Dynamic robust optimal reorder point with uncertain lead time and changeable demand distribution

In fixed order quantity systems, uncertainty in lead time is expressed as a set of scenarios with occurrence probabilities, and the mean and variance in demand distribution are supposed to be changeable according to a known pattern. A new concept of “dynamic robust optimal reorder point” is proposed in this paper and its value is calculated as a “robust optimal reorder point function with respect to reorder time”. Two approaches were employed in determining the dynamic optimal reorder point. The first is a shortage rate satisfaction approach and the second is a backorder cost minimization approach. The former aims at finding the minimum value of reorder point at each reorder time which satisfies the condition that the cumulative distribution function (CDF) of shortage rate under a given set of scenarios in lead time is greater than or equal to a basic CDF of shortage rate predetermined by a decision-maker. In the latter approach, the CDF of closeness of reorder point is defined at each reorder time to express how close to the optimal reorder points under the set of scenarios, and the dynamic optimal reorder point is defined according to stochastic ordering. Some numerical examples demonstrate the features of these dynamic robust optimal reorder points.