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

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.
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https://hal-uphf.archives-ouvertes.fr/hal-03396848
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Submitted on : Friday, October 22, 2021 - 5:53:17 PM
Last modification on : Monday, November 15, 2021 - 5:50:02 PM

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Abdelhak El Idrissi, Rachid Benmansour, Mohammed Benbrahim, David Duvivier. Mathematical formulations for the parallel machine scheduling problem with a single server.. International Journal of Production Research, Taylor & Francis, 2020, 59 (20), pp.6166-6184. ⟨10.1080/00207543.2020.1807637⟩. ⟨hal-03396848⟩

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