Dynamic Inventory Allocation with Demand Learning for Seasonal Goods

We study a multi-period inventory allocation problem in a one-warehouse multiple-retailer setting with lost sales. At the start of a finite selling season, a fixed amount of inventory is available at the warehouse. Inventory can be allocated to the retailers over the course of the selling horizon (transshipment is not allowed). The objective is to minimize the total expected lost sales and holding costs. In each period, the decision maker can use the realized and possibly censored demand observations to dynamically update demand forecast and consequently make allocation decisions. Our model allows a general demand updating framework, which includes ARMA models or Bayesian methods as special cases. We propose a computationally tractable algorithm to solve the inventory allocation problem under demand learning using a Lagrangian relaxation technique, and show that the algorithm is asymptotically optimal. We further use this technique to investigate how demand learning would affect inventory allocation decisions in a two-period setting. Using a combination of theoretical and numerical analysis, we show that demand learning provides an incentive for the decision maker to withhold inventory at the warehouse rather than allocating it in early periods.