Infinite-horizon models for inventory control under yield uncertainty and disruptions

Abstract

We consider a firm facing supply chain risk in two forms: disruptions and yield uncertainty. We demonstrate the importance of analyzing a sufficiently long time horizon when modeling inventory systems subject to supply disruptions. Several previous papers have used single-period newsboy-style models to study supply disruptions, and we show that such models underestimate the risk of supply disruptions and generate sub-optimal solutions. We consider one case where a firm's only sourcing option is an unreliable supplier subject to disruptions and yield uncertainty, and a second case where a second, reliable (but more expensive) supplier is available. We develop models for both cases to determine the optimal order and reserve quantities. We then compare these results to those found when a single-period approximation is used. We demonstrate that a single-period approximation causes increases in cost, under-utilizes the unreliable supplier, and distorts the order quantities that should be placed with the reliable supplier in the two-supplier case. Moreover, using a single-period model can lead to selecting the wrong strategy for mitigating supply risk.