The robust cyclic job shop problem

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-andcolumn generation algorithms are the most common. In this paper, we propose a branch-and-bound 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 branch-and-bound method. Finally, encouraging preliminary results on numerical experiments performed on randomly generated instances are presented. (c) 2023 Elsevier B.V. All rights reserved.

Automated summary

This paper addresses the cyclic job shop problem with uncertain task durations in a polyhedral uncertainty set. A two-stage robust optimization model is formulated, and a branch-and-bound algorithm is proposed to minimize the cycle time. Encouraging preliminary results are presented from numerical experiments.