Reducing the number of variables in integer and linear programming problems (Q1326508)

A procedure is developed for the analysis of large scale knapsack problems with the aim of reducing the number of variables prior to starting the solution method. The procedure is based on comparing pairs of columns of the constraint matrix. If a pair of columns thus compared meets certain conditions, then the integer programming problem has an optimal solution, in which a variable corresponding to one of the columns in the pair is equal to zero. The presented results of computational experiments illustrate the efficiency of the developed procedure.