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Hadley G. — Linear programming
Hadley G. — Linear programming

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Название: Linear programming

Автор: Hadley G.

Аннотация:

Linear programming (LP, or linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (mathematical optimization).


Язык: en

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1962

Количество страниц: 532

Добавлена в каталог: 12.02.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abadic, J.      420
Activity vector      76 450 481
Addition, of matrices      25
Addition, of matrices, of vectors      37
Adjoint      33
Aggregation problem      493
Allen, R. G. D.      104
Alternative activities      501
Alternative optima      99
And extreme points      100
Artificial variables      118
Artificial vectors      118
Back-substitution      51
Basic solutions      54
Basic variables      54 85
Basis      43
Basis matrix      84
Beale, E. M. L.      190 196 266
Berge, C.      373
Birkhoff, G.      67
Blending problems      458
Boles, J. N.      463
Bowman, E. H.      463
Branch      286 331
Capacitated transportation problem      395
Case study      433
Caterer problem      465
Charnes, A.      20 104 120 175 196 293 322 463 472
Closed Leontief model      499
Cofactor      31
Column vector      37
Complementary slackness      239
Components of a vector      37
Cone      65
Cone, convex      65
Cone, polyhedral      65
Connected graph      333
Constraint      4 6
Convex combination      58 61 99
Convex polyhedron      61
Convex set      18 58 61
Convex set, extreme point of      18 59 100
Cooper, W. W.      20 104 196 293 322 463 472
Cut in a network      349
Cut in a network, capacity of      349
Cycling      113 174
Cycling, example      190
Cycling, prevention of      181 185
Dantzig, G. B.      19 20 149 175 183 196 197 218 258 266 293 318 322 373 398 400 417 420 463 502 508
Decomposable Leontief systems      495
Decomposition principle      400
Degeneracy      54 81 113
Degeneracy, examples      187
Degeneracy, in transportation problems      299
Degeneracy, resolution of      174
Dennis, J. B.      322
Dependence, linear      40
Determinant      30
Diet problem      462
Dorfman, R.      508
Dual electrical networks      226
Dual linear programming problems      222
Dual linear programming problems, economic interpretation      483
Dual simplex algorithm      242
Dual simplex algorithm, example of      253
Dual simplex algorithm, geometric interpretation      255
Dual simplex algorithm, initial solution      252
Dynamic Leontief models      504
Edge of a convex set      65 165
Edge of a network      331
Eisemann, K      318 322 463
Euclidean space      40
Extended requirements space      161
Extreme points      59 100
feasible      77 80
Feasible solution      6 71 80
Ferguson, A. R.      318 322
Flood, M. M.      322 431 463
Flows in networks      334
Flows in networks, definition of      335
Flows in networks, max flow-min cut theorem      351
Flows in networks, maximal      335
Flows in networks, steady state      335
Ford, L. R., Jr      258 266 340 351 368 373 374 395 420
Fulkerson, D. R.      258 266 340 351 368 373 374 395 420 463
Gainen, L.      464
Gale, D.      20 374 417 420
Gasoline blending      458
Gass, S. I.      104 118 420
Gaussian reduction      51
Generalized linear programming problems      183
Generalized transportation problems      314
Generalized transportation problems, example      315
Geometric interpretation of the simplex method      19 158 162
Georgescu — Roegen, N.      506
Goldman, A. J.      266
Graph      331
Guillemin, E. A.      266 374
Gunther, P.      463
Hadley, G.      67
Half-line      65
Half-space      58
Half-space, closed      58
Half-space, extreme supporting      66
Half-space, open      58
Henderson, A.      104 196 463
Hitchcock, F. L.      21
Hoffman, A. J.      190 196
Honig, D. P.      464
Houthakker, H. S.      323
Hyperplane      58
Hyperplane, extreme supporting      66
Hyperplane, supporting      62
Identity matrix      26
Inconsistency      121
Independence      40
Industrial applications      429
Initial solution      116 181 184
Input-output analysis      487
Integrality property for transportation problems      280
Interindustry models      227 487
Intersection      56
Inverse matrix      34
Inverse matrix, computation of by partitioning      35
Inverse matrix, power series      36
Inverse matrix, product form      48
Jacobs, W. W.      465
Johnson, S.      444 464
Kantorovitch, L.      20 21
Karlin, S.      104
Kemeny, J. G.      67
Konig, D.      374
Koopmans, T. C.      20 21 67 104 323 493 508
Kuhn, H. W.      20 368 374 417 420
Lagrange multipliers      18
Lemke, C. E.      243 266
Leontief, W.      20 22 227 487
Lexicographically ordered vectors      183
Line      57
linear combination      40
Linear dependence      40
