Abstract—The Aggregate Production Plan (APP) is a schedule of the organization’s overall operations over a planning horizon to satisfy demand while minimizing costs. It is the baseline for any further planning and formulating the master production scheduling, resources, capacity and raw material planning. This paper presents a methodology to model the Aggregate Production Planning problem, which is combinatorial in nature, when optimized with Genetic Algorithms. This is done considering a multitude of constraints of contradictory nature and the optimization criterion – overall cost, made up of costs with production, work force, inventory, and subcontracting. A case study of substantial size, used to develop the model, is presented, along with the genetic operators. Keywords—Aggregate Production Planning, Costs, and Optimization. I. INTRODUCTION GGREGATE Production Plans (APP) concern about the allocation of resources of the company to meet the demand forecast. Optimizing the APP problem implies minimizing the cost over a finite planning horizon. This can be done by adjusting production load as well as inventory and employment levels over a certain period of time to achieve the lowest cost while satisfying demand and considering the specific constraints for each particular case (company dependent). A good APP has the capacity to positively influence the bottom line and also permit a long-term view of the organization performance. This avoids having to make short-term decisions and fire-fight problems, adversely affecting the organization’s long term perspective [1]. Managers have access to the break-down monthly or weekly demand forecast for the next planning horizon, Paper submitted for review on August 29, 2006. This research is conducted as Mr. Fahimnia’s master thesis at the University of South Australia, School of Advanced Manufacturing & Mechanical Engineering. Behnam Fahimnia is a PhD candidate at the University of South Australia, School of Advanced Manufacturing & Mechanical Engineering. Mawson Lakes Campus, SA 5095, Australia (phone: 0061-8-82605176; fax: 0061-8- 83023380; e-mail: behnam.fahimnia@postgrads.unisa.edu.au). Prof. L H S Luong is the head of school and a lecturer at the University of South Australia, School of Advanced Manufacturing & Mechanical Engineering. Mawson Lakes Campus, SA 5095, Australia (e-mail: lee.luong@unisa.edu.au). Dr. Romeo M. Marian is a lecturer and program director at the University of South Australia, School of Advanced Manufacturing & Mechanical Engineering. Mawson Lakes Campus, SA 5095, Australia (e-mail: romeo.marian@unisa.edu.au). normally 1 year. In practice, managers capitalize on the forecasted demand to achieve long-run profitability. They face major constraints in the number of workers, facilities and plant capacity to fulfill the demand. Therefore, not only all the demand must be met in each planning period (month/week), but costs have to be minimized. Managers may decide if meeting market demand results in lower long-term profit, to backorder and/or ask the subcontractors to do a part of the products. The APP problem deals with how to employ the available workforce, resources and facilities, including external contractors, to best satisfy the demand which is defined through APP [1]. Although a number of production planning approaches have been developed in order to improve planning automation and increase efficiency of production planning [2], but a lot of problems in the area of production planning are subject to highly complex constraints which make them very difficult to solve using traditional optimization methods and approaches. Despite the importance of APP which forms the basis for the formulation for all other schedules and materials management, the results of the APP optimization are far from perfect, leaving way to major improvements. This paper uses Genetic Algorithm (GA), and presents an optimization approach to APP modeling, which permits the search for an optimum, while considering, simultaneously, a large number of constraints of contradictory nature. A realistic case study illustrates the model and the development of the GA to an APP problem with the conditions found in an industrial context is presented. II. LITERATURE REVIEW The APP problem considering minimum changes in workforce level as well as inventory and backorders minimization simultaneously was solved for an 8-period planning horizon [3]. In 1998, the APP problem was solved using Mixed Integer Programming and considering different optimization criteria, including revenue maximization as well as inventory, backorder and set-up cost minimization [4]. Baykasoglu added further constraints to the previous models such as subcontractor selection and set-up decisions [5]. Later on, a number of artificial intelligence approaches, alone or combined with mathematical programming models have been used to solve the production planning problems Modeling and Optimization of Aggregate Production Planning - A Genetic Algorithm Approach B. Fahimnia, L.H.S. Luong, and R. M. Marian A International Journal of Applied Mathematics and Computer Sciences Volume 1 Number 1 1