A Compact Linearisation of Euclidean Single Allocation Hub Location Problems

Hub location problems are strategic network planning problems. They formalise the challenge of mutually exchanging shipments between a large set of depots. The aim is to choose a set of hubs (out of a given set of possible hubs) and connect every depot to a hub so that the total transport costs for exchanging shipments between the depots are minimised. In classical hub location problems, the unit cost for transport between hubs is proportional to the distance between the hubs. Often these distances are Euclidean distances: Then is possible to replace the quadratic cost term for hub-hub-transport in the objective function by a linear term and a set of linear inequalities. The resulting model can be solved by a row generation scheme. The strength of the method is shown by solving all AP instances to optimality.