Dynamic Inventory Allocation with Demand Learning for Seasonal Goods

Abstract

We study an inventory allocation problem in a two-echelon (single-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, and can be allocated to the retailers over the course of the selling horizon with the objective of minimizing total expected lost sales costs and holding costs. We are particularly interested in demand learning in this context, where the decision maker can use historical demand observations to predict future demand, and consequently make allocation decisions. We thus model demand in order to capture learning, and show that our model can describe both demand forecasting (e.g. ARMA) frameworks, as well as a Bayesian framework. Then, we pose the questions of (1) how to solve the inventory allocation problem under demand learning in a computationally tractable way, and (2) how demand learning impacts effective inventory allocation policies. To address the first question, we adopt a Lagrangian relaxation-based technique. We show under general assumptions that the resulting heuristic remains near-optimal in our setting, compared to the original dynamic program. Finally, we use this analysis to investigate the relationship between demand learning and early allocation decisions. We show through a combination of theoretical and numerical analysis the following result: Demand learning provides an incentive for the decision maker to withhold inventory at the warehouse rather than allocating it in earlier periods.