On a multi-stage stochastic programming model for inventory planning

This paper considers a stochastic dynamic inventory problem involving a single item, linear cost structures, and finite distributions (but not necessarily independent) for the stochastic cost and demand parameters. We develop primal and dual algorithms for a multi-stage stochastic linear programming formulation for the problem. The complexity of the proposed algorithms is shown to be within O(N2), where N is the number of nodes in the scenario tree used to model the stochastic parameters.