Dynamic capacity management with uncertain demand and dynamic price

Inspired from practices of Chinese real estate firms, we study dynamic capacity management problems for a firm that sells homogeneous goods over a finite or infinite selling horizon, provided that demand is uncertain, retail price is exogenous but changes according to an auto-regressive process, and there is holding cost for remaining inventory in each period. The capacity problems facing the firm include to determine an initial stock at the beginning of the selling season and to allocate the remaining quantity for the current and future sale in each period to maximize the firm׳s total expected discounted profit. By using Markov decision processes, we show the optimality of a so-called save-up-to level policy (i.e., it is optimal to allocate as much as the save-up-to level to future periods if possible in each period) and the existence of the optimal initial stock. Moreover, we characterize monotone properties of the optimal save-up-to level and the optimal initial stock. Numerical analysis shows that compared to the policy with zero save-up-to level (i.e., always allocating all the remaining inventory to the current period), the advantage of the policy proposed in the present paper is significant when price rising trend is large, holding cost is low, initial price is high, or demand variation is either high or low.