Uniform distribution of inventory positions in two-echelon periodic review systems with batch-ordering policies and interdependent demands

We consider a two-level inventory system in which there are one supplier and multiple retailers. The retailers face stochastic, interdependent customer demands. Each location employs a periodic-review (R, nQ), or lot-size reorder point, inventory policy. We show that each location's inventory positions are stationary and the stationary distribution is uniform and independent of any other's. (C) 2002 Elsevier Science B.V. All rights reserved.