Evaluating echelon stock (R,nQ) policies in serial production/inventory systems with stochastic demand

This paper studies echelon stock (R,nQ) policies in serial production/inventory systems with stochastic demand. We provide a recursive procedure to compute the steady state echelon inventory levels of the systems, which can be used to evaluate the long-run average holding and backorder costs as well as other performance measures. The procedure is based upon an observation of a relationship between the inventory status of adjacent stages in a serial system. We also derive exact formulas for replenishment frequencies and setup costs. Our results apply to both continuous-review systems with compount Poisson demand and periodic-review systems with independent, identically distributed demands. A preliminary numerical study was conducted to explore the cost effectiveness of echelon stock (R,nQ) policies. For two-stage systems with simple Poisson demand, we compared among the minimum costs of echelon stock (R,nQ) policies, a lower bound on the minimum achievable costs, and the minimum costs of installation stock (R,nQ) policies. Finally, we present a modification of an existing approximate evaluation procedure.