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 139
... artificial variable x , as shown next . - 0.6x + 0.4x2 0.6x1 + 0.4x2 - X5 0.6x1 + 0.4x2 - ≥6 = = 6 x5 + x6 = 6 ( x5 ... variables in the objective function are + M , in- stead of -M , because we now are minimizing Z. Thus , even though x4 > ...
... artificial variable x , as shown next . - 0.6x + 0.4x2 0.6x1 + 0.4x2 - X5 0.6x1 + 0.4x2 - ≥6 = = 6 x5 + x6 = 6 ( x5 ... variables in the objective function are + M , in- stead of -M , because we now are minimizing Z. Thus , even though x4 > ...
Page 144
... 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 ...
... 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 artificial variables are used to ...
... 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 ...
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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