A tight approximation for an EOQ model with supply disruptions

Abstract

We consider a continuous-review inventory model for a firm that faces deterministic demand but whose supplier experiences random supply disruptions. The supplier experiences “wet” and “dry” (operational and disrupted) periods whose durations are exponentially distributed. The firm follows an EOQ-like policy during wet periods but may not place orders during dry periods; any demands occurring during dry periods are lost if the firm does not have sufficient inventory to meet them.This paper introduces a simple but effective approximation for this model that maintains the tractability of the classical EOQ and permits analysis similar to that typically performed for the EOQ. We provide analytical and numerical bounds on the approximation error in both the cost function and the optimal order quantity. We prove that the optimal power-of-two policy has a worst-case error bound of 6%. Finally, we demonstrate numerically that the results proved for the approximate cost function hold, at least approximately, for the original exact function.