Demand point aggregation analysis for a class of constrained location models: a penalty function approach

Abstract

Many location models involve location cost functions that depend on the distances between demand points and new facility locations. There can be so many demand points that they must be aggregated to obtain a tractable model. We consider a class of such problems where the location cost functions appear in both the objective and the constraints. By using the concept of a penalty function we obtain error bounds, that is, upper bounds on the errors introduced by aggregation. The error bounds can be used to drive demand point aggregation schemes, and consider both objective error and constraint error.

Acknowledgements

We are happy to acknowledge the numerous constructive comments of the referees. This research has been supported in part by the National Science Foundation, grant DMI-9908124.