Motivations and analysis of the capacitated lot-sizing problem with setup times and minimum and maximum ending inventories

Abstract

This paper first analyzes the negative impact of the end-of-horizon effect when solving the capacitated multi-item lot-sizing problem with setup costs and times on a rolling horizon. Maximum ending inventories for items and a global minimum ending inventory are considered to define a new optimization problem whose optimal solutions are much less impacted by the end-of-horizon effect. Then, a generation scheme is proposed to create new instances with initial inventories and ending inventories. This scheme relies on the analysis of the cyclical production planning problem to derive relevant parameters. Computational experiments are carried out to compare the solutions obtained for original instances of the literature and for the new instances, and to analyze the relevance of the new instances on a rolling horizon.