MONTAJ HATLARINDA YENİDEN İŞLEME İSTASYON POZİSYONUNUN OPTİMİZASYONU İÇİN BİR KARIŞIK-TAMSAYILI PROGRAMLAMA MODELİ

Yıl 2018, Cilt: 23 Sayı: 3, 273 - 288, 31.12.2018

Fatih Çavdur , Elif Kaymaz , Aslı Sebatlı

https://doi.org/10.17482/uumfd.420001

Öz

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.

Anahtar Kelimeler

Montaj hattı dengeleme, Yeniden işleme istasyonu, İstasyon pozisyonu belirlenmesi, Çevrim süresi minimizasyonu, Karışık-tamsayılı programlama

A Mixed-Integer Programming Model for Assembly Line Balancing: Using Rework Station for Standard Tasks and Optimizing Station Position

Öz

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.

 

Anahtar Kelimeler

Assembly line balancing, Rework station, Determination of station position, Cycle time minimization, Mixed-integer programming

Kaynakça

• 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: 10.1080/00207543.2014.9552184
• 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: 10.1080/00207543.2011.6315994
• 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.2010.08.0064
• 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.2016.759754
• 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.2016.11.0014
• 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.2016.06.0274
• 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.2004.07.0264
• 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.3695294
• 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.2012.10.0204
• 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.32.8.9094
• 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/s00170-005-0322-44
• 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.2004.07.0234
• 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.2006.10.0104
• Bryton, B. (1954). Balancing of a continuos production line, M.Sc Thesis, Northwestern University, Evanston. 4
• 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.2005.01.055.4
• 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).4
• 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)00115-54
• Faccio, M., Gamberi, M. and Bortolini, M. (2016) Hierarchical approach for paced mixed-model assembly line balancing and sequencing with jolly operators, International Journal of Production Research, 54(3), 761-777. doi: 10.1080/00207543.2015.10599654
• 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: 10.1080/002075489089425744
• 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. 4
• 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.2004.09.0214
• 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)00123-64
• 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)00142-34
• 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.2005.12.0014
• 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-y4
• 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 4
• 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.2017.03.0344
• Kottas, J. F. and Lau, H. S. (1973) A Cost-Oriented Approach to Stochastic Line Balancing, AIIE Transactions, 5(2), 164-171. doi: 10.1080/056955573089748974
• 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: 10.1080/074081787089754214
• 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.2017.08.0304
• Özcan, U. and Toklu, B. (2010) Balancing two-sided assembly lines with sequence-dependent setup times, International Journal of Production Research, 48(18), 5363-5383. doi: 10.1080/002075409031407504
• 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: 10.1080/00207543.2015.10553444
• 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.2008.11.0174
• Salveson, M. E. (1955) The assembly line balancing problem, The Journal of Industrial Engineering, 18-25.4
• 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.2004.07.0224
• 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: 10.1080/002075484089424504
• 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.2016.12.0264
• 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.32.4.4554
• 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-y4
• 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: 10.1080/17509653.2008.106710324
• Tapkan, P., Ozbakir, L. and Baykasoglu, A. (2012) Modeling and solving constrained two-sided assembly line balancing problem via bee algorithms, Applied Soft Computing, 12(11), 3343-3355. doi: 10.1016/j.asoc.2012.06.0034
• 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.2012.11.0064
• 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)00248-24
• 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.2011.05.0154