Research on Logistics Capability of the Supply Chain in Food Production Enterprise Based on AHP and Fuzzy Entropy

As the third profit source, logistics plays an extremely important role to reduce costs, improve efficiency and enhance the enterprise market competitiveness. This study describes the logistics capability of the supply chain in food production enterprise. The logistics capability is summarized as the ability to control the logistics cost, the ability of logistics service, the ability of logistics elements and the ability of logistics organization and management. Through the analysis of logistics capability of the supply chain in food production enterprise, this study establishes an evaluation system of logistics capability of the supply chain from the above four aspects. The Analytic Hierarchy Process (AHP) is used to determine weights of the subspace dimension indicators and the membership function in fuzzy theory is used to determine the indicators of the level of the matrix. Combined with the theory of entropy, integrated weight of logistics capability of the supply chain of the matrix can be determined and quantified indicators will be achieved as an evaluation criterion. Finally, the indicator system and evaluation method are integrated to analyze the logistics capabilities of the supply chain in food production enterprise via a case study, which proves to be valid.


INTRODUCTION
With the rapid development of economic globalization and technology advance, the enterprises have to face the global competition and the challenge, to shorten the delivery time, improve quality, improve the service and meet the personalized needs.At present, it becomes more and more difficult that the enterprises only rely on the ability to create ways to obtain the sustainable competitive advantage.Based on this, the enterprises began to turn their attention to the logistics field, which is called "the third profit source" of the enterprises.
In the past decades, some experts and scholars at home and abroad had made a lot of research on the logistics capability of the supply chain.Daugherty and Pittman (1995) studied the supply chain from the speed of product distribution, information exchange and flexibility.Logistics capability of the supply chain should include the customer's response speed, customer service level, delivery on time and delay or shortage of the advance notice (Daugherty et al., 1998).Morash et al. (1996) made a study on strategic logistics capabilities for competitive advantage and firm success.Logistics capability of the supply chain should include processing ability and the value-added capacity and the relationship between them was analyzed (Sameer, 2008).Huang (2008) put forward some problemsolving measures to improve the logistics capability of supply chain.Shang et al. (2009) summarized the logistics capability from four aspects and evaluated the logistics capability of a case based on the fuzzy evaluation method.
On the whole, most of experts and scholars performed some empirical studies on logistics capabilities of supply chain by means of some evaluation methods, including the Analytic Hierarchy Process (AHP), fuzzy evaluation and entropy theory and so on.At the same time, every evaluation method has its advantages and disadvantages.This study tries to make good use of their benefits and establish logistics capability of supply chain evaluation system in food production enterprise through model calculation of AHP and fuzzy entropy from four aspects, including the ability to control the logistics cost, the ability of logistics service, the ability of logistics elements and the ability of logistics organization and management.1).

TO DETERMINE WEIGHTS AMONG THE SECOND-LEVEL INDICATORS BY MEANS OF AHP
Analytic Hierarchy Process (AHP) is a functional decision process proposed and gradually improved by the American mathematician Saaty T. L. in the 1970's (Saaty, 1990).It is appropriate to use the AHP method to determine weights among the second-level indicators and weighted calculation.Finally, this study uses the AHP method to establish a model, whose main steps are as follows (Duan et al., 2011): To establish the hierarchical structure model: According to the Table 1 and the theory of AHP, the hierarchical structure model can be easily established.
To construct the judgment matrices of each level: Assuming the vector Then the following data matrix will be obtained (Chen and Li, 2011): where, To perform hierarchical single sorting and consistency check: By means of the Matlab software, the hierarchical single sorting can be easily solved.Then the consistency check will be made, whose equation is as follows: , the results of hierarchical sorting will satisfy the requirement for consistency, otherwise the judgment matrix will need to be adjusted.

