Learning Censored Demand for One Period Inventory Decisions

Abstract

Sales cease to reveal demand when stock runs out. We examine the decision cost of ignoring that fact in an executed twenty-four-item, one-period inventory study. Each item has a fixed generated Poisson demand rate, five hundred historical days with exogenous stock levels, and twenty thousand independent evaluation demands. A sales-mean estimate is compared with a grid maximum-likelihood estimate that treats stock-equal sales as right-censored observations. Both feed the same newsvendor rule with shortage cost nine and overage cost one. Mean evaluation cost is 13.6830 for the sales-mean policy, 5.7428 for censored likelihood, and 5.7136 for a known-rate reference. Rate RMSE falls from 3.7571 to 0.2770. A conserved unit-flow graphic, censored-tail diagram, likelihood ridges, and order staircase connect data recording to economic consequences. Results depend on stationary Poisson demand, correctly recorded stock, and a fixed historical sampling design. They establish neither dynamic-policy regret nor a retail deployment result, but show why an accurate model of the observation process belongs inside a learning-to-decision pipeline.