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U-şekilli hatlarda iş yükü dengelemeli tip-2 montaj hattı dengeleme probleminin çözümü için melez tavlama benzetimi-tabu arama algoritmaları

Year 2024, Volume: 39 Issue: 3, 1733 - 1744

Murat Arıkan

https://doi.org/10.17341/gazimmfd.1274474

Abstract

Son yıllarda, tam zamanında üretim felsefesini benimseyen işletmelerin artmasıyla birlikte U-şekilli montaj hatlarının kullanımı yaygınlaşmıştır. Dolayısıyla, U-şekilli montaj hattı dengeleme problemlerinin çözüm yöntemleri üzerine yapılan çalışmalar çoğalmaktadır. Bu çalışmada, iş yükü düzgünleştirme amacını ikincil amaç olarak dikkate alan, tip-2 U-şekilli basit montaj hattı dengeleme probleminin çözümü için, literatürde daha önce geliştirilmiş ve farklı problemler üzerinde etkinliği gösterilmiş olan, iki adet farklı yapıda melez tavlama benzetimi-tabu arama algoritması kullanılmıştır. Biri tavlama benzetimi, diğeri tabu arama üzerine inşa edilmiş bu algoritmalar ilk defa U-şekilli bir montaj hattı dengeleme problemine uygulanmaktadır. Bunun yanında, bu iki melez algoritma, performans karşılaştırma amacıyla, ilk defa bir problemin çözümünde beraberce kullanılmıştır. Melez algoritmaların performansları, literatürden alınmış test problemleri üzerinde, birbirleriyle ve tavlama benzetimi ve tabu arama algoritmalarının saf versiyonlarıyla karşılaştırılmıştır. Hesaplama sonuçları, çekirdeğini tabu aramanın oluşturduğu melez algoritmanın diğerlerine üstünlük sağladığını göstermektedir.

Keywords

U-şekilli montaj hatları tip-2 montaj hattı dengeleme tavlama benzetimi tabu arama melez meta-sezgiseller

