The P-Hub maximal covering problem and extensions for gradual decay functions

•We introduced partial coverage to the hub location literature.•We developed efficient MILP formulations for binary and partial coverage.•We proved that both problems are NP-Hard.•Extensive computational study was carried out with the CAB and TR data sets.

The p-hub maximal covering problem aims to find the best locations for hubs so as to maximize demands within a coverage distance with a predetermined number of hubs. Classically, the problem is defined in the framework of binary coverage only; an origin–destination pair is covered if the cost (time, etc.) is lower than the critical value, and not covered at all if the cost is greater than the critical value. In this paper, we extend the definition of coverage, introducing “partial coverage”, which changes with distance. We present new and efficient mixed-integer programming models that are also valid for partial coverage for single and multiple allocations. We present and discuss the computational results with different data sets.