## 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 71

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**bound**technique avoids this increased effort by removing the upper**bound**constraints from the functional constraints and treating them separately , essentially like nonnegativity constraints . Removing the upper**bound**constraints in ...Page 319

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**bound**technique uses the following rule to make this choice : Rule : Begin with choice 1 . = Whenever x ; O , use choice 1 , so x ; is nonbasic . Whenever x ; = uj , use choice 2 , so yj = O is nonbasic . Switch choices only when the ...Page 607

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**Bound**for subproblem 1 :**Bound**for subproblem 2 : Z≤9 , Z ≤ 16 . Figure 12.5 summarizes these results , where the numbers given just below the nodes are the bounds and below each**bound**is the optimal solution obtained for the LP ...### 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 cost CPF solution CPLEX decision variables described dual problem dynamic programming entering basic variable example feasible region feasible solutions final simplex tableau final tableau following problem formulation functional constraints Gaussian elimination given goal goal programming graphical identify increase initial BF solution integer interior-point iteration leaving basic variable linear programming model linear programming problem LINGO LP relaxation lution 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 shown simplex method slack variables solve the model Solver spreadsheet step subproblem surplus variables Table tion values weeks Wyndor Glass x₁ zero