Planar Location Problems with Line Barriers
نویسنده
چکیده
The Weber Problem for a given nite set of existing facilities Ex = fEx 1 ; Ex 2 ; : : : ; Ex M g IR 2 with positive weights w m (m = 1; : : : ; M) is to nd a new facility X such that P M m=1 w m d(X; Ex m) is minimized for some distance function d. 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. Structural results as well as algorithms for this non-convex optimization problem depending on the distance function and on the number and location of passages through the barrier are presented. A reduction to convex optimization problems is used to derive eecient algorithms.
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تاریخ انتشار 1996