An online algorithm for the inventory retrieval problem with an uncertain selling duration, uncertain prices, and price-dependent demands

We study a multi-period inventory retrieval problem with uncertain selling duration, uncertain future prices, and price-dependent demands. At the beginning of a finite selling horizon, a fixed amount of inventory is available for sale in future periods. In each period, the decision-maker observes the current market price and makes the retrieval decision, and only at the beginning of the last period, he knows that it is the last period. The objective is to maximize the expected total revenue and the difficulty stems from the lack of information on probability distributions of both the selling duration and future market prices, which also causes uncertainty in the random demands. Proposing an online algorithm ALG-IR to solve the problem based on competitive analysis theory, we derive its constant competitive ratio, which is optimal under certain conditions, showing the robust performance of the algorithm. We further indicate that, when applying other price-dependent demand models or considering the impact of reference prices on the current demand, the adjusted algorithm ALG-IR-M retains all the theoretical properties. When considering the holding cost of inventory, a similar algorithm ALG-IR-H is proposed to solve the problem. Through numerical studies, we show the algorithm achieves good performance in both optimality and robustness, especially when the market is not over-supplied or the selling duration will not suddenly end at an early period.