Note---A Note on the Dynamic Lot-Size Model with Uncertainty in Demand and Supply Processes

In this paper we give some extensions of a result of Nevison and Burstein (Nevison, C. H., M. Burstein. 1984. The dynamic lot-size model with stochastic lead times. Management Sci. 30 100--109.), 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 we give a more precise characterization, and show 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 we use is different from that used by Nevison and Burstein.