A mathematical model and artificial bee colony algorithm for the lexicographic bottleneck mixed-model assembly line balancing problem
Typically, the total number of required workstations are minimised for a given cycle time (this problem is referred to as type-1), or cycle time is minimised for a given number of workstations (this problem is referred to as type-2) in traditional balancing of assembly lines. However, variation in workload distributions of workstations is an important indicator of the quality of the obtained line balance. This needs to be taken into account to improve the reliability of an assembly line against unforeseeable circumstances, such as breakdowns or other failures. For this aim, a new problem, called lexicographic bottleneck mixed-model assembly line balancing problem (LB-MALBP), is presented and formalised. The lexicographic bottleneck objective, which was recently proposed for the simple single-model assembly line system in the literature, is considered for a mixed-model assembly line system. The mathematical model of the LB-MALBP is developed for the first time in the literature and coded in GAMS solver, and optimal solutions are presented for some small scale test problems available in the literature. As it is not possible to get optimal solutions for the large-scale instances, an artificial bee colony algorithm is also implemented for the solution of the LB-MALBP. The solution procedures of the algorithm are explored illustratively. The performance of the algorithm is also assessed using derived well-known test problems in this domain and promising results are observed in reasonable CPU times.
KeywordsLexicographic bottleneck Assembly line balancing Mixed-model lines Mathematical model Artificial bee colony algorithm
- Baykasoglu, A., & Dereli, T. (2009). Simple and U-type assembly line balancing by using an ant colony based algorithm. Mathematical & Computational Applications, 14(1), 1–12.Google Scholar
- Hamta, N., Ghomi, S. M. T. F., Jolai, F., & Shirazi, M. A. (2013). A hybrid PSO algorithm for a multi-objective assembly line balancing problem with flexible operation times, sequence-dependent setup times and learning effect. International Journal of Production Economics, 141(1), 99–111.CrossRefGoogle Scholar
- Haq, A. N., Rengarajan, K., & Jayaprakash, J. (2006). A hybrid genetic algorithm approach to mixed-model assembly line balancing. International Journal of Advanced Manufacturing Technology, 28(3–4), 337–341.Google Scholar
- Karaboga, D. (2005). An idea based on honey bee swarm for numerical optimization. Technical report TR06. In Computer Engineering Department, Engineering Faculty, Erciyes University, Turkey.Google Scholar
- Kucukkoc, I., & Zhang, D. Z. (2014). Mathematical model and agent based solution approach for the simultaneous balancing and sequencing of mixed-model parallel two-sided assembly lines. International Journal of Production Economics, 158, 314–333. doi: 10.1016/j.ijpe.2014.08.010.CrossRefGoogle Scholar
- Kucukkoc, I., & Zhang, D. Z. (2015d). Integrating ant colony and genetic algorithms in the balancing and scheduling of complex assembly lines. The International Journal of Advanced Manufacturing Technology. doi: 10.1007/s00170-015-7320-y.
- Liao, L. M., Huang, C. J., & Huang, J. H. (2012). Applying multi-agent approach to mixed-model assembly line balancing. In Proceedings of the IEEE ICMIT.Google Scholar
- Liu, S. B., Ong, H. L., & Huang, H. C. (2004). A bidirectional heuristic for stochastic assembly line balancing Type II problem. The International Journal of Advanced Manufacturing Technology, 25(1–2), 71–77.Google Scholar
- Pastor, R., García-Villoria, A., Laguna, M., & Martí, R. (2015). Metaheuristic procedures for the lexicographic bottleneck assembly line balancing problem. Journal of the Operational Research Society. doi: 10.1057/jors.2014.138.
- Satoglu, S. I., & Ethem Sahin, I. (2012). Design of a just-in-time periodic material supply system for the assembly lines and an application in electronics industry. The International Journal of Advanced Manufacturing Technology, 65(1–4), 319–332.Google Scholar
- Zhang, D. Z., & Kucukkoc, I. (2013). Balancing mixed-model parallel two-sided assembly lines. In L. Amodeo, A. Dolgui, & F. Yalaoui Proceedings of 2013 international conference on industrial engineering and systems management, IEEE–IESM 2013, art. no. 6761429, 28–30 October, Rabat, Morocco (pp. 391–401).Google Scholar