Fuzzy Comprehensive Evaluation on the Selection of Material Management Project Partner

INTRODUCTION

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Generally, a large material management project is often offered by a stronger supplier as the general contractor. Then the general contractor organizes itself and some other subcontractors, who are weak in overall strength but are specialized in their own fields, so as to complete the whole project cooperatively (Jie-He, 2003). Thus, for a general contractor, to select suitable project partners, subcontractors, becomes crucial. Before selection, it is necessary to make a scientific comprehensive evaluation to all the partners. But the influencing factors of material management project partners evaluation are multitudinous, involved in both quantitative indexes and qualitative indexes. Even quantitative indexes are due to a variety of subjective and objective reasons can't get the concrete numerical value of index. And there are many indicators of evident fuzziness, no clear criteria. This leads to the project partner evaluation index of fuzziness, uncertainty and difficult to measure. In view of the above reasons, this study tries to use a method of fuzzy comprehensive evaluation which based on the fuzzy mathematical theory for evaluation on the material management project partner selection.

EVALUATION PROCESS

The evaluation process includes: Establishing fuzzy evaluation sets, sure comments level domain, determine evaluation membership matrix, determines the index weight, comprehensive evaluation, result analysis, etc (Crainic et al., 2009).

Establish fuzzy evaluation set: According to the existing evaluation index system, construct a fuzzy evaluation set, U={u₁,u₂,u₃,…,u_i},u_i means the ist primary index. And in u_i={u_i1,u_i2,…,u_ij}, u_ij means the jst secondary index in the ist primary index.

Make sure comments level domain: Before fuzzy comprehensive evaluation, comments level should be determined. In setting the comments level, the grad of levels usually take the odd number which less than 9 larger than 4. Too many comments levels would make it difficult to determine the discriminatory power of semantic level of economic benefit belongs. On the other hand, too little comments level grads can not meet the quality requirements of fuzzy comprehensive evaluation. And odd number grades will have a middle class, facilitate judgment on partner level.

Make sure evaluation membership matrix: After setting comments grade, the membership rate for enterprise to each index can be judged. Membership rate means the degree of one index belongs to a comment level (Zhong-Bao, 2008). We can use the number of people who choice certain comment level to show it. Under the same level of all the indexes of membership in comments level, it got a fuzzy relation matrix. Select a certain number of experts to constitute the jury, Evaluate factors of the second layer in the evaluation index system. We choice the questionnaire survey and analyze the result to get single-factor fuzzy judgment matrix.

(1)

In the formula, i mean the number of index in first class index; m is the number of target factors concentrated elements; n is the number of evaluation concentration elements.

Make sure the index weight: In comprehensive evaluation system of material management project partner selection, various factors important degree is not the same, so it is necessary to distribute their weights. In order to overcome the weight coefficient method to determine the indicated existing scientific sent, subjectivity big defects, this study used the Analytic Hierarchy Process (AHP) established the mathematical model for solving the weight of each factor (Yan and Wen-Sheng, 2009). Specific operation process is as follows:

First, determine the evaluation factors judgment matrix. Compare partner comprehensive evaluation factors system factors and child factors and their judgment matrixes can be obtained respectively. For example, binary comparison on factor or child factors, get this matrix:

(2)

This matrix is the judgment matrix of factors or child factors. In the matrix, a_ij is listed element and did the value of the elements compare. Its value standard is: Important degree equal value is 1, slightly important is 3, obviously important for 5, very important for 7, extremely important for 9, between two adjacent degrees, respectively 2,4,6,8. Conversely compared, the numbers are the reciprocals of above; those are 1-1/9.

Second, calculating the maximum eigenvalue of judgment matrix and the eigenvectors W of λ_max. Normalization of W for later, the value of the corresponding, W_i is representative of the evaluation factors weights or comments relative to a son factors weights of evaluation factors. This can work out management ability U₁, employee ability U₂, production capacity of U₃, financial cost U₄ factors under the weight and their weight.

Third, validate the consistency. Consistency index CR = IC/IR, type: IC (λ_max-n)/(n-1) (n is for the evaluation factors in number or the number of child factors), IR is the relevant index n order number. If CR <0.10 judgment matrix is satisfactory consistency, or need to adjust judgment matrix.

