A computational study of a nonlinear minsum facility location problem

A discrete location problem with nonlinear objective is addressed. A set of p plants is to be open to serve a given set of clients. Together with the locations, the number p of facilities is also a decision variable. The objective is to minimize the total cost, represented as the transportation cost between clients and plants, plus an increasing nonlinear function of p.Two Lagrangean relaxations are considered to derive lower bounds. Dual information is also used to design a core heuristic.Computational results are given, showing that nearly optimal solutions are obtained in short running times.