Robust Optimization on Unrelated Parallel Machine Scheduling With Setup Times

Abstract

The parallel machine scheduling problem has been a popular topic for many years due to its theoretical and practical importance. This paper addresses the robust makespan optimization problem on unrelated parallel machine scheduling with sequence-dependent setup times, where the processing times are uncertain, and the only knowledge is the time intervals they take values from. We propose a robust optimization model with the min-max regret criterion to formulate this problem. To solve this problem, we prove that the worst-case scenario with the maximum regret for a given solution belongs to a finite set of extreme scenarios. Based on this theoretical analysis, a procedure to obtain the maximum regret is proposed and an enhanced regret evaluation method (ERE) is designed to accelerate this process, which is of great significance to improve the efficiency of the algorithm. A multi-start decomposition-based heuristic algorithm (MDH) based on the analysis of properties is proposed to solve this problem. Computational experiments are conducted to justify the performance and robustness of these methods. Note to Practitioners—Various uncertainties may occur in the production process, which brings great challenges to production and operations management. A robust production schedule is of great significance for factories to make full use of production capacity and deal with production abnormalities. This study is motivated by an R&D and assembly task scheduling problem encountered in a high-end equipment manufacturing factory in which the processing time of each job is uncertain, and its distribution is also unknown due to limited information. In this study, with the consideration of sequence-dependent setup time and uncertain job-processing time, we view the labor groups with different skill levels as unrelated parallel machines and build a robust (min-max regret) scheduling model to formulate this problem so as to reduce the production makespan. An enhanced regret evaluation method is developed to improve the evaluation efficiency for a given solution, and a multi-start decomposition-based heuristic algorithm is proposed to solve this problem. This study can be applied in practice to release schedulers from burdensome work and provide high-quality robust schedules for this complicated production environment.