optimizing a hierarchical hub covering problem with mandatory dispersion of central hubs

The hierarchical hub location problem is encountered three-level network that is applied in production-distribution system, education system, emergency medical services, telecommunication network, etc. this paper addresses the hierarchical hub covering problem with single assignment accounting for mandatory dispersion of central hubs restriction as a special case. this formulation with incorporating mandatory distance and covering constraints has not been remarked in the hierarchical hub location problem literature. to test the performance of the problem on the turkish data, computational experiments carried out and the model outcomes give useful insight associating with the model sensitivity to its parameters.