Optimal (, , ) batch-ordering policy under stationary demand

We consider the control of a single-echelon inventory system under the standard batch-ordering policy. Demand follows a stationary stochastic process and, when unsatisfied, is backordered. Under a standard cost structure, we seek to minimise total average cost per unit time. In contrast to previous research, all three policy variables (i.e. reorder level r, batch size Q and review interval T) are simultaneously optimised. While average total cost is not convex, analytic properties for two new cost bounds and a Newsboy characterisation of the optimal solution lead to an exact search algorithm with guaranteed convergence to the global optimum. Computational results demonstrate that the inclusion of the review interval as a decision variable in the optimisation problem can offer substantial cost savings.