Effects on undershoots and lost sales on the cycle service level for periodic and continuous review policies

One of the most usual measures of customer service is the cycle service level (CSL) which indicates the specific probability of no stockout per replenishment cycle. This definition can be applied to any stock policy and demand pattern, given a known stock level at the beginning of the cycle. Some approximations have been used to compute this stock level in some scenarios not including undershoots or neglecting the probability of no demand during the cycle depending on the stock policy. However, in practice a number of different scenarios take place those basically depend on the market rules and the demand characteristics. A general approach is presented in this paper to compute the exact cycle service level in different scenarios for both periodic and continuous review policies. Additionally, this paper examines the deviations observed when the classical approximations are used. This paper is focused on uncorrelated, discrete and stationary demand with a known pattern.