P-hub maximal covering problem and extensions for gradual decay functions
Kara, Bahar Y.
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Hubs are special facilities that serve as switching, transshipment and sorting nodes in many to many distribution systems. The hub location problem deals with the selection of the locations of hub facilities and finding assignments of demand nodes to hubs simultaneously. The p-hub maximal covering problem, that is one of the variations of the hub location problems, aims to find locations of hubs so as to maximize the covered demand that are within the coverage distance with a predetermined number of hubs. In the literature of hub location, p-hub maximal covering problem is conducted in the framework of only binary coverage; origin-destination pairs are covered if the total path length is less than coverage distance and not covered at all if the path length exceeds the coverage distance. Throughout this thesis, we extend the definition of coverage and introduce “partial coverage” that changes with the distance, to the hub location literature. In this thesis, we study the p-hub maximal covering problem for single and multiple allocations and provide new formulations that are also valid for partial coverage. The problems are proved to be NP-Hard. We even show that assignment problem with a given set of hubs for the single allocation version of the problem is also NP-Hard. Computational results for all the proposed formulations with different data sets are presented and discussed.