Introduction to Operations ResearchCD-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 151
... nonnegative variables x ; = x ; † − xj , + where x 0 , xj ≥ 0 . xj † ≥ + - Since x and x can have any nonnegative values , this difference x − x , can have any value ( positive or negative ) , so it is a legitimate substitute for x ...
... nonnegative variables x ; = x ; † − xj , + where x 0 , xj ≥ 0 . xj † ≥ + - Since x and x can have any nonnegative values , this difference x − x , can have any value ( positive or negative ) , so it is a legitimate substitute for x ...
Page 300
... nonnegative values of 0 over which this basic solution is feasible . ( c ) Determine the range of nonnegative values of 0 over which this basic solution is both feasible and optimal . Determine the best choice of 0 over this range . 6.7 ...
... nonnegative values of 0 over which this basic solution is feasible . ( c ) Determine the range of nonnegative values of 0 over which this basic solution is both feasible and optimal . Determine the best choice of 0 over this range . 6.7 ...
Page 310
... nonnegative coefficients in Eq . ( 0 ) , until all the variables are nonnegative . Such a basic solution is feasible ( it satisfies all the equations ) and is , therefore , optimal by the simplex method criterion of nonnegative ...
... nonnegative coefficients in Eq . ( 0 ) , until all the variables are nonnegative . Such a basic solution is feasible ( it satisfies all the equations ) and is , therefore , optimal by the simplex method criterion of nonnegative ...
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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 Courseware CPLEX decision variables dual problem dual simplex method dynamic programming entering basic variable estimates example feasible region feasible solutions final simplex tableau final tableau following problem formulation functional constraints Gaussian elimination given goal programming graphical identify increase initial BF solution integer 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 resource right-hand sides sensitivity analysis shadow prices shown slack variables solve the model Solver spreadsheet step subproblem surplus variables Table tion unit profit values weeks Wyndor Glass x₁ zero