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English version:
Journal of Applied and Industrial Mathematics, 2019, 13:2, 250-260
Volume 26, No 2, 2019, P. 79-97
UDC 519.8
K. G. Kuzmin and V. R. Haritonova
Estimating the stability radius of an optimal solution to the simple assembly line balancing problem
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.
Bibliogr. 24.
Keywords: sensitivity analysis, uncertain operation duration, assembly line, stability radius, optimal balance.
DOI: 10.33048/daio.2019.26.626
Kirill G. Kuzmin 1
Veronica R. Haritonova 2
1. Georgia State University,
1 Park Place, Atlanta, GA 30303
2. Belarusian State University,
4 Nezavisimosti Avenue, 220030 Minsk, Belarus
e-mail: kuzminkg@gmail.com, haritonova.veronica@gmail.com
Received August 6, 2018
Revised February 25, 2019
Accepted February 27, 2019
References
[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, No. 3, 18–35, 2015. Translated in J. Appl. Ind. Math., 9, No. 3, 358–366, 2015.[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, No. 3, 79–83, 2007. Translated in Discrete Math. Appl., 17, No. 4, 349–354, 2007.
[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. Upravl., No. 5, 45–51, 2007. Translated in J. Comput. Syst. Sci. Int., 46, No. 5, 714–720, 2007.
[4] V. A. Emelichev and K. G. Kuzmin, Stability criteria in vector combinatorial bottleneck problems in terms of binary relations, Kibern. Sist. Anal., No. 3, 103–111, 2008. Translated in Cybern. Syst. Anal., 44, No. 3, 397–404, 2008.
[5] 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, No. 4, 27–35, 2013.
[6] V. A. Emelichev and D. P. Podkopaev, Stability and regularization of vector integer linear programming problems, Diskretn. Anal. Issled. Oper., Ser. 2, 8, No. 1, 47–69, 2001.
[7] 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, No. 5, 30–51, 2015. Translated in J. Appl. Ind. Math., 9, No. 4, 527–539, 2015.
[8] K. G. Kuzmin and V. R. Haritonova, The measure of stability for solutions to a simple assembling linear balancing problem SALBP-E, in Tr. X Mezh?dunar. konf. “Diskretnye modeli v teorii upravlyayushchikh sistem” (Proc. 10th Int. Conf. “Discrete Models in the Theory of Control Systems”), Moscow, Russia, May 23–25, 2018, pp. 175–178, MAKS Press, Moscow, 2018.
[9] I. V. Sergienko and V. P. Shilo, Discrete Optimization Problems: Problems, Solution Methods, Research, Naukova dumka, Kiev, 2003.
[10] 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, Int. J. Prod. Econ., 145, 761–772, 2013.
[11] 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.
[12] 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, No. 2, 115–125, 2018.
[13] V. A. Emelichev and D. P. Podkopaev, Quantitative stability analysis for vector problems of 0-1 programming, Discrete Optim., 7, No. 1–2, 48–63, 2010.
[14] R. Gamberini, A. Grassi, and B. Rimini, A new multiobjective heuristic algorithm for solving the stochastic assembly line rebalancing problem, Int. J. Prod. Econ., 102, 226–243, 2006.
[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.
[16] 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.
[17] K. G. Kuzmin, Yu. V. Nikulin, and M. Mäkelä, On necessary and sufficient conditions for stability and quasistability in combinatorial multicriteria optimization, Control Cybern., 46, No. 4, 361–382, 2017.
[18] 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.
[19] 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, Eur. J. Oper. Res., 274, 466–481, 2019.
[20] 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, Eur. J. Oper. Res., 228, 33–45, 2013.
[21] A. Scholl, Balancing and Sequencing of Assembly Lines, Physica-Verl., Heidelberg, 1999.
[22] Yu. N. Sotskov, A. B. Dolgui, and M.-C. Portmann, Stability analysis of optimal balance for assembly line with fixed cycle time, Eur. J. Oper. Res., 168, No. 3, 783–797, 2006.
[23] 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. Ind. Eng., 90, 241–258, 2015.
[24] 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, pp. 135–149, Springer, New York, 2005 (Appl. Optim., Vol. 94).
