Power Approximation for Computing (s, S) Policies Using Service Level

The paper presents an analytic approximation for computing (s, S) policies for single items under periodic review with fixed ordering costs, linear holding costs and a service level requirement. The replenishment lead time is fixed and unfilled demand is backlogged. The approximation is similar to Ehrhardt's "Power Approximation." However, we do not assume the knowledge of shortage costs, which are difficult to estimate in practice. We define a \gamma -service level which measures the average backlog relative to the average demand. This quantity is easy to understand and frequently used in practice. The resulting power approximation policies are easy to compute and require only knowledge of the mean and variance of demand. Computational results show that the approximation gives a \gamma -service level which is within one percentage point of the required service level in most cases. Furthermore, the expected total costs of the approximation, taking into consideration a penalty cost for stockouts, are well within one percent of optimal.