Optimization in Operations ResearchProblem solving with mathematical models - Deterministic optimization models in operations research - Improving search - Linear programming models - Simplex search for linear programming - Interior point methods for linear programming - Duality and sensitivity in linear programming - Multiobjetive optimization and goal programming - Shortest paths and discrete dynamic programming - Network flows - Discrete optimization models - Discrete optimization methods - Unconstrained nonlinear programming - Constrained nonlinear programming. |
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Page 190
... basic solution is obtained by choosing x1 , X2 , X3 , X4 to be basic and X5 , X6 to be nonbasic . Fixing xs = x6 = 0 leaves the equality system + X1 + X3 = 1000 + x2 + X4 = 1500 + X1 + x2 + ( 0 ) = 1750 + 4x1 + 2x2 + ( 0 ) = 4800 The ...
... basic solution is obtained by choosing x1 , X2 , X3 , X4 to be basic and X5 , X6 to be nonbasic . Fixing xs = x6 = 0 leaves the equality system + X1 + X3 = 1000 + x2 + X4 = 1500 + X1 + x2 + ( 0 ) = 1750 + 4x1 + 2x2 + ( 0 ) = 4800 The ...
Page 197
Ronald L. Rardin. ( c ) Points corresponding to each basic solution of part ( b ) are indicated on the plot of part ( a ) . Confirming property 5.19 , basic feasible x ( 1 ) , x ( 2 ) , and x ( 3 ) correspond to extreme points of the ...
Ronald L. Rardin. ( c ) Points corresponding to each basic solution of part ( b ) are indicated on the plot of part ( a ) . Confirming property 5.19 , basic feasible x ( 1 ) , x ( 2 ) , and x ( 3 ) correspond to extreme points of the ...
Page 210
... basic feasible solution to basic feasible solution . Each simplex iteration begins by checking the sign of objective function coefficients c ; on nonbasic variables . If none is negative for a minimize problem ( positive for a maximize ) ...
... basic feasible solution to basic feasible solution . Each simplex iteration begins by checking the sign of objective function coefficients c ; on nonbasic variables . If none is negative for a minimize problem ( positive for a maximize ) ...
Contents
CHAPTER | 1 |
IN OPERATIONS RESEARCH | 23 |
IMPROVING SEARCH | 77 |
Copyright | |
17 other sections not shown
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Optimization in Operations Research: Pearson New International Edition Ronald L. Rardin No preview available - 2013 |
Common terms and phrases
active Algorithm Analysis arcs assignment basic solution basic variables branch and bound CFPL choose class optimization software components compute convex corresponding cycle direction d₁ decision variables demand Determine digraph direction Ax discrete example feasible direction feasible set feasible solution Figure Formulate global goal program gradient graph improving feasible improving search incumbent solution inequality infeasible integer integer linear program iteration Lagrange multipliers linear program local optimum LP relaxation main constraints matrix max s.t. maximize maximum minimize move direction multiobjective multiplier negative dicycle network flow node nonbasic nonlinear program nonnegative objective function objective function value objective value optimal path optimal solution optimal value optimization model partial solution posynomial primal principle produce quadratic SAMPLE EXERCISE schedule Section sequence shortest path shortest path problems shows simplex algorithm simplex direction slack solve standard form Step Table tion unconstrained v₁ vector w₁ x₁ y₁