The Capacitated Lot-Sizing Problem (CLSP) and its variants are important challenging optimization problems. Constructive heuristics known to be the most intuitive fastest methods for finding good feasible solutions CLSPs therefore often used as a subroutine in building more sophisticated exact or metaheuristic approaches. Classical constructive heuristics, such period-by-period lot elimination ...

NP{hard cases of the single{item capacitated lot{sizing problem have been the topic of extensive research and continue to receive considerable attention. However, surprisingly few theoretical results have been published on approximation methods for these problems. To the best of our knowledge, until now no polynomial approximation method is known which produces solutions with a relative deviati...

Non-stationary stochastic lot sizing problem appears in many industrial environments where demand is nonstationary and stochastic, and replenishments require fixed freight fees. This paper presents the cost performance assessment of three inventory control strategies proposed for the stochastic lot sizing problem, namely Hua et al. (2008)’s strategy (HYHX), Tarim and Kingsman (2006)’s model (TK...

We consider several variants of the two-level lot-sizing problem with one item at the upper level facing dependent demand, and multiple items or clients at the lower level, facing independent demands. We first show that under a natural cost assumption, it is sufficient to optimize over a stock-dominant relaxation. We further study the polyhedral structure of a strong relaxation of this problem ...

In this paper we consider a multi-item, multi-machine discrete lot sizing and scheduling problems (DLSP) which consists of finding a minimal cost production schedule over a finite discrete horizon, where in each period a machine may be either producing one item at full capacity or is idle. The demand for each item in each period is known, and can be satisfied either by production in the period,...

In this paper we discuss two basic geometric techniques that can be used to speed up certain types of dynamic programs. We first present the algorithms in a general form, and then we show how these techniques can be applied to the economic lot-sizing problem and extensions. Furthermore, it is illustrated that the geometric techniques can be used to give elegant and insightful proofs of structur...