6533b836fe1ef96bd12a087d

RESEARCH PRODUCT

Efficiency in constrained continuous location

Christian MichelotMalick Ndiaye

subject

Information Systems and ManagementGeneral Computer ScienceFeasible regionRegular polygonProjection propertyManagement Science and Operations ResearchTopologyIndustrial and Manufacturing EngineeringPlanarCompact spaceModeling and SimulationNorm (mathematics)Convex functionMathematics

description

Abstract We present a geometrical characterization of the efficient, weakly efficient and strictly efficient points for multi-objective location problems in presence of convex constraints and when distances are measured by an arbitrary norm. These results, established for a compact set of demand points, generalize similar characterizations previously obtained for uncontrained problems. They are used to show that, in planar problems, the set of constrained weakly efficient points always coincides with the closest projection of the set of unconstrained weakly efficient points onto the feasible set. This projection property which are known previously only for strictly convex norms, allows to easily construct all the weakly efficient points and provides a useful localization property for efficient and strictly efficient points.

https://doi.org/10.1016/s0377-2217(97)00184-7