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arXiv · 2402.08629

Efficient arc-flow formulations for makespan minimisation on parallel machines with a common server

Alessandro Druetto·Andrea Grosso·Jully Jeunet·Fabio Salassa
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Abstract

We consider the problem of scheduling non preemptively a set of jobs on parallel identical machines with prior setup operations on a single shared server, where the objective is to minimise the makespan. We develop an arc-flow formulation to the problem with two multigraphs, one for the machines and one for the server, with a same set of nodes representing points in time, and arcs associated with job execution, and with machines or server idleness. The resulting Flow-Flow formulation (FFF) and its tuned version (FFT) are compared with the best existing model in the literature, TIV I, on benchmark instances with up to 200 jobs and 7 machines. Computational results showed that our Flow-Flow models outperformed TIV I for instances with 100 jobs and produced optimal solutions to the vast majority of problems with 150 and 200 jobs for which TIV I failed to even find integer solutions within the standard limited runtime of 3600 s. When non optimal, solutions provided by our models exhibited very low gaps to best bound.

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Alessandro Druetto, Andrea Grosso, Jully Jeunet, Fabio Salassa. 2024-02-13. Efficient arc-flow formulations for makespan minimisation on parallel machines with a common server. https://doi.org/10.1016/j.cor.2024.106911

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