Ward, J. E., and R. E. Wendell. 1980. A new norm for measuring distance which yields linear location problems. Operations Researcli 28:836-844.

Weber, A. 1909. Ueberden standort der industrien. TUbingen (English translation: Friedrich, C. J. (translator) 1929. Theory of the location of industries. Chicago: University of Chicago Press).

Weiszfeld, E. 1936. Sur un probleme de minimum dans Iespace. Tdhoku Mathematical Journal 42:274-280.

-. 1937. Sur le point lequel la somme des distances de n points donnes est

minimum. Tdhoku Mathematical Journal 43:355-386.

Wendell, R. E., and A. P. Hurter. 1973. Location theory, dominance, and convexity. Operations Research 21:314-320.

Wendell, R. E., A. P. Hurter, and T. J. Lowe. 1977. Efficient points in location problems. Transactions 9:338-346.

Wersan, S. J., J. E. Quon, and A. Charnes. 1962. Systems analysis of refuse collection and disposable practices. American Public Works Association, Yearbook A95-2\\.

Wesolowsky, G. O. 1970. Facilities location using rectangular distances. Ph.D.

Dissertation, University of Wisconsin-Madison. -. 1972. Rectangular distance location under the minimax optimality criterion. Transportation Science 6AOi-lli.

-. 1973. Dynamic facihty location. Management Science 19:1241-1247.

-. 1974. Location of the median line for weighted points. Environment and

Planning A 7:163-170.

1977. The Weber problem with rectangular distances and randomly dis-

tributed destinations. Journal of Regional Science 17:53-60.

-. 1982. Location problems on a sphere. Regional Science and Urban Eco-

nomics 12:495-508.

Wesolowsky, G. O., and R. F. Love. 1971a. Location of facilities with rectangular distances among point and area destinations. Naval Research Logistics Quarterly 18:83-90.

-. 1971b. The optimal location of new facilities using rectangular distances.

Operations Research 19:124-130.

-. 1972. A nonlinear approximation method for solving a generalized rec-

tangular distances Weber problem. Management Science 18:656-663.

Wesolowsky, G. O., and W. G. Truscott. 1975. The multiperiod location-allocation problem with relocation of facihties. Management Science 22:57-65.

Westwood, J. B. 1977. A transport planning model for primary distribution. Interfaces 8/1:1-10.

White, J. A. 1971. A note on the quadratic facility location problem. AIIE Transactions 3:156-157.

Wimmert, R. J. 1958. A mathematical model of equipment location. The Journal of Industrial Engineering 9:498-505.

Witzgall, C. 1964. Optimal location of a central facility: Mathematical models and concepts. National Bureau of Standards Report 8388, Gaithersberg, Maryland.

Wolfe, P. 1961. A duality theorem for non-linear programming. Quarterly Journal of Applied Mathematics 19:239-244.

Woolsey, R. E. D. 1986. The fifth column: On the minimization of need for new facilities, or space wars, lack of presence, and Delphi. Interfaces 16/5:53-55.

Wyman, Samuel D. Ill, and L. G. Callahan. 1975. Evaluation of computerized layout algorithms for use in design of control panel layouts. In Proceedings, Fourteenth Annual U.S. Army Operations Research Symposium, Fort Lee, Virginia, November, Vol. 2, 993-1002, Maryland: Director, U.S. Army Material Systems Analysis Activity, Aberdeen Proving Ground.

