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Bazaraa M.S., Jarvis J.J. — Linear Programming and Network Flows
Bazaraa M.S., Jarvis J.J. — Linear Programming and Network Flows

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Название: Linear Programming and Network Flows

Авторы: Bazaraa M.S., Jarvis J.J.

Аннотация:

The authoritative guide to modeling and solving complex problems with linear programming—extensively revised, expanded, and updated

The only book to treat both linear programming techniques and network flows under one cover, Linear Programming and Network Flows, Fourth Edition has been completely updated with the latest developments on the topic. This new edition continues to successfully emphasize modeling concepts, the design and analysis of algorithms, and implementation strategies for problems in a variety of fields, including industrial engineering, management science, operations research, computer science, and mathematics.


Язык: en

Рубрика: Технология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1977

Количество страниц: 565

Добавлена в каталог: 17.04.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Active constraint      214
Activity level      2
Adding, new activity      271
Adding, new constraint      272
Addition, matrices      45
Addition, vectors      40
Additivity assumption      4
Adjacent, bases      480
Adjacent, extreme directions      234
Adjacent, extreme points      233 234
Adjoint matrix      54
Air quality problem      34
Aircraft assignment problem      301
Algorithm, assignment      388
Algorithm, Benders      348
Algorithm, bounded simplex      208
Algorithm, Busacker — Gowen      517
Algorithm, cutting plane      274 342
Algorithm, Dantzig — Wolfe      309 351
Algorithm, decomposition      309
Algorithm, dual simplex      253
Algorithm, Klein      518
Algorithm, labeling      424 462 480 490
Algorithm, maximal flow      478 480
Algorithm, multicommodity flows      496
Algorithm, negative circuit      491 516
Algorithm, network simplex      413 420 424
Algorithm, out-of-kilter      458 462
Algorithm, primal-dual simplex      260 263
Algorithm, revised simplex      190
Algorithm, shortest path      484 487 490
Algorithm, simplex      109 117
Algorithm, transportation      367
Alternative optimal solutions      17 102 103
Analysis, big-M method      157 162
Analysis, two-phase method      146
Applications of linear programming, capital budgeting      11
Applications of linear programming, cutting stock      9
Applications of linear programming, feed-mix      7
Applications of linear programming, production scheduling      8
Applications of linear programming, tanker scheduling      12
Applications of linear programming, transportation      10
ARC      404
Arc disjoint paths      508
Arc-path formulation      510
Artificial technique, single constraint      265
Artificial technique, single variable      163
Artificial variable      140
Assignment problem, covering      386 400 510
Assignment problem, definition      283
Assignment problem, dual problem      384
Assignment problem, finite convergence      390
Assignment problem, Hungarian algorithm      388
Assignment problem, independent cells      386 400 510
Assignment problem, modifying dual variables      387
Assignment problem, partial solution      386
Assignment problem, reduced matrix      384
Assumptions in linear programming      3
Augmented matrix      50 54
Back substitution      49 358 371 414 416
Basic feasible solution, bounded variables      202
Basic feasible solution, definition      85
Basic feasible solution, degenerate      86 89 202
Basic feasible solution, existence      92
Basic feasible solution, improving      94
Basic feasible solution, initial      137
Basic feasible solution, nondegenerate      86 202
Basic feasible solution, optimal      93 218
Basic feasible solution, relationship to extreme point      90
Basic solution      56 85
Basic variables      86
Basis, adjacent      480
Basis, assignment problem      401
Basis, complementary dual      255
Basis, definition      43 55 86
Basis, entry criterion      95
Basis, exit criterion      95
Basis, maximal flow problem      480
Basis, multicommodity flow problem      502
Basis, network flow problem      419 421
Basis, number of      88 204
Basis, optimal      101
Basis, relationship to trees in networks      361 364 411
Basis, transportation      361
Benders's partitioning procedure      350
Big-M method, analysis      157 162
Big-M method, comparison with two-phase method      163
Big-M method, description      154
Binding constraints      214
Block diagonal constraint matrix      328
Block pivoting      122 467 480
Blocking constraint      101
Blocking variable      99 101
Bounded set      66
Bounded variable      201
Breakthrough      459 462 478
Busacker — Gowen algorithm      517
Canonical form of duality      237
Canonical form of linear program      5 6
Capacitated transportation problem      399
Capacity, arc      474
Capacity, cut-set      475
Capacity, disconnecting set      521
Capital budgeting problem      11
Car pooling problem      514
Chain in graph      406
Chain in transportation tableau      360
Change in basis      43 96
Change of constraint coefficients      270
Change of cost vector      268
Change of right-hand side      269
Chord      64
Circuit      407 441
Circulation      441
Closed set      523
Cofactor      52
Column generation scheme      310
Column pivoting      227
Column rank      54
Column simplex method      227
Combination, convex      58
Combination, linear      42
Command and control network      508
Comparison of simplex and revised simplex      194
Comparison of two-phase and big-M methods      163
Complementary, basic dual solution      255
Complementary, slackness conditions      213 245 442
Complicating constraints      305
Concave function      64
Cone, convex      62
Cone, generated by vectors      63
