Facility location in the presence of forbidden regions, I: Formulation and the case of Euclidean distance with one forbidden circle
| Autor: | Leon Cooper, I. Norman Katz |
|---|---|
| Rok vydání: | 1981 |
| Předmět: |
Path (topology)
Information Systems and Management General Computer Science Plane (geometry) Weber problem Management Science and Operations Research Euclidean distance matrix Industrial and Manufacturing Engineering Euclidean distance Combinatorics Euclidean shortest path Modeling and Simulation Shortest path problem Point (geometry) Mathematics |
| Zdroj: | European Journal of Operational Research. 6:166-173 |
| ISSN: | 0377-2217 |
| DOI: | 10.1016/0377-2217(81)90203-4 |
| Popis: | A constrained form of the Weber problem is formulated in which no path is permitted to enter a prespecified forbidden region R of the plane. Using the calculus of variations the shortest path between two points x , y ∉ R which does not intersect R is determined. If d( x , y ) is unconstrained distance, we denote the shortes distance along a feasible path by d ( x y ) . The constrained Weber problem is, then: given points x j ∉ R and positive weights wj, j = 1,2,…,n, find a point x ∉ R such that f( x )= Σ n j=1 d( x , x j ) is a minimum. An algorithm is formulated for the solution of this problem when d( x , y ) is Euclidean distance and R is a single circular region. Numerical results are presented. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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