Dynamic lot sizing with stochastic demand timing

In this paper, a novel way of modeling uncertainty on demand in the single item dynamic lot sizing problem is proposed and studied. The uncertainty is not related to the demand quantity, but rather to the demand timing, i.e., the demand fully occurs in a single period of a given time interval with a given probability and no partial delivery is allowed. The problem is first motivated and modeled. Our modeling naturally correlates uncertain demands in different periods contrary to most of the literature in lot sizing. Dynamic programs are then proposed for the general case of multiple demands with stochastic demand timing and for several special cases. We also show that the most general case where the backlog cost depends both on the time period and the stochastic demand is NP-hard.