Euclidean Distances

Definition of Euclidean distance, Francis and White (1974, p. 169)

Examples where Euclidean distance is appropriate, Francis and White (1974, pp. 169, 187)

Properties of Euclidean distance, Francis et al. (1992, p. 189)

Francis, Richard L. and White, John A. Facilities Layout and Location, Prentice Hall, Englewood Cliffs, NJ, 1974.

Francis, Richard L., McGinnis, Leon F., Jr. and White, John A. Facilities Layout and Location, 2nd. ed., Prentice Hall, Englewood Cliffs, NJ, 1992.

2007-01-29 10:25 pm

Minisum Single-Facility Location Problem with Euclidean Distances

Examples where Euclidean distance is appropriate, Francis and White (1974, pp. 169, 187)

Historical Background, Francis and White (1974, p. 186)

Mathematical formulation, Francis and White (1974, p. 186) and Francis et al. (1992, pp. 200-201)

Solution by Kuhn’s modified gradient procedure, Francis and White (1974, pp. 187-189)

Solved small numerical example, Francis and White (1974, p. 189)

Matricial optimal solution, Francis et al. (1992, pp. 204-207)

Solution by Weiszfeld’s algorithm, Francis et al. (1992, pp. 199-201, 207)

Solved small numerical examples, Francis et al. (1992, pp. 207-208)

Stopping criterion for iterative solution procedures, Francis and White (1974, p. 194) and Francis et al. (1992, pp. 207-209)

Solution by Hyperboloid Approximation Procedure (HAP), Francis and White (1974, p. 190)

Solution of colinear problem, Francis et al. (1992, pp. 201-202)

Solution by mechanical analog, Francis et al. (1992, p. 187)

Majority theorem, Francis et al. (1992, p. 187)

Convex hull, Francis et al. (1992, p. 188)

Triangle inequality, Francis and White (1974, pp. 190-191) and Francis et al. (1992, p. 202)

Triangle inequality for numerical example, Francis and White (1974, p. 191) and Francis et al. (1992, p. 202)

Geometric solution for four and three existing facilities with equal weights, Francis and White (1974, pp. 189-190)

Countour lines for a single existing facility and two existing facilities, Francis and White (1974, pp. 191-192)

Contour lines construction procedure, Francis and White (1974, pp. 191-193)

Evaluation of alternative locations using contour lines, Francis et al. (1992, pp. 209-210)

Francis, Richard L. and White, John A. Facilities Layout and Location, Prentice Hall, Englewood Cliffs, NJ, 1974.

Francis, Richard L., McGinnis, Leon F., Jr. and White, John A. Facilities Layout and Location, 2nd. ed., Prentice Hall, Englewood Cliffs, NJ, 1992.

2006-10-11 11:04 pm

Minisum Multifacility Location Problem with Euclidean Distances

Mathematical formulation, Francis and White (1974, p. 227)

Solution by Hyperboloid Approximation Procedure (HAP), Francis and White (1974, pp. 228-230) and Francis et al. (1992, pp. 365- 367, 370-373)

Solved small numerical example, Francis et al. (1992, p. 367)

Solution when all existing facilities locations are collinear, Francis et al. (1992, p. 368)

Solved small numerical example, Francis et al. (1992, pp. 368-369)

Triangle inequality, Francis and White (1974, p. 231) and Francis et al. (1992, p. 369)

Triangle inequality for numerical examples, Francis and White (1974, pp. 231-232) and Francis et al. (1992, pp. 369-370)

Geometric solution for special case, Francis and White (1974, p. 232)

Francis, Richard L. and White, John A. Facilities Layout and Location, Prentice Hall, Englewood Cliffs, NJ, 1974.

Francis, Richard L., McGinnis, Leon F., Jr. and White, John A. Facilities Layout and Location, 2nd. ed., Prentice Hall, Englewood Cliffs, NJ, 1992.

2007-02-02 9:50 pm

Minimax Single-Facility Location Problem with Euclidean Distances

Examples where Euclidean distance is appropriate, Francis and White (1974, pp. 396-397)

Mathematical formulation with equal weights, Francis and White (1974, p. 396)

Geometric interpretation with equal weights, Francis and White (1974, p. 386)

Geometric solution, Francis and White (1974, pp. 397-398)

Solved small numerical example, Francis and White (1974, pp. 398-399)

Mathematical formulation with addends, Francis and White (1974, p. 399)

Francis, Richard L. and White, John A. Facilities Layout and Location, Prentice Hall, Englewood Cliffs, NJ, 1974.

2007-01-29 11:00 pm

Minimax Multifacility Location Problem with Euclidean Distances

Mathematical formulation, Francis and White (1974, p. 400)

Solved small numerical example, Francis and White (1974, pp. 400-401)

Francis, Richard L. and White, John A. Facilities Layout and Location, Prentice Hall, Englewood Cliffs, NJ, 1974.

2007-01-29 11:05 pm