STUDY OF THE DEGENERACY CASE OF BASIC FEASIBLE SOLUTIONS IN THE SIMPLEX METHOD

Abstract

Aim. We describe the degeneracy case of basic feasible solutions in the simplex method for use by lecturers both in the classroom and in self-study of students. Methodology. The basic concepts of linear programming are formulated and the problems caused by excessive constraints in the problem conditions are considered. The reasons for the occurrence of such a special case in the simplex method as the degeneracy of basic feasible solutions are presented. The cases of temporal degeneracy and cycling are described. A rule is given to avoid cycling. All of the above is illustrated by concrete examples. Since the transition to the general case raises a problem related to the inability to see mathematical objects, the method of visualization of mathematical objects is used. Results. A detailed description of the degeneracy case of basic feasible solutions in the simplex method is presented. Research implications. The work is of practical significance, since it can be used in the study of one of the four special cases that arise when using the simplex method.

Keywords

• mathematical programming
• linear programming
• simplex method
• basic feasible solutions
• degenerate basic feasible solutions