ЗАДАЧИ БАЛАНСИРОВКИ СБОРОЧНЫХ ЛИНИЙ С НЕОПРЕДЕЛЕННЫМИ ЧИСЛОВЫМИ ПАРАМЕТРАМИ
Аннотация
Рассматриваются задачи балансировки сборочных линий с неточными исходными данными (длительностями сборочных операций). Приводятся постановки задач балансировки сборочных линий с детерминированными, стохастическими и неопределенными параметрами. Описываются различные подходы к решению задач балансировки сборочных линий с неточными длительностями сборочных операций. Предлагается новая постановка задачи с неопределенными (интервальными) параметрами, когда для длительностей сборочных операций заданы только нижние и верхние гра-ницы (интервалы) их возможных значений. Обосновывается необходимость исследования задачи балансировки сборочных линий с интервальными параметрами.
Об авторах
Ю. Н. СотсковРоссия
О. С. Затюпо
Россия
Список литературы
1. Salveson, M.E. The assembly line balancing problem / M.E. Salveson // The J. of Industrial Engineering. – 1955. – Vol. 6, № 3. – P. 18–25.
2. Baybars, I. A survey of exact algorithms for the simple assembly line balancing problem /I. Baybars // Management Science. – 1986. – Vol. 32. – P. 909–932.
3. Boysen, N. A classification of assembly line balancing problems / N. Boysen, M. Fliener, A. Scholl // European J. of Operational Research. – 2007. – Vol. 183. – P. 674–693.
4. Thomopoulos, N.T. Line balancing – sequencing for mixed model assembly / N.T. Thomopoulos // Management Science. – 1967. – Vol. 14. – P. 59–75.
5. Dar-El, E.M. Mixed-model assembly line sequencing problems / E.M. Dar-El // Omega. –1978. – Vol. 6. – P. 317–323.
6. Sparling, D. The mixed-model U-line balancing problem / D. Sparling, J. Miltenburg // International J. of Operational Research. – 1998. – Vol. 36. – P. 485–501.
7. Ege, Y. Assembly line balancing with station paralleling / Y. Ege, M. Azizoglu, N. Ozdemirel // Computers & Industrial Engineering. – 2009. – Vol. 57. – P. 1218–1225.
8. Tonge, F.M. A Heuristic program for assembly line balancing / F.M. Tonge. – Englewood Cliffs, NJ : Prentice-Hall, 1961. – 362 p.
9. Pinto, P.A. A branch and bound algorithm for assembly line balancing with paralleling /P.A. Pinto, D.G. Dannenbring, B.M. Khumawala // International J. of Production Res. – 1975. –Vol. 13. – P. 183–196.
10. Mansoor, E.M. Assembly line balancing – an improvement on the ranked positional weight technique / E.M. Mansoor // J. Industrial Engineering. – 1964. – Vol. 15. – P. 73–78.
11. Freeman, D.R. A general line balancing model / D.R. Freeman // Proc. 19th Annual Conf. AIIE. – Tampa, FLA, 1968. – P. 230–235.
12. Scholl, A. Balancing and sequencing of assembly line / A. Scholl; Second ed. – Heidelberg : Physical-Verlag, 1999. – 532 p.
13. Erel, E. A survey of the assembly line balancing procedures / E. Erel, S.C. Sarin // Production Planning and Control. – 1998. – Vol. 9. – P. 414–434.
14. Scholl, A. Balancing assembly lines effectively – A computational comparison / A. Scholl, R. Klein // European J. of Operational Research. – 1999. – Vol. 144. – P. 50–58.
15. Kottas, J.F. A cost oriented approach to stochastic line balancing / J.F. Kottas, H.S. Lau // AIIE Transactions. – 1973. – Vol. 5. – P. 164–171.
16. Reeve, N.R. Balancing stochastic assembly lines / N.R. Reeve, W.H. Thomas // AIIE Transactions. – 1973. – Vol. 5. – P. 223–229.
17. Kottas, J.F. A cost oriented approach to stochastic line balancing / J.F. Kottas, H.S. Lau // AIIE Transactions. – 1973. – Vol. 5. – P. 164–171.
18. Silverman, F.N. A cost- based methodology for stochastic line balancing with intermittent line stoppages / F.N. Silverman, J.C. Carter // Management Science. – 1986. – Vol. 32. – P. 455–463.
