A note on the rationing policies of multiple demand classes with lost sales

Abstract

We study inventory rationing in a system with multiple demand classes and lost sales. It is assumed to have at most one outstanding order, resulting in two periods in an order cycle separated by the time of order release. We review the most related work by Melchiors (2001, 2003) (Ph.D. thesis, University of Aarhus, Int. J. Prod. Econ. 81–82, (11), 461–468), and find that the existing approximated and optimal policies are not easy to obtain due to computational complexity. Also as the rationing issue before order release is not well addressed in literature, in this paper we prove the static rationing being optimal. Furthermore in such a system with two distinct periods, the optimal rationing policy is a combination of a dynamic policy during the replenishment lead time and a static policy before order release. In order to make the rationing policies to be readily used in practice, we introduce two approximated methods for calculating the rationing levels in two periods, respectively. The results, in particular the combination of static and dynamic rationing, outperform the existing approximations in literature. In addition, the computation is obviously simplified due to the efficient algorithm of dynamic rationing and the explicit expressions of static rationing.