Dynamic Inventory Models and Stochastic Programming

A wide class of single-product, dynamic inventory problems with convex cost functions and a finite horizon is investigated as a stochastic programming problem. When demands have finite discrete distribution functions, we show that the problem can be substantially reduced in size to a linear program with upper-bounded variables. Moreover, we show that the reduced problem has a network representation; thus network flow theory can be used for solving this class of problems. A consequence of this result is that, if we are dealing with an indivisible commodity, an integer solution of the dynamic inventory problem exists. This approach can be computationally attractive if the demands in different periods are correlated or if ordering cost is a function of demand.