Index

Absolute deviations, 258 Adcock, R.J., 73 Addends, 119

Aggregation of demand points, 196-199,

212-213 Aikens, C.H., 224 Aly, A.A., 73, 169 Ambulance station location, 175 Antipode, 38, 41 Area destinations, 43-51 Armour, G.C., 254

bounds (upper) on distances in location models, 131-132, 182 Brady, S.D., 113, 119, 140 Brady-Rosenthal Algorithm, 119 Branch-and-bound solution of dynamic location problem, 64-66

solution of quadratic assignment problem, 231-242 Broeckx, F., 254 Buffa, E.S., 254 Burkard, R.E., 254 Burness, R.C., 274

Balinski, M.L., 95, 223 Barber, G.M., 51 Bainnol, W.J., 95, 223 Bazaraa, M.S., 251, 254 Beckenbach, E.F., 110 Belardo, S., 223 Bellman, R., 110

Benders decomposition method, 203-212, 224

Bergman,L., 223 Bias, directional, 257 Bilde, O., 223 Bindschedler, A.E., 31 Bjorck, A., 31 Bos, H.D., 169 Bounds

bound (lower) on objective function of location models, 16-17, 34-35, 89, 93, 119, 122, 134, 141, 205, 225

bound (lower) for solving the quadratic assignment problem, 233-236

Cabot, A.V., 92, 109

Calami, P.H., 93

Callahan, L.G. 229

Center-of-gravity, 4-5, 15, 17

Chaiken, J.M., 178

Chained facilities, 87

Chalmet, L.G., 169

Chandrasekaran, R., 115, 1)7, 139

Charalambous, C, 31, 92, 122, 140

Charnes, A., 92

Chatelon, J.A., 136, 140

Chen, R., 169

Christofides, N., 9, 274

Church, R.L., 182, 183, 184, 185, 223

Circles

covering, 118

great, 268-271

market area, 163

unit, 257-258, 265 Concavity of location-allocation problem, 158

Conn, A.R., 93 Connors, M., 254 Constraints dual formulation of constrained problems, 101-102, 106-107 on distances in minimax location

problems, 131-132 on locations in rectangular distance location problems, 83 Continuous existing facilities, 43-51, 162-164

Continuous location-allocation, 162-164 Contours, 131, 269 Converse, A.O., 146 Convex sets

convex hull, 15-16, 88, 118, 153-157

convex polygon, 16, 115

convex set on sphere, 39 Convexity (of functions)

definition, 13, 32, 39

empirical metrics, 266-268

Euclidean distance function, 14, 31

hyperbolic approximation, 25

R,. distance function, 23-24, 33

rectangular distance function, 18

spherical distance, 39, 13-14 Cooper, L., 73, 169, 273 Cornuejols, G., 223

Cost structures and capacity restrictions, 193, 195

CRAFT heuristic for floor layout

problems, 242-244, 251 Criterion for locating at an existing facility

location, 14, 24, 40 Crowston, W.B., 254 Cutting plane procedure, 177

Dahlquist, G., 31

Data considerations, 187-188, 202-203 Dearing, P.M., 135, 140 Decomposition method to solve dual

problem, 107 Deviations, absolute and squared, 258-259 Directional bias, 257-258 Direction vectors, 1 1 1 11 5 of dual

solutions as, 100 Discontinuities in the derivatives of the

distance function, 87 Distribution centers, 143-145, 200 Dohrn, P.J., 274 Domschke, W., 9 Donnay, J.D.H., 74 Dowling, P.D., 31, 93, 263 Drexl, A., 9

Drezner, Z., 31, 35, 43, 69, 73, 133, 134,

140, 152, 169 Drezner-Wesolowsky Algorithm, 134

Duality minimax dual, 129-131 multi-facility Euclidean dual, 102-104 multi-facility jP,, dual, 104-107 single-facility Euclidean dual, 95-101 solution methods, 107 structural properties of location-allocation problem, 158

DUALOC, 189-193

Dynamic location, 60-66

Eddison, R.T., 9

Edge descent method for solving muhi-

facility problems, 83-86 Efficient point, 169 Efroymson, M.A., 223 Ellon, S., 9, 274 Elshafei, A.N., 227, 251, 254 Elzinga-Heam Algorithm, 118, 123 Elzinga,!., 9, 31, 118, 123, 140 Empirical studies (of distance functions),

