Optimality and Computation of (\sigma, S) Policies in the Multi-Item Infinite Horizon Inventory Problem

A multi-item inventory system with periodic review, single set-up cost K plus linear ordering cost c for changing stock levels, and holding and shortage cost l(x) for being in stock position x at the beginning of a period is considered. Demand in any period is assumed to be \xi with probability \phi (x,\xi ), where x is the stock level at the beginning of the period. The infinite horizon optimum policies found consist of ordering up to S for any point x in \sigma, the reorder region, and not ordering at x not in \sigma. A computational procedure is given, bounds are derived, and, for further assumptions on l, \sigma is further characterized.