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Journal of Applied and Industrial Mathematics

, Volume 13, Issue 2, pp 250–260 | Cite as

Estimating the Stability Radius of an Optimal Solution to the Simple Assembly Line Balancing Problem

  • K. G. KuzminEmail author
  • V. R. HaritonovaEmail author
Article

Abstract

The simple assembly line balancing problem (SALBP) is considered. We describe the special class of problems with an infinitely large stability radius of the optimal balance. For other tasks we received the lower and the upper reachable estimates of the stability radius of optimal balances in the case of an independent perturbation of the parameters of the problem.

Keywords

sensitivity analysis uncertain operation duration assembly line stability radius optimal balance 

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Notes

Acknowledgment

The authors thank an anonymous reviewer for the valuable comments which promote to a significant improvement of this article.

References

  1. 1.
    E. N. Gordeev, “Comparison of Three Approaches to Studying Stability of Solutions to Problems of Discrete Optimization and Computational Geometry,” Diskretn. Anal. Issled. Oper. 22 (3), 18–35 (2015) [J. Appl. Indust. Math. 9 (3), 358–366 (2015)].zbMATHGoogle Scholar
  2. 2.
    V. A. Emelichev and K. G. Kuzmin, “A General Approach to Studying the Stability of a Pareto Optimal Solution of a Vector Integer Linear Programming Problem,” Diskretn. Mat. 19 (3), 79–83 (2007) [Discrete Math. Appl. 17 (4), 349–354 (2007)].CrossRefzbMATHGoogle Scholar
  3. 3.
    V. A. Emelichev and K. G. Kuzmin, “On a Type of Stability of a Milticriteria Integer Linear Programming Problem in the Case of a Monotone Norm,” Izv. RAN Teor. Sist. Upravleniya No. 5, 45–51 (2007) [J. Comput. Syst. Sci. Int. 46 (5), 714–720 (2007)].Google Scholar
  4. 4.
    V. A. Emelichev and K. G. Kuzmin, “Stability Analysis of the Efficient Solution to a Vector Problem of a Maximum Cut,” Diskretn. Anal. Issled. Oper. 20 (4), 27–35 (2013).MathSciNetGoogle Scholar
  5. 5.
    V. A. Emelichev and D. P. Podkopaev, “Stability and Regularization of Vector Integer Linear Programming Problems,” Diskretn. Anal. Issled. Oper. Ser. 2, 8 (1), 47–69 (2001).MathSciNetzbMATHGoogle Scholar
  6. 6.
    V. A. Emelichev and D. P. Podkopaev, “Quantitative Stability Analysis for Vector Problems of 0–1 Programming,” Discrete Optim. 7 (1–2), 48–63 (2010).MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    V. A. Emelichev and Yu. V. Nikulin, “Strong Stability Measures for Multicriteria Quadratic Integer Programming Problem of Finding Extremum Solutions,” Comput. Sci. J.Mold. 26 (2), 115–125 (2018).MathSciNetGoogle Scholar
  8. 8.
    V. A. Emelichev and Yu. V. Nikulin, “Aspects of Stability for Multicriteria Quadratic Problems of Boolean Programming,” Bul. Acad. Stiinte Repub. Mold. Mat., No. 2, 30–40 (2018).Google Scholar
  9. 9.
    K. G. Kuzmin, Yu. V. Nikulin, and M. Mäkelä, “On Necessary and Sufficient Conditions for Stability and Quasistability in Combinatorial Multicriteria Optimization,” Control Cybernet. 46 (4), 361–382 (2017).MathSciNetzbMATHGoogle Scholar
  10. 10.
    V. A. Emelichev and K. G. Kuzmin, “Stability Criteria in Vector Combinatorial Bottleneck Problems in Terms of Binary Relations,” Kibernet. Sist. Anal. No. 3, 103–111 (2008) [Cybernet. Syst. Anal. 44 (3), 397–404 (2008)].Google Scholar
