New integer optimization models and an approximate dynamic programming algorithm for the lot-sizing and scheduling problem with sequence-dependent setups

Abstract

In this paper, we propose new integer optimization models for the lot-sizing and scheduling problem with sequence-dependent setups, based on the general lot-sizing and scheduling problem. To incorporate setup crossover and carryover, we first propose a standard model that straightforwardly adapts a formulation technique from the literature. Then, as the main contribution, we propose a novel optimization model that incorporates the notion of time flow. We derive a family of valid inequalities with which to compare the tightness of the models’ linear programming relaxations. In addition, we provide an approximate dynamic programming algorithm that estimates the value of a state using its lower and upper bounds. Then, we conduct computational experiments to demonstrate the competitiveness of the proposed models and the solution algorithm. The test results show that the newly proposed time-flow model has considerable advantages compared with the standard model in terms of tightness and solvability. The proposed algorithm also shows computational benefits over the standard mixed integer programming solver.