A Tight Approximation for a Continuous-Review Inventory Model with Supply Disruptions

We consider a continuous-review inventory model for a retailer who faces deterministic demand but whose supplier is unreliable. The supplier experiences “wet” and “dry” (operational and disrupted) periods whose durations are exponentially distributed. The retailer 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 retailer does not have sufficient inventory to meet them. This paper introduces a simple but tight approximation for such a model that maintains the tractability of the classical EOQ and permits analysis similar to that typically performed on the EOQ. We provide analytical and empirical bounds on the approximation error in both the cost function and the optimal order quantity. We prove that prove that the optimal powerof-two policy has a worst-case error bound of 6%. Finally, we demonstrate empirically that the results proved for the approximate cost function hold, at least approximately, for the original exact function.