An O(N2)-time algorithm for the stochastic uncapacitated lot-sizing problem with random lead times

In this paper, we develop a dynamic programming algorithm for the scenario-tree-based stochastic uncapacitated lot-sizing problem with random lead times. Our algorithm runs in O(N^2) time, where N is the input size of the scenario tree, and improves the recently developed algorithm that runs in O(N^3) time.