Geometric methods to solve max-ordering location problems

Location problems with Q (in general conflicting) criteria are considered. After reviewing previous results of the authors dealing with lexicographic and Pareto location the main focus of the paper is on max-ordering location s. In these location problems the worst of the single objectives is minimiz ed. After discussing some general results (including reductions to single-c riterion problems and the relation to lexicographic and Pareto locations) t hree solution techniques are introduced and exemplified using one-location problem class, each: The direct approach, the decision space approach and t he objective space approach. In the resulting solution algorithms emphasis is on the representation of the underlying geometric idea without fully exp loring the computational complexity issue. A further specialization of max- ordering locations is obtained by introducing lexicographic max-ordering lo cations, which can be found efficiently. The paper is concluded by some ide as about future research topics related to max-ordering location problems. (C) 1999 Elsevier Science B.V. All rights reserved.