Parallel machine scheduling with multiple processing alternatives and sequence-dependent setup times

This paper examines a parallel machine scheduling problem in which jobs can be processed either in multiple parts or in a complete form and the number of possible job splitting alternatives of jobs is more than one. There are sequence-dependent setup times between different jobs (or parts), and the objective is to minimise makespan by choosing an appropriate processing alternative for each job, assigning parts (or jobs) to machines, and determining the sequence of parts on the machines. This work is motivated from a 3D printer-based manufacturing system that produces customised products for individuals or start-up companies. When 3D printers are used as processing machines, a product can be printed in diverse forms composed of different parts. To address the problem, we first propose a mixed integer programming model and then develop a hybrid genetic algorithm which is combined with a travelling salesman problem-based heuristic algorithm. The experimental results show that the average gap between a solution from the proposed algorithm and an optimal one solved with CPLEX or a lower bound is very small. The paired t-test shows that there is a significant improvement for processing jobs with multiple alternatives.