Robust Optimization on Unrelated Parallel Machine Scheduling with Setup Times

TL;DR

This paper develops a robust optimization model for unrelated parallel machine scheduling with sequence-dependent setup times under uncertain processing times, introducing a heuristic algorithm and an enhanced evaluation method to improve solution quality.

Contribution

It formulates a min-max regret robust model for scheduling with setup times and proposes a multi-start heuristic with an accelerated regret evaluation technique.

Findings

The worst-case regret scenarios are finite and identifiable.

The proposed heuristic effectively finds high-quality solutions.

Computational results demonstrate the method's efficiency and robustness.

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 intervals they take values from. We propose a robust optimization model with 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, the procedure to obtain the maximum regret is proposed and an enhanced regret evaluation method (ERE) is designed to accelerate this process. A multi-start decomposition-based heuristic algorithm (MDH) is proposed to solve this problem. High-quality initial solutions and an upper bound are examined to help better solve the problem. Computational experiments are conducted to justify the performance of these methods.