Outsourcing some of the logistic activities is a useful strategy for companies in recent years. This makes it possible for firms to concentrate on their main issues and processes and presents facility to improve logistics performance, to reduce costs, and to improve quality. Therefore provider selection and evaluation in thirdparty logistics become important activities for companies. Making a strategic decision like this is significantly hard and crucial. In this study we proposed a fuzzy multicriteria decision making (MCDM) approach to effectively select the most appropriate provider. First we identify the provider selection criteria and build the hierarchical structure of decision model. After building the hierarchical structure we determined the selection criteria weights by using fuzzy analytical hierarchy process (AHP) technique. Then we applied fuzzy technique for order preference by similarity to ideal solution (TOPSIS) to obtain final rankings for providers. And finally an illustrative example is also given to demonstrate the effectiveness of the proposed model.
Supply chain management involves the design and management of seamless, valueadded processes across organizational boundaries to meet the real needs of the end customer [
Estimates indicate that the proportion of companies in the US implementing this approach has increased by 5–8% annually between 1996 and 2004 [
Third it can be defined as a managed process of transferring activities to be performed by others. Logistics outsourcing or third party logistics (3PL) involves the use of external companies to perform logistics functions that have traditionally been performed within an organization [
Outsourcing involves the procurement of physical and/or service inputs from outside organizations either through cessation of an activity that was previously performed internally or abstention from an activity that is well within the capability of the firm [
Finding the right partner requires careful screening and can be a timeconsuming process. Developing an understanding of partners’ expectations and objectives can also take time [
Multiple criteria decisionmaking (MCDM) is a powerful tool widely used for evaluating problems containing multiple, usually conflicting criteria [
The proposed method integrates fuzzy AHP and fuzzy TOPSIS techniques for provider selection that satisfies the needs of ThirdParty Logistics company. First, the weights of criteria have been calculated using fuzzy AHP, and fuzzy TOPSIS is used for the selection of providers.
The remainder of the study is arranged as follows: Section
AHP [
In this study we use the Chang’s extent analysis method for fuzzy AHP. According to Chang [
The value of fuzzy synthetic extent with respect to the
When
The degree possibility for a convex fuzzy number to be greater than
Assume that
For
Via normalization, the normalized weight vectors are
The TOPSIS [
TFNs appear to be a valid tool, offering a well balanced compromise between computational costs and accuracy in the final ranking [
The steps of fuzzy TOPSIS are as follows [
Choose the appropriate linguistic variables for the alternatives with respect to criteria. The linguistic variables are described by TFNs, such as
Construct the fuzzy decision matrix and the normalized fuzzy decision matrix:
Calculate the weighted normalized fuzzy decision matrix. The weighted normalized value
Identify positiveideal (
Calculate the distance of each alternative from
Determine the similarities to ideal solution
Rank the preference order.
The model proposed for the provider selection problem consists of two different kinds of fuzzy MCDM approaches: fuzzy AHP, which we used for calculating weights of criteria, and fuzzy TOPSIS for the ranking of alternative providers.
At first step, a decision making group is organized from experts, managers, and academics. Decision makers determined the selection criteria and provider alternatives, then they built the hierarchical structure of decision model.
After building the hierarchical structure, pairwise comparison matrix is established to identify the weights of criteria. The weights have been calculated by Chang’s [
Finally, provider ranks have been determined by fuzzy TOPSIS in accordance with the linguistic variable values of providers. The alternative having the maximum
Decision making group which is composed of experts, managers, and academics determined 6 important criteria out of 30 criteria. They eliminate the less important criteria in accordance with their experiments and knowledge. And the same group also determined 5 provider alternatives out of 15 firms. In order to take into account the uncertainty in judgements and vagueness in reasoning and by the help of membership functions we can exactly measure the perceptions. Therefore we used fuzzy linguistic variables applied. Figure
The linguistic scale of fuzzy triangular numbers.
Provider selection criteria in 3PL are decided as follows. Figure
Price (PR);
General reputation (GR);
Customer services (CS);
Ontime delivery (OD);
Information technologies (IT);
Flexibility (FL).
Hierarchical structure of the model.
Table
Triangular fuzzy conversion scale.
Linguistic scale for importance degrees  Triangular fuzzy scale  Triangular fuzzy reciprocal scale 

Equally important  (1/2, 1, 3/2)  (2/3, 1, 2) 
Weakly important  (1, 3/2, 2)  (1/2, 2/3, 1) 
Moderately important  (3/2, 2, 5/2)  (2/5, 1/2, 2/3) 
Fairly important  (2, 5/2, 3)  (1/3, 2/5, 1/2) 
Strongly important  (5/2, 3, 7/2)  (2/7, 1/3, 2/5) 
Strongly more important  (3, 7/2, 4)  (1/4, 2/7, 1/3) 
Very strongly important  (7/2, 4, 9/2)  (2/9, 1/4, 2/7) 
Absolutely important  (4, 9/2, 5)  (1/5, 2/9, 1/4) 
The pairwise comparison matrix of criteria.
PR  GR  CS  OD  IT  FL  

PR  —  MI  WI  EI  SI  VSI 
GR  —  SMI  
CS  WI  —  
OD  SI  —  WI  SI  
IT  SMI  MI  —  
FL  WI  EI  MI  — 
Weights of criteria.

0.293 

0.101 

0.038 

0.299 

0.19 

0.079 
In this section we used the Chen’s fuzzy linguistic scale as shown in Table
Chen’s fuzzy scale.
Linguistic variable  Fuzzy scale 

Very low (VL)  (0, 0, 0.1) 
Low (L)  (0, 0.1, 0.3) 
Medium low (ML)  (0.1, 0.3, 0.5) 
Medium (M)  (0.3, 0.5, 0.7) 
Medium high (MH)  (0.5, 0.7, 0.9) 
High (H)  (0.7, 0.9, 1) 
Very high (VH)  (0.9, 1, 1) 
After the calculations according to Table
Fuzzy evaluation matrix for providers.
PR  GR  CS  OD  IT  FL  

P1  M  ML  MH  MH  H  M 
P2  H  MH  L  ML  MH  M 
P3  VH  ML  ML  H  MH  H 
P4  MH  ML  H  ML  MH  MH 
P5  M  H  MH  H  ML  H 
Fuzzy TOPSIS results.
Alternatives 



Ranking 

P1  5.387  0.639  0.106  3 
P2  5.411  0.616  0.102  5 
P3  5.196  0.817  0.136  1 
P4  5.398  0.629  0.104  4 
P5  5.358  0.666  0.111  2 
Same calculation steps are applied to all alternatives. Based on the
Due to the rapid growth of industries and increased global competition, firms must take care of all processes of business. In order to enrich competitive advantages in market, firms are considering different strategies. Logistic outsourcing is one of these strategies. An effective provider selection plays a vital role both for outsourcing company and the provider. In general the necessary data for MCDM problems are imprecise and uncertain. Solving problems through fuzzy techniques eliminates the limitation of crisp values. The importance of the model is the vagueness of the subjective decision making, taken into account by using fuzzy techniques in fuzzy environment. More dependable, more sensitive, and more flexible results can be obtained through fuzzy approaches. Weights of provider selection criteria are determined through FAHP and providers ranked through fuzzy TOPSIS. This model integrates different fuzzy MCDMs in order to take advantages of different approaches. Owing to the hybrid structure the disadvantages of dependency to only one method is eliminated. The hybrid model aims to integrate the strong aspects of different fuzzy methods.
Future researches may try to extend this study as an integration of more fuzzy MCDM techniques to solve many other decision making problems in many other disciplines.