We consider a continuous-review inventory problem for a retailer who faces random disruptions both internally and externally (from its supplier). We formulate the expected inventory cost at this retailer and analyze the properties of the cost function. In particular, we show that the cost function is quasi-convex and therefore can be efficiently optimized to numerically find the optimal order size from the retailer to the supplier. Computational experiments provide additional insight into the problem. In addition, we introduce an effective approximation of the cost function. Our approximation can be solved in closed form, which is useful when the model is embedded into more complicated supply chain design or management models. Key Words: Inventory Model; Supply Disruptions

We consider a continuous-review inventory model for a firm that faces deterministic demand but whose supplier experiences random 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.

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Recent events have brought attention to the importance of retailer’s strategies before disruptions may occur such as a hurricane or other events that have some sort of warning. This paper explores several cases to determine the best course of action for retailers when deciding how they should approach possible demand disruptions. Numerical analysis was performed to determine whether retailers should be reactive or proactive before a possible demand surge. This is the first paper that uses minimax decision criterion to make inventory decisions regarding a disruption. The results give managers insight into whether they should be proactive or reactive in their ordering strategy before a demand surge depending on the circumstances.