A note on the dynamic lot-size model with uncertainty in demand and supply processes

This paper gives some extensions of a result of Nevison and Burstein, who discuss a dynamic lot-sizing model with stochastic lead times. They consider a situation in which the lead time distribution is unaltered by the amount which is ordered, but is otherwise arbitrary, and characterize the optimal solution in terms of points at which there is zero inventory. Here the paper gives a more precise characterization, and shows that these results can be extended to a situation in which the demands are also stochastic, and in which there is uncertainty relating to quantity as well as to the timing of demands and order arrivals. The method of proof that is used is different from that used by Nevison and Burstein.