Cone, polyhedral      66
Connected graph      407
Conserving flow      441 443 448
Constraint, active (binding, tight)      214
Constraint, artificial      265
Constraint, definition      2
Constraint, matrix      2
Constraint, nonnegativity      2
Construction of basic feasible solutions      93
control variable      9
Convergence, assignment algorithm      390
Convergence, dual simplex method      256
Convergence, maximal flow algorithm      477
Convergence, out-of-kilter algorithm      457
Convergence, primal-dual method      265
Convergence, shortest path algorithm      484 490
Convergence, simplex method      110 170
Convex combination      58
Convex cone      62 63 66
Convex function      64
Convex set      58
Convexity constraint      329 337
Corner point      16
Cost coefficient      2
Court scheduling problem      33
Covering in assignment problem      386 400 510
Cramer's rule      54 359
Critical path problem      472 515
Cut      272 274
Cut-set      475
Cutting plane algorithms      275 342
Cutting stock problem      9 345
Cycle in graph      407 448 505
Cycle in transportation tableau      360
Cycle method, for computing $z_{ij} - c_{ij}$      370 403 416
Cycling, example of      166
Cycling, prevention rule      169
Cycling, validation of prevention rule      171
Dantzig — Wolfe decomposition principle      305 309 351
Decision variables      2
Decomposition principle, algorithm      309
Decomposition principle, block diagonal structure      328
Decomposition principle, economic interpretation      336
Decomposition principle, getting started      320
Decomposition principle, lower bound on objective function      310 331
Decomposition principle, unbounded subproblem      321
Degeneracy in assignment problem      383
Degeneracy in basic feasible solution      86 89 202
Degeneracy in transportation problem      378 381 395
Degeneracy, relationship to cycling      165
Dependent constraints      55
Dependent vectors      42
Destination in transportation problem      353
Determinant of matrix      52 53
Dimension of basis      43
Dimension of Euclidean space      42
Dimension of matrix      45
Dimension of vector      39
Directed arc      404
Directed cycle      441
Directed network      404
Direction of convex set      60
Direction of polyhedral set      60
Direction of ray      60 105
Direction, associated with unbounded optimum      105 131
Direction, distinct      62
Direction, extreme      62 78
Disconnecting set      520
Discrete control problem      345
Distribution problem      34
Divisibility assumption      4
Dual canonical form      237
Dual complementary basis      255
Dual of assignment problem      384
Dual of dual      239 240
Dual of maximal flow problem      476
Dual of out-of-kilter formulation      441
Dual simplex method, finite convergence      256 295 296
Dual simplex method, getting started      265
Dual simplex method, summary of      253
Dual variables      213 237 249
Dual, feasibility and primal optimality      250
Dual, mixed forms      240 241
Dual, standard form      238
Duality and Kuhn — Tucker conditions      243
Duality and Lagrangian multipliers      213
Duality, economic interpretation of      248
Duality, gap      290
Duality, theorems      245 246 302
Economic interpretation of decomposition      336
Economic interpretation of duality      248
Elementary matrix      195
Elementary matrix operations      47
Empty feasible region      18
End of a tree      363 407 414
Entry criterion      95 252
Euclidean norm      41
Euclidean space      42
Exit criterion      95 253
Extreme direction      62 78
Extreme point, adjacent      233 234
Extreme point, definition      59
Extreme point, optimality at      82
Extreme point, relationship to basic solutions      90
Extreme point, representation theorem      67 68
Face      64
Facility location      27
Farkas's theorem      70
Feasible flow      441
Feasible region      2
Feasible solution      2
Feasible system      21
Feed mix problem      7 25 26
Finite convergence      see "Convergence"
Finite optimal solution      83 93
Flow in arc      405
Flow with gains      434 439
Flow, conservation equations      405
Flow, maximal      474
Flow, minimal cost      404
Flow, multicommodity      492
Forest in graph      362
Full rank matrix      54
Fundamental theorem of duality      245
Game      291
Gaussian reduction      49 57
General solution of linear equations      57
Generalized linear programming problem      351
Generalized transportation problem      396
Geometric interpretation, Farkas's theorem      70
Geometric interpretation, Kuhn — Tucker conditions      214 216
Geometric redundancy      178
Geometric solution of linear programs      14
Gradient      25
Graph      361
Halfline      62
Halfspace      60
Housing renewal planning problem      33
Hungarian method      388
Hyperplane, definition      59
Hyperplane, normal to      59
Hyperplane, separating      523
Identity matrix      46
Improving basic feasible solution      94
In kilter      443
Inactive constraint      214
incident      404
Inconsistent system      18 21
Independent cells in assignment problem      386
Independent vectors      42
Initial basic feasible solution      137
Inner product      41
Integer programming problem      274 383
Integer property in assignment problems      383
Integer property in network flow problems      411
Integer property in transportation problems      359
Integer variable      274
Inverse matrix, calculation of      50 54
Inverse matrix, condition for existence      49
Inverse matrix, definition      49
Inverse matrix, investment problem      28
Inverse matrix, product form of      195
Iteration      110
Kilter number      444 445
Kilter state      444
Kirchhoff equations      405
Klein's algorithm      518
Knapsack problem      125 223
Kuhn — Tucker conditions for equality constraints      217
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