H Karimi - University of Bojnord, Department of industrial engineering, Bojnord, Iran
M Bashiri - Shahed University, Department of industrial engineering, Tehran, Iran
S Nickel - Institute for Operations Research, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany

The goals of hub location problems are finding the location of hub facilities and determining theallocation of non-hub nodes to these located hubs. In this work, we discuss the multi-modal singleallocation capacitated p-hub covering problem over fully interconnected hub networks. Therefore, weprovide a formulation to this end. The purpose of our model is to find the location of hubs and the hublinks between them at a selected combination of modes for each origin-destination. Furthermore, itdetermines the allocation of non-hub nodes to the located hubs at the best mode for each allocationsuch that the travel time between any origin–destination pair is not greater than a given time bound. Inaddition, the capacity of hub nodes is considered. Six valid inequalities are presented to tighten thelinear programming lower bound. We present a heuristic tabu search based algorithm and test theperformance of it on the Australian Post (AP) data set.

Hub LocationCovering; Multi-modalTabu SearchValid InequalityCapacity