Warehouse procurement decisions are strongly affected by demand uncertainty and purchase lead-time variability. When stockouts lead to lost sales (rather than backorders), both the control problem and the underlying data become challenging: demand is censored by inventory availability, and replenishment arrives after uncertain delays. This paper develops a data-driven framework for periodic-review, single-item warehouse procurement with stochastic, i.i.d.\ lead times and lost sales. We formulate a finite-horizon stochastic optimization model as a Markov decision process over on-hand and pipeline inventory and define a cost structure capturing ordering, holding, and lost-sales penalties. To enable data-driven computation, we derive a sample average approximation (SAA) program and summarize convergence and consistency results under standard regularity conditions. We propose two implementable solution pathways: (i) policy-class SAA that optimizes parameters of structured replenishment rules using historical observations and (ii) scenario-based multistage SAA with non-anticipativity constraints and decomposition considerations. Finally, we outline a numerical experiment design—including demand/lead-time generators, metrics, and suggested plots—to quantify trade-offs among service, cost, and robustness.

Keywords

Stochastic Lead Times, Lost Sales, Inventory Control, Sample Average Approximation, and Data-driven Procurement.