Fuzzy mathematical programming for assembly line balancing problem with uncertain parameters
Abstract
Assembly line balancing models aim at minimizing cycle time, and the number of stations becomes quite complex with precedence relations and various resource constraints. Various heuristic and fuzzy-based methods are used to ease the solution in such assembly line balancing models. This study proposes a two-stage model that simultaneously minimizes cycle time and the number of stations for a real-life case. The paper shows how to formulate a mixed integer non-linear programming model for an assembly line balancing problem. After the constraints on production size and task durations are fuzzy transformed, the model acquires new constraints. In the new model, the α coefficient takes values in the range [0,1], bringing the fuzzy parameters closer to the lower or upper range. In cases where uncertain task duration and production size parameters are fuzzy, better results are achieved with the fuzzy model than the basic model. The fuzzy model provides to expand value range for parameters and evaluates different solution alternatives. In the study, the reflection of the value change in the parameters on the solution was examined with the experimental data set created in line with 112 different α coefficients. One-way ANOVA test was used to understand whether the fuzzy parameter values created a significant difference in the solution. The proposed model improves the solution quality through scenarios, provides a 7% saving for the total duration of the tasks at the stations within a cycle time and suggests a more suitable station layout for efficient production.
Keywords
Assembly line balancing, uncertain parameters, fuzzy approach, ANOVA
Ethical Statement
References
- Bukchin, Y., Raviv, T., “Constraint programming for solving various assembly line balancing problems” Omega, 78, (2018), 57-68. https://doi.org/10.1016/j.omega.2017.06.008.
- Kalender, F. Y., Yılmaz, M., Türkbey, O., “Montaj hattı dengeleme problemine bulanık bir yaklaşım” Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, 23(1), (2008), 129-138.
- Mirzaei, N., Mahmoodirad, A., Niroomand, S., “An uncertain multi-objective assembly line balancing problem: a credibility-based fuzzy modeling approach” International Journal of Fuzzy Systems, 21(8), (2019), 2392-2404. https://doi.org/10.1007/s40815-019-00734-7.
- Baybars, I, “A survey of exact algorithms for the simple assembly line balancing problem”, Management Science, 32(8), (1986), 909-932.
- Topaloglu, S., Salum, L., Supciller, A. A., “Rule-based modeling and constraint programming-based solution of the assembly line balancing problem”, Expert Systems with Applications, 39(3), (2012), 3484-3493. https://doi.org/10.1016/j.eswa.2011.09.038.
- Pınarbaşı, M., Alakaş, H. M., “Atama kısıtlı tip-1 montaj hattı dengeleme problemi: Bir kısıt programlama modeli yaklaşımı”, Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, 27(4), (2021), 532-541.
- Xu, W., Xiao, T. “Mixed model assembly line balancing problem with fuzzy operation times and drifting operations” in 2008 Winter Simulation Conference, IEEE, 2008. pp. 1752-1760.
- Bagher, M., Zandieh, M., Farsijani, H., “Balancing of stochastic U-type assembly lines: an imperialist competitive algorithm”, The International Journal of Advanced Manufacturing Technology, 54, (2011), 271-285. https://doi.org/10.1007/s00170-010-2937-3.
- Diri, Z., Mete, S., Çil, Z. A., Ağpak, K., “Stokastik sıra-bağımlı hazırlık zamanlı montaj hattı dengeleme problemi”, Pamukkale University Journal of Engineering Sciences, 21(4), (2015), 152-157.
- Delice, Y., Aydoğan, E. K., Özcan, U., İlkay, M. S., “Balancing two-sided U-type assembly lines using modified particle swarm optimization algorithm”, 4OR, 15, (2017), 37-66. https://doi.org/10.1007/s10288-016-0320-4.