Value of Demand Observability for Inventory Control with Markovian Demand and Lost Sales

We present a partially observed Markov decision process model of a single product supply chain system with lost sales, in which a single decision maker selects a replenishment quantity at each decision epoch. Demand is modeled using an exogenous Markov chain, such that the distribution of demand in a period is dependent on the demand level in the prior period. The objective is to maximize expected total discounted profit over a finite planning horizon. We assume that inventory levels are completely observed, but that demand observations may be noise corrupted. We present an algorithm for determining an optimal policy and the optimal expected total discounted profit. We also present three computationally attractive heuristic algorithms. We use two extreme cases of this model, the completely-observed case and the sales-only-observed case, to determine a bound on the maximum expected increase in system profitability due to demand observability. Finally, we demonstrate the bounding technique for a set of example problem scenarios and investigate the impact of scenario characteristics on the potential value of observability. In the scenarios considered, the maximum profitability gain varies significantly from about 2% to over 30%.