Continuous covering and cooperative covering problems with a general decay function on networks

Abstract

A cooperative covering location problem anywhere on the networks is analysed. Each facility emits a signal that decays by the distance along the arcs of the network and each node observes the total signal emitted by all facilities. A node is covered if its cumulative signal exceeds a given threshold. The cooperative approach differs from traditional covering models where the signal from the closest facility determines whether or not a point is covered. The objective is to maximize coverage by the best location of facilities anywhere on the network. The problems are formulated and analysed. Optimal algorithms for one or two facilities are proposed. Heuristic algorithms are proposed for location of more than two facilities. Extensive computational experiments are reported.

Keywords:

• location
• networks
• continuous covering
• cooperative covering
• big segment small segment
• simulating annealing

Acknowledgements

This research was supported, in part, by the Natural Sciences and Engineering Research Council of Canada.