A new characterization for the dynamic lot size problem with bounded inventory

In this paper, we address the dynamic lot size problem with storage capacity. As in the unconstrained dynamic lot size problem, this problem admits a reduction of the state space. New properties to obtain optimal policies are introduced. Based on these properties a new dynamic programming algorithm is devised. Superiority of the new algorithm to the existing procedure is demonstrated. Furthermore, the new algorithm runs in O(T) expected time when demands vary between zero and the storage capacity. Computational results are reported for randomly generated problems.