Skip to main content
Log in

Stability, parametric, and postoptimality analysis of discrete optimization problems

  • Published:
Cybernetics Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature Cited

  1. S. A. Ashmanov, “Stability conditions for linear programming problems,” Zh. Vychisl. Mat. Mat. Fiz.,21, No. 6, 1402–1410 (1981).

    Google Scholar 

  2. L. F. Verina, “On the solution of parametric quadratic programs,” Vestn. Akad. Nauk BSSR, Ser. Fiz.-Mat. Nauk, No. 2, 17–22 (1980).

    Google Scholar 

  3. I. N. Vil'yams, Parametric Programming in Economics [in Russian], Statistika, Moscow (1976).

    Google Scholar 

  4. S. I. Gass, Linear Programming, McGraw-Hill (1969).

  5. E. G. Gol'shtein and D. B. Yudin, New Trends in Linear Programming [in Russian], Sovetskoe Radio, Moscow (1966).

    Google Scholar 

  6. É. N. Gordeev and V. K. Leont'ev, “Parametric optimization problems,” in: 5th Soviet Conf. on Topics of Theoretical Cybernetics [in Russian], Abstracts of Papers, IM, Novosibirsk (1980), pp. 54–55.

    Google Scholar 

  7. I. I. Eremin and N. N. Astaf'ev, Introduction to the Theory of Linear and Convex Programming [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  8. P. P. Zapletin and B. K. Kazbekov, “Algorithms for a one-parameter integer linear programming problem with a parameter in the functional,” in: Application and Improvement of Mathematical Economic Methods and Models in National Economic Planning [in Russian], Kazakh. Univ., Alma-Ata (1980), pp. 97–114.

    Google Scholar 

  9. L. N. Kozeratskaya, “On systems of linear Diophantine equations with a parameter,” Dokl. Akad. Nauk UkrSSR, No. 9, 11–14 (1980).

    Google Scholar 

  10. L. N. Kozeratskaya, “On the solution of one type of linear parametric programming problems,” Kibernetika, No. 1, 81–87 (1981).

    Google Scholar 

  11. V. K. Leont'ev, “Stability of the traveling salesman problem,” Zh. Vychisl. Mat. Mat. Fiz.,15, No. 5, 1298–1309 (1975).

    Google Scholar 

  12. V. K. Leont'ev, “Stability in combinatorial choice problems”, Dokl. Akad. Nauk SSSR,228, No. 1, 23–25 (1976).

    Google Scholar 

  13. V. K. Leont'ev, “Stability in linear discrete problems,” Probl. Kibern., No. 35, 169–184 (1979).

    Google Scholar 

  14. A. A. Pervozvanskii, Mathematical Models in Industrial Management [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  15. I. V. Sergienko and L. N. Kozeratskaya, “On the solution of one-parametric integer programming problem,” Kibernetika, No. 3, 80–84 (1982).

    Google Scholar 

  16. I. V. Sergienko, T. T. Lebedeva, and V. A. Roshchin, Approximate Methods for the Solution of Discrete Optimization Problems [in Russian], Naukova Dumka, Kiev (1980).

    Google Scholar 

  17. I. V. Sergienko, T. T. Lebedeva, and N. V. Filonenko, “Approximate solution of integer programming problems with a parameter in the constraints,” in: Computational Aspects of Application Program Packages [in Russian], Inst. Kibern. Akad. Nauk UkrSSR, Kiev (1980), pp. 3–7.

    Google Scholar 

  18. I. V. Sergienko and N. V. Filonenko, “Solution of some stability problems in integer programming,” Dokl. Akad. Nauk UkrSSR, No. 6, 79–82 (1982).

    Google Scholar 

  19. M. G. Baily and B. E. Gillet, “Parametric integer programming analysis: a contraction approach,” J. Oper. Res. Soc.,31, No. 3, 257–262 (1980).

    Google Scholar 

  20. B. Bank, “Qualitative Stabilitatsuntersuchungen rein- und gemischtganzzahliger linearer parametrischer Optimierungsprobleme,” Seminarber. Humboldt-Univ.,14, No. 6, 1–111 (1978).

    Google Scholar 

  21. B. Bank, “Stability analysis in pure and mixed integer programming,” Lecture Notes Control Inform. Sci., No. 23, 148–153 (1978).

    Google Scholar 

  22. M. W. Cooper, “Postoptimality analysis in nonlinear integer programming: the right-hand side case,” Naval Res. Logist. Quart.,28, No. 2, 301–307 (1981).

    Google Scholar 

  23. A. V. Fiacco and W. P. Hutzler, “Basic results in the development of sensitivity and stability analysis in nonlinear programming,” Comput. Oper. Res.,9, No. 1, 9–28 (1982).

    Google Scholar 

  24. A. M. Geoffrion and R. Nauss, “Parametric and postoptimality analysis in integer linear programming,” Manag. Sci.,23, No. 5, 453–466 (1977).

    Google Scholar 

  25. J. Guddat, “On qualitative stability in the nonlinear parametric programming,” Stud. Math. Program., No. 1, 69–82 (1980).

