FATİH ÇAVDUR, Elif KAYMAZ, Aslı SEBATLI

MONTAJ HATLARINDA YENİDEN İŞLEME İSTASYON POZİSYONUNUN OPTİMİZASYONU İÇİN BİR KARIŞIKTAMSAYILI PROGRAMLAMA MODELİ

Montaj hatlarında, ürünün önceden belirlenen birtakım özelliklere uygun olmaması (hatalı olması) durumunda, ürün, hata giderme çalışmalarının gerçekleştirilmesi için yeniden işleme istasyonuna gönderilmektedir. Yeniden işleme istasyonuna gönderilen hatalı ürün sayısı ise montaj hattının hata oranına bağlıdır. Yeniden işleme istasyonunun kullanım oranının düşük olması durumunda, bu istasyon hata giderme işlemlerine ek olarak standart görevlerin gerçekleştirilmesi için de kullanılabilir. Yeniden işleme istasyonunun bu amaçla kullanılması ile hattın çevrim süresi azaltılabilir. Yeniden işleme istasyonu genellikle montaj hattının sonunda konumlandırılmakla birlikte, standart görevlerin gerçekleştirilmesi için de kullanılması durumunda pozisyonunun değiştirilmesi avantajlı olabilir. Bu çalışmada, hata giderme işlemlerine ek olarak standart görevlerin gerçekleştirilmesi için de kullanılan bir yeniden işleme istasyonunun dinamik olarak pozisyonunun belirlenmesi ile çevrim süresini minimize eden bir doğrusal olmayan-karışık-tamsayılı programlama modeli önerilmektedir. Önerilen modelin doğrusal olmayan yapısı değişken dönüşümleri ile doğrusal hale dönüştürülmüştür. Yeniden işleme istasyon pozisyonunun seçimi, görevler arasındaki öncelik ilişkilerine bağlı olarak bu istasyona atanabilecek olan potansiyel görev sayısını etkilemektedir. Bu çalışmada, önerilen model kullanılarak yeniden işleme istasyon pozisyonu optimize edilmektedir. Yeniden işleme istasyonuna atanabilecek olan potansiyel görev sayısını etkileyen diğer bir faktör de montaj hattı hata oranıdır. Çalışma kapsamında önerilen model literatürde yer alan farklı örneklemler kullanılarak test edilmiştir. Problemlerin optimal çözümleri elde edilerek, sonuçlar analiz edilmiştir.

A Mixed-Integer Programming Model for Optimizing Rework Station Position in Assembly Line Balancing

In an assembly line, if a product does not meet some pre-defined specifications (i.e., if it is defective), it is generally sent to a rework station where necessary correction (rework) operations are performed. On the other hand, the number of products sent to the rework station for rework operations depends on the rework (defect) rate of the assembly line. If the defect rate is relatively low, the rework station can be used to perform standard tasks in addition to rework operations. Using the rework station for this purpose might decrease the cycle time of the assembly line. Although rework stations are generally positioned at the end of an assembly line, it might be advantageous to change its position if it is also used for performing standard tasks. In this study, a nonlinear-mixed-integer programming model is proposed to minimize the cycle time of an assembly line by dynamically positioning the rework station which is also used to perform standard tasks in addition to rework operations. The nonlinear structure of the proposed model is linearized using some variable transformations. The position of the rework station affects the number of potential tasks assigned to this station depending on the precedence relationships of the tasks. In this study, the position of the rework station is optimized using the proposed model. Another factor that affects the number of potential tasks assigned to the rework station is defect rate of the assembly line. The proposed model is tested for different defect rates using some sample problems from the literature. The problems are solved to optimality and the results are analyzed.

