Newsvendor Networks: Inventory Management and Capacity Investment with Discretionary Activities

We introduce a class of models, called newsvendor networks, that allow for multiple products and multiple processing and storage points and investigate how their single-period properties extend to dynamic settings. Such models provide a parsimonious framework to study various problems of stochastic capacity investment and inventory management, including assembly, commonality, distribution, flexibility, substitution and transshipment. Newsvendor networks are stochastic models with recourse that are characterized by linear revenue and cost structures and a linear input-output transformation. While capacity and inventory decisions are locked in before uncertainty is resolved, some managerial discretion remains via ex-post input-output activity decisions. Ex-post decisions involve both the choice of activities and their levels and can result in subtle benefits. This discretion in choice is captured through alternate or “nonbasic” activities that can redeploy inputs and resources to best respond to resolved uncertain events. Nonbasic activities are never used in a deterministic environment; their value stems from discretionary flexibility to meet stochastic demand deviations from the operating point.

The optimal capacity and inventory decisions balance overages with underages. Continuing the classic newsvendor analogy, the optimal balancing conditions can be interpreted as specifying multiple “critical fractiles” of the multivariate demand distribution; they also suggest appropriate measures for and trade-offs between product service levels. This paper shows that the properties of optimal newsvendor network solutions extend to a dynamic setting under plausible conditions. Indeed, we establish dynamic optimality of inventory and capacity policies for the lost sales case. Depending on the nonbasic activities, this also extends to the backordering case. Analytic- and simulation-based solution techniques and graphical interpretations are presented and illustrated by a comprehensive example that features discretionary input commonality and a flexible processing resource.