Purchasing demand information in a stochastic-demand inventory system

This paper studies a periodic-review, stochastic-demand inventory system in which the manager has the opportunity each period to purchase information about demand in the upcoming period before deciding how much product to order. We analyze the information-purchase and product-replenishment decisions for both perfect and imperfect demand information. Under perfect information, we provide a characterization of the optimal policy for both finite and infinite horizon problems, and also establish useful managerial insights into the behavior of the system. We show that future demand information becomes less valuable at higher inventory levels, and more valuable when longer horizons remain. When the initial inventory is zero, solving the perfect-information problem reduces to computing a single quantity, for which we provide a closed form expression. As a result, this problem is shown to be equivalent to one in which the manager purchases perfect information over the entire horizon with a single lump-sum payment at the beginning of the horizon. Our analytical and numerical results demonstrate that most of the insights from the perfect-information scenario carry over to the imperfect-information case.