Lost-sales inventory systems with a service level criterion

► We model a period-review inventory system with lost sales and a service level. ► There are no restrictions on the lead time or the number of outstanding orders. ► We examine optimal policies as well as base-stock policies and (R, s, S) policies. ► New heuristic procedures are proposed to set the reorder level and base-stock level. ► The heuristics result in cost increases of 1-2% and satisfy the service level in 80-95%.