19. Shin, D. An efficient heuristic for solving stochastic assembly line balancing problem /D. Shin // Computers and Industrial Engineering. – 1990. – Vol. 18. – P. 285–295.
20. Shin, D. Uniform assembly line balancing with stochastic task limes in just-in-time manufacturing / D. Shin, H. Min // International J. of Operations and Production Management. – 1991. –Vol. 11, №. 8. – P. 23–34.
21. Gen, M. Solving fuzzy assembly-line balancing problem with genetic algorithms / M. Gen, Y. Tsujimura, E. Kubot // Computers inc. Engineering. – 1995. – Vol. 29. – P. 543–547.
22. Gen, M. Fuzzy assembly line balancing using genetic algorithms / M. Gen, Y. Tsujimura, Y. Li // Computers inc. Engineering. – 1996. – Vol. 31. – P. 631–634.
23. Rabbani, M. Considering the conveyer stoppages in sequencing mixed-model assembly lines by a new fuzzy programming approach / M. Rabbani, F. Radmehr, N. Manavizadeh // International J. of Advance Manufacture Technology. – 2010. – Vol. 10. – P. 170-180.
24. Ozcan, U. Multiple-criteria decision-making in two-sided assembly line balancing: A goal programming and a fuzzy goal programming models / U. Ozcan, B. Toklu // Computers & Operations Research. – 2009. – Vol. 36. – P. 1955 – 1965.
25. Mastor, A.A. An experimental investigation and comparative evaluation of production line balancing techniques / A.A. Mastor // Management Science. – 1970. – Vol. 16. – P. 728-746.
26. Sotskov, Yu. Stability analysis of optimal balance for assembly line with fixed cycle time / Yu. Sotskov, A. Dolgui, M.-C. Portmann // European J. of Operational Research. – 2006. – Vol. 168. – P. 783–797.
27. Сотсков, Ю.Н. Теория расписаний. Системы с неопределенными числовыми параметрами / Ю.Н. Сотсков, Н.Ю. Сотскова. – Минск : ОИПИ НАН Беларуси, 2004. – 290 c.
28. Zatsiupa, A. Enumeration of the stable optimal line balances for a simple assembly line balancing problem with fixed cycle time / A. Zatsiupa, Yu.N. Sotskov, A. Dolgui // 22-nd Intern. Conf. on Production Research. – Brazil, Iquassu, 2013. – P. 1–6.
29. Stability of optimal line balance with given station set / Yu.N. Sotskov [et al.] // A chapter in the book «Supply Chain Optimization», Applied Optimization. – Vol. 94. – USA, N.Y. : Springer, 2005. – P. 135–149.
30. Sotskov, Yu. Calculation of the stability radius of an optimal line balance / Yu. Sotskov, F. Werner, A. Zatsiupa // 14th IFAC symposium on information control problems in manufacturing. – Bucharest, Romania, 2012. – P. 192–197.
31. Sotskov, Yu. Stable optimal line balances with a fixed set of the working stations /Yu. Sotskov, А. Zatsiupa, A. Dolgui // IFAC conference MIM 2013. – St. Petersburg, Russia, 2013.
32. Gurevsky, E. Stability measure for a generalized assembly line balancing problem /E. Gurevsky, O. Battaïa, A. Dolgui // Discrete Applied Mathematics. – 2013. – Vol. 161. – P. 377–394.
33. Hifi, M. Sensitivity of the optimum to perturbations of the profit or weight of an item in the binary knapsack problem / M. Hifi, H. Mhalla, S. Sadfi // J. of Combinatorial Optimization. – 2005. – Vol. 10, № 3. – P. 239–260.
34. Hifi, M. An adaptive algorithm for the knapsack problem: perturbation of the profit or weight of an arbitrary item / M. Hifi, H. Mhalla, S. Sadfi // European J. of Industrial Engineering. – 2008. – Vol. 2, №. 2. – P. 134–152.
35. Stability aspects of the traveling salesmen problem based on -best solutions / M. Libura [et al.] // Discrete Applied Mathematics. – 1998. – Vol. 87, № 1–3. – P. 159–185.
