Hierarchical maximal covering location problem with referral in the presence of partial coverage

Töreyen, Özgün
We consider a hierarchical maximal covering location problem to locate p health centers and q hospitals in such a way that maximum demand is covered, where health centers and hospitals have successively inclusive hierarchy. Demands are 3 types: demand requiring low-level service only, demand requiring high-level service only, and demand requiring both levels of service at the same time. All types of requirements of a demand point should be either covered by hospital providing both levels of service or referred to hospital via health center since a demand point is not covered unless all levels of requirements are satisfied. Thus, a health center cannot be opened unless it is suitable to refer its covered demand to a hospital. Referral is defined as coverage of health centers by hospitals. We also added partial coverage to this complex hierarchic structure, that is, a demand point is fully covered up to the minimum critical distance, non-covered after the maximum critical distance and covered with a decreasing quality while increasing distance to the facility between minimum and maximum critical distances. We developed an MIP formulation to solve the Hierarchical Maximal Covering Location Problem with referral in the presence of partial coverage. We solved small-size problems optimally using GAMS. For large-size problems we developed a Genetic Algorithm that gives near-optimal results quickly. We tested our Genetic Algorithm on randomly generated problems of sizes up to 1000 nodes.


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Citation Formats
Ö. Töreyen, “Hierarchical maximal covering location problem with referral in the presence of partial coverage,” M.S. - Master of Science, Middle East Technical University, 2007.