] T X Han Y F Wang and W M Liu ldquoERP performanceevaluation method study in electric power enterpriserdquo Journalof East China Power vol 35 pp 1064ndash1069 2007
[12] Y Z Li and X Zhang ldquoThe application of principle exten-sion method in evaluating enterprise performancerdquo Journal ofChengdu University (Social Science Edition) vol 17 no 2 pp103ndash107 2010
[13] Y W Zhou ldquoPerformance evaluation based on the entropyweight and matter-element modelrdquo Enterprise Economy no 3pp 76ndash79 2012
[14] L L Yang ldquoThe research on the evaluation index system ofthe ERP system effectrdquo Qingdao University of Science andTechnology 2010
[15] W Cai C Y Yang and W Lin Extension Engineering MethodScience Press Beijing China 1997
[16] Y XHe A YDai J ZhuH YHe and F Li ldquoRisk assessment ofurban network planning in china based on the matter-elementmodel and extension analysisrdquo International Journal of ElectricalPower and Energy Systems vol 33 no 3 pp 775ndash782 2011
[17] X P Zhang ldquoThe fuzzy comprehensive evaluation result setchange based on the close degreerdquo Journal of Shandong Univer-sity vol 39 no 2 pp 25ndash29 2004
[18] C T Lin C B Chen and Y C Ting ldquoAn ERP model forsupplier selection in electronics industryrdquo Expert Systems withApplications vol 38 no 3 pp 1760ndash1765 2011
[19] B Pang and S Bai ldquoAn integrated fuzzy synthetic evaluationapproach for supplier selection based on analytic networkprocessrdquo Journal of Intelligent Manufacturing vol 24 no 1 pp163ndash174 2011
[20] Y C Hu J H Wang and R Y Wang ldquoEvaluating the per-formance of Taiwan homestay using analytic network processrdquoMathematical Problems in Engineering vol 2012 Article ID827193 24 pages 2012
Submit your manuscripts athttpwwwhindawicom
OperationsResearch
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Abstract and Applied Analysis
ISRN Applied Mathematics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2013
International Journal of
Combinatorics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Journal of Function Spaces and Applications
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
ISRN Geometry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Discrete Dynamicsin Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2013
Advances in
Mathematical Physics
ISRN Algebra
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
ProbabilityandStatistics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
ISRN Mathematical Analysis
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Journal ofApplied Mathematics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Advances in
DecisionSciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Stochastic AnalysisInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawi Publishing Corporation httpwwwhindawicom Volume 2013
The Scientific World Journal
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
ISRN Discrete Mathematics
Hindawi Publishing Corporationhttpwwwhindawicom
DifferentialEquations
International Journal of
Volume 2013
Mathematical Problems in Engineering 9
to analyze the performance of ERP project an index sys-tem of comprehensive benefit evaluation including financecustomer and operation management is established in thispaper An ANP was proposed to determine the weight ofeach index which fully took the relationship between variousindicators into account Due to the limitations and inadequa-cies of traditionalmatter-element extensionmodel when per-forming the comprehensive evaluation an improved matter-element extensionmodel was proposed And then taking oneenterprisersquos ERP project as an example the comprehensiveevaluation was done The empirical analysis results show theperformance of ERPproject in our case belongs to ldquohighrdquo leveland our proposed hybrid evaluation model is feasible andpractical Finally a sensitivity analysis is performed to findsensitive index in the ERP project evaluation The analysisresults show that total asset turnover ratio and data transferefficiency are sensitive indexes so this enterprise should paymore attention to them
Acknowledgments
This study is supported by theNationalNatural Science Foun-dation of China (Grant no 70971038) and the Humanitiesand Social Science project of the Ministry of Education ofChina (Project no 11YJA790217) The authors are grateful tothe editor and anonymous reviewers for their suggestions onimproving the quality of the paper
References
[1] J S Zhang and W Tan ldquoResearch on the performance eval-uation of logistics enterprise based on the analytic hierarchyprocessrdquo Energy Procedia vol 14 pp 1618ndash1623 2012
[2] I Ertugrul and N Karakasoglu ldquoPerformance evaluation ofTurkish cement firms with fuzzy analytic hierarchy process andTOPSISmethodsrdquo Expert Systems with Applications vol 36 no1 pp 702ndash715 2009
[3] H Saranga and R Moser ldquoPerformance evaluation of purchas-ing and supply management using value chain DEA approachrdquoEuropean Journal of Operational Research vol 207 no 1 pp197ndash205 2010
[4] H Y Wu Y K Lin and C H Chang ldquoPerformance evaluationof extension education centers in universities based on thebalanced scorecardrdquo Evaluation and Program Planning vol 34no 1 pp 37ndash50 2011
[5] J Y Li ldquoThe effect evaluation of ERP system based on BP neuralnetworkrdquo Technology Square no 8 pp 25ndash27 2010
