Abstract: With today's large number of data, the use of linear programming is facing the real big size of applications with increasing complexity, so data presolving techniques for solving linear programming problems become very important. Duality not only help to solve the original problems (such as dual simplex method), but also is an important part of presolving techniques before solving the problems. For presolving, based on a model of linear programming problems with upper and lower bounds, two methods:dominated columns and duplicated columns in detail to realize using duality in presolving are analyzed and summarized, and the nature of weak dominated columns is proved by using invalid constraints concept. Finally, algorithm is implemented with C programming language for testing standard internationally accepted linear programming problems with number of variables greater than 1500. The results for tested problems show that:(1) For general linear programming problems, using duality in presolving can reduce the size of the problems effectively in two ways:by directly reducing the number of variables and non-zero elements of the problem and by influencing other presolving methods to reduce the number of constraints indirectly. (2) From the view of reducing problem size, most of the problems have shown that results of presolving process for dominated columns are better than those for duplicated columns. Apart from verifying and proving the importance and feasibility of using duality in presolving, new references are also provided for future researchers on presolving methods and techniques in order to come up with more valuable presolving methods.

Key words: linear programming, presolving, duality, dominated columns, duplicated columns