Two Branch & Bound Methods for a Generalized Class of Location-Allocation Problems

In this paper we consider a generalized class of location-allocation problems, in which N new facilities are to be located in the plane with respect to M objects. We assume each object to be associated with a non-negative convex cost function, specifying the expenses for serving the object from any location in the plane. For the resulting multi-dimensional mixed-integer optimization problem two different branch & bound methods are presented, one branching on the discrete assignment variables, the other on the continuous location variables. A relatively new instance of this class of location problems, the multi connection location problem under the Euclidean metric is used for evaluating both methods.