An Interactive Goal Programming Approach for Multi Period Multi Product Production Planning Problem...

4th International Conference of Fuzzy Information & Engineering 14‐15 October 2010 Shomal University, Amol, Iran 1 An interactive fuzzy goal programming approach for multi product multi period production planning problem Kaveh Taghizadeh 1,* ,Iraj Mahdavi 2 , Morteza Bagherpour 3 1,* Department of Industrial Engineering, Mazandaran University of Science & Technology, [email protected] 2 Department of Industrial Engineering, Mazandaran University of Science & Technology, [email protected] 3 Department of Industrial Engineering, Iran University of Science & Technology, [email protected] Abstract This study addresses an interactive multiple Fuzzy Goal Programming (FGP) approach for solving the Multi Period Multi Product (MPMP) production planning problem in an imprecise environment. The proposed model attempts to simultaneously minimize total production costs, rates of changes in labor levels, and maximizing machine utilization, while considering individual production routes of parts, inventory levels, labor levels, machine capacity, warehouse space, and the time value of money. Piecewise linear membership functions are utilized to represent Decision Maker’s (DM’s) overall satisfaction levels. A numerical example demonstrates the feasibility of applying the proposed model to MPMP problem. Furthermore, the proposed interactive approach facilitates the DM with a systematic framework of decision making process which enables DM to modify the search direction to reach the most satisfactory results during solving process. Keywords: Multi Period Multi Product production planning, Fuzzy goal programming, Piecewise linear membership functions. 1. Introduction MPMP production planning problem is a well known problem in production environment, which has attracted considerable attention from both practitioners and academia [1]. MPMP production planning typically encompasses a time horizon between 3 weeks to 3 months. From the planning point of view MPMP production planning falls between medium decisions of medium-range planning and highly specific and detailed short- range planning decisions. Planners in the process of MPMP planning conventionally make decisions regarding production, inventory, and backorder volumes, regarding issues such as fluctuated market demand, available inventory space, production capacity of machines, and available labor levels. While MPMP production planning problem attempts to match production rates of individual product types with fluctuated demand of market, Aggregate Production Planning (APP) considers the planning problem from an aggregated viewpoint, which utilizes an aggregate production unit such as the “average” items or in term of weight, volume, production time, and currency value to aggregate a family of similar products with small differences. Thus, both MPMP and APP production planning problems share same concepts and notions. Since Holt et al. [2] proposed the HMMS rule in 1955, researchers have developed numerous models to help solving MPMP and APP problems each with their own pros and constraints, however, in real world MPMP production planning problems input data or parameters such a demand, resources, and also objective values cannot be expressed precisely due to incomplete or unobtainable information [3]. Fuzzy sets theory proposed by Zadeh [4] in 1965 is a type of imprecision that has no well-defined boundaries for its description. Fuzzy sets theory is highly applicable in the area where human judgments, evaluations, and decisions are important [5]. Inclusion of fuzzy sets theory and linear programming (LP) systems can results in reduction of information costs and avoidance of unrealistic modeling [6].

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