Deriving near-optimality conditions using approximation procedures for an inventory control system with lost sales

Inventory theory often assumes that demands during out-of-stock periods are backordered, although lost demands are arguably more realistic, especially in retail settings. This is, to a large extent, due to the fact that lost-sales systems are harder to analyse, especially if multiple orders can be outstanding. This paper considers the classic single-item, single-location, continuous review (R, Q) inventory model with lost sales under a cost minimization objective, where reorder level R is optimi