Improved formulations and new valid inequalities for a Hybrid Flow Shop problem with time-varying resources and chaining time-lag

Abstract

This paper proposes revised and improved mathematical integer formulations for the Hybrid Flow Shop problem under time-varying resources and chaining time-lag constraints. First, we provide a structural classification and a complexity analysis of the tackled problem. Then, we prove the correctness of our novel modeling techniques. To reinforce the formulations, two valid inequalities are developed. The revised formulations are benchmarked, and the results show that the valid inequalities improve significantly the performance. Finally, we propose a hybrid model that outperforms the best formulations and can be applied in an industrial application.