A D.C. biobjective location model
Journal of Global Optimization
The big cube small cube solution method for multidimensional facility location problems
Computers and Operations Research
Locating a semi-obnoxious covering facility with repelling polygonal regions
Discrete Applied Mathematics
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Given a finite set of points in the plane anda forbidden region R, we want to find a point X ∉ int(R), such thatthe weighted sum to all given points is minimized.This location problem is a variant of the well-known Weber Problem, where wemeasure the distance by polyhedral gauges and alloweach of the weights to be positive ornegative. The unit ballof a polyhedral gauge may be any convex polyhedron containingthe origin. This large class of distance functions allows verygeneral (practical) settings – such as asymmetry – to be modeled. Each given point isallowed to have its own gaugeand the forbidden region Renables us to include negative information in the model. Additionallythe use of negative and positive weights allows to include thelevel of attraction or dislikeness of a new facility.Polynomial algorithms and structural properties for this globaloptimization problem (d.c. objective function and anon-convex feasible set) based on combinatorial and geometrical methodsare presented.