VESTNIK
Bashkirskogo universiteta

RUSSIAN
ISSN 1998-4812

Archive | Volume 19, 2014, No. 3.

REPLACEMENT OF COEFFICIENTS AS THE METHOD OF SOLUTION OF THE PROBLEM OF LINEAR PROGRAMMING WITH VARIABLE COEFFICIENTS ON THE SET OF ALL REAL NUMBERS

Vestnik Bashkirskogo Universiteta. 2014. Vol. 19. No. 3. Pp. 791-798.
Salimonenko D. A.
Bashkir State University
32 Zaki Validi St., 450076 Ufa, Republic of Bashkortostan, Russia.

Abstract

The method of solution of a problem of linear programming with variable coefficients in a case when criterion function reaches optimum value under conditions of negativity of one or several variables that the simplex method because usually it is applied only in the field of no negativity of each of variables is expansion of range of definition is studied. Known ways of replacement of variables allow to solve successfully LP problem at negative values of variables but provided that coefficients of a task are constants. Instead of a well-known method of replacement of variables (which is difficult for realizing when coefficients of a problem of linear programming are variables) the method of replacement of coefficients is offered at the corresponding variables. The offered method is universal (i.e. it can be applied to any problem of linear programming with variable coefficients). Computer realization of replacement of variable coefficients isn’t difficult and can be easily feasible within any, already available program intended for the solution of a problem of linear programming on a basis of the simplex method (under a condition, of course, that the initial code of such program is available). Besides, the algorithm flowchart provided in the real work according to offered improvement of the simplex method.

Keywords

  • • problem of linear programming with variable coefficients
  • • simplex method
  • • a method of generation of columns
  • • replacement of variables
  • • replacement of coefficients
  • • negative values of variables
  • • range of definition

References

  1. Gass S. Lineinoe programmirovanie [Linear Programming]. Moscow: Fizmatgiz, 1961.
  2. Kasatkin A. S., Nemov M. V. Elektrotekhnika. Moscow: Vysshaya shkola, 2011.
  3. Martynov A. P., Salimonenko E. A., Amirov Ya. S., Abyzgil'din A. Yu., Telyashev E. G., Saifullin N. R., Davletkulov R. G. Sistemnoe modelirovanie proizvodstvennykh protsessov (na baze metoda generatsii stolbtsov) [System Modeling of Industrial Processes (Based on the Method of Column Generation)]. Ufa: Gilem, 1998.
  4. Martynov A. P., Salimonenko D. A., Salimonenko E. A. Elektrotekhnika. 1998. No. 2. Pp. 59–62.
  5. Murtaf B. Sovremennoe lineinoe programmirovanie [Modern Linear Programming]. Moscow: Mir, 1984.
  6. Salimonenko D. A. Matematicheskaya obrabotka eksperimenta metodami lineinogo programmirovaniya s peremennymi koeffitsientami: dis. … kand. fiz-mat. nauk. Ufa, 1999.