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51

Location-allocation, site-selecting

(continued) data considerations, 187-188, 202-203 demand point aggregation issues, 196-

199, 212-213 DUALOC, 189-193 model representation and linear

programming relaxation, 188-189 set-covering models for site selection,

173-185 single-stage, single-commodity

distribution system design, 186-199 solution by Benders decomposition,

203-212, 224-226 two-stage, multi-commodity distribution

system design, 199-212 Longitude, 38, 269

Love, R.F., 24, 31, 73, 78, 92, 93, 97, 109,

140, 169, 254, 256, 258, 263, 273 Lowe, T.J., 136, 169 jfp distance

definition, 6, 11

models, 23-27, 86-89, 113-117

properties, 23

MacKinnon, R.D., 51

Mairs, T.G, 202, 256

Manne, A.S., 223

Marucheck, A.S., 169

Mavrides, L.P., 223

Maximin problem, 114, 133-135

Maximal covering location, 182-183

McGinnis, L.F., 9

McGrew, M.C., 167

Mercator projection, 269-271

Metrics, 255-271. See also Travel

distances Miehle, W., 92 Minieka, E., 179, 223 Minimax location

contours, 131-132

convex programming approach, 132

dual problem, 129-131

Euclidean distances, 117-125

maximin location, 133-135

multi-facility, 120-125

rectangular distances, 125-131

set covering, 178-181

upper bounds on distances and location constraints, 131 Minkowski inequality, 34, 93 m-median problem, 155-156, 188, 223 Modeling philosophy, 99 Moore, J.M., 31

Morris, J.G., 31, 73, 92, 93, 97, 140, 169,

223, 256, 258, 273 Multi-facility locaiion e,, distance minimum sum model, 80-86

INDEX

minimax model, 120-132 properties and solution methods, 80-90 rectangular distance minimum sum model, 80-86

Nair, K.P.K., 115, 117, 139

Nemhauser, G.L., 223

Nobert, Y., 274

Nonlinear programming

formulation of minimax location

problems, 116-117, 132 solution of dual problem, 100, 107 solution of multi-facility minimum sum problems, 89

Norback, J.P., 73

Norm, 264

Norm, one-infinity, 264-266 Nugent, C.E., 254

Odoni, A.R., 178 OKelly, M.E., 169 One-infinity norm, 264-266 Ostresh, L.M., Jr., 31, 92, 146, 169

Pair exchanging heuristic. See CRAFT

heuristic for floor layout problems Parameters, of distance functions, 258-265 Pardalos, P.M., 169 Pearson, K., 73 Peeters, D., 9, 273 Pelletier, P., 274 Perreur, J., 273 Perturbation function, 158 Pierce, J.F., 254 Pintelon, L.M., 169 Planchart, A., 109 Plane, D.R.. 174 Plyter, N.V., 254 Polya, G., 232 Positivity property

of a metric, 255

of a norm, 264 Powers, R.F., 187 Pritsker, A.A.B., 92

Probabilistic destination location, 66-69 Projection, mercator, 269-271 Pruzan, P.M., 223

Quadratic assignment problem. See Floor layout-quadratic assignment problem

INDEX

Quadratic equivalence, 245-246 Quadratic placement problem, 245-251 Quasilinearization, 96-107, 109 Quon, J.E., 92

Rao, M.R., 92 Ray, T.L., 223 Rectangular bound on location models, 31, 34, 93 distance models, 18, 43-51, 80-86, 125-

132, 152-157 metric, 257 Rectangular destinations, 43-51 Rectangular hull, 153-157 Rectilinear. See Rectangular Reduction, of branch-and-bound method of solving floor layout problem, 233-235

Restriction, of branch-and-bound method of solving floor layout problem, 235-236

Revelle, C.S., 182, 183, 184, 185, 223

Reutzel, E.T., 255

Rhumb line, 269

Ritzman, L.P., 254

Road distances, 259-262

Road network data, 255

Robinson, S.M., 220

Rockafellar, R.T., 109

Roodman, G.M., 73

Rosen, J.B., 169

Rosenthal, R.E., 113, 119, 140

Ruml, J., 254

Rural road distances, 259-262

Schrage, L., 223 Schwartz inequality, 35 Schwarz, L.B., 73 Scon, A.J., 179, 180 Scriabin, M., 254

Separability of rectangular distance

problem, 18, 80 Set-covering models, 173-185 Sherali, A.D., 169, 254 Shetty, ., 169 Shortest arc distance, 38, 270 Simple plant location problem, 189-193,

Single-facility location dynamic model, 60-66 Euclidean distance minimum sum

model 12-18 linear facility. 51-60 H,, distance minimum sum model, 23-27 minimax model, 113, 117-120

one-infinity norm model, 264-266 point and area destinations, 43-51 probabilistic destinations, 66-69 properties and solution methods, 11-27 rectangular distance minimum sum model, 18-23

Single-stage, single-commodity distribution system design, 186-199

Soland, R.M., 169, 274

Spath, H., 139

Sphere

location on a sphere, 38-43

spherical circle, 39

spherical disc, 39

spherical distances, 38-39 Spielberg, K., 202, 223 Squared distances models

facility location, 5, 9, 21

quadratic placement, 245-251 Stary, M.A., 92 Steinberg, L., 254

Stopping criterion for terminating iterative solution procedures, 16-17, 88-90

Straight-line distances. See Euclidean distances

Stratmann, K.H., 254

Sum of squares, goodness-of-fit criterion, 259

Swain, R., 223

Thisse, J.F., 9, 169, 273

Toregas, C, 223

Tour-distances, 271

Trade-off curves, 179-181, 193

Travel distances (mathematical models of) applications of, 255-256 empirical distance functions, 256-258 empirical metrics, convexity, optimal

location, 266-268 empirical studies, 258-265 large region metrics, 268-271 modeling vehicle tour-distances, 271 weighted one-infinity norm, 264-266

Tree, for branch-and-bound method of solving dynamic location problem, 64-66

of solving floor layout problem, 238 Triangle inequality, 34, 255, 264, 266, 275 Truscott, W.G., 73

Two-stage, multi-commodity distribution system design, 199-212

Unit circles, 257-258, 265 Urban road distances, 259-262 Urquhart, M., 227



Van Roy, T.J., 73, 223 Van Wassenhove, L.N., 169 Variations on the single-facility model

dynamic location, 60-66

linear facility, 51-60

point and area destinations, 43-51

probabilistic destinations, 66-69

spherical location, 38-43 Varignon frame, 8, 27-28 Verdini, W.A., 31, 92 Vergin, R.C., 254 Vijay, J., 140 Vollmann, . ., 254

Wakefield, G.W., 202

Walker, W.E., 174, 175, 177, 178

Wallace, W.A., 223

Ward, J.A., 169, 223, 264, 273

Watson-Gandy, C.D.T., 9, 274

Weber, A., 8

Weiszfeld, E., 8, 10, 31, 40, 92, 120, 271 Weiszfeld iterative solution method, 14-

15, 25-26, 40-41 Wendell, R.E., 41, 43, 169, 264, 273 Werson, S.J., 92

Wesolowsky, G.O., 31, 42, 43, 73, 92, 93,

133, 134, 140 Westwood, J.B., 256 Whinston, A.B., 254 White, J.A., 9, 31, 92, 273 Wierwille, W.W., 31, 92 Wimmert, R.J., 254 Witzgall, C, 109, 273 Wolfe, P., 95, 223 Wong, J.Y., 254 Wyman, S.D., 229

Yeong, W.Y., 31, 93 Yerex, L., 78 Young, D., 140



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