On the (S  1, S) Lost Sales Inventory Model with Priority Demand Classes R. Dekker, 1 R.M. Hill, 2 M.J. Kleijn, 1 R.H. Teunter 1 1 Erasmus University Rotterdam, Econometric Institute, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands 2 University of Exeter, School of Mathematical Sciences, Laver Building, North Park Road, Exeter EX4 4QE, United Kingdom Received 8 February 2000; revised 31 July 2001; accepted 7 February 2002 Abstract: In this paper an inventory model with several demand classes, prioritised according to importance, is analysed. We consider a lot-for-lot or ( S - 1, S) inventory model with lost sales. For each demand class there is a critical stock level at and below which demand from that class is not satisfied from stock on hand. In this way stock is retained to meet demand from higher priority demand classes. A set of such critical levels determines the stocking policy. For Poisson demand and a generally distributed lead time, we derive expressions for the service levels for each demand class and the average total cost per unit time. Efficient solution methods for obtaining optimal policies, with and without service level constraints, are presented. Numer- ical experiments in which the solution methods are tested demonstrate that significant cost reductions can be achieved by distinguishing between demand classes. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 593– 610, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10032 Keywords: inventory; demand classes; spare parts; lost sales; rationing 1. INTRODUCTION Nowadays we live in an era where customer service is becoming more and more important. An important aspect of service is product availability, which is related to service levels in inventory systems. In this respect not every customer needs the same kind of service level. For example, in a major oil refinery in The Netherlands a multimillion dollar inventory of spare parts is held (see Dekker, Kleijn, and De Rooij [4]). The customers of this inventory are in fact the equipment needing the parts for repair. Within the refinery the equipment is categorized into three classes, viz. vital, essential, and auxiliary, and different service levels are defined for each type. This poses a problem if parts are installed in several items of equipment of different criticality. According to our empirical research this is the case for some 6000 out of the more than 30,000 parts related to equipment at the refinery. If all demands are satisfied from the same inventory in a first-come-first-served (FCFS) order, as is usually done in inventory systems, then Correspondence to: R. Dekker © 2002 Wiley Periodicals, Inc.