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.