Linear equations      50
Linear forms      5
Linear inequalities      4
Linear programming problems      4 71 76 175 183
Linear transformation      55
Loop      287 332
Loop, directed      287
Loop, simple      288
Lower bounds      394
Machine-assignment problems      437
MacKenzie, H. C.      464
MacLane, S. A.      67
Manne, A. S.      420 458 464
Matrices      24
Matrices, addition      25
Matrices, adjoint      33
Matrices, diagonal      27
Matrices, element      24
Matrices, identity      26
Matrices, inverse      34
Matrices, multiplication      25
Matrices, null      27
Matrices, skew-symmetric      28
Matrices, symmetric      28
Matrices, transposed      27
Matrix solution      344
Max Flow-Min Cut Theorem      351
Maximal flow in a network      334
Maximal flow in a network, examples      337 346
Maximal flow in a network, intuitive approach      334
Maximal flow in a network, labeling technique      340
Maximal flow in a network, proofs      349
Mellon, B.      463
Minimax theorem      415
Minor      32
Mirkil, H.      67
Morgenstern      0 417 508
Network      334
Node      331
Non-negative variables      5 71
Non-negativity restrictions      6 71
Nondcgenerate      54
Nondegenerate basic feasible solution      81 176
Nonsingular matrix      34
Null matrix      27
Objective function      6 76
Optimal basic feasible solution      97
Optimal product mix      447
Optimality criterion      95 97
Orchard — Hays, W.      197 218 266 420
Orden, A.      125 149 183 196 218 266 373 374
Orthant, non-negative      60
Parametric programming      380
Parametric programming, example      386
Parametric programming, of price vector      380
Parametric programming, of requirements vector      382
Partitioning of matrices      28
Path      285 332
Path, simple      288
Pauli, A. E.      464
Personnel-assignment problems      367
Perturbed problem      175
Petroleum-refinery operations      452
Phase I      150 205
Phase II      151 206
Polyhedron, convex      61 158
Postoptimality problems      379
Primal problem      223
Primal-dual algorithm      257
Primal-dual algorithm, example of      263
Primal-dual algorithm, for transportation problems      351
Product form of inverse      48 217
Production scheduling      439
Programming problems      1
Rank      47
Redundancy      121 153
Regular-time, overtime production      439
Reinfeld, N. V.      323
Requirements space      158
Revised simplex method      197
Revised simplex method, example      211
Revised simplex method, Standard Form I      201
Revised simplex method, Standard Form II      205
Revised simplex method, tableau for      204
Row vector      37
S simplex method, change of basis in      87 109
S surplus variable      72
S Tornheim, L.      67
Saaty, T. L.      420
Saddle point      413
Samuelson, P. A.      508
Scalar product      39
Schlaifer, R.      463
Secondary constraints      398
Set      55
Set, convex      58
Set, point      55
Shapley, L. S.      417
Simonnard, M. A.      323
Simplex method      17 71 10
Simplex method, examples of      134
Simplex method, initial solution for      116
Simplex method, summary of      132
Simplex method, tableau for      124
Simplex method, vector to enter basis      111
Simplex method, vector to leave basis      113
Sink      334
Skew-symmetric matrix      28
Slack variable      72
Snell, J. L.      67
Snow, R. N.      417
Solow, R.      508
Solutions space      162
Source      334
Spanning set      43
Square matrix      25
Stanley, E. D.      464
Stigler, G. J.      22 463
Strategy      412
Strategy, mixed      414
Strategy, pure      414
subspace      47
Sum check      14
Symmetric game      419
Symmetric matrix      28
Symonds, G. H.      464
Tanker routing problems      431 472
Theory of the firm      476 481
Thompson, G. L.      67
Thrall, R. M.      67
Ties, breaking of      112 113 181 185 18
Transformation formulas      114
Transhipment problem      368
Transportation problem      7 273
Transportation problem, $uv$-method for      309
Transportation problem, capacitated      395
Transportation problem, initial solutions to      304
Transportation problem, integral solutions to      280
Transportation problem, primal-dual algorithm for      351
Transportation problem, resolution of degeneracy in      299
Transportation problem, stepping-stone method for      291
Transportation problem, tableaux for      284
TRANSPOSE      27
TREE      289 333
Tucker, A. W.      266 417 420
Two-phase method      149
Unbounded solutions      14 93
Unimodular property      277
union      56
Unit vectors      38
Unrestricted variables      168
Upper bounds      387
Upper bounds, on transportation problems      395
Vajda, S.      104 464
Value of a game      415
Variables      4 5 71
Variables, artificial      118
Variables, basic      85
Variables, dual      223
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