Target-oriented robust satisficing models for the single machine scheduling problems with release time

Abstract

In this paper, we investigate single machine scheduling problems with release times and random processing times, where the release times can be either deterministic or random. The objective is to determine a scheduling sequence that exhibits strong out-of-sample performance. To achieve this, we employ target-oriented robust satisficing models to obtain the scheduling sequence. For the scheduling problem with deterministic release times, we derive an equivalent mixed-integer linear program and an approximate reformulation to address cases involving a large number of jobs. For the scheduling problem with random release times, we first demonstrate the challenges associated with providing an equivalent reformulation. To overcome this intractability, we propose an approximate reformulation based on the linear decision rule. Numerical experiments are conducted to demonstrate the superiority of our solutions through comparisons with several benchmarks. Furthermore, the numerical results demonstrate that a relatively higher target should be chosen if the worst-case performance is valued, otherwise, the decision-maker should set a relatively lower target to obtain better average performance.