Generalization of simplex method with analytical and computational techniques for solving linear programming problem

Abstract

In this thesis, we have studied the established traditional simplex methods of Dantzig for solving linear programming problem (LP) by replacing one basic variable by one non-basic variable at each simplex iteration, suggest to generalize the traditional simplex methods for solving linear programming problem (LP) by replacing more than one (P, where P • 1) basic variables by non-basic variables at each simplex iteration and compare the methods between themselves. To apply these methods on large-scale real life linear programming problem, we need computer-oriented program of these methods. To fulfill this purpose, we developed computer program based on (MATHEMATICA) language of these methods and apply on a sizable large-scale real life linear programming problem of a garment industry and textile mill scheduling problem. In this thesis we also developed a computational technique using mathematica codes to show the feasible region of two-dimensional linear programming problems accurately as well as this method also gives the optimal solution. Finally, conclusion is drawn in favour of the developed generalized simplex method.