Nebojša V. Stojković

Two direct methods in linear programming

Abstract In this paper, we introduce two direct methods for solving some classes of linear programming problems. The first method produces the extreme vertex or a neighboring vertex with respect to the extreme point. The second method is based on the game theory. Both these methods can be used in the preparation of the starting point for the simplex method. The efficiency of the improved simplex method, whose starting point is constructed by these introduced methods, is compared with the original simplex method and the interior point methods, and illustrated by examples. Also, we investigate the elimination of excessive constraints.

Stabilization of Mehrotra's primal-dual algorithm and its implementation

Abstract In this paper we apply a stabilization procedure proposed by Kovacevic-Vujcic and Asic to the Mehrotras primal–dual interior-point algorithm for linear programming. Transformations of the dual problem corresponding to the stabilization procedure are considered. The stabilization procedure and Mehrotras algorithm are implemented in the package MATHEMATICA . A number of highly degenerate test examples are used to compare the modified Mehrotras method with respect to the original one and the codes PCx , LIPSOL and MOSEK . We also provide numerical results on some examples from the Netlib test set.

Modification and implementation of two-phase simplex method

We investigate the problem of finding the initial basic feasible solution in the simplex algorithm. Two modifications of the two-phase simplex method are presented. Implementations of the two-phase simplex method and its modifications in the programming package MATHEMATICA and the programming language Visual Basic are written. We report computational results on numerical examples from the Netlib test set.

RESEARCH ON ELEMENTARY SCHOOL TEACHER SATISFACTION IN THE REPUBLIC OF SERBIA

Abstract Employees’ satisfaction is one of the frequently analyzed subgroups of human attitudes connected to organizational environment. The authors’ aim is to study different categories of satisfaction or dissatisfaction of teachers in elementary schools in the Republic of Serbia, as a specific category of employees. The results of the research carried out have shown that teachers are dissatisfied with salaries, awards and benefits. The next category concerning the intensity of dissatisfaction is teachers’ dissatisfaction with operational procedures. On the other hand, teachers are mostly satisfied with the work they are doing, with their superiors, their colleagues and system of communicating within schools.

On the Simplex Algorithm Initializing

This paper discusses the importance of starting point in the simplex algorithm. Three different methods for finding a basic feasible solution are compared throughout performed numerical test examples. We show that our two methods on the Netlib test problems have better performances than the classical algorithm for finding initial solution. The comparison of the introduced optimization softwares is based on the number of iterative steps and on the required CPU time. It is pointed out that on average it takes more iterations to determine the starting point than the number of iterations required by the simplex algorithm to find the optimal solution.

Symbolic implementation of interior point method for linear programming problem

In this article we describe an implementation of the Mehrotras primal–dual interior-point method in the package . Usage of ’s computer algebra system in our software is described. Both augmented and normal equation system approach are implemented. Described implementation is compared with main LP solvers. Algorithm for generating an efficient starting point as well as algorithm for the elimination of zero variables and the stabilization algorithm are incorporated in the developed code.