Multi-item capacitated lot-sizing with demand uncertainty

Abstract

We consider a stochastic version of the classical multi-item Capacitated Lot-Sizing Problem (CLSP). Demand uncertainty is explicitly modeled through a scenario tree, resulting in a multi-stage mixed-integer stochastic programming model with recourse. We propose a plant-location-based model formulation and a heuristic solution approach based on a fix-and-relax strategy. We report computational experiments to assess not only the viability of the heuristic, but also the advantage (if any) of the stochastic programming model with respect to the considerably simpler deterministic model based on expected value of demand. To this aim we use a simulation architecture, whereby the production plan obtained from the optimization models is applied in a realistic rolling horizon framework, allowing for out-of-sample scenarios and errors in the model of demand uncertainty. We also experiment with different approaches to generate the scenario tree. The results suggest that there is an interplay between different managerial levers to hedge demand uncertainty, i.e. reactive capacity buffers and safety stocks. When there is enough reactive capacity, the ability of the stochastic model to build safety stocks is of little value. When capacity is tightly constrained and the impact of setup times is large, remarkable advantages are obtained by modeling uncertainty explicitly.

Keywords:

• Capacitated lot-sizing problem
• Stochastic programming
• Scenario generation

Acknowledgements

We gratefully acknowledge the financial support of both the Fondazione CRT (research grant for Supply Chain Management Under Uncertainty) and the Italian Ministry of University and Research (PRIN 2001 project Stochastic Mixed-integer Programming: An Application to Master Production Scheduling With Uncertain Demand, prot. 2001011353). The comments of an anonymous referee lead to an improved presentation.