PDF

___

Ağpak, K. and Zolfaghari, S. (2015) Mathematical models for parallel two-sided assembly line balancing problems and extensions, International Journal of Production Research, 53(4), 1242-1254. doi: 10.1080/00207543.2014.955218
Ağpak, K., Yegül, M. F. and Gökçen, H. (2012) Two-sided U-type assembly line balancing problem, International Journal of Production Research, 50(18), 5035-5047. doi: 10.1080/00207543.2011.631599
Akpınar, S. and Bayhan, G. M. (2011) A hybrid genetic algorithm for mixed model assembly line balancing problem with parallel workstations and zoning constraints, Engineering Applications of Artificial Intelligence, 24(3), 449-457. doi: 10.1016/j.engappai.2010.08.006
Akpınar, Ş. (2017) Large neighbourhood search algorithm for Type-II assembly line balancing problem, Pamukkale University Journal of Engineering Sciences, 23(4), 444-450. doi: 10.5505/pajes.2016.75975
Akpinar, S., Elmi, A. and Bektaş, T. (2017) Combinatorial Benders cuts for assembly line balancing problems with setups, European Journal of Operational Research, 259(2), 527- 537. doi: 10.1016/j.ejor.2016.11.001
Altekin, F. T., Bayındır, Z. P. and Gümüşkaya, V. (2016) Remedial actions for disassembly lines with stochastic task times, Computers & Industrial Engineering, 99, 78-96. doi: 10.1016/j.cie.2016.06.027
Amen, M. (2006) Cost-oriented assembly line balancing: Model formulations, solution difficulty, upper and lower bounds, European Journal of Operational Research, 168(3), 747-770. doi: 10.1016/j.ejor.2004.07.026
Arıkan, M. (2017) İş yükü dengelemeli ikinci tip basit montaj hattı dengeleme problemi için bir tabu arama algoritması, Gazi Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi, 32(4), 1169-1180. doi: 10.17341/gazimmfd.369529
Battaia, O. and Dolgui, A. (2013) A taxonomy of line balancing problems and their solution approaches, International Journal of Production Economics, 142(2), 259-277. doi: 10.1016/j.ijpe.2012.10.020
Baybars, I. (1986) A survey of exact algorithms for the simple assembly line balancing problem, Management science, 32(8), 909-932. doi: 10.1287/mnsc.32.8.909
Baykasoğlu, A. and Özbakır, L. (2007) Stochastic U-line balancing using genetic algorithms, The International Journal of Advanced Manufacturing Technology, 32(1-2), 139-147. doi: 10.1007/s00170-005-0322-4
Becker, C. and Scholl, A. (2006) A survey on problems and methods in generalized assembly line balancing, European journal of operational research, 168(3), 694-715. doi: 10.1016/j.ejor.2004.07.023
Boysen, N., Fliedner, M. and Scholl, A. (2007) A classification of assembly line balancing problems, European journal of operational research, 183(2), 674-693. doi: 10.1016/j.ejor.2006.10.010
Bryton, B. (1954). Balancing of a continuos production line, M.Sc Thesis, Northwestern University, Evanston.
Bukchin, Y. and Rabinowitch, I. (2006) A branch-and-bound based solution approach for the mixed-model assembly line-balancing problem for minimizing stations and task duplication costs, European Journal of Operational Research, 174(1), 492-508. doi: 10.1016/j.ejor.2005.01.055.
Çerçioğlu, H., Özcan, U., Gökçen, H. ve Toklu, B. (2009) Paralel montaj hattı dengeleme problemleri için bir tavlama benzetimi yaklaşımı, Gazi Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi, 24(2).
Erel, E. and Gokcen, H. (1999) Shortest-route formulation of mixed-model assembly line balancing problem, European Journal of Operational Research, 116(1), 194-204. doi: 10.1016/S0377-2217(98)00115-5
Faccio, M., Gamberi, M. and Bortolini, M. (2016) Hierarchical approach for paced mixedmodel assembly line balancing and sequencing with jolly operators, International Journal of Production Research, 54(3), 761-777. doi: 10.1080/00207543.2015.1059965
Ghosh, S. and Gagnon, R. J. (1989) A comprehensive literature review and analysis of the design, balancing and scheduling of assembly systems, The International Journal of Production Research, 27(4), 637-670. doi: 10.1080/00207548908942574
Gokcen, H. and Erel, E. (1997) A goal programming approach to mixed-model assembly line balancing problem, International Journal of Production Economics, 48(2), 177-185.
Gökçen, H. and Ağpak, K. (2006) A goal programming approach to simple U-line balancing problem, European Journal of Operational Research, 171(2), 577-585. doi: 10.1016/j.ejor.2004.09.021
Gökçen, H. and Baykoç, Ö. F. (1999) A new line remedial policy for the paced lines with stochastic task times, International Journal of Production Economics, 58(2), 191-197. doi: 10.1016/S0925-5273(98)00123-6
