An exact calculation of the cycle service level in a generalized periodic review system M Cardo´s*, C Miralles and L Ros Universidad Polite´cnica de Valencia, Valencia, Spain This paper is focused on the exact calculation of the cycle service level for a generalized periodic review system accepting any discrete demand with a known probability function and any cycle service target. Previously, it was necessary to modify the definition of the cycle service level metric (also known as non stock out probability) so that it could be applied to these cases. The purpose of the proposed (R, S) system is to handle simultaneously fast-moving items, slow- moving items and intermittent or sporadic demand items any of them with high, medium or low cycle service targets. Journal of the Operational Research Society (2006) 57, 1252–1255. doi:10.1057/palgrave.jors.2602121 Published online 23 November 2005 Keywords: inventory; periodic review; slow-moving items; cycle service level Introduction A major regional retailer replenishes more than 60 shops from a central warehouse using a periodic review system, usually delivering two to four times per week to every shop in order to achieve the high service standard they have imposed. Table 1 shows the inventory profile of a typical shop where the items are classified depending on the item’s average daily demand rate. Class III items are just 2% of the items but they are responsible for 29% of the units sold and 11% of the stock, while class I items are 69% of the items and account just for 14% of the units sold but 40% of the stock. Obviously, the retailer defined service target for every items depending on its demand rate. This retailer, as many others in the industry, has to cope with a critical task: to establish and maintain the periodic review parameters for literally thousands of items in every shop at least every 3 months looking for the right balance between stock and cycle service. Therefore, a reliable and efficient method is needed to process these massive data and maintain inventory levels at a minimum. The most widely analysed periodic review models in the literature share the simplifying hypothesis detailed by Silver et al (1998), including the following ones especially relevant to the purpose of this paper: (a) there is a negligible chance of no demand between two consecutive reviews, so every review places a replenishment order; and (b) the usual level of backorders is negligibly small when compared with the average stock level. This simplified approach is called classical approximation in the rest of this paper. Unfortunately, the classical method is not suitable for many of the items shown in Table 1 as they violate the hypotheses (a) and (b). Moreover, van der Heijden and de Kok (1998) point out that cost optimal control policies in multi-echelon systems often imply low service levels at intermediate nodes, resulting in a violation of the (b) hypothesis. Additionally, even when a retail chain is chasing a high global service level, Cardo´ s and Garcı´a (2005) show that the service level required for slow-moving items is usually low, resulting in a violation of the (a) hypothesis. Different models have been developed to manage slow- moving items and sporadic-demand items (Williams, 1984). More recently, some interesting papers highlight the implications of size orders on slow-moving items (Johnston et al, 2003) and evaluate periodic review policies and forecasting methods applied to low and intermittent demand items (Sani and Kingsman, 1997). However, no reference could be found on the calculation of low cycle service levels. Therefore, this paper is primarily concerned with the exact calculation of the cycle service level when a periodic review system is applied and the demand is intermittent, even for low cycle service levels. At the extent of the authors’ knowledge, this is the first time the (R, S) system has been generalized to include intermittent demand and slow-moving items instead of developing specialized models, and the first time low cycle service levels can be suitably computed. The proposed method only needs discrete demand with a known probability function. The periodic review system Periodic review systems place replenishment orders every R fixed periods to restore a predefined level called the order up to level. The replenishment order is received r periods after *Correspondence: M Cardo ´s, Departamento de Organizacio ´n de Empre- sas, Universidad Polite ´cnica de Valencia, Camı´ de Vera s/n, 46071 Valencia, Spain. E-mail: mcardos@omp.upv.es Journal of the Operational Research Society (2006) 57, 1252–1255 r 2006 Operational Research Society Ltd. All rights reserved. 0160-5682/06 $30.00 www.palgrave-journals.com/jors