Linear facility location. Solving extensions of the basic problem. (English) Zbl 0499.90025
Summary: The basic problem is to locate a linear facility to minimize the sum of weighted shortest Euclidean distances from demand points to the facility. We extend the analysis to locating a constrained linear facility, a radial facility, a linear facility where distances are rectangular and a linear facility under the minimax criterion. Each case is shown to admit a simple solution technique.
MSC:
| 90B85 | Continuous location |
Keywords:
linear facility location; minimization of the sum of weighted shortest Euclidean distances; constrained linear facility; radial facility; minimax criterion; solution technique; rectangular distanceReferences:
| [1] | Appa, G.; Smith, C., On \(L_1\) and Chebyshev estimation, Math. Programming, 5, 73-87 (1973) · Zbl 0271.41021 |
| [2] | Charnes, A.; Cooper, W. W.; Ferguson, R. O., Optimal estimation of executive compensation by linear programming, Management Sci., 1, 138-150 (1955) · Zbl 0995.90590 |
| [3] | Francis, R. L.; Lowe, T. J.; Ratliff, H. D., Distance contraints for tree network multifacility location problems, Operations Res., 26, 570-596 (1978) · Zbl 0385.90112 |
| [4] | MacKinnon, R. D.; Barber, G. M., A new approach to network generationand map representation: The linear case of the location-allocation problem, Geographical Anal., 4, 156-168 (1972) |
| [5] | Morris, J. G.; Norback, J. P., A simple approach to linear facility location, Transportation Sci., 14, 1-8 (1980) |
| [6] | Norback, J. P.; Love, R. F., Geometric approaches to solving the traveling salesman problem, Management Sci., 23, 1208-1223 (1977) · Zbl 0373.90074 |
| [7] | Wagner, H. M., Linear programming techniques for regression analysis, J. Amer. Statist. Assoc., 54, 206-212 (1957) · Zbl 0088.35702 |
| [8] | Wesolowsky, G. O., Location of the median line for weighted points, Environment and Planning A, 7, 163-170 (1975) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
