Replenishment planning in discrete-time, capacitated, non-stationary, stochastic inventory systems

In this paper, we examine a single-product, discrete-time, non-stationary, inventory replenishment problem with both supply and demand uncertainty, capacity limits on replenishment quantities, and service level requirements. A scenario-based stochastic program for the static, finite-horizon problem is presented to determine replenishment orders over the horizon. We propose a heuristic that is based on the first two moments of the random variables and a normal approximation, whose solution is compared with the optimal from a simulation-based optimization method. Computational experiments show that the heuristic performs very well (within 0.25% of optimal, on average) even when the uncertainty is non-normal or when there are periods without any supply. We also present insights obtained from sensitivity analyses on the effects of supply parameters, shortage penalty costs, capacity limits, and demand variance. A rolling-horizon implementation is illustrated.

Acknowledgements

We are grateful to Dr. Donald R. Smith and Dr. Narayan Raman of Lucent Technologies for providing insights, encouragement and ideas on this problem. We thank the editors, Dr. Candace Yano and Dr. Ton de Kok, and two anonymous referees for their many useful comments that helped us improve the paper.