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.

本文研究了一个并行机器调度问题，在该问题中，作业可以以多个部分或完整的形式处理，并且作业的可能作业拆分替代方案的数量不止一个。不同作业（或零件）之间存在顺序相关的设置时间，目标是通过为每个作业选择合适的加工替代方案、将零件（或作业）分配给机器并确定机器上零件的顺序来最小化制造时间. 这项工作的动机来自基于 3D 打印机的制造系统，该系统为个人或初创公司生产定制产品。当3D打印机用作加工机器时，产品可以打印成由不同零件组成的多种形式。为了解决这个问题，我们首先提出了一个混合整数规划模型，然后开发了一种混合遗传算法，该算法与基于旅行商问题的启发式算法相结合。实验结果表明，所提出算法的解与使用 CPLEX 或下界求解的最优解之间的平均差距非常小。配对 t 检验表明，处理具有多种选择的作业有显着改进。