## Introduction to Operations Research, Volume 1CD-ROM contains: Student version of MPL Modeling System and its solver CPLEX -- MPL tutorial -- Examples from the text modeled in MPL -- Examples from the text modeled in LINGO/LINDO -- Tutorial software -- Excel add-ins: TreePlan, SensIt, RiskSim, and Premium Solver -- Excel spreadsheet formulations and templates. |

### From inside the book

Results 1-3 of 17

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**LP relaxation**once by the simplex method , namely , when the optimal solution to the latter problem turns out to satisfy the integer restriction of the IP problem . When this situation occurs , this solution must be optimal for the IP ...Page 607

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**LP relaxation**of subproblem 1 :**LP relaxation**of subproblem 2 : ( X1 , X2 , X3 , X4 ) = ( 0 , 1 , 0 , 1 ) with Z = 9 . 4 ( X1 , X2 , X3 , X4 ) = 1 , 0 , with Z = 16 16 . 5 The resulting bounds for the subproblems then are Bound for ...Page 619

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**LP relaxation**of this problem by deleting the set of constraints that x , is an integer for j = 1 , 2 , 3. Applying the simplex method to this**LP relaxation**yields its optimal solution below .**LP relaxation**of whole problem : ( X1 , X2 ...### Other editions - View all

Introduction to Operations Research Frederick S. Hillier,Gerald J. Lieberman No preview available - 2001 |

### Common terms and phrases

activity algebraic algorithm allowable range artificial variables b₂ basic solution c₁ c₂ changes coefficients column Consider the following corresponding cost Courseware CPF solution CPLEX decision variables dual problem dynamic programming entering basic variable estimates example feasible region feasible solutions final simplex tableau final tableau flow following problem formulation functional constraints Gaussian elimination given graphical identify increase initial BF solution integer interior-point iteration leaving basic variable linear programming model linear programming problem LINGO LP relaxation lution Maximize subject Maximize Z maximum flow problem Minimize needed node nonbasic variables nonnegativity constraints objective function obtained optimal solution optimality test parameters path plant presented in Sec primal problem Prob procedure range to stay right-hand sides sensitivity analysis shadow prices simplex method slack variables solve the model Solver spreadsheet step subproblem surplus variables Table tion values weeks Wyndor Glass x₁ zero