In this paper, we first propose a perturbation procedure for achieving dual feasibility, which starts with any basis without introducing artificial variables. This procedure and the dual simplex ...

Now, to get started on the simplex method, we set all the original variables (x1 and x2 in the case of the XYZ company) to zero, and let the slack variables be non-zero. So for the XYZ problem, the ...

In this paper, a modification of the bisection simplex method is made for more general purpose use. Organized in an alternative simpler form, the modified version exploits information of the optimal ...

Eventually linear programming came to be used in everything from manufacturing to diet planning. George Bernard Dantzig was born in Portland, Ore., on Nov. 8, 1914.

The book also addresses linear programming duality theory and its use in algorithm design as well as the Dual Simplex Method, Dantzig-Wolfe decomposition, and a primal-dual interior point algorithm.

The Interior-Point algorithm often solves network problems and linear programming (LP) problems much faster than the Simplex algorithm, and it can solve problems that are very large. LP problems that ...