References

  • 1. Kılınçcı, Ö., Assembly line balancing problem with resource and sequence-dependent setup times (ALBPRS), Journal of the Faculty of Engineering and Architecture of Gazi University, 38 (1), 557-570, 2023.
  • 2. Scholl, A., Voß, S., Simple assembly line balancing—Heuristic approaches, J. Heuristics, 2, 217-244, 1996.
  • 3. Scholl, A., Klein, R., ULINO: Optimally balancing U-shaped JIT assembly lines. Int. J. Prod. Res, 37 (4), 721-736, 1999.
  • 4. Erel, E., Sabuncuoglu, I., Aksu, B.A., Balancing of U-type assembly systems using simulated annealing, Int. J. Prod. Res, 39 (13), 3003-3015, 2001.
  • 5. Miltenburg, G.J., Wijngaard, J., The U-line line balancing problem, Manage. Sci., 40 (10), 1378-1388, 1994.
  • 6. Gökçen, H., Agpak, K., A goal programming approach to simple U-line balancing problem, Eur. J. Oper. Res., 171 (2), 577-585, 2006.
  • 7. Kara, Y., Paksoy, T., Chang, C.T., Binary fuzzy goal programming approach to single model straight and U-shaped assembly line balancing, Eur. J. Oper. Res., 195 (2), 335-347, 2009.
  • 8. Jonnalagedda, V., Dabade, B., Application of simple genetic algorithm to U-shaped assembly line balancing problem of type II, IFAC proceedings volumes, 47 (3), 6168-6173, 2014.
  • 9. Şahin, M., Kellegöz, T., An efficient grouping genetic algorithm for U-shaped assembly line balancing problems with maximizing production rate, Memet. Comput., 9, 213-229, 2017.
  • 10. Li, M., Tang, Q., Zheng, Q., Xia, X., Floudas, C.A. Rules-based heuristic approach for the U-shaped assembly line balancing problem, Appl. Math. Modell., 48, 423-439, 2017.
  • 11. Li, Z., Janardhanan, M.N. Rahman, H.F., Enhanced beam search heuristic for U-shaped assembly line balancing problems, Eng. Optim., 53 (4), 594-608, 2021.
  • 12. Nakade, K., Ohno, K., Shanthikumar, J.G., Bounds and approximations for cycle times of a U-shaped production line, Oper. Res. Lett., 21, 191-200, 1997.
  • 13. Şahin, M., Kellegöz, T., Increasing production rate in U-type assembly lines with sequence-dependent set-up times. Eng. Optim., 49 (8), 1401-1419, 2017b.
  • 14. Zhang, Z., Tang, Q., Han, D., Li, Z., Enhanced migrating birds optimization algorithm for U-shaped assembly line balancing problems with workers assignment, Neural Comput. Appl., 31, 7501-7515, 2019.
  • 15. Li, Z., Janardhanan, M.N., Ashour, A S., Dey, N., Mathematical models and migrating birds optimization for robotic U-shaped assembly line balancing problem, Neural Comput. Appl., 31, 9095-9111, 2019.
  • 16. Wang, T., Fan, R., Peng, Y., Wang, X., Optimization on mixed-flow assembly u-line balancing problem, Cluster Comput., 22, 8249-8257, 2019.
  • 17. Pınarbaşı, M., New mathematical and constraint programming models for U-type assembly line balancing problems with assignment restrictions, Eng. Optim., 54 (8), 1289-1304, 2022.
  • 18. Arikan, M., A Tabu Search Algorithm for Type-2 U-Shaped Simple Assembly Line Balancing Problem, Sixteenth International Conference on Management Science and Engineering Management, Ankara-Türkiye, 435-449, 4-5 August, 2022.
  • 19. Gonçalves, J. F., De Almeida, J. R., A hybrid genetic algorithm for assembly line balancing, J. Heuristics, 8, 629-642, 2002.
  • 20. Triki, H., Mellouli, A., Hachicha, W., Masmoudi, F., A hybrid genetic algorithm approach for solving an extension of assembly line balancing problem, Int. J. Comput. Integr. Manuf., 29 (5), 504-519, 2016.
  • 21. Zhang, J. H., Li, A.P., Liu, X.M., Hybrid genetic algorithm for a type-II robust mixed-model assembly line balancing problem with interval task times, Adv. Manuf., 7, 117-132, 2019.
  • 22. Álvarez-Miranda, E., Pereira, J., Torrez-Meruvia, H., Vilà, M., A hybrid genetic algorithm for the simple assembly line balancing problem with a fixed number of workstations, Mathematics, 9 (17), 2157, 2021.
  • 23. Salehi, M., Maleki, H. R., Niroomand, S., Solving a new cost-oriented assembly line balancing problem by classical and hybrid meta-heuristic algorithms, Neural Comput. Appl., 32, 8217-8243, 2020.
  • 24. Tasan, S. Ö., Tunali, S., Improving the genetic algorithms performance in simple assembly line balancing, Computational Science and Its Applications-ICCSA 2006: International Conference, Springer Berlin Heidelberg, 78-87, 2006.
  • 25. Suwannarongsri, S., Limnararat, S., Puangdownreong, D., A new hybrid intelligent method for assembly line balancing, 2007 IEEE International Conference on Industrial Engineering and Engineering Management, 1115-1119, December, 2007.
