Logistics Mode Selection Model Based on Fuzzy multi-objective Programming

Logistics mode selection is one of the most important activities of supply chain management. An important way to make competitor advantage is select an optimal Logistics mode for the enterprise. Logistics mode selection is a multi-criterion decision making problem in which criteria have different relative importance. In practice, many input information are known precisely. The fuzzy set theories can be used due to the imprecision of information. In this paper, a fuzzy multi-objective decision-making model which is equivalent to solving crisp model by using max-min approach is developed to handle effectively the vagueness of input data in the process of Logistics mode selection. Also, an additive model taking into account the objectives’ weights is presented further in the end of this paper. Indexing terms/


INTRODUCTION
Modern logistics is considered to be the third source of profit to enterprise. Logistic mode is the synthesis of logistics system operating mode, forms of structural organization and the services. Domestic logistics business has experienced so far the first party logistics (self-logistics), the second party logistics (part of the equipment or rental of logistics services form), third-party logistics (logistics outsourcing) and fourth-party logistics. With the higher increasing demand for logistics services, fourth party logistics mode was made in 1996 by Accenture. It is the enterprise in the global supply chain, outsourcing capital flow, business flow, information flow and technology services to a unified one-stop integrated service provider, which is an integrated logistics mode, and focus on their business core business.Fourth party logistics mode as new modes of operation, is a breakthrough in theory and practice, and already enhance the efficiency and mode of innovation.They co-exist and promote the development of each other.
There is a great deal of confusion to select the appropriate logistics business mode with The rapid development of logistics service mode. It have to be decide thatwhich is to choose from self-logistics, logistics outsourcing, third party logistics or integrated logistics service mode, or according to the business adjust their strategic orientation is the use of lean logistics, on-time logistics, rapid response logistics or agile logistics. It is necessary to consider internal and external factors, and may in some of the factors under conditions of uncertainty, a comprehensive evaluation, in order to choose their own mode of logistics services, and to enhance competitive advantage and competitiveness. Therefore, the scientific effective way to select the most requested logistics enterprise has bee become the most important issue for decision-makers [3][4]. Logistics modeselection involves the evaluation criteria and evaluation methods of choice. William [5] and other supplier summary the selection criteria about dozens of types, the most widely followed by quality, cost, delivery, service, management, technology and research and development; the selection of suppliers, there are mainly DEA , AHP, ANP, linear programming, as well as their integration.
In this paper, for the first time, afuzzy multi-objective programming model has been developedfor logistics mode selection,in which the vague criteria and constraints of the logistics mode selection. At the same time, the max-min operator is developed to handle effectively the vagueness and imprecision of input data. Finally, the paper proposed how to further optimize the solution when considering target weight, so that the objectives and factors taken into account the ambiguity of the role and influence of varying sizes, to better ensure the right to re-order and higher degree of membership sort of consistency, to help decision-making who better to pick out the logistics service provider.
The paper is organized as follows: in Section 2 the basic theories are given; Section 3 the fuzzy multi-objective model and crisp formulation for the logistics mode selection problem is presented in which the objectives are equally important and have the same weights. First, a general linear multi-objective formulation for this problem is considered and then an appropriate approach for solving the problem is discussed. Finally, the concluding remarks are presented in Section 4.

Multi-objective programming theory
The method of Multi-objective optimization is presented firstly by the French economist Pareto in 1896.According to Weber and Current [6], a general multi-objective model for the supplier selection problem can be started as follows: In the above model, 12  In practical decision-making, decision-making criteria or decision on the impact of qualification, completely accurate information did not been get by decision makers, such as the level of cost, quality good or bad, service level. These are some of the more vague concept, which need to combine the theory of fuzzy decision optimization model. S e p t e m b e r , 2 0 1 3

Fuzzy decision theory
Fuzzy theory is developed on the basis of the University of fuzzy set by L.A.zadeh from California in 1965 [7].For the purpose of clarity, definitions of the related terms are given as follows.

Normal or Body Text Multi-objective programming model
The rapid development of modern logistics industry was more consolidated its third profit source as an important business position, and each company should choose their own single logistics mode or integrated logistics modefrom the selflogistics mode, logistics outsourcing mode, third-party mode and the emerging fourth party logistics mode based on their own development strategies and macro environment. The evaluationof each logistic mode, which is a multi-objective decision-making problem,can be assessed from the cost of the service (or product), efficiency, portability, and so many angles. In this process, the cost of self-logistics modelcan be measuredby the opportunity cost.
To have a typical model, the criteria of logistic modeor logistic product are assumed tobe quality, net price and delivery in this paper, that is to say, decision-makers assume that other factors, such as decision-makers preferences, the macroeconomic environment are fixed in the process of the mode selection for logistics. In order to formulate this model, the following notations are defined: i n  (9) In this model, three objective functions are considered.They are minimizing the total cost of logistics mode (including selflogistic mode) and maximizingthe servicelevel and the level of delivery on time.Three constraints are also considered. Constraint (7) ensures that demand is satisfied. Constraint set (8) means that the use service quantities to each logistics service provider can not exceed its service capacity. Constraint (9) requires that all decision variables meet the nonnegative.

Fuzzy multi-objective programming model
In a real situation for a logistics mode selection problem, all objectives might not be achieved simultaneously under the system constraints, and the decision maker may define a tolerance limit. This is a vague concept. Meanwhile, the restrictions in some of the factors may not be clear. So the proposed general multi-objective programming model (1) -(3) (Weber and Current) to express the multi-objective program problem will become a fuzzy multi-objective program problem. At this point, the determination of the general multi-objective programming model can be expressed as the following general form of fuzzy multi-objective model: The objective functions: In this model, the sign ~ indicates the fuzzy environment. The symbol in the constraints set demotes the fuzzified version of  and has linguistic interpretation "essentially smaller than or equal to" and the symbol  has linguistic interpretation "essentially greater than or equal to".