Continuous review (s,S) inventory model with limited backlogging levels and stochastic lead times

An (s,S) inventory policy is studied for a continuous review inventory model in which backloggings are restricted at limited levels and stochastic lead tmes are allowed. The model assumes that at most one order is outstanding and demands occur in a Poisson process. The steady-state probability distributions of the inventory levels are derived so as to determine the long-run expected average cost. Then, an optimal solution is characterized and its computational procedure is presented.