An analytical model for service level and tardiness in a single machine MTO production system

In this paper an analytical model to calculate service level, FGI and tardiness for a make-to-order (MTO) production system based on the production leadtime, utilisation and WIP is presented. The distribution of customer required leadtime is linked to the already available equations for an M/M/1 production system from queuing theory. Explicit equations for service level, FGI, FGI leadtime and tardiness are presented for an M/M/1 production system within an MTO environment. For a G/G/1 production system an approximation based extension is provided - discussing the influence of variation in the inter-arrival and processing time distribution in this framework. Moreover, the integration of a work ahead window (WAW) work release policy is discussed. Based on a numerical study, a high potential to decrease FGI (up to 97% FGI reduction) when applying such a WAW strategy is found and it is shown that the higher the targeted service level is, the higher the FGI reduction potential. The paper contributes to a better understanding of the relationship between customer required leadtime distribution and the M/M/1 production system. By applying this model a decision maker can base his capacity investment decisions on the service level and expected tardiness for certain levels of FGI and WIP and can additionally define the optimal WAW policy.