The Random-Yield Newsvendor with Initial Inventory: Inflation Rules, Information, and Robustness

Firms often place orders before knowing how much usable supply they will actually receive. A common response is to inflate the classical newsvendor order by the inverse of average yield. We study when such simple inflation is structurally justified in a state-dependent newsvendor problem with initial inventory, stochastic demand, and propor- tional random yield. We show that simple inflation is neither universally right nor universally wrong but depends on the information available in the forecast. With full distributional information, the optimal order generally depends nonlinearly on the inventory state, although exact linearity is recovered in important boundary cases such as deterministic demand. With limited information, the recommended rule depends on what the manager can credibly estimate. If only support bounds are trusted, a linear inflation rule is robust-optimal for both sample-wise and distributionally robust formulations. If only first and second moments are trusted, the robust policy becomes nonlinear because ordering more increases both expected receipts and receipt variance. Numerical comparisons illustrate that different inflation rules perform well in different inventory regions, while two-slope and moment-based policies provide more balanced performance over broad state ranges. The results provide guidance on when managers can safely use simple yield inflation, when they should use state-dependent ordering rules, and what demand and yield information is most valuable for improving decisions.