Managing perishable inventory when strategic customers form a reference on product availability

Our framework deals with stochastic dynamic inventory models for stocking decisions of a retailer selling a single perishable product in the presence of strategic customers who time their purchases. Each short period, the retailer determines a stocking quantity before random demand is realized. Strategic customers use their reference on product availability to purchase at a regular price or wait for a markdown and learn from the retailer’s stocking quantity to update their reference. We characterize the structural properties such as the concavity of single- and two-period profit functions. On an infinite horizon, we show that a steady-state reference distribution is ergodic and an optimal stocking quantity is unique for a given reference. We conduct extensive numerical studies on an infinite horizon to compare an optimal dynamic policy and the corresponding optimal static policy which sets a fixed stocking quantity over time. A near-optimal performance of optimal static policy with an average profit gap of less than 1% is remarkable and contrasts with that in the two-period model which may be far worse. Thus, a well-chosen fixed stocking quantity on a planning horizon with many short periods tends to yield a high performance without having to change stocking quantities over time.