Fuzzy Multi-Objective Optimization for Network Design of Logistic and Production Systems M. Dotoli, M.P. Fanti, A.M. Mangini, G. Tempone Politecnico di Bari Via Re David 200 70 125 Bari Italy {dotoli, fanti, mangini}@deemail.poliba.it, gtempone@inwind.it Abstract Global competition has given rise to Logistic and Production Systems (LPSs), that are distributed manufacturing systems integrating international logistics and information technologies with production. This paper builds upon an LPS network design model previously proposed by some of the authors. The recalled technique formulates and solves a multi- criteria optimization problem to select the partners in the different stages of the production chain and the links connecting them. In this paper, in order to rank the equally optimal Pareto solutions of such a problem, we propose to employ fuzzy multi-criteria optimization. Two fuzzification techniques and two different multi- criteria methods are considered. In addition, the methodology is illustrated by way of a case study. Moreover, a discussion on the different advantages and limitations of the proposed techniques is provided. Keywords: logistic and production systems, network design, optimization, fuzzy logic, performance indices. 1. Introduction Global competition imposes an improved efficiency on companies, that respond to this pressure by reengineering their processes, integrating international logistics and information technologies with production. This process has given rise to the formation of Logistic and Production Systems (LPSs), defined as a collection of independent companies, possessing complementary skills and integrated with streamlined material, information and financial flow [4, 9, 2]. Significant literature deals with the problem of LPS network design and a detailed survey can be found in [5]. However, although several conceptual models for LPSs are proposed and discussed in the related literature, research efforts are lagging behind in the development of formal decision models for LPS design [9]. In order to fill such a gap, we propose a configuration strategy for LPSs that determines the structure of both the logistic and production networks, considering also the e-business relationships between operators and the network environmental impact. This paper builds upon the configuration strategy for LPSs proposed in [2], that describes the structure of the LPS by a digraph, where nodes are partners and edges are links. Moreover, different costs are assigned to each link (edge), so that the performance indices can be obtained by the digraph structure. In order to optimize the LPS structure, a multi-criteria objective problem is formulated and different Pareto-optimal LPS solutions are obtained by an integer linear programming problem. However, selecting one of such LPS alternative configurations may be a complex task if the dimension of the solutions set is very large. Hence, in this paper the solutions are ranked using fuzzy multi- criteria optimization. Indeed, fuzzy logic provides a natural framework to incorporate qualitative knowledge with quantitative information such as real data. Therefore, fuzzy multi-objective optimization is particularly suitable for choosing, on the basis of the subjective and qualitative knowledge provided by the decision makers, the LPS configuration from the set of available and equally optimal alternatives. In particular, two fuzzification methods are taken into account and two different fuzzy optimization strategies proposed in the related literature are considered. The methodology is illustrated by way of a case study, and a discussion on the different advantages and limitations of the proposed techniques is provided. The paper is organized as follows. Section 2 recalls the digraph-based LPS model and Section 3 defines the optimization model and the fuzzy techniques to rank the obtained Pareto optimal solutions. Moreover, in Section 4 the case study is analyzed and solved. Finally, Section 5 summarizes the conclusions. 2. The Network Model A Logistic and Production System (LPS) can be defined as a hyper-network of material flows overlaid with an e-business information network. The LPS