Abstract-This paper proposes the two phase approximation method (2-PAM) based primarily on the concept of dynamic programming and metaheuristic. The multi-objective aggregate production planning (APP) model is solved by a pair of mathematical approaches. The desirability function approach was implemented to compromise all objectives of the aggregate production planning decision problem. The metaheuristic of bat and bee algorithms are first applied to provide the initial solutions in each stage. The dynamic programming approach is followed to combine all solutions. It was found that the results obtained from the proposed method based on bat algorithm can provide more effective and informative APP and more chance to achieve the optimal disaggregate plan when compared to the other variant of 2-PAM with bee algorithm.Index Terms-Aggregate production planning, desirability function, two phase approximation algorithm, bat algorithm, bee algorithm, dynamic programming.
I. INTRODUCTIONConventional optimisation algorithms search for a single optimum based on a weighted sum of all objectives. If these objectives simultaneously get better or worse, mathematical approaches such as linear, non-linear and dynamic programming can effectively can guarantee global optimum. However, in real world problems if the objectives are conflicting and there is an increase in the number of decision variables, then there is not a single optimum and the number of evaluations of the recursive functions would exponentially increase. In order to find satisfactory solutions for these hard optimisation problems, meta-heuristics have been introduced to overcome the deficiencies of conventional algorithms. Meta-heuristics are widely used to solve complex problems in industry and services, in various areas and in this case it is applied to the engineering problem. Aggregate production planning (APP) is concerned with the determination of production, inventory, and work force levels. It has been used to plan the future process capacity to meet fluctuating or uncertain sales demand requirements over a medium-time horizon ranging from six months to one year. Conventionally, the scarce resources of the company are assumed to be constant during the planning horizon of interest and the planning eff ort is oriented toward the best utilisation of those resources, given the external demand requirements. The APP Manuscript received June 25, 2017; revised December 12, 2017. This work was supported in part by Thammasat University.P. Luangpaiboon is with Industrial Statistics and Operational Research Unit (ISO-RU), Department of Industrial Engineering, Faculty of Engineering, Thammasat University, 12120, Thailand (e-mail: lpongch@engr.tu.ac.th). considers various operation strategies over appropriate scarce resources. They consist of hiring, overtime, layoffs, backorders, subcontracting and inventory level. An aim is to simultaneously optimise all customer requirements via multiple objectives over a fixed planning horizon. The data based on the APP model from Th...