Computational difficulties in solving the Integer Programming Problems (IPP) are caused to a considerable degree by the number of variables. If the number of variables is small, then even NP-complete problems usually can be solved with a reasonable expenditure of effort.A procedure is developed for the analysis of large scale IPP 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 of the IPP. If a pair of columns thus compared meets certain conditions, then the IPP has an optimal solution, in which a variable corresponding to one of the columns in the pair is equal to zero. Corresponding theorems for Knapsack and Multidimensional Knapsack problems and for general IPP are presented. The procedure is extended to Linear and Mixed Integer Programming Problems. The presented results of computational experiments illustrate the efficiency of the developed procedure.
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