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

Abstract

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.

Keywords:

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

Acknowledgement

We would like to thank Stefan Minner and Richard Hartl for their support and comments on the article. Their input led to a considerable increase in the quality of this publication.

Notes

Notes

1. For a Poisson process with rate λ and events of type 1 and type 2, the assignment of type 1 and type 2 is given with probability p and 1 − p independent of all the other events, the two resulting streams of events for types 1 and 2 are again Poisson streams with rate ϕ = pλ and ψ = (1 - p)λ, respectively (see Tijms 2003).

2. The merge of two Poisson streams of events with rates ψ and ϕ lead to a Poisson stream of events with rate λ = ϕ + ψ (see Tijms 2003).