Demand point aggregation method for covering problems with gradual coverage

Abstract

Real world location problems often involve a large number of demand point (DP) data such that the location models become computationally intractable. DP aggregation is a viable means to address the problem by aggregating the original DPs to a smaller set of representative DPs. Most inevitably, though, DP aggregation accompanies a loss of information in the original data and results in errors in the location solution. As such, there is an inherent trade-off between the extent of aggregation and the amount of errors. For covering problems, Current and Schilling (1990) [3] developed an error-free aggregation method based on a key concept that we define in this paper as common reachability set (CRS). While their method provides error-free aggregation solutions to covering problems with binary coverage, it is not applicable to more general and practical cases where the coverage of facilities gradually decreases. We address this limitation by refining the CRS concept. Our method, which we call an approximate CRS (ACRS) method, can be viewed as a generalized version of the original method by Current and Schilling. Using randomly generated DPs data and data from a real world application, we demonstrate the effectiveness of the ACRS method.