MILP models to minimise makespan in additive manufacturing machine scheduling problems

Abstract

Additive manufacturing (AM), also known as 3D printing, is gaining enormous importance in the production of highly customised quality and lightweight products in low quantities. In addition to AM's use in producing fully functional industrial components, it is also seen as a technology of the future that will enable civilisation in space. Although the cost structures for AM facilities have been sufficiently studied in the literature, no effort has been made to investigate the scheduling problem of AM machines with the aim of optimising processing time-related performance measures. This paper focuses on the scheduling problem of single and multiple AM machines and proposes mathematical models for optimisation. Mixed-integer linear programming models allocate parts into jobs to be produced on AM machines to minimise makespan. The problem was handled by considering different machine configurations (i.e. single machine, parallel identical machines, and parallel non-identical machines). The models were coded in IBM ILOG CPLEX Optimization Studio (v12.8.0) and solved through the CPLEX solver. This paper presents detailed solutions for numerical examples. A comprehensive computational study was also conducted, and the results are presented. The optimum solutions are reported for most problems. The best solutions obtained within the time limit (i.e. 1800 and 2400 s) are reported for the parallel identical and non-identical AM machine scheduling problems if optimum solution could not be verified.