258-265

Erlenkotter, D., 73, 190, 193, 223 Euclidean distances

dual models, 95-104

location models, 12-18, 113-115, 117-125

Euclidean metric, 257 Eyster, J.W., 31, 92

Fire engine travel time, 174, 256 Fire station location, 173-178 Fisher, M.L., 223 Floor layout-quadratic assignment problem

branch-and-bound solution method, 231-242

Hall Quadratic Placement Algorithm, 245-251

heuristic procedures-CRAFT and HC63-66, 242-244, 251 Francis, R.L., 9, 31, 92, 109, 135, 137, 140, 169

Gavett, J.W., 254 Gelders, L.F., 169

Geoffrion, A.M., 109, 158, 162, 169, 178,

187, 195, 199, 206, 223, 224 Ghare, P.M., 92 Gilmore, P.C., 254 Ginsburgh, v., 255 Goldstein, J.M., 9 Gomory, R.E., 223

Graphics

exclusion property, 156

inclusion property, 153-155

interactive computer graphics, 118, 133 Graves, G.W., 199, 206, 224, 254 Great circle metrics, 38, 268-271

Haldane, J.B.S., 73 Hall, K.M., 245, 254

Hall Quadratic Placement Algorithm, 245-251

Hamburger, M.J., 199, 223 Handler, G.Y., 169 Hansen, P., 9, 169, 255, 273 Hardy, G.H., 232 Harrald, J., 223 Hausner, J., 174

Hearn, D.W., 9, 31, 118, 123, 136, 140

Hendrick, . ., 174

Heragu, S.S., 254

Hertz, D.B., 9

Heuristics

for floor layout, quadratic assignment problems, 242-244

for site-generating location-allocation problems, 157-162

for set-covering problems, 177-178 Hillier, F.S., 254 Hogan, K.. 223 Helders inequality, 110 Homogeneity property of a norm, 264 Hull

convex hull, 15-16, 118, 153, 157 rectangular hull, 153-154, 169-170

Hurler, A.P., Jr., 109, 169

Hyperbolic approximation, 24, 31, 87

Identity property

of a metric, 255

of a norm, 264 Ignall, E.J., 178

Infinity, one-infinity norm, 264-266 Instrument panel layout, 229 Intercity road distances, 262

Johnson, E.L., 202

Juel, H., 24, 31, 92, 109, 169

Juel-Love Algorithm, 86

Katz, I.N., 31, 73 Kaufman, L., 254

Kermack, K.A., 73 Khumawala, B.M., 190, 223 Kirca, O., 254 Kleindorfer, G.B., 255 Kochenberger, G.A., 255 Kolen, A.J.W., 138, 169 Kolesar, P., 174, 175, 177 Kolesar-Walker Heuristic, 177 Kraemer, S.A., 109, 140 Krarup, J., 223 Kuehn, A.A., 199, 223 Kuenne, R.E., 169, 274 Kuhn, H.W., 9, 31, 109 Kusiak, A., 254

Lagrange multipliers, 99, 110, 121, 246, 247

Lagrangian function, 110, 246, 247 Land, A.H., 254 Laporte, G., 274 Large region metrics, 268-271 Urson, R.C., 178 Latitude, 38, 269 Lawler, E.L., 254 Lawson, C.L., 122, 125, 140 Lawson-Charalambous Algorithm, 122-125

Layout. See Floor layout-quadratic

assignment problem Leamer, E.E., 169 Lee, S., 206

Linear facility location, 51-60 Linear programming minimax location, rectangular distances, 126-131

minimum sum location, rectangular

distances, 80-83 one-infinity norm models, 265-266 relaxation of set covering model, 177 relaxation of distribution model, 188-

Littlewood, J.E., 232

Litwhiler, D.W., 73

Location-allocation, site-generating continuous existing facilities, 162-164 heuristics for solving, 157-162 hull properties of, 153-157, 169, 170 one-dimensional problem solved by dynamic proamming, 146-150 perturbation solution scheme, 158 solved as m-median problem, 152-156 structural properties, 158 two-facility with Euclidean distances, 150-152

Location-allocation, site-selecting cost structures and capacity restrictions, 193-196