Most models of multilevel production and distribution systems assume unlimited production capacity at each site. When capacity limits are introduced, an ineffective policy may lead to increasingly large order backlogs: The stability of the system becomes an issue. In this paper, the authors examine the stability of a multi-echelon system in which each node has limited production capacity and operates under a base-stock policy. They show that if the mean demand per period is smaller than the capacity at every node, then every node, then inventories and backlogs are stable, having a stationary distribution to which they converge from all initial states. Under i.i.d. demands the authors show that the system is a Harris ergodic Markov chain and is thus wide-sense regenerative. Under a slightly stronger condition, inventories return to their target levels infinitely often, with probability one. The authors discuss cost implications of these results, and give extensions to systems with random lead times and periodic demands.
