A heuristic algorithm for identical parallel machine scheduling: splitting jobs, sequence-dependent setup times, and limited setup operators

Abstract

We examine a parallel machine scheduling problem with a job splitting property, sequence-dependent setup times, and limited setup operators, for minimizing makespan. Jobs are split into arbitrary (job) sections that can be processed on different machines simultaneously. When a job starts to be processed on a machine, a setup that requires an operator is performed, and the setup time is sequence-dependent. The number of setup operators is limited, and hence not all of the machines can be set up at the same time. For this problem, we propose a mathematical programming model and analyze a lower bound. We then develop a simple but efficient heuristic algorithm so that it can be used in practice, and analytically derive a worst-case bound of the algorithm. We finally evaluate the performance of the proposed algorithm numerically with various scenarios.