TO ESTABLLISH EVALUATION SYSTEM OF SUPPLY CHAIN LOGISTICS ABILITY BASED ON THE FUZZY ENTROPY MODEL
To determine the evaluation set: In the model of rough sets and fuzzy entropy, the evaluation set of the logistics capability of the supply chain is C = (C 1 , C 2 , C 3 , C 4 , C 5 ), C k (k = 1, 2, 3, 4, 5) represents, respectively five grades, which include the higher, high, general, low and lower.And the above five grades are given the assignment A= {90, 80, 70, 60, 30}.
To construct the membership degree matrix: If any element x in the domain is corresponding to a number of ( ) A x , ( ) A x is the fuzzy set in the domain.When element x has a change in the domain, ( ) A x can be considered as the membership function.If ( ) A x is closer to 1, it denotes that membership degree of x to ( ) A x is higher; at the same time, ( ) A x is closer to 0; it denotes that membership degree of x to ( ) A x is lower (Yu et al., 2010).
Then membership functions are used to establish the membership of indicators on levels.It is calculated as follows: • To calculate the membership and make normalized processing: Supposing the number of each level indicator of logistics capability of the supply chain is n, the logistics capability of the index i is i x and the corresponding membership ( ) i x µ can be calculated by the Eq. ( 3): where, 1, 2,3, 4; i = a = 1, 3/4, 1/2, 1/4, 0 And subspace dimension indexes of supply chain logistics capabilities are either positive or negative, either high or low; the indicators will be converted into the same trend changes via the following Eq.( 4): The indicator number of subspace dimension in the four aspects n = The number of the evaluation grade (n = 5) ijn µ = The membership degree of the j to the grade of n responding to the aspect i

To determine the entropy values and weight of evaluation index:
• To calculate the weighted coefficient of subspace dimension and make normalization: where, j = 1, 2, 3, 4 • To calculate the value of supply chain logistics capabilities:

CASE STUDY
In this study, the logistics capability of supply chain of a food production enterprise in 2011 is evaluated by the models of AHP and fuzzy entropy.

To determine weights among the second-level indicators by means of AHP:
According to the expert scoring and results of the questionnaires, the hierarchical analysis matrix will be built so as to determine the internal weights of evaluation index level.The maximum eigenvalue of all judgment matrices of every level is as follows and all the results of hierarchical sorting satisfy the requirement for consistency check.
• The calculation of the judgment matrix U 1 (Table 3): • The calculation of the judgment matrix U 2 (Table 4): • The calculation of the judgment matrix U 3 (Table 5): • The calculation of the judgment matrix U 4 (Table 6):

To calculate the membership of indicators:
According to the Eq. ( 3) and ( 4), the membership of indicators can be which can be shown in Table 7: According to the Eq. ( 5), weighted coefficient of subspace dimension can be obtained:   According to the Eq. ( 6), the entropy values of the first-indicator can be obtained: The evaluation of calculation results: By the above calculation, the conclusion can be drawn that the capability of the enterprise in food production enterprise is at the secondary level and the capability of four aspects is in general, which is consistent with the actual situation.

CONCLUSION
In this study, an evaluation system of supply chain logistics capabilities is established from four aspects.A model of AHP and fuzzy entropy is used to analyze the logistics capabilities supply chain in food production enterprise.And the result of an empirical analysis proved to be valid.
O 2 , ..., Om 4 ) represent respectively the vector which is composed of each first-level indicator and represent respectively the number of the second-level indicators responding to their own first-level indicator.
2, 3, 4 k = The adjustment coefficient ( 1 log k n = ) n = The number of evaluation grade ( 5 n = ) z ij = The element of a normalized matrix • To convert the entropy values into the weight values: 1 2212, 0.2752, 0.2955, 0.2081)   d d d d d = =According to the Eq.(8), value of supply chain logistics capabilities can be obtained:

Table 1 :
The evaluation indicator system of supply chain logistics capabilities supply chain.Based on the results of previous research, according to the comparison and summary, an evaluation indicator system of supply chain logistics capabilities can be established from four aspects (Table 1) To adjust the judgment matrix and hierarchical ranking model: If necessary, the judgment matrix and hierarchical ranking model may be corrected and adjusted.If 0.1 CR <

Table 2 :
The indicator of average random consistency

Table 3 :
The judgment matrix U 1 and its interior weights w 1

Table 6 :
The judgment matrix U 4 and its interior weights w 4

Table 7 :
The membership of indicators based on fuzzy entropy