The Dynamic Lot-Size Model with Stochastic Lead Times

Optimal solutions for the dynamic lot-sizing problem with deterministic demands but stochastic lead times are “lumpy.” If lead time distributions are arbitrary except that they are independent of order size and do not allow orders to cross in time, then each order in an optimal solution will exactly satisfy a consecutive sequence of demands, a natural extension of the classic results by Wagner and Whitin. If, on the other hand, orders can cross in time, then optimal solutions are still “lumpy” in the sense that each order will satisfy a set, not necessarily consecutive, of the demands. An example shows how this characterization can be used to find a solution to a problem where interdependence of lead times is critical. This characterization of optimal solutions facilitates dynamic programming approaches to this problem.