Inventory models with minimal service level constraints

This paper investigates inventory models in which the stockout cost is replaced by a minimal service level constraint (SLC) that requires a certain level of service to be met in every period. The minimal service level approach has the virtue of simplifying the computation of an optimal ordering policy, because the optimal reorder level is solely determined by the minimal SLC and demand distributions. It is found that above a certain ‘critical’ service level, the optimal (s,S) policy ‘collapses’ to a simple base-stock or order-up-to level policy, which is independent of the cost parameters. This shows the minimal SLC models to be qualitatively different from their shortage cost counterparts. We also demonstrate that the ‘imputed shortage cost’ transforming a minimal SLC model to a shortage cost model does not generally exist. The minimal SLC approach is extended to models with negligible set-up costs. The optimality of myopic base-stock policies is established under mild conditions.