Replenishment Policy with Limited Price Information

In this paper, we seek to provide real-time replenishment policy for a capacitated company that faces an exogenous demand and has to procure and store sufficient quantities of certain items with uncertain procurement prices. The objective is to minimize the total cost of the procuring cost and inventory holding cost without stock out. Motivated by the fact that a large variability in the price process often makes forecasting difficult, in contrast to the traditional approaches of the stochastic inventory theory, we study this problem from the perspective of competitive analysis who is free of any price distribution assumption. We propose an online replenishment model, which generalizes several previous online models. We give a real-time replenishment policy whose decisions are made based entirely on the past and present prices and the current inventory level. We prove that our policy achieves superior performance, and outperforms all of the previous theoretical results. Furthermore, we present the numerical studies to show that our replenishment policy achieves an even better empirical performance.