Robust Optimal Reorder Points with Uncertain Lead Time(Theory and Methodology)

Abstract

In fixed order quantity systems, uncertainty of procurement lead time is expressed as a set of scenarios with occurrence probabilities, and a cumulative distribution function (c.d.f.) of shortage rate is evaluated under the set of scenarios for any value of reorder point. According to stochastic ordering, a "robust optimal reorder point based on an allowable shortage rate" is defined as the minimum value of the reorder point satisfying the condition that the c.d.f. of shortage rate is greater than or equal to the basic c.d.f of shortage rate predetermined by a decision maker. For the other case when the reorder point is determined to minimize the total additional cost consisting of safety stock holding cost and backordering cost, an optimal reorder point is found under each scenario and the closeness for any value of reorder point is evaluated under every scenario, resulting in the c.d.f. of closeness for the set of scenarios. The rank for any value of the reorder point is calculated according to stochastic ordering to express how close the reorder point is to the optimal reorder points under the set of scenarios. A "robust optimal reorder point" is defined as the value of the reorder point with the minimum rank. These robust optimal reorder points are obtained and their features are investigated for some numerical examples.