## 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. |

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Page 318

Therefore , having a large number of upper

Therefore , having a large number of upper

**bound**constraints among the functional constraints greatly increases the computational effort required . The upper**bound**technique avoids this increased effort by removing the upper**bound**...Page 319

Replace x ; by u ; – yj , where 0 = y ; Suj . u < The upper

Replace x ; by u ; – yj , where 0 = y ; Suj . u < The upper

**bound**technique uses the following rule to make this choice : Rule : Begin with choice 1 . Whenever x ; 0 , use choice 1 , so x ; is nonbasic . Whenever x ; = Uj , use choice 2 ...Page 607

9 ( 0 , 1 , 0 , 1 ) LP relaxation of subproblem 2 : ( x1 , X2 , X3 , X4 ) = ( 1,5.0.5 ) with 2 = 16 Z = All 16 ( à 1,0,1 ) 5 1 The resulting

9 ( 0 , 1 , 0 , 1 ) LP relaxation of subproblem 2 : ( x1 , X2 , X3 , X4 ) = ( 1,5.0.5 ) with 2 = 16 Z = All 16 ( à 1,0,1 ) 5 1 The resulting

**bounds**for the subproblems then are**Bound**for subproblem 1 : Z < 9 ,**Bound**for subproblem 2 ...### What people are saying - Write a review

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### Other editions - View all

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

### Common terms and phrases

activity additional algorithm allowable amount apply assignment basic solution basic variable BF solution bound boundary called changes coefficients column complete Consider constraints Construct corresponding cost CPF solution decision variables demand described determine direction distribution dual problem entering equal equations estimates example feasible feasible region FIGURE final flow formulation functional constraints given gives goal identify illustrate increase indicates initial iteration linear programming Maximize million Minimize month needed node nonbasic variables objective function obtained operations optimal optimal solution original parameters path Plant possible presented primal problem Prob procedure profit programming problem provides range remaining resource respective resulting shown shows side simplex method simplex tableau slack solve step supply Table tableau tion unit weeks Wyndor Glass zero