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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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