## 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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**artificial variable**x6 , as shown next . 0.6x1 + 0.4x2 0.6x1 + 0.4x2 - x5 = ≥ 6 6 ( xs ≥ 0 ) ( xs ≥0 , X60 ) ... variables in the objective function are + M , in- stead of -M , because we now are minimizing Z. Thus , even though 4 > 0 and / ...Page 144

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**artificial variables**as needed to obtain an obvious initial BF solution for the artificial problem . Phase 1 : The objective for this phase is to find a BF solution for the real problem . To do this , Minimize Z = Σ artificial ...Page 252

... variables play the role of slack variables , their coefficients in row 0 now provide the values of the corresponding dual variables in the complementary basic solution for the dual problem . Since

... variables play the role of slack variables , their coefficients in row 0 now provide the values of the corresponding dual variables in the complementary basic solution for the dual problem . Since

**artificial variables**are used to ...### 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