Valid inequalities and extended formulations for lot-sizing and scheduling problem with sequence-dependent setups

Abstract

In this paper, we propose new valid inequalities and extended formulations for the lot-sizing and schedul-ing problem with sequence-dependent setups, which are derived by investigating the single-period sub-structure of the problem. Specifically, we derive two new families of valid inequalities and identify their facet-defining conditions. Additionally, we demonstrate that these inequalities can be separated in poly-nomial time. After introducing the existing extended formulations for the problem, we provide new ex-tended formulations adapting decision variables representing the time-flow and compare the theoretical strengths of the various formulations and valid inequalities, including the proposed ones. Finally, we con-duct computational experiments to demonstrate the effectiveness of the proposed inequalities and for-mulations. The test results indicate that the proposed inequalities and extended formulations facilitate tightening the linear programming relaxation bounds.(c) 2023 Elsevier B.V. All rights reserved.