Modelling and optimising the capacity and production network planning in plastics processing factories

This paper deals with the capacity planning and production network planning in plastics processing factories. We lay emphasis on the opportunity and – potentially – necessity to move machines, tools and material. Furthermore, we consider the option to outsource production to external suppliers. Demand is deterministic and has to be satisfied in the same period. We present a linear mixed integer programming model representing the problem to find a minimum-cost production plan where total cost accounts for variable production cost, setup cost, transportation cost, relocation cost and cost caused by machine purchases. The decisions to be made are the allocation of machines to plants. This includes to decide for investments or relocating machines between plants. In addition, the allocation of products to machines and the determination of the corresponding optimal quantities of production, purchase and transportation within the network of suppliers, plants and customers are decided. We provide a computational study validating the model and conduct a sensitivity analysis of the run time using an off-the-shelf solver. Finally, we present a real-world case of an international automobile supplier. Tackling the instance with an off-the-shelf solver the problem cannot be solved in reasonable time. Thus we apply a simple decomposition scheme to provide decision support for the real-world case.