A general approximation for the single product lot sizing model with queueing delays

The objective of this paper is to derive a general approximation for the single product lot sizing model with queueing delays, explicitly including a non-zero setup time. Most research focuses on bulk (batch) arrival and departure processes. In this paper we assume an individual arrival and departure process allowing the modelling of more realistic demand patterns. A general approximation of the expected lead time and the variance of the lead time is derived. The lead time probability distribution is approximated by means of a lognormal distribution. This allows the manufacturer to quote lead times satisfying a specified customer service level as a function of the lot size. The main result is a convex relationship of the expected lead time and the quoted lead time as a function of the lot size. The results are illustrated by means of numerical examples.