A capacitated lot-sizing model with sequence-dependent setups, parallel machines and bi-part injection moulding

Abstract

This paper aims to propose a model for solving a capacitated lot-sizing problem with sequence-dependent setups (CLSD) and parallel machines in a bi-part injection moulding (BPIM) context that consists of injecting two different parts or products into the same mould in separate injection cavities. These two parts require the same sequence order and available capacity at the same instant, but generate different part inventories. The addressed problem should be considered a multi-machine CLSD-BPIM one. We provide a mixed integer linear programming (MILP) model for it. The proposed model is based on a real-world case study from a second-tier supplier of the automotive sector. In sequence setup, inventory and resource setup costs terms, the benefits of the proposed multi-machine CLSD-BPIM model are validated by comparing it with a single-machine CLSD-BPIM model that replicates the current planning scenario carried out in the company under study. Additionally, random instances based on the real problem have been generated and tested. The computational results exhibit optimal solutions for the small instances with an average of 0.2-second solution time, the medium instances present average gaps of 0.47% with 2.6 h and large instances present average gaps of 4% with 6 h solution time.