A Continuous-Review Inventory Model with Disruptions at Both Supplier and Retailer

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.