A two-stage sequential approach for scheduling with lot-sizing decisions in the context of plastic injection systems

This study addresses a planning problem for plastics injection systems, where final products are assembled of compatible plastic pieces. Additionally, the production of pieces requires the use of dedicated molds that are installed on compatible injection machines (leading to long setup times). Then, our Manufacturing Planning Problem determines the lot-size of each product in terms of the number of cycles for each piece-mold-machine combination and the scheduling of molds for each injection machine in a single planning period to maximize the total profit. We consider constraints for machines' available time and avoid mold overlapping on different machines. Moreover, we define a mixed-integer linear program for our problem, and we obtain high-quality solutions for medium-size instances using a commercial solver in minutes. Still, the convergence to optimal solutions for large instances is slower. In response, we propose a two-stage sequential approach that takes advantage of the mathematical formulation to obtain better solutions for large instances in short computational times.