This paper addresses the parallel machine scheduling problem with family dependent setup times and total weighted completion time minimization. In this problem, when two jobs j and k are scheduled consecutively on the same machine, a setup time is performed between the finishing time of j and the starting time of k if and only if j and k belong to different families. The problem is strongly NP-hard and is commonly addressed in the literature by heuristic approaches and by branch-and-bound algorithms. Achieving proven optimal solution is a challenging task even for small size instances. Our contribution is to introduce five novel mixed integer linear programs based on concepts derived from one-commodity, arc-flow and set covering formulations. Numerical experiments on more than 13000 benchmark instances show that one of the arc-flow models and the set covering model are quite efficient, as they provide on average better solutions than state-of-the-art approaches, with shorter computation times, and solve to proven optimality a large number of open instances from the literature.

Mathematical formulations for scheduling jobs on identical parallel machines with family setup times and total weighted completion time minimization / Kramer, A.; Iori, M.; Lacomme, P.. - In: EUROPEAN JOURNAL OF OPERATIONAL RESEARCH. - ISSN 0377-2217. - 289:3(2021), pp. 825-840. [10.1016/j.ejor.2019.07.006]

Mathematical formulations for scheduling jobs on identical parallel machines with family setup times and total weighted completion time minimization

Kramer A.
;
Iori M.;
2021

Abstract

This paper addresses the parallel machine scheduling problem with family dependent setup times and total weighted completion time minimization. In this problem, when two jobs j and k are scheduled consecutively on the same machine, a setup time is performed between the finishing time of j and the starting time of k if and only if j and k belong to different families. The problem is strongly NP-hard and is commonly addressed in the literature by heuristic approaches and by branch-and-bound algorithms. Achieving proven optimal solution is a challenging task even for small size instances. Our contribution is to introduce five novel mixed integer linear programs based on concepts derived from one-commodity, arc-flow and set covering formulations. Numerical experiments on more than 13000 benchmark instances show that one of the arc-flow models and the set covering model are quite efficient, as they provide on average better solutions than state-of-the-art approaches, with shorter computation times, and solve to proven optimality a large number of open instances from the literature.
5-lug-2019
289
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825
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Mathematical formulations for scheduling jobs on identical parallel machines with family setup times and total weighted completion time minimization / Kramer, A.; Iori, M.; Lacomme, P.. - In: EUROPEAN JOURNAL OF OPERATIONAL RESEARCH. - ISSN 0377-2217. - 289:3(2021), pp. 825-840. [10.1016/j.ejor.2019.07.006]
Kramer, A.; Iori, M.; Lacomme, P.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1186979
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