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

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27 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1827-1850
Number of pages24
JournalInternational Journal of Production Research
Issue number7
Publication statusPublished - 1 Apr 2011


  • MTO
  • production economics
  • production management
  • queuing theory
  • service level
  • tardiness

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