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Modification and implementation of two-phase simplex method. (English) Zbl 1172.65031
The authors study modifications of the two-phase simplex method for solving linear programs and proposes alternatives to the calculation of the initial simplex basic feasible solution. The first two sections present the necessary background to linear programming and the features of the simplex method for solving such problems. The third section contains the main contribution of the paper and proposes alternative ways of selecting the leaving and entering non-basic variables of the linear program which improve the performance of the simplex algorithm. The article concludes with a list of numerical results carried out in Mathematica and Visual Basic software and using the Netlib set of test problems.
MSC:
65K05Mathematical programming (numerical methods)
90C05Linear programming
90-08Computational methods (optimization)
Software:
Mathematica