Exact makespan minimization of unrelated parallel machines

Åblad, Edvin¹ ; Strömberg, Ann-Brith² ; Spensieri, Domenico¹

¹ Fraunhofer-Chalmers Research Centre and Chalmers University of Technology, Gothenburg, Sweden
² Chalmers University of Technology and University of Gothenburg, Gothenburg, Sweden

Open Journal of Mathematical Optimization, Tome 2 (2021), article no. 2, 15 p.

Résumé

We study methods for the exact solution of the unrelated parallel machine problem with makespan minimization, generally denoted as $R\left|\right|C_{\text{max}}$. Our original application arises from the automotive assembly process where tasks needs to be distributed among several robots. This involves the solutions of several $R\left|\right|C_{\text{max}}$ instances, which proved hard for a MILP solver since the makespan objective induces weak LP relaxation bounds. To improve these bounds and to enable the solution of larger instances, we propose a branch–and–bound method based on a Lagrangian relaxation of the assignment constraints. For this relaxation we derive a criterion for variable fixing and prove the zero duality gap property for the case of two parallel machines. Our computational studies indicate that the proposed algorithm is competitive with state-of-the-art methods on different types of instances. Moreover, the impact of each proposed feature is analysed.

Détail

Reçu le : 2020-04-02
Révisé le : 2021-04-01
Accepté le : 2021-04-25
Publié le : 2021-05-11

DOI : 10.5802/ojmo.4

Keywords: unrelated parallel machine problem, makespan, variable fixing, binary knapsack, Lagrangian relaxation

Licence : CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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