    Google Scholar 

  26. J. Guddat, “On some actual questions in parametric optimization,” in: Mathematical Methods in Operations Research, Int. Conf., Sofia, Nov. 22, 1980, Sofia (1981), pp. 39–54.

  27. S. Holm and D. Klein, “Discrete right-hand-side parametrization for linear integer programs,” Europ. J. Oper. Res.,2, No. 1, 50–53 (1978).

    Google Scholar 

  28. J. Hrouda, “The Benders method and parametrization on the right-hand sides in the mixed integer linear programming problem,” Appl. Math.,21, No. 5, 327–364 (1976).

    Google Scholar 

  29. R. E. Jensen, “Sensitivity analysis and integer linear programming,” Account. Rev.,43, No. 3, 425–446 (1968).

    Google Scholar 

  30. D. Klein and S. Holm, “Integer programming postoptimal analysis with cutting planes,” Manag. Sci.,25, No. 1, 64–72 (1979).

    Google Scholar 

  31. M. Libura, “Stability regions for optimal solutions of the integer programming problems,” in: Working Paper MPD 3-76, System Res. Inst. Polish Acad. Sci., Warsaw (1976).

    Google Scholar 

  32. M. Libura, “Integer programming problems with inexact objective function,” Control Cybernet.,9, No. 4, 189–202 (1980).

    Google Scholar 

  33. M. Lucertini, A. Marchetti Spaccamela, “Approximate solutions of an integer linear programming problem with resonance variations,” Lecture Notes Control Inform. Sci., No. 18, 207–219 (1979).

    Google Scholar 

  34. L. Lupsa, “Sur une class de problemes de programmation parametrique en nombres entiers,” in: Proc. 6th Conf. Probability Theory (Brasov, Sept. 10–15, 1979), Bucharest (1979), pp. 535–536.

  35. R. D. McBride and J. S. Yormark, “Finding all solutions for a class of parametric quadratic integer programming problems,” Manag. Sci.,26, No. 8, 784–795 (1980).

    Google Scholar 

  36. H. Mine, M. Fuchshima, and Y.-J. Ryang, “Methods of parametric nonlinear programming,” Int. J. Syst. Sci.,12, No. 1, 95–110 (1981).

    Google Scholar 

  37. T. L. Morin and R. E. Marsten, “An algorithm for knapsack problem,” Manag. Sci.,22, 1147–1158 (1976).

    Google Scholar 

  38. H. Noltemeier, “Sensitivitätsanalyse bei discreten lineare Optimierungsproblemen,” Lecture Notes Oper. Res. Math. Syst. Theory, No. 30, 95–110 (1970).

    Google Scholar 

  39. C. J. Piper and A. A. Zoltners, “Implicit enumeration based algorithms for postoptimizing zero-one programs,” Naval Res. Logist. Quart.,22, No. 4, 791–809 (1975).

    Google Scholar 

  40. C. J. Piper and A. A. Zoltners, “Some easy postoptimality analysis for zero-one programming,” Manag. Sci.,22, No. 7, 759–765 (1976).

    Google Scholar 

  41. G. M. Roodman, “Postoptimality analysis in zero-one programming,” Manag. Sci.,19, No. 3, 435–447 (1972).

    Google Scholar 

  42. G. M. Roodman, “Postoptimality analysis in integer programming by implicit enumeration: the mixed integer case,” Naval. Res. Logist. Quart.,21, No. 4, 595–607 (1974).

    Google Scholar 

  43. J. Seeländer, “Einige Bemerkungen zur Bestimmung von Stabilitätsbereichen in der reinganzzahligen linearen Optimierung,” Math. Operationsforsch. Statistic, Ser. Optimization,11, No. 2, 261–271 (1980).

    Google Scholar 

  44. J. Seeländer, “Über die Bestimmung von Stabilitätsbereichen bei speziellen gemischtganzzahligen linearen Optimierungsproblemen,” ibid., No. 3, 447–454 (1980).

    Google Scholar 

  45. J. F. Shapiro, “Sensitivity analysis in integer programming,” Ann. Discrete Math., No. 1, 647–677 (1977).

    Google Scholar 

  46. J. Travnicek, “An approach to the solution of the parametric zero-one integer programming problem with the parameter in one right-hand side,” Econ.-Mat. Obzor,8, No. 1, 83–98 (1972).

    Google Scholar 

  47. J. Travnicek, “Parametric zero-one programming with the parametrized objective function,” Econ.-Mat. Obzor., No. 4, 417–425.

  48. L. A. Wolsey, “Ingeger programming duality: price functions and sensitivity analysis,” Math. Program.,20, No. 2, 173–195 (1981).

    Google Scholar 

Download references

Authors

Additional information

Translated from Kibernetika, No. 4, pp. 71–80, July–August, 1983.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kozeratskaya, L.N., Lebedeva, T.T. & Sergienko, I.V. Stability, parametric, and postoptimality analysis of discrete optimization problems. Cybern Syst Anal 19, 522–535 (1983). https://doi.org/10.1007/BF01068340

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01068340

Keywords

Navigation