Modeling the evolution of dependency between demands, with application to inventory planning

Abstract

This article shows that the progressive realization of uncertain demands across successive discrete time periods through additive or multiplicative forecast updates results in the evolution of the conditional covariance of demand in addition to its conditional mean. A dynamic inventory model with forecast updates is used to illustrate the application of the proposed method. It is shown that the optimal inventory policy depends on conditional covariances, and a model without information updates is used to quantify the benefit of using the available forecast information in the presence of additive forecast updates. The proposed approach yields significant reductions in system costs and is applicable to a wide range of production and inventory models. It is also shown that the proposed approach can be extended to the case of multiplicative forecast updates and directions for future work are suggested.