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Pré-Publication, Document De Travail Année : 2024

The robust cyclic job shop problem

Idir Hamaz
Sonia Cafieri
  • Fonction : Auteur

Résumé

This paper deals with the cyclic job shop problem where the task durations are uncertain and belong to a polyhedral uncertainty set. We formulate the cyclic job shop problem as a two-stage robust optimization model. The cycle time and the execution order of tasks executed on the same machines correspond to the here-and-now decisions and have to be decided before the realization of the uncertainty. The starting times of tasks corresponding to the wait-and-see decisions are delayed and can be adjusted after the uncertain parameters are known. In the last decades, different solution approaches have been developed for two-stage robust optimization problems. Among them, the use of affine policies, row and row-and-column generation algorithms are the most common. In this paper, we propose a branch-andbound algorithm to tackle the robust cyclic job shop problem with cycle time minimization. The algorithm uses, at each node of the search tree, a robust version of the Howard's algorithm to derive a lower bound on the optimal cycle time. Moreover, we design a row generation algorithm and a column-and-row generation algorithm and compare it to the branchand-bound method. Finally, encouraging preliminary results on numerical experiments performed on randomly generated instances are presented.
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Dates et versions

hal-03683608 , version 1 (31-05-2022)
hal-03683608 , version 2 (08-09-2023)

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Idir Hamaz, Laurent Houssin, Sonia Cafieri. The robust cyclic job shop problem. 2023. ⟨hal-03683608v2⟩
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