Fuzzy mathematical programming for assembly line balancing problem with uncertain parameters

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.