An improved (Q, R) formulation when the stockout cost is incurred on a per-stockout basis

When an order for an out-of-stock inventory item is received, sometimes a fixed cost independent of the order size is incurred to expedite the order (e.g., by running a special production batch or chartering a helicopter). This paper shows that the current standard “textbook formulation” for this situation contains a number of conceptual flaws. We then present an improved formulation and an associated solution procedure, followed by numerical illustrations. It is shown that the improved formulation leads to substantially improved solutions.