Minisum Single-Facility Location Problems

Typical examples, Francis et al. (1992, pp. 185-186)

General formulation, Francis et al. (1992, p. 186-187)

Model validity, Francis and White (1974, p. 169)

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.

2006-10-05 11:21 pm

Minisum Single-Facility Location Problem with Rectilinear Distances

Examples where rectilinear distance is appropriate, Francis and White (1974, pp. 169-170)

Mathematical formulation, Francis et al. (1992, p. 190)

Properties of optimal solution, Francis and White (1974, p. 171) and Francis et al. (1992, pp. 190-194)

Discussion of “median,” Francis and White (1974, p. 171) and Francis et al. (1992, p. 194)

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

Solved small numerical examples, Francis and White (1974, pp. 171-172), Francis et al. (1992, pp. 191-194) and Tompkins et al. (1996, pp. 536-537)

Force analogy, Tompkins and White (1984, p. 492)

Solved small numerical example, Tompkins and White (1984, p. 492)

Solved large numerical example, Francis and White (1974, pp. 172-173)

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

Cost of alternative locations, Tompkins et al. (1996, pp. 537-538)

Definition of contour or iso-cost lines or level curves, Francis and White (1974, p. 173)

Importance of contour lines, Francis and White (1974, pp. 173, 194) and Francis et al. (1992, pp. 194-196)

Contour lines construction procedure, Francis and White (1974, pp. 173-175), Francis et al. (1992, p. 196-199), Tompkins and White (1984, pp. 492-495) and Tompkins et al. (1996, p. 538)

Countour lines for small numerical example, Francis and White (1974, pp. 175-176), Francis et al. (1992, pp. 195-1997) and Tompkins and White (1984, pp. 492-495)

Justification of contour lines construction procedure, Francis and White (1974, pp. 175, 177, 179-183)

Plots of x and y optimization for small numerical example, Francis and White (1974, pp. 177-178) and Francis et al. (1992, pp.192-193)

Importance of plots of x and y optimization, Francis and White (1974, p. 179)

Countour lines for a single existing facility and two existing facilities, Francis and White (1974, pp. 178-179)

Insights, Francis et al. (1992, p. 199)

Area locations for existing facilities, Tompkins and White (1984, pp. 494-497)

Solved small numerical example by force analogy, Tompkins and White (1984, pp. 495-497)

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.

Tompkins, James A. and White, John A. Facilities Planning, John Wiley and Sons, New York, 1984.

Tompkins et al. Facilities Planning, 2nd. ed., John Wiley and Sons, New York, 1996.

2007-02-27 6:14 pm

Minisum Single-Facility Location Problem with Squared Euclidean Distances

Example where squared Euclidean distance is appropriate, Francis and White (1974, p. 170)

Model validity, Francis and White (1974, p. 184) and Francis et al. (1992, p. 203)

Mathematical formulation, Francis and White (1974, p. 184) and Francis et al. (1992, p. 203)

Algebraic optimal solution, Francis and White (1974, p. 184)

Solved small numerical example, Francis and White (1974, pp. 184-185)

Matricial optimal solution, Francis et al. (1992, pp. 203-204)

Contour lines, Francis and White (1974, pp. 185-186) and Francis et al. (1992, p. 204)

Evaluation of alternative locations using contour lines, Francis et al. (1992, p. 204)

Countour lines for a single existing facility and two existing facilities, Francis and White (1974, p. 185)

Data availability, Francis and White (1974, pp. 194-195)

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 10:31 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 Problems

Typical examples, Francis and White (1974, pp. 167-169)

General formulation, Francis and White (1974, pp. 210-213) and Francis et al. (1992, pp. 338-339)

Model validity, Francis and White (1974, pp. 211-213)

Table form for small example data, Francis et al. (1992, pp. 335-337, 339-340)

Weight graph, Francis et al. (1992, pp. 335-337, 339-340)

Weight graph for small example data, Francis et al. (1992, pp. 335-337, 339-340)

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 11:35 pm

Minisum Multifacility Location Problem with Rectilinear Distances

Mathematical formulation, Francis et al. (1992, pp. 335-339, 345-347)

Model validity, Francis and White (1974, p. 217)

Solution by linear programming, Francis and White (1974, pp. 213-217) and Francis et al. (1992, pp. 347-348)

Solved small numerical example, Francis and White (1974, pp. 215-217)

Application, Francis et al. (1992, pp. 342-345)

Multiple optimal solutions, Francis and White (1974, pp. 216-217)

Properties of optimal solution, Francis and White (1974, pp. 217-218, 221-224) and Francis et al. (1992, pp. 341, 349)

Solution by iterative procedure, Francis and White (1974, pp. 218-220)

Solved small numerical examples, Francis and White (1974, pp. 218-219)

Limitation of iterative procedure, Francis and White (1974, p. 219)

Solution using coordinate descent, Francis et al. (1992, pp. 349-351)

Dual formulation, Francis and White (1974, pp. 220-221)

Minimum-cost network flow solution procedure, Francis et al. (1992, pp. 352-354, 358-361)

Solved small numerical examples, Francis et al. (1992, pp. 354-357, 361-362)

Arc saturation in order of increasing costs heuristic, Francis et al. (1992, pp. 354-357)

Computational check, Francis et al. (1992, pp. 355-356)

Node labeling algorithm, Francis et al. (1992, pp. 354-357)

Source, sink and transshipment nodes, Francis et al. (1992, p. 356)

Solution by Hyperboloid Approximation Procedure (HAP), Francis and White (1974, pp. 230-231)

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.

2007-01-31 11:00 pm

Minisum Multifacility Location Problem with Squared Euclidean Distances

Example where squared Euclidean distance is appropriate, Francis and White (1974, p. 170)

Model validity, Francis and White (1974, p. 227)

Mathematical formulation, Francis and White (1974, p. 224)

Algebraic optimal solution, Francis and White (1974, pp. 224-226) and Francis et al. (1992, pp. 363- 364)

Solved small numerical examples, Francis and White (1974, pp. 226-227) and Francis et al. (1992, pp. 364- 365)

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 9:45 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 Problems

Typical examples, Francis and White (1974, pp. 378-379)

Model validity, Francis and White (1974, pp. 378-379)

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

2006-10-16 10:46 pm

Minimax Single-Facility Location Problem with Rectilinear Distances

Examples where rectilinear distance is appropriate, Francis and White (1974, pp. 380-381)

Mathematical formulation with equal weights, Francis and White (1974, p. 380)

Addends, Francis and White (1974, pp. 381-382, 384)

Mathematical formulation with equal weights and addends, Francis and White (1974, p. 381)

Solution by linear programming, Francis and White (1974, pp. 382-384)

Optimal solution, Francis and White (1974, p. 381)

Solved small numerical examples, Francis and White (1974, pp. 381-382) and Tompkins et al. (1996, p. 539)

Mathematical formulation with addends, Francis and White (1974, p. 384)

Solution by linear programming, Francis and White (1974, pp. 386-387)

Solved small numerical example, Francis and White (1974, pp. 387-388)

Properties of optimal solution, Francis and White (1974, pp. 388-389)

Contour lines construction procedure, Francis and White (1974, pp. 384-385)

Countour lines for small numerical example, Francis and White (1974, pp. 382, 385-386)

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

Tompkins et al. Facilities Planning, 2nd. ed., John Wiley and Sons, New York, 1996.

2007-03-06 00:34 am