Mathematical formulations for the parallel machine scheduling problem with a single server

Abdelhak Elidrissi, Rachid Benmansour, Mohammed Benbrahim and David Duvivier

International Journal of Production Research, 2021, vol. 59, issue 20, 6166-6184

Abstract: This paper addresses the problem of scheduling independent jobs on identical parallel machines with a single server to minimise the makespan. We propose mixed integer programming (MIP) formulations to solve this problem. Each formulation reflects a specific concept on how the decision variables are defined. Moreover, we present inequalities that can be used to improve those formulations. A computational study is performed on benchmark instances from the literature to compare the proposed MIP formulations with other known formulations from the literature. It turns out that our proposed time-indexed variables formulation outperforms by far the other formulations. In addition, we propose a very efficient MIP formulation to solve a particular case of the problem with a regular job set. This formulation is able to solve all regular instances for the case of 500 jobs and 5 machines in less than 5.27 min, where all other formulations are not able to produce a feasible solution within 1 h.

Date: 2021
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DOI: 10.1080/00207543.2020.1807637

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