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 scheduling problem with sequence-dependent setups, which are derived by investigating the single-period substructure 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 polynomial time. After introducing the existing extended formulations for the problem, we provide new extended 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 conduct computational experiments to demonstrate the effectiveness of the proposed inequalities and formulations. The test results indicate that the proposed inequalities and extended formulations facilitate tightening the linear programming relaxation bounds.