A new algorithm for solving planar multiobjective location problems involving the Manhattan norm

This paper is devoted to the study of unconstrained planar multiobjective location problems, where distances between points are defined by means of the Manhattan norm. We characterize the nonessential objectives and, by eliminating them, we develop an effective algorithm for generating the whole set of efficient solutions as the union of a special family of rectangles and line segments. We prove the correctness of this algorithm, analyze its complexity, and present illustrative computational results obtained by a MATLAB-based implementation.