A Dynamic and Data-Driven Approach to the News Vendor Problem Under Cyclical Demand

We consider the problem of managing the inventory of perishable goods when the demand is cyclical with unknown distribution. While traditional inventory management under uncertainty assumes the precise knowledge of the underlying probabilities, such information is difficult to obtain for time-varying processes in many real-life applications, as the evolution over time of the deterministic seasonal trend interferes with the analysis of the stochastic part of the demand. To address this issue, we propose a dynamic and data-driven approach that builds directly upon the historical observations and addresses seasonality by creating and recombining clusters of past demand points. This allows the decision maker to place his order at each time period based only on the most relevant data. The algorithm we present requires the estimation of only one parameter, the demand periodicity; furthermore, system performance is protected against estimation errors through a cluster aggregation subroutine, which recombines clusters as needed. We present extensive numerical experiments to illustrate the approach. The key contribution of the chapter is to address a logistics challenge faced by many practitioners, namely, the lack of distributional information for nonstationary demand, by integrating historical data directly into the decision-making module through an algorithm devised specifically for cyclical processes.