## 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

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**Optimality test**: Consider any linear programming problem that possesses at least one optimal solution . If a CPF solution has no adjacent CPF solutions that are better ( as measured by Z ) , then it must be an optimal solution . Thus ...Page 119

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**Optimality test**Iteration 1 Step 1 Step 2 Step 3**Optimality test**Iteration 2 Step 1 Step 2 Step 3**Optimality test**solution . Not optimal , because moving along either edge from ( 0 , 0 ) increases Z. Move up the edge lying on the x2 ...Page 375

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**optimality test**for the sim- plex method ( see Sec . 4.3 ) to the following for the transportation problem :**Optimality test**: A BF solution is optimal if and only if ci ; u ; v ; ≥ 0 for every ( i , j ) such that x ;; is nonbasic ...### 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