Fuzzy comprehensive evaluation: By weight vectors and fuzzy relation matrix, make the following comprehensive evaluation:

(3)

(4)

(5)

In the formula, is the comprehensive evaluation value of subgoal; B is the comprehensive evaluation value of final goal. Mark “°” said the synthesis operations, generalized. Select a specific computational operation according to the actual situation.

APPLICATION EXAMPLE

Background information: ZSD-XA is a large material circulation enterprises in our country electric power industry, is one of the main supply channels in China's hydropower and thermal power production and construction. In its partner selection of one project (we called project A), ZSD-XA has to choose one from these three companies. Here we call them partner SV, partner DK and partner DF. In these three companies, SV’s strength is strong. Now their subsidiaries have branches all over the country. They use advanced materials management information system based on Internet, can integrate storage, transportation, distribution various aspects resources. In the eastern and southern China, they have strong transportation and business network but have no experience on cooperation with construction enterprise. Partner DK long-term bear ZSD-XA in Shanxi area material management programs and they kept the good cooperation relations. DK and ZSD-XA have deeper cooperation relationship, the trust mechanism and customer relations have been better but they don’t have advanced information system. Partner DF is a material management company founding not too long. The company has strong financial strength, staff quality level is high but compare to the above two companies, the experience is smaller. So, how to choose a better one? This is a question to ZSD–XA’s company leadership group.

Comprehensive evaluation of ZSD-XA’s material management project partners: First identify the evaluation index system of material management project partner. Space constraints permit longer write index system construction process. Then determine the index weight, as stated above, use AHP method (Cao and Gao, 2005). According to the characteristic of material management project partners, the evaluation index system and index weight shown in Table 1.

This study make a questionnaire survey to partner SV, DK and DF and make a single factor simulation evaluate aim at the secondary indexes according to Table 1.We select the ZSD-XA company A project team and material management relevant persons as respondents. Comments are divided into five rating. Accordingly, comments sets V={v₁,v₂,v₃,v₄,v₅}, v₁ says very satisfied, v₂ satisfied, v₃ general, v₄ says not quiet satisfied, v₅ says not satisfied. Different comment level can reflect different satisfactory level. Through questionnaires recovery, sorting and counting, we can the single-factor fuzzy judgment membership list of partner SV. The list shows in Table 2.

According to index weights in Table 1, we can calculation comprehensive evaluation score.

From formula (3) and W₁=( 0.493,0.507), we can get the evaluation vector of team building ability:

B1 = W1*R1 = (0.249, 0.449, 0.302, 0, 0)

In the same way, ability of team building:

B2 = W2*R2 = (0.460, 0.250, 0.290, 0, 0)

•	Ability of Project plan: B3=W3*R3= (0.360, 0.250, 0.290, 0, 0)
•	Ability of Project control: B4=W4*R4=( 0.484, 0.308, 0.139, 0.068, 0)
•	Quality level of project: B5=W5*R5=( 0.401, 0.266, 0.100, 0.233, 0)
•	Stakeholder satisfaction level: B6=W6*R6=( 0.289, 0.406, 0.213, 0.092, 0)
•	High-level support level: B7=W7*R7=( 0.414, 0.236, 0.235, 0.115, 0)

According to formula (5), we can get comprehensive evaluation vector:

B = W*R = ( 0.373, 0.335, 0.234, 0.058, 0.000)

Because of:

it isn’t necessary to normalize.

Table 1:	Evaluation indexes weights of ZSD-XA material management project partner

Table 2:	Partners SV single-factor fuzzy judgment membership

In order to facilitate comparison results, the judge set V, respectively corresponding score v₁ = 90, v₂ and v₃ = = 80 v₄ = 60, 70, v₅ = 50, so comprehensive score for:

VI = B*VT = (0.373, 0.335, 0.234, 0.058, 0.000)* (90, 80, 70, 60, 50)T = 80.228

From the result we can see the partner SV between very satisfied and satisfaction. In the same way, composite scores for partners DK is V_II=76.346 and composite scores for partners DF is V_?=75.062.

See from this, the evaluation of partner SV is better than partner DF and DK. So in further cooperate, should first consideration partners SV as A project partners.