Infinite-horizon models for inventory control under yield uncertainty and disruptions, Work.pdf

Infinite-horizon models for inventory control under yield uncertainty and disruptions, Work.pdf

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

Infinite-Horizon Models for Inventory Control under Yield Uncertainty and Disruptions Amanda J. Schmitt Lawrence V. Snyder Dept. of Industrial and Systems Engineering Lehigh University Bethlehem, PA, USA October 17, 2007 ABSTRACT We demonstrate the importance of using a sufficiently long time horizon analysis when modeling inventory systems subject to supply disruptions. Several publications use single- period newsboy models to study supply disruptions, and we show that such models underes- timate the risk of supply disruptions and generate sub-optimal solutions. We examine a firm with an unreliable supplier that is subject to supply yield uncertainty as well as complete supply disruptions. We consider one case where the unreliable supplier is the only supply option, 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 which 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. Key Words: supply chain disruptions, yield uncertainty, dual-sourcing, inventory management 1 Introduction Inventory models are frequently constructed using a single-period time horizon and often provide excellent results. However, when supply disruptions are possible, single-period mod- els can grossly underestimate the risk that disruptions pose to the system. In this paper we demonstrate that single-period models do not generate solutions that provide enough protection from disruptions. 1 We consider two types of supply uncertainty: yield uncertainty and disruptions. Yield uncertainty occurs when the quantity of su

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