36. Ramaswamy, R. Sensitivity analysis for shortest path problems and maximum capacity path problems in undirected graphs / R. Ramaswamy, J. Orlin, N. Chakravarti // Mathematical Programming. – 2005. – Vol. 102, № 2. – P. 355–369.
37. Bräsel, H. Stability of a schedule minimizing mean flow time / H. Bräsel, Yu. Sotskov, F. Werner // Mathematical and Computer Modelling. – 1996. – Vol. 24, № 10. – P. 39–53.
38. Kravchenko, S. Optimal schedules with infinitely large stability radius / S. Kravchenko, Yu. Sotskov, F. Werner // Optimization. – 1995. – Vol. 33, № 3. – P. 271–280.
39. Sotskov, Yu. Stability of an optimal schedule / Yu. Sotskov // European J. of Operational Research. – 1991. – Vol. 55, № 1. – P. 91–102.
40. Scheduling under uncertainty: Theory and Algorithms / Yu. Sotskov [et al.]. – Minsk : Belorusskaya Nauka, 2010. – 326 p.
41. Sotskov, Yu. Stability of an optimal schedule in a job shop / Yu. Sotskov, N. Sotskova, F. Werner // Omega. – 1997. – Vol. 25, № 4. – P. 397-414.
42. Sotskov, Yu. Stability radius of an optimal schedule: a survey and recent developments /Yu. Sotskov, V. Tanaev, F. Werner // Industrial Applications of Combinatorial Optimization. – 1998. – Vol. 16. – P. 72–108.
43. Sotskov, Yu. On the calculation of the stability radius of an optimal or an approximate schedule / Yu. Sotskov, A. Wagelmans, F. Werner // Annals of Operations Research. – 1998. – Vol. 83. – P. 213–252.
44. Schedule execution for two-machine flow-shop with interval processing times / N.M. Matsveichuk [et al.] // Mathematical and Computer Modelling. – 2009. – Vol. 49. – Р. 991–1011.
45. Sotskov, Yu.N. Minimizing total weighted flow time of a set of jobs with interval processing times / Yu.N. Sotskov, N.G. Egorova, T.-C. Lai // Mathematical and Computer Modelling. – 2009. – Vol. 50. – Р 556–573.
46. Two-machine flow-shop minimum-length scheduling with interval processing times / C.T. Ng [et al.] // Asia-Pacific Journal of Operational Research. – 2009. – Vol. 26, № 6. – Р. 715–734.
47. Sotskov, Yu.N. Minimizing total weighted completion time with uncertain data: A stability approach / Yu.N. Sotskov, N.G. Egorova, F. Werner // Automation and Remote Control. – 2010. – Vol. 71, № 10. – Р. 2038–2057.
48. Sotskov, Yu.N. Minimizing total weighted flow under uncertainty using dominance and a stability box / Yu.N. Sotskov, T.-C. Lai // Computers & Operations Research. – 2012. – Vol. 39. – Р. 1271–1289.
49. Matsveichuk, N.M. The dominance digraph as a solution to the two-machine flow-shop problem with interval processing times / N.M. Matsveichuk, Yu.N. Sotskov, F. Werner // Optimization. – 2011. – Vol. 60, № 12. – Р. 1493–1517.
50. Sotskov, Yu.N. Measures of problem uncertainty for scheduling with interval processing times / Yu.N. Sotskov, T.-C. Lai, F. Werner // OR Spectrum. – 2013. – Vol. 35. – Р. 659–689.
51. Sotskov, Yu.N. Measure of uncertainty for Bellman-Johnson problem with interval data /Yu.N. Sotskov, N.M. Matsveichuk // Cybernetics and System Analysis – 2012. – Vol. 48, № 5. – P. 641–652.
Рецензия
Для цитирования:
Сотсков Ю.Н., Затюпо О.С. ЗАДАЧИ БАЛАНСИРОВКИ СБОРОЧНЫХ ЛИНИЙ С НЕОПРЕДЕЛЕННЫМИ ЧИСЛОВЫМИ ПАРАМЕТРАМИ. Информатика. 2013;(4):54-65.
For citation:
Sotskov Yu.N., Zatsiupa A.S. ASSEMBLY LINE BALANCING PROBLEMS WITH UNCERTAIN NUMERICAL PARAMETERS. Informatics. 2013;(4):54-65. (In Russ.)