  • 26. Jian-sha, L., Ling-ling, J., Xiu-lin, L., Hybrid particle swarm optimization algorithm for assembly line balancing problem-2, 2009 16th International Conference on Industrial Engineering and Engineering Management, 979-983, October, 2009.
  • 27. Dong, J., Zhang, L., Xiao, T., A hybrid PSO/SA algorithm for bi-criteria stochastic line balancing with flexible task times and zoning constraints, J. Intell. Manuf., 29, 737-751, 2018.
  • 28. Hamta, N., Ghomi, S. F., Jolai, F., Shirazi, M.A., A hybrid PSO algorithm for a multi-objective assembly line balancing problem with flexible operation times, sequence-dependent setup times and learning effect, Int. J. Prod. Econ., 141 (1), 99-111, 2013.
  • 29. Yuan, B., Zhang, C., Shao, X., Jiang, Z., An effective hybrid honey bee mating optimization algorithm for balancing mixed-model two-sided assembly lines, Comput. Oper. Res., 53, 32-41, 2015.
  • 30. Cakir, B., Altiparmak, F., Dengiz, B., Multi-objective optimization of a stochastic assembly line balancing: A hybrid simulated annealing algorithm, Comput. Ind. Eng., 60 (3), 376-384, 2011.
  • 31. Yildiz, S. T., Yildiz, G., Okyay, R., Assembly line balancing problem with hierarchical worker assignment, positional constraints, task assignment restrictions and parallel workstations, Int. J. Ind. Eng. Theory Appl. Pract., 27 (3), 345-377, 2020.
  • 32. Niroomand, S., Hybrid artificial electric field algorithm for assembly line balancing problem with equipment model selection possibility, Knowledge-Based Syst., 219, 106905, 2021.
  • 33. Roshani, A., Paolucci, M., Giglio, D., Tonelli, F., A hybrid adaptive variable neighbourhood search approach for multi-sided assembly line balancing problem to minimise the cycle time, Int. J. Prod. Res, 59 (12), 3696-3721, 2021.
  • 34. Suwannarongsri, S., Puangdownreong, D., Optimal balancing of multi-objective U-shaped assembly lines using the TSGA method, 2008 IEEE International Conference on Industrial Engineering and Engineering Management, 307-311, December, 2008.
  • 35. Nejad, G. M., Husseinzadeh Kashan, A., Shavarani, S.M., A novel competitive hybrid approach based on grouping evolution strategy algorithm for solving U-shaped assembly line balancing problems, Prod. Eng., 12 (5), 555-566, 2018.
  • 36. Khorram, M., Eghtesadifard, M., Niroomand, S., Hybrid meta-heuristic algorithms for U-shaped assembly line balancing problem with equipment and worker allocations, Soft Comput., 26 (5), 2241-2258, 2022.
  • 37. Zolfaghari, S., Liang, M., Jointly solving the group scheduling and machining speed selection problems: a hybrid tabu search and simulated annealing approach, Int. J. Prod. Res, 37 (10), 2377-2397, 1999.
  • 38. Zhang, C. Y., Li, P., Rao, Y., Guan, Z. A very fast TS/SA algorithm for the job shop scheduling problem, Comput. Oper. Res., 35 (1), 282-294, 2008.
  • 39. Arıkan M., A tabu search algorithm for the simple assembly line balancing problem of type-2 with workload balancing objective, Journal of the Faculty of Engineering and Architecture of Gazi University 32 (4), 1169-1179, 2017.
  • 40. Arıkan, M., Type-2 Assembly Line Balancing with Workload Smoothing Objective: A Reactive Tabu Search Algorithm, GU J Sci., 34 (1), 162-178, 2021.
  • 41. Rachamadugu, R., Talbot, B., Improving the quality of workload assignments in assembly lines. Int. J. Prod. Res, 29 (3), 619-633, 1991.
  • 42. Driscoll, J., Thilakawardana, D., The definition of assembly line balancing difficulty and evaluation of balance solution quality, Rob. Comput. Integr. Manuf., 17 (1-2), 81-86, 2001.
  • 43. Scholl, A., Data of assembly line balancing problems. Techn. Hochsch., Inst. für Betriebswirtschaftslehre, 1995.
  • 44. Kirkpatrick, S., Gelatt Jr, C. D., Vecchi, M. P., Optimization by simulated annealing. Science, 220 (4598), 671-680, 1983.
  • 45. Glover, F., Tabu search—part I, ORSA Journal on computing, 1 (3), 190-206, 1989.
  • 46. Glover, F., Tabu search—part II, ORSA Journal on computing, 2 (1), 4-32, 1990.
  • 47. Glover, F., Taillard, E., Taillard, E., A user's guide to tabu search, Ann. Oper. Res., 41 (1), 1-28, 1993.
  • 48. Glover F, Laguna M., Tabu search. Dordrecht: Kluwer Academic Publishers, 1997.
  • 49. Swarnkar, R., Tiwari, M K., Modeling machine loading problem of FMSs and its solution methodology using a hybrid tabu search and simulated annealing-based heuristic approach, Rob. Comput. Integr. Manuf., 20 (3), 199-209, 2004.
  • 50. Ben-Ameur, W., Computing the initial temperature of simulated annealing, Comput. Optim. Appl., 29, 369-385, 2004.

