Restricted planar location problems and applications

Abstract

Facility location problems in the plane are among the most widely used tools of Mathematical Programming in modeling real‐world problems. In many of these problems restrictions have to be considered which correspond to regions in which a placement of new locations is forbidden. We consider center and median problems where the forbidden set is a union of pairwise disjoint convex sets. As applications we discuss the assembly of printed circuit boards, obnoxious facility location and the location of emergency facilities. © 1995 John Wiley & Sons, Inc.

A modelling framework for solving restricted planar location problems using phi-objects

“…They present some basic examples to test their algorithms. Hamacher and Nickel (1995) extend their previous work to multi-facility median and centre problems, where the forbidden region is again a union of pairwise disjoint convex sets. They present a heuristic algorithm that consists of a sequential solution of p single facility problems for the p-median problem with a forbidden region, and an efficient solution algorithm based on level sets and lines for the 1-centre problem with Manhattan and Chebyshev distance metrics.…”

“…In these models the either-or constraints are used to define the maximum constraints. In the second and third model, a linearization method is applied, which has resulted in a mixedinteger programming formulation, using the linearization technique for rectilinear and Chebyshev distance functions in Hamacher and Nickel (1995). The first model remains a MINLP, as the distance metric is squared Euclidean.…”

“…The first model remains a MINLP, as the distance metric is squared Euclidean. In the third model, Chebyshev distance function is transformed to rectilinear distance function (Hamacher and Nickel, 1995).…”

“…There are various applications of such types of problems. Assembly of printed circuit boards (Foulds and Hamacher, 1993), obnoxious facility planning (Carrizosa and Plastria, 1993) and location of emergency facilities are some examples for problems with forbidden regions (Hamacher and Nickel, 1995), whereas urban applications considering lakes, parks, cemeteries and rivers can be listed as examples for problems with barriers.…”

Bilinear Programming Formulations for Weber Problems With Continuous and Network Distances

“…The need for realistic representations of [10] Drezner and Hamacher [6] [18]). [10] and Nickel [14].…”