مقدار ترکیبی یکپارچه قضاوت های فازی و متدولوژی برنامه ریزی غیر خطی

ABSTRACT An integrated synthetic value of fuzzy judgments and nonlinear programming methodology for ranking the facility layout patterns

A FLD problem is applied for determining the location of facilities or departments, directly, influences the total cost of manufacturing a product or offering a service, in view of the governing constraints or objectives. Although in manufacturing industrials, the material handling cost (the material handling cost is determined based on the flow of materials and the distances between departments) is the most important factor for determining the efficiency of layout and it encompasses 20–50% of the total operating cost and 15–70% of the total cost for manufactured goods (Tompkins et al., 1996), other important criteria may affect the selection of facility layout. Inappropriate facility layout can cause the major time and cost overruns (Liang & Chao, 2008; Pardalos & Du, 1998). Hence, a FLD depends on the number of objectives and criteria such as the adjacency of facilities, distance between facilities, locations of facilities, flexibility and accessibility. The FLD problem has different formulations such that it can be solved by existing approaches of optimization. Most of plant layout design literatures are either algorithmic or procedural (Yang & Hung, 2007). Over the past 20 years, numerous papers were proposed to solve the different FLD problems.

The optimization problems include assigning the facilities or departments within the spaces, in view of becoming one objective or multi-objectives and related constraints in the problem. When the factory site is divided into the rectangular grids (discrete) and each of facilities adopts one or more of these grids, it is often considered as Quadratic Assignment Problems (QAPs). The QAP goal is to minimize the distance-based transportation cost which is expressed as the quantity of workflow and the traveled distance. Although, the QAP can be solved by approaches such as cutting plane, branch and bound or other operations research techniques, finding the optimal solutions for practical QAP instances still seems extremely challenging from both theoretical results and practical experience. Also, unfortunately these problems belong to the class of NP-hard (Sahni & Gonzalez, 1976) and it is addressed as one of the hardest problems that is almost impossible to be optimally solved in an acceptable time for more than 25 facilities/cells (Solimanpur, Vrat, & Shankar, 2004), particularly, when the important qualitative criteria affects FLD, it results in prohibitive computation time for large problems (Ertay, Ruan, & Tuzkaya, 2006). In many articles, the layout representation is continual (Heragu & Kusiak, 1990), where the FLD problem is often formulated as Mixed Integer Programming (MIP). In these models, each facility is represented as a rectangle of known sizes, while inter-facility distances are defined as the rectilinear distances between facility centers. Both exact algorithms and heuristics have been developed to solve continuous facility layout (CFL) problem.

The exact approaches often obtain the optimal solutions. When equal-sized and rectangular-shaped facilities are considered, the exact solution can be obtained for small problem sizes (for example, 15–20 facilities), in a reasonable time (Moghaddain & Shayan, 1998). Also, these approaches can be applied for CFL (Xie & Sahinidis, 2008), dynamic layout problem (DLP) (Rosenblatt, 1986) and other problems.

The near-optimal methods can generally be classified into two classes, namely heuristics and metaheuristics. Heuristic methods are grouped into two groups including the procedural approaches such as systematic layout planning (SLP) (Muther, 1973) and constructed algorithmic approaches as ALDEP (Seehof & Evans, 1967) and improved as CRAFT (Armour & Buffa, 1963). Among the approaches based on metaheuristics, one can distinguish global search methods (Chiang & Kouvelis, 1996), simulated annealing (Chwif, Pereira Barretto, & Moscato, 1998), genetic algorithm (Azadivar & Wang, 2000; Mavridou & Pardalos, 1997) and ant colony algorithms (Baykasoglu, Dereli, & Sabuncu, 2006). The great advantage of these methods is to avoid being caught in local optima by sometimes accepting moves that worsen the objective function (Chwif et al., 1998). Unfortunately, the metaheuristics approaches may be complex and, sometimes, their learning is difficult for factory designers. When some qualitative criteria together with the quantitative criteria are accommodated with a FLD problem, it can be solved by multi-attribute decision making (MADM) techniques. For example, Cambron and Evans (1991), Foulds and Partovi (1998) and Yang, Su, and Hsu (2000) applied AHP to evaluate the design patterns. Yang and Kuo (2003) applied an integrated AHP–DEA methodology for ranking FLPs, where the AHP and the spiral commercial software were used for generating the performance measures of the qualitative criteria and determining the performance measures of the quantitative criteria, respectively, and finally DEA was applied for solving the layout performance frontiers problem simultaneously by considering both the quantitative and qualitative data. However, they inserted the measures of qualitative criteria for ranking FLPs while solving FLD, the used DEA model might ignores the scores of some criteria in total score. Furthermore, Yang and Hung (2007) presented the fuzzy technique for order preference by similarity to ideal solution (FTOPSIS) for ranking the FLPs and then the obtained results were compared with TOPSIS and YK-model.

In this paper, we present an integrated methodology based on the SVFJ–NLP for ranking the FLPs generated by commercial CRAFT software. Here the qualitative criteria data are obtained by SVFJ and quantitative data earned by commercial software and by designers, respectively. Besides, an NLP model is proposed to solve the layout design problem.

The remainder of this paper is organized as follows. In Section 2, the proposed model is presented for ranking the FLPs. An illustrative example is presented to implement the proposed model in Section 3 and finally, in Section 4, conclusions and limitation are given.