The unlimited newsvendor: A general solution to a class of two-period newsvendor problems

We study a scheduling system in which a manufacturer, who sells to a retailer, determines the stocking level for a single product. The manufacturer has two opportunities to make a stocking decision. At the beginning of the first period, the manufacturer sets a preliminary stocking level based upon a set of initial demand estimates, possibly obtained from several sources, which consists of N demand distributions and the probabilities that final demand will be drawn from any of these distributions. The uncertainty about which demand distribution will be realized is resolved after the first period, leaving the manufacturer with a known demand distribution but unknown final demand. At this point, the manufacturer can change the preliminary stocking level by either expediting additional supply or cancelling some—or all—of the initial stocking order. Expediting and cancelling carry a penalty cost. We develop a process for identifying the optimal initial and revised order quantities that can be applied regardless of the number of initial demand distributions. We also present a heuristic approach that can significantly simplify the process and, in many cases, maintain the quality of the solution.