Given Q different objective functions, three types of single-facility problems are considered: lexicographic, Pareto and max ordering problems. After discussing the interrelation between the problem types, a complete characterization of lexicographic locations and some instances of Pareto and max ordering locations is given. The characterizations result in efficient solution algorithms for finding these locations. The paper relies heavily on the theory of restricted locations developed by the same authors, and can be further extended, for instance, to multi-facility problems with several objectives. The proposed approach is more general than previously published results on multicriteria planar location problems and is particularly suited for modelling real-world problems.