Year 2024, Volume: 39 Issue: 3, 1733 - 1744

Murat Arıkan

https://doi.org/10.17341/gazimmfd.1274474

Abstract

References

  • 1. Kılınçcı, Ö., Assembly line balancing problem with resource and sequence-dependent setup times (ALBPRS), Journal of the Faculty of Engineering and Architecture of Gazi University, 38 (1), 557-570, 2023.
  • 2. Scholl, A., Voß, S., Simple assembly line balancing—Heuristic approaches, J. Heuristics, 2, 217-244, 1996.
  • 3. Scholl, A., Klein, R., ULINO: Optimally balancing U-shaped JIT assembly lines. Int. J. Prod. Res, 37 (4), 721-736, 1999.
  • 4. Erel, E., Sabuncuoglu, I., Aksu, B.A., Balancing of U-type assembly systems using simulated annealing, Int. J. Prod. Res, 39 (13), 3003-3015, 2001.
  • 5. Miltenburg, G.J., Wijngaard, J., The U-line line balancing problem, Manage. Sci., 40 (10), 1378-1388, 1994.
  • 6. Gökçen, H., Agpak, K., A goal programming approach to simple U-line balancing problem, Eur. J. Oper. Res., 171 (2), 577-585, 2006.
  • 7. Kara, Y., Paksoy, T., Chang, C.T., Binary fuzzy goal programming approach to single model straight and U-shaped assembly line balancing, Eur. J. Oper. Res., 195 (2), 335-347, 2009.
  • 8. Jonnalagedda, V., Dabade, B., Application of simple genetic algorithm to U-shaped assembly line balancing problem of type II, IFAC proceedings volumes, 47 (3), 6168-6173, 2014.
  • 9. Şahin, M., Kellegöz, T., An efficient grouping genetic algorithm for U-shaped assembly line balancing problems with maximizing production rate, Memet. Comput., 9, 213-229, 2017.
  • 10. Li, M., Tang, Q., Zheng, Q., Xia, X., Floudas, C.A. Rules-based heuristic approach for the U-shaped assembly line balancing problem, Appl. Math. Modell., 48, 423-439, 2017.
  • 11. Li, Z., Janardhanan, M.N. Rahman, H.F., Enhanced beam search heuristic for U-shaped assembly line balancing problems, Eng. Optim., 53 (4), 594-608, 2021.
  • 12. Nakade, K., Ohno, K., Shanthikumar, J.G., Bounds and approximations for cycle times of a U-shaped production line, Oper. Res. Lett., 21, 191-200, 1997.
  • 13. Şahin, M., Kellegöz, T., Increasing production rate in U-type assembly lines with sequence-dependent set-up times. Eng. Optim., 49 (8), 1401-1419, 2017b.
  • 14. Zhang, Z., Tang, Q., Han, D., Li, Z., Enhanced migrating birds optimization algorithm for U-shaped assembly line balancing problems with workers assignment, Neural Comput. Appl., 31, 7501-7515, 2019.
  • 15. Li, Z., Janardhanan, M.N., Ashour, A S., Dey, N., Mathematical models and migrating birds optimization for robotic U-shaped assembly line balancing problem, Neural Comput. Appl., 31, 9095-9111, 2019.
  • 16. Wang, T., Fan, R., Peng, Y., Wang, X., Optimization on mixed-flow assembly u-line balancing problem, Cluster Comput., 22, 8249-8257, 2019.
  • 17. Pınarbaşı, M., New mathematical and constraint programming models for U-type assembly line balancing problems with assignment restrictions, Eng. Optim., 54 (8), 1289-1304, 2022.
  • 18. Arikan, M., A Tabu Search Algorithm for Type-2 U-Shaped Simple Assembly Line Balancing Problem, Sixteenth International Conference on Management Science and Engineering Management, Ankara-Türkiye, 435-449, 4-5 August, 2022.
  • 19. Gonçalves, J. F., De Almeida, J. R., A hybrid genetic algorithm for assembly line balancing, J. Heuristics, 8, 629-642, 2002.
  • 20. Triki, H., Mellouli, A., Hachicha, W., Masmoudi, F., A hybrid genetic algorithm approach for solving an extension of assembly line balancing problem, Int. J. Comput. Integr. Manuf., 29 (5), 504-519, 2016.
  • 21. Zhang, J. H., Li, A.P., Liu, X.M., Hybrid genetic algorithm for a type-II robust mixed-model assembly line balancing problem with interval task times, Adv. Manuf., 7, 117-132, 2019.
  • 22. Álvarez-Miranda, E., Pereira, J., Torrez-Meruvia, H., Vilà, M., A hybrid genetic algorithm for the simple assembly line balancing problem with a fixed number of workstations, Mathematics, 9 (17), 2157, 2021.
  • 23. Salehi, M., Maleki, H. R., Niroomand, S., Solving a new cost-oriented assembly line balancing problem by classical and hybrid meta-heuristic algorithms, Neural Comput. Appl., 32, 8217-8243, 2020.
  • 24. Tasan, S. Ö., Tunali, S., Improving the genetic algorithms performance in simple assembly line balancing, Computational Science and Its Applications-ICCSA 2006: International Conference, Springer Berlin Heidelberg, 78-87, 2006.
  • 25. Suwannarongsri, S., Limnararat, S., Puangdownreong, D., A new hybrid intelligent method for assembly line balancing, 2007 IEEE International Conference on Industrial Engineering and Engineering Management, 1115-1119, December, 2007.
