Identifying potential bottlenecks in production systems using dual prices from a mathematical programming model

Abstract

The importance of identifying bottlenecks in production systems for effective production control and continuous improvement is well recognised. A useful definition of a bottleneck is the station to whose performance the performance of the overall production system is most sensitive. However, obtaining accurate estimates of the impact of changes in a given station's performance on the performance of a production system is often difficult. This paper uses the dual prices associated with production resources in a production planning model to support the identification of bottlenecks as the product mix in the system changes over time. The planning model considers queueing behaviour at production resources using non-linear clearing functions. Relationships between the dual prices of different resources are derived, and the bottleneck information obtained is compared to that from a model that does not consider queueing behaviour.

Keywords:

• production planning
• linear programming
• duality theory
• bottlenecks
• clearing functions

Acknowledgements

The opinions expressed in the paper are those of the authors, and do not reflect those of the National Science Foundation. The authors would like to thank Dr Erinc Albey of North Carolina State University and Prof. Hubert Missbauer of the University of Innsbruck for their many insightful comments on an earlier draft of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Science Foundation [grant number 0559136], [grant number 1029706]; Intel Research Council.