integer programming problem: A new approach

Abstract

The methods for solving integer programming problems depend on solving the linear programming problem using a known method, such as the Simplex method. If the values of the basic variables are integers, this is required. However, suppose the optimal solution includes non-integer values. In that case, the rounding methods, the optimal break level (1985), or the geometric-Shemkhi and Salman method (1988) are used to obtain a solution close to the optimal solution with integer variables. These methods sacrifice part of the optimality of the objective function, which in turn leads to the disabling of the use of some available resources, requiring that some of the dummy variables not be zeros.