Compiling capacitated single-item lot-sizing problem in a CostMDD

Abstract

This paper deals with capacitated single-item lot sizing problem (CLSP) in an interactive support system context. The interaction is done thanks to queries to the system: The decision-maker makes partial choices and asks about the consequences in terms of costs but also about possible inventory levels. Hence, three fundamental queries are investigated: Find production plans with a cost less than K; Find possible plans with conditioning on a pair of variables (production and inventory); Find the production plans that simultaneously satisfy the previous queries. A knowledge compilation approach is used and composed of two phases: offline and online. Offline, a top-down algorithm computes cost multivalued decision diagrams. While online, we show how cost multivalued decision diagrams can improve the reactivity of answers to queries.The proposed approach is compared to classical constraint programming with CP Optimizer. Tests indicate that our algorithm is more efficient than CP re-solving in terms of computation time.