Facility location in the presence of forbidden regions,I: Formulation and the case of Euclidean distance with one forbidden circle |
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Authors: | INorman Katz Leon Cooper |
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Institution: | Department of Systems Science and Mathematics, Washington University, St. Louis, U.S.A.;Department of Operations Research, Southern Methodist University, Dallas, U.S.A. |
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Abstract: | A constrained form of the Weber problem is formulated in which no path is permitted to enter a prespecified forbidden region of the plane. Using the calculus of variations the shortest path between two points which does not intersect is determined. If is unconstrained distance, we denote the shortes distance along a feasible path by . The constrained Weber problem is, then: given points and positive weights wj, j = 1,2,…,n, find a point such that is a minimum.An algorithm is formulated for the solution of this problem when is Euclidean distance and is a single circular region. Numerical results are presented. |
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Keywords: | Facility location optimal location constrained optimization |
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