  11. 11.
    K. G. Kuzmin, “A General Approach to the Calculation of Stability Radii for the Max-Cut Problem with Multiple Criteria,” Diskretn. Anal. Issled. Oper. 22 (5), 30–51 (2015) [J. Appl. Indust. Math. 9 (4), 527–539 (2015)].Google Scholar
  12. 12.
    I. V. Sergienko and V. P. Shilo, Discrete Optimization Problems: Problems, Solution Methods, Research (Naukova Dumka, Kiev, 2003) [in Russian].Google Scholar
  13. 13.
    T.-S. Lai, Yu. N. Sotskov, A. B. Dolgui, and A. Zatsiupa, “Stability Radii of Optimal Assembly Line Balances with a Fixed Workstation Set,” Int. J. Prod. Econ. 182, 356–371 (2016).CrossRefGoogle Scholar
  14. 14.
    A. Scholl, Balancing and Sequencing of Assembly Lines (Physica, Heidelberg, 1999).CrossRefGoogle Scholar
  15. 15.
    E. E. Gurevsky, O. Battaïa, and A. B. Dolgui, “Balancing of Simple Assembly Lines under Variations of Task Processing Times,” Ann. Oper. Res. 201, 265–286 (2012).MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    M. Chica, O. Gordon, S. Damas, and J. Bautista, “A Robustness Information and Visualization Model for Time and Space Assembly Line Balancing under Uncertain Demand,” Internat. J. Prod. Econ. 145, 761–772 (2013).CrossRefGoogle Scholar
  17. 17.
    A. Otto, C. Otto, and A. Scholl, “Systematic Data Generation and Test Design for Solution Algorithms on the Example of SALBPGen for Assembly Line Balancing,” European J. Oper. Res. 228, 33–45 (2013).MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Yu. N. Sotskov, A. B. Dolgui, and M.-C. Portmann, “Stability Analysis of Optimal Balance for Assembly Line with Fixed Cycle Time,” European J. Oper. Res. 168 (3), 783–797 (2006).MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Yu. N. Sotskov, A. B. Dolgui, N. Yu. Sotskova, and F. Werner, “Stability of Optimal Line Balance with Given Station Set,” in Supply Chain Optimization (Springer, New York, 2005), pp. 135–149.CrossRefGoogle Scholar
  20. 20.
    E. E. Gurevsky, O. Battaïa, and A. B. Dolgui, “Stability Measure for a Generalized Assembly Line Balancing Problem,” Discrete Appl. Math. 161, 377–394 (2013).MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Yu. N. Sotskov, A. B. Dolgui, T.-S. Lai, and A. Zatsiupa, “Enumerations and Stability Analysis of Feasible and Optimal Line Balances for Simple Assembly Lines,” Comput. Indust. Eng. 90, 241–258 (2015).CrossRefGoogle Scholar
  22. 22.
    K. G. Kuzmin and V. R. Haritonova, “The Measure of Stability for Solutions to a Simple Assembling Linear Balancing Problem SALBP-E,” in Proceedings of 10th International Conference “Discrete Models in the Theory of Control Systems,” Moscow, Russia, May 23–25, 2018 (MAKS Press, Moscow, 2018), pp. 175–178.Google Scholar
  23. 23.
    T.-S. Lai, Yu. N. Sotskov, and A. B. Dolgui, “The Stability Radius of an Optimal Line Balance with Maximum Efficiency for a Simple Assembly Line,” European J. Oper. Res. 274, 466–481 (2019).MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    R. Gamberini, A. Grassi, and B. Rimini, “A New Multiobjective Heuristic Algorithm for Solving the Stochastic Assembly Line Rebalancing Problem,” Internat. J. Prod. Econ. 102, 226–243 (2006).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Georgia State UniversityAtlantaUSA
  2. 2.Belarusian State UniversityMinskBelarus

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