[6] S G Chen and Y K Lin ldquoOn performance evaluation ofERP systems with fuzzy mathematicsrdquo Expert Systems WithApplications vol 36 pp 6362ndash6367 2010
[7] X H Zhan X Xu and H Z Liu ldquoERP performance evaluationof power supply engineering Company Based on Gray TriangleWhiten Functionrdquo Systems Engineering Procedia vol 4 pp 116ndash123 2012
[8] L Xu ldquoThe evaluation of ERP sandtable simulation based onAHPrdquo Physics Procedia vol 33 pp 1924ndash1931 2012
[9] J Razmi M S Sangari and R Ghodsi ldquoDeveloping a practicalframework for ERP readiness assessment using fuzzy analyticnetwork processrdquoAdvances in Engineering Software vol 40 no11 pp 1168ndash1178 2009
[10] I C Chang H G Hwang H C Liaw M C Hung S LChen and D C Yen ldquoA neural network evaluation model forERP performance from SCM perspective to enhance enterprisecompetitive advantagerdquo Expert Systems with Applications vol35 no 4 pp 1809ndash1816 2008
[11] T X Han Y F Wang and W M Liu ldquoERP performanceevaluation method study in electric power enterpriserdquo Journalof East China Power vol 35 pp 1064ndash1069 2007
[12] Y Z Li and X Zhang ldquoThe application of principle exten-sion method in evaluating enterprise performancerdquo Journal ofChengdu University (Social Science Edition) vol 17 no 2 pp103ndash107 2010
[13] Y W Zhou ldquoPerformance evaluation based on the entropyweight and matter-element modelrdquo Enterprise Economy no 3pp 76ndash79 2012
[14] L L Yang ldquoThe research on the evaluation index system ofthe ERP system effectrdquo Qingdao University of Science andTechnology 2010
[15] W Cai C Y Yang and W Lin Extension Engineering MethodScience Press Beijing China 1997
[16] Y XHe A YDai J ZhuH YHe and F Li ldquoRisk assessment ofurban network planning in china based on the matter-elementmodel and extension analysisrdquo International Journal of ElectricalPower and Energy Systems vol 33 no 3 pp 775ndash782 2011
[17] X P Zhang ldquoThe fuzzy comprehensive evaluation result setchange based on the close degreerdquo Journal of Shandong Univer-sity vol 39 no 2 pp 25ndash29 2004
[18] C T Lin C B Chen and Y C Ting ldquoAn ERP model forsupplier selection in electronics industryrdquo Expert Systems withApplications vol 38 no 3 pp 1760ndash1765 2011
[19] B Pang and S Bai ldquoAn integrated fuzzy synthetic evaluationapproach for supplier selection based on analytic networkprocessrdquo Journal of Intelligent Manufacturing vol 24 no 1 pp163ndash174 2011
[20] Y C Hu J H Wang and R Y Wang ldquoEvaluating the per-formance of Taiwan homestay using analytic network processrdquoMathematical Problems in Engineering vol 2012 Article ID827193 24 pages 2012
Submit your manuscripts athttpwwwhindawicom
OperationsResearch
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Abstract and Applied Analysis
ISRN Applied Mathematics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2013
International Journal of
Combinatorics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Journal of Function Spaces and Applications
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
ISRN Geometry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Discrete Dynamicsin Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2013
Advances in
Mathematical Physics
ISRN Algebra
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
ProbabilityandStatistics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
ISRN Mathematical Analysis
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Journal ofApplied Mathematics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Advances in
DecisionSciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Stochastic AnalysisInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawi Publishing Corporation httpwwwhindawicom Volume 2013
The Scientific World Journal
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
ISRN Discrete Mathematics
Hindawi Publishing Corporationhttpwwwhindawicom
DifferentialEquations
International Journal of
Volume 2013
Submit your manuscripts athttpwwwhindawicom
OperationsResearch
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Abstract and Applied Analysis
ISRN Applied Mathematics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2013
International Journal of
Combinatorics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Journal of Function Spaces and Applications
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
ISRN Geometry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Discrete Dynamicsin Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2013
Advances in
Mathematical Physics
ISRN Algebra
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
ProbabilityandStatistics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
ISRN Mathematical Analysis
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Journal ofApplied Mathematics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Advances in
DecisionSciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
Stochastic AnalysisInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawi Publishing Corporation httpwwwhindawicom Volume 2013
The Scientific World Journal
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013
ISRN Discrete Mathematics
Hindawi Publishing Corporationhttpwwwhindawicom
DifferentialEquations
International Journal of
Volume 2013