Gökçen, H. ve Erel, E. (1998) Binary integer formulation for mixed-model assembly line balancing problem, Computers & Industrial Engineering, 34(2), 451-461. doi: 10.1016/S0360-8352(97)00142-3
Gökçen, H., Ağpak, K. and Benzer, R. (2006) Balancing of parallel assembly lines, International Journal of Production Economics, 103(2), 600-609. doi: 10.1016/j.ijpe.2005.12.001
Güden, H. and Meral, S. (2016)An adaptive simulated annealing algorithm-based approach for assembly line balancing and a real-life case study, The International Journal of Advanced Manufacturing Technology, 84(5-8), 1539-1559. doi: 10.1007/s00170-015-7802- y
Kara, Y., Özgüven, C., Yalçın, N. and Atasagun, Y. (2011) Balancing straight and U-shaped assembly lines with resource dependent task times, International Journal of Production Research, 49(21), 6387-6405. doi: 10.1080/00207543.2010.535039
Koltai, T. and Kalló, N. (2017) Analysis of the effect of learning on the throughput-time in simple assembly lines, Computers & Industrial Engineering, 111, 507-515. doi: 10.1016/j.cie.2017.03.034
Kottas, J. F. and Lau, H. S. (1973) A Cost-Oriented Approach to Stochastic Line Balancing, AIIE Transactions, 5(2), 164-171. doi: 10.1080/05695557308974897
Lau, H. S. and Shtub, A. (1987) An exploratory study on stopping a paced line when incompletions occur, IIE transactions, 19(4), 463-467. doi: 10.1080/07408178708975421
Oksuz, M. K., Buyukozkan, K. and Satoglu, S. I. (2017) U-shaped assembly line worker assignment and balancing problem: A mathematical model and two meta-heuristics, Computers & Industrial Engineering, 112, 246-263. doi: 10.1016/j.cie.2017.08.030
Özcan, U. and Toklu, B. (2010) Balancing two-sided assembly lines with sequencedependent setup times, International Journal of Production Research, 48(18), 5363-5383. doi: 10.1080/00207540903140750
Polat, O., Kalayci, C. B., Mutlu, Ö. and Gupta, S. M. (2016) A two-phase variable neighbourhood search algorithm for assembly line worker assignment and balancing problem Type-II: an industrial case study, International Journal of Production Research, 54(3), 722-741. doi: 10.1080/00207543.2015.1055344
Sabuncuoglu, I., Erel, E. and Alp, A. (2009) Ant colony optimization for the single model U-type assembly line balancing problem, International Journal of Production Economics, 120(2), 287-300. doi: 10.1016/j.ijpe.2008.11.017
Salveson, M. E. (1955) The assembly line balancing problem, The Journal of Industrial Engineering, 18-25.
Scholl, A. and Becker, C. (2006) State-of-the-art exact and heuristic solution procedures for simple assembly line balancing, European Journal of Operational Research, 168(3), 666- 693. doi: 10.1016/j.ejor.2004.07.022
Shtub, A. (1984) The effect of incompletion cost on line balancing with multiple manning of work stations, The Internatıonal Journal Of Productıon Research, 22(2), 235-245. doi: 10.1080/00207548408942450
Sikora, C. G. S., Lopes, T. C., Schibelbain, D. and Magatão, L. (2017) Integer based formulation for the simple assembly line balancing problem with multiple identical tasks, Computers & Industrial Engineering, 104, 134-144. doi: 10.1016/j.cie.2016.12.026
Silverman, F. N. and Carter, J. C. (1986) A cost-based methodology for stochastic line balancing with intermittent line stoppages, Management Science, 32(4), 455-463. doi: 10.1287/mnsc.32.4.455
Sivasankaran, P. and Shahabudeen, P. (2014) Literature review of assembly line balancing problems, The International Journal of Advanced Manufacturing Technology, 73(9-12), 1665-1694. doi: 10.1007/s00170-014-5944-y
Suwannarongsri, S. and Puangdownreong, D. (2008) Optimal assembly line balancing using tabu search with partial random permutation technique, International Journal of Management Science and Engineering Management, 3(1), 3-18. doi: 10.1080/17509653.2008.10671032
Tapkan, P., Ozbakir, L. and Baykasoglu, A. (2012) Modeling and solving constrained twosided assembly line balancing problem via bee algorithms, Applied Soft Computing, 12(11), 3343-3355. doi: 10.1016/j.asoc.2012.06.003
Tuncel, G. and Topaloglu, S. (2013) Assembly line balancing with positional constraints, task assignment restrictions and station paralleling: A case in an electronics company, Computers & Industrial Engineering, 64(2), 602-609. doi: 10.1016/j.cie.2012.11.006
Uğurdağ, H. F., Rachamadugu, R. and Papachristou, C. A. (1997) Designing paced assembly lines with fixed number of stations, European Journal of Operational Research, 102(3), 488-501. doi: 10.1016/S0377-2217(96)00248-2
Wei, N. C. and Chao, I. M. (2011) A solution procedure for Type E simple assembly line balancing problem, Computers & Industrial Engineering, 61(3), 824-830. doi: 10.1016/j.cie.2011.05.015