A Two-Stage Newsvendor Problem with a Service Constraint

Abstract

We extend the classical newsvendor problem by introducing a service constraint and a demand forecast update. The newsvendor orders an initial amount and has the possibility to adjust the initial order after she observes a demand updating signal. She also commits to a target service level before any forecast update is available. The resulting problem does not permit a dynamic programming formulation. We use the method of Lagrange multipliers to solve the problem, and we derive an analytical expression for the optimal ordering decisions. Various properties of the optimal policy are discussed, and numerical results are presented to provide further insights into the newsvendor's behavior.

Keywords: Inventory, newsvendor problem, service constraint, forecast update, two-stage ordering

JEL Classification: M11, C61