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Bazaraa M.S., Jarvis J.J. — Linear Programming and Network Flows
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Название: Linear Programming and Network FlowsАвторы: Bazaraa M.S., Jarvis J.J. Аннотация: The authoritative guide to modeling and solving complex problems with linear programming—extensively revised, expanded, and updated
Язык: Рубрика: Технология /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1977Количество страниц: 565Добавлена в каталог: 17.04.2010Операции: Положить на полку |
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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 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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