A Bi-Objective Median Location Problem With a Line Barrier

Abstract

The multiple objective median problem (MOMP) involves locating a new facility with respect to a given set of existing facilities so that a vector of performance criteria is optimized. A variation of this problem is obtained if the existing facilities are situated on two sides of a linear barrier. Such barriers, like rivers, highways, borders, or mountain ranges, are frequently encountered in practice. In this paper, theory of an MOMP with line barriers is developed. As this problem is nonconvex but specially structured, a reduction to a series of convex optimization problems is proposed. The general results lead to a polynomial algorithm for finding the set of efficient solutions. The algorithm is proposed for bicriteria problems with different measures of distance.

An efficient solution method for Weber problems with barriers based on genetic algorithms

“…In Klamroth (2001a,b) it was shown that an optimal solution of the non-convex barrier problem can be found by solving a finite and, in the case of line barriers, polynomial number of related unconstrained subproblems, a result which will be used extensively in this paper. A generalization to multi-criteria problems was discussed in Klamroth and Wiecek (2002).…”

The Capacitated Location-Allocation Problem in the Presence of <i>k</i> Connections

“…In the case of line barriers, Klamroth [10] considered a limited number of passages with any distance measure, separated the plane into two sub-planes and showed that an optimal solution of the non-convex barrier problem can be attained by solving a polynomial number of related unconstrained sub-problems. Klamroth and Wiecek [11] generalized this result to multi-criteria problems. Huang et al [12] find the optimal location of k connections in the plane for uncapacitated and capacitated location problems.…”

Planar Location Problems with Block Distance and Barriers

“…For the case of polyhedral barrier sets, Klamroth (2001a) and Klamroth (2001b) showed that an optimal solution of the non-convex barrier problem can be found by solving a finite (and in the case of line barriers a polynomial) number of related unconstrained subproblems. This result was generalized to the multi-criteria case in Klamroth and Wiecek (2002).…”