Inventory replenishment decisions with uncertain price and demand

This paper studies the multiple period inventory replenishment problem for a capacitated warehouse when procurement prices and market demands are both uncertain, with the goal to minimise the procuring and holding costs. We analyse this problem under the framework of competitive analysis, where neither probabilistic distributions nor sets are available to characterise the unknown price and demand parameters. An efficient online real-time replenishment algorithm is developed, which is free of any distribution assumption, and the decisions are made based entirely on past and present information. We derive an instance-independent competitive ratio of the algorithm, which provides a worst-case theoretical performance guarantee, and shows that the proposed algorithm performs well for situations with high volatility uncertainty over time and is naturally risk-averse. Finally, a set of numerical experiments further verifies the effectiveness of the algorithm.