Dynamic Inventory Management with Learning About the Demand Distribution and Substitution Probability

A well–known result in the Bayesian inventory management literature is: If lost sales are not observed, the Bayesian optimal inventory level is larger than the myopic inventory level (one should ‘stock more’ to learn about the demand distribution). This result has been proven in other studies under the assumption that inventory is perishable, so the myopic inventory level is equal to the Bayesian optimal inventory level with observed lost sales. We break that equivalence by considering nonperishable inventory. We prove that with nonperishable inventory, the famous ‘stock more’ result is often reversed to ‘stock less,’ in that the Bayesian optimal inventory level with unobserved lost sales is lower than the myopic inventory level. We also prove that making lost sales unobservable increases the Bayesian optimal inventory level; in this specific sense, the famous ‘stock more’ result of other studies generalizes to the case of nonperishable inventory.