A fast LP-based solution to the production planning problem with capacity constraints including setup considerations

Purpose - Resource capacity and product changeovers must be both considered in the preparation of a realistic production plan. The purpose of this paper is to present a heuristic for enforcing resource availability and the accompanying changeover realities into a continuous-variable linear programming formulation that would otherwise require a mixed-integer model. The results from both approaches are compared in terms of objective function values and computational requirements; the effectiveness of the heuristic approach is demonstrated. Design/methodology/approach - A case study search was conducted to identify relevant data sets that could be used to exercise the optimization and heuristic models. The case studies found in the literature were too small and simple compared to the problem complexity desired. The authors developed a case study based on the development of a production plan for a typical flashlight. It includes two end-products that differ in their bills of materials and process requirements. Basic processes include plastic part preparation and final assembly; various raw materials with pre-defined lead times are purchased from external suppliers. The results of the LP-based heuristic and the mixed-integer programming (MIP) optimization algorithm are then compared through a statistical experiment. The experiment includes four factors: number of products, number of periods, number of machines, and percentage line capacity utilization. Findings - When a MIP algorithm is applied to obtain the results, most of the time the planner would have to wait days or even weeks for the algorithm to provide a solution. However, the authors' linear programming-based procedure provides the same quality of solution in minutes and for some problems in seconds. Originality/value - The originality of the heuristic approach resides on the avoidance of the lengthy MIP computer runs. At each iteration, the authors solve the LP production planning problem without changeover considerations, and then subtract from the original capacity the time associated with the changeovers resulting from the last LP solution. After a small number of iterations the heuristic always converges to the optimal MIP solution. The contribution of this research can be appreciated by someone who is using this tool to generate a production plan in a real world factory where setups are important and the results can immediately suggest changes to some of the assumptions or parameters used in the planning exercise.