  • 26. Jian-sha, L., Ling-ling, J., Xiu-lin, L., Hybrid particle swarm optimization algorithm for assembly line balancing problem-2, 2009 16th International Conference on Industrial Engineering and Engineering Management, 979-983, October, 2009.
  • 27. Dong, J., Zhang, L., Xiao, T., A hybrid PSO/SA algorithm for bi-criteria stochastic line balancing with flexible task times and zoning constraints, J. Intell. Manuf., 29, 737-751, 2018.
  • 28. Hamta, N., Ghomi, S. F., Jolai, F., Shirazi, M.A., A hybrid PSO algorithm for a multi-objective assembly line balancing problem with flexible operation times, sequence-dependent setup times and learning effect, Int. J. Prod. Econ., 141 (1), 99-111, 2013.
  • 29. Yuan, B., Zhang, C., Shao, X., Jiang, Z., An effective hybrid honey bee mating optimization algorithm for balancing mixed-model two-sided assembly lines, Comput. Oper. Res., 53, 32-41, 2015.
  • 30. Cakir, B., Altiparmak, F., Dengiz, B., Multi-objective optimization of a stochastic assembly line balancing: A hybrid simulated annealing algorithm, Comput. Ind. Eng., 60 (3), 376-384, 2011.
  • 31. Yildiz, S. T., Yildiz, G., Okyay, R., Assembly line balancing problem with hierarchical worker assignment, positional constraints, task assignment restrictions and parallel workstations, Int. J. Ind. Eng. Theory Appl. Pract., 27 (3), 345-377, 2020.
  • 32. Niroomand, S., Hybrid artificial electric field algorithm for assembly line balancing problem with equipment model selection possibility, Knowledge-Based Syst., 219, 106905, 2021.
  • 33. Roshani, A., Paolucci, M., Giglio, D., Tonelli, F., A hybrid adaptive variable neighbourhood search approach for multi-sided assembly line balancing problem to minimise the cycle time, Int. J. Prod. Res, 59 (12), 3696-3721, 2021.
  • 34. Suwannarongsri, S., Puangdownreong, D., Optimal balancing of multi-objective U-shaped assembly lines using the TSGA method, 2008 IEEE International Conference on Industrial Engineering and Engineering Management, 307-311, December, 2008.
  • 35. Nejad, G. M., Husseinzadeh Kashan, A., Shavarani, S.M., A novel competitive hybrid approach based on grouping evolution strategy algorithm for solving U-shaped assembly line balancing problems, Prod. Eng., 12 (5), 555-566, 2018.
  • 36. Khorram, M., Eghtesadifard, M., Niroomand, S., Hybrid meta-heuristic algorithms for U-shaped assembly line balancing problem with equipment and worker allocations, Soft Comput., 26 (5), 2241-2258, 2022.
  • 37. Zolfaghari, S., Liang, M., Jointly solving the group scheduling and machining speed selection problems: a hybrid tabu search and simulated annealing approach, Int. J. Prod. Res, 37 (10), 2377-2397, 1999.
  • 38. Zhang, C. Y., Li, P., Rao, Y., Guan, Z. A very fast TS/SA algorithm for the job shop scheduling problem, Comput. Oper. Res., 35 (1), 282-294, 2008.
  • 39. Arıkan M., A tabu search algorithm for the simple assembly line balancing problem of type-2 with workload balancing objective, Journal of the Faculty of Engineering and Architecture of Gazi University 32 (4), 1169-1179, 2017.
  • 40. Arıkan, M., Type-2 Assembly Line Balancing with Workload Smoothing Objective: A Reactive Tabu Search Algorithm, GU J Sci., 34 (1), 162-178, 2021.
  • 41. Rachamadugu, R., Talbot, B., Improving the quality of workload assignments in assembly lines. Int. J. Prod. Res, 29 (3), 619-633, 1991.
  • 42. Driscoll, J., Thilakawardana, D., The definition of assembly line balancing difficulty and evaluation of balance solution quality, Rob. Comput. Integr. Manuf., 17 (1-2), 81-86, 2001.
  • 43. Scholl, A., Data of assembly line balancing problems. Techn. Hochsch., Inst. für Betriebswirtschaftslehre, 1995.
  • 44. Kirkpatrick, S., Gelatt Jr, C. D., Vecchi, M. P., Optimization by simulated annealing. Science, 220 (4598), 671-680, 1983.
  • 45. Glover, F., Tabu search—part I, ORSA Journal on computing, 1 (3), 190-206, 1989.
  • 46. Glover, F., Tabu search—part II, ORSA Journal on computing, 2 (1), 4-32, 1990.
  • 47. Glover, F., Taillard, E., Taillard, E., A user's guide to tabu search, Ann. Oper. Res., 41 (1), 1-28, 1993.
  • 48. Glover F, Laguna M., Tabu search. Dordrecht: Kluwer Academic Publishers, 1997.
  • 49. Swarnkar, R., Tiwari, M K., Modeling machine loading problem of FMSs and its solution methodology using a hybrid tabu search and simulated annealing-based heuristic approach, Rob. Comput. Integr. Manuf., 20 (3), 199-209, 2004.
  • 50. Ben-Ameur, W., Computing the initial temperature of simulated annealing, Comput. Optim. Appl., 29, 369-385, 2004.
There are 50 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Makaleler
Authors

