## Abstract

The objective of classic cover location models is for facilities to cover demand within a given distance. Locating a given number of facilities to cover as much demand as possible is referred to as max-cover. Finding the minimum number of facilities required to cover all the demand is the set covering problem. The gradual (or partial) cover replaces abrupt drop from full cover to no cover by defining gradual decline in cover. If classic cover models consider 3 miles as the cover distance, then at 2.99 miles a demand point is fully covered while at 3.01 miles it is not covered at all. In gradual cover, a cover range is set. For example, up to 2 miles the demand is fully covered, beyond 4 miles it is not covered at all, and between 2 and 4 miles it is partially covered. In this paper, we propose, analyze, and test a new rule for calculating the joint cover of a demand point which is partially covered by several facilities. The algorithm is tested on a case study of locating cell phone towers in Orange County, California. The new approach provided better total cover than the cover obtained by existing procedures.

## Keywords

Cover location models Partial cover Gradual cover## Mathematics Subject Classification

90B80 90B85 90C27## References

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