An Ecient Procedure for Computing an Optimal (R,Q) Policy in Continuous Review Systems with Poisson Demands and Constant Lead Time


Department of Industrial Engineering,Sharif University of Technology


In this paper, a continuous review inventory system is considered in which an order in
a batch of size Q is placed immediately after the inventory position reaches R. Transportation time is
constant and demands are assumed to be generated by a stationary Poisson process with one unit demand
at a time. Demands not covered immediately from the inventory are backordered. In a recent paper, the
exact evaluation of batch-ordering policies for two-level inventory systems was derived. This evaluation is
based on a recursive procedure for determining the exact policy costs in case of one-for-one replenishment
policies. In this paper, we show how this result can be applied to nd the optimal solution of a (R;Q)
policy. To obtain the optimal policy for this system, considering a one-for-one policy, we will rst solve
the base stock model by setting the inventory position at the supplier to a certain value. By considering
ordering cost, we next derive the cost function of the de ned (R;Q) model and nd the optimal solution
for the exact value of the expected system costs using a search method. In demonstrating the applicability
of the proposed method, we resort to solving an example.