The “Price of Information”: Inventory Management with Limited Information about Demand

Traditional stochastic inventory models assume full knowledge of the demand distribution. However, in practice, it is often difficult to completely characterize the demand distribution, especially with little or outdated historical data. In these uncertain environments, good inventory management has to be robust, i.e., perform well under most demand scenarios. In this paper, we study the newsvendor problem with limited information about the demand distribution. In particular, we derive robust order quantities that minimize the maximum regret, defined as the opportunity cost from not acting optimally, had we had full information about the demand distribution. In addition, we quantify the value of additional information and highlight that knowing that the demand distribution has a regular shape is in general more valuable than knowing its mean and variance. In the newsvendor model, a firm has to decide how much to order, denoted by Q, before a selling season, without knowing the demand, in order to maximize its expected profit ΠF (Q), that is