مدل برنامه ریزی تولید کل برای دو سیستم تولید فاز: حل با الگوریتم ژنتیک و TS

Aggregate production planning (APP) is a medium-term capacity planning to determine the quantity of production, inventory and work force levels to satisfy fluctuating demand over a planning horizon. The goal is to minimize costs and instabilities in the work force and inventory levels. This paper is concentrated on multi-period, multi-product and multi-machine systems with setup decisions. In this study, we develop a mixed integer linear programming (MILP) model for general two-phase aggregate production planning systems. Due to NP-hard class of APP, we implement a genetic algorithm and tabu search for solving this problem. The computational results show that these proposed algorithms obtain good-quality solutions for APP and could be efficient for large scale problems.

Aggregate production planning is medium-term capacity planning often from 3 to 18 months ahead. It is concerned with the lowest-cost method of production planning to meet customer‘s requirements and to satisfy fluctuating demand over the planning horizon. A survey of models and methodologies for APP has been represented by Nam and Ogendar (1992). Some researchers have used a hierarchical approach for production planning that called hierarchical production planning (HPP) (Ari and Axsater, 1988, Axsater, 1986 and Bitran et al., 1982). Also, the multi criteria decision making (MCDM) approach has been used for production planning (Masud and Hwang, 1980 and Tabucanon and Majumdar, 1989). Nowadays, meta-heuristic methods are used to solve NP-hard problems and due to NP-hard class of aggregate production planning, these approaches have been used for solving APP (Fahimnia et al., 2006 and Jiang et al., 2008). Researchers have used fuzzy approach with genetic algorithm to formulate and solve APP (Aliev et al., 2007 and Hsu and Lin, 1999). Other methods such as hybrid algorithms (Ganesh and Punniyamoorthy, 2005 and Mohan Kumar and Noorul Haq, 2005) and tabu search algorithm (Baykasogluy, 2006 and Pradenas and Peñailillo, 2004) have been implemented to solve APP. But these presented methods are generality concentrated on the solution algorithm but not on a general model. On the other hand, the consideration of the all parameters in an APP model makes it more difficult. So researchers have not presented a comprehensive and general model to formulate real production environments. The majority of models in the APP are relevant to single product and single stage systems and they are not compatible to real production systems. In this paper a general and comprehensive aggregate production planning model is represented and is solved by meta-heuristic approaches. This paper considers a multi-period, multi-product multi-machine and two-phase system in which involves setup costs and setup times. If a specific product is produced in a period then each required machine must be set up exactly once in that period. Since there is setup decisions in this system so we must formulate this model as a mixed integer programming (MIP) problem (Hung & Hu, 1998). The rest of this paper is organized as follows. In Section 2, the proposed aggregate production planning model is demonstrated. In Sections 3 and 4, genetic algorithm and tabu search for solving the problem are described. In Section 5, the computational results are given and in last section we present our conclusion

The purpose of this paper is to formulate and solve aggregate production planning model for two phase production systems in which the objective function is to minimize the costs of production over the planning horizon. This paper is concentrated on multi-period, multi-product, multi-machine and two stage systems with setup decisions. We develop a mixed integer linear programming model that can be used to compute optimal solution for the problems by an operation research solver. We presented genetic algorithm and tabu search for solving this problem. To verify the effectiveness of the presented approaches, computational experiments are performed on a set of random small-sized instances by LINGO. Due to NP-hard class of APP, the computational results show that these implemented algorithms obtain good solutions for APP within a reasonable computational time.