Murat Arıkan 0000-0003-1437-8939

Early Pub Date January 19, 2024
Publication Date
Submission Date March 31, 2023
Acceptance Date August 30, 2023
Published in Issue Year 2024 Volume: 39 Issue: 3

Cite

APA Arıkan, M. (2024). U-şekilli hatlarda iş yükü dengelemeli tip-2 montaj hattı dengeleme probleminin çözümü için melez tavlama benzetimi-tabu arama algoritmaları. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, 39(3), 1733-1744. https://doi.org/10.17341/gazimmfd.1274474
AMA Arıkan M. U-şekilli hatlarda iş yükü dengelemeli tip-2 montaj hattı dengeleme probleminin çözümü için melez tavlama benzetimi-tabu arama algoritmaları. GUMMFD. January 2024;39(3):1733-1744. doi:10.17341/gazimmfd.1274474
Chicago Arıkan, Murat. “U-şekilli Hatlarda Iş yükü Dengelemeli Tip-2 Montaj Hattı Dengeleme Probleminin çözümü için Melez Tavlama Benzetimi-Tabu Arama Algoritmaları”. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 39, no. 3 (January 2024): 1733-44. https://doi.org/10.17341/gazimmfd.1274474.
EndNote Arıkan M (January 1, 2024) U-şekilli hatlarda iş yükü dengelemeli tip-2 montaj hattı dengeleme probleminin çözümü için melez tavlama benzetimi-tabu arama algoritmaları. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 39 3 1733–1744.
IEEE M. Arıkan, “U-şekilli hatlarda iş yükü dengelemeli tip-2 montaj hattı dengeleme probleminin çözümü için melez tavlama benzetimi-tabu arama algoritmaları”, GUMMFD, vol. 39, no. 3, pp. 1733–1744, 2024, doi: 10.17341/gazimmfd.1274474.
ISNAD Arıkan, Murat. “U-şekilli Hatlarda Iş yükü Dengelemeli Tip-2 Montaj Hattı Dengeleme Probleminin çözümü için Melez Tavlama Benzetimi-Tabu Arama Algoritmaları”. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 39/3 (January 2024), 1733-1744. https://doi.org/10.17341/gazimmfd.1274474.
JAMA Arıkan M. U-şekilli hatlarda iş yükü dengelemeli tip-2 montaj hattı dengeleme probleminin çözümü için melez tavlama benzetimi-tabu arama algoritmaları. GUMMFD. 2024;39:1733–1744.
MLA Arıkan, Murat. “U-şekilli Hatlarda Iş yükü Dengelemeli Tip-2 Montaj Hattı Dengeleme Probleminin çözümü için Melez Tavlama Benzetimi-Tabu Arama Algoritmaları”. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, vol. 39, no. 3, 2024, pp. 1733-44, doi:10.17341/gazimmfd.1274474.
Vancouver Arıkan M. U-şekilli hatlarda iş yükü dengelemeli tip-2 montaj hattı dengeleme probleminin çözümü için melez tavlama benzetimi-tabu arama algoritmaları. GUMMFD. 2024;39(3):1733-44.