MIP–based heuristic for the unrelated parallel machine scheduling problem with sequence and machine-dependent setup times

Abstract

In this paper we study the unrelated parallel machine scheduling problem with sequence and machine-dependent setup times. We consider the objective of minimizing the maximum completion time of the latest job, usually referred to as makespan. We propose a new MIP-based heuristic combining atomic moves such as insertion, ejection and closure, in order to generate sequences of such atomic moves minimizing the makespan. This heuristic employs a commercial solver to search the neighborhood in a multi-start algorithm. Our approach performed well in computational experiments targeting two sets of benchmark instances previously used in the literature.