A Distributionally Robust Optimization Method for Mixed-Model U Shaped Assembly Line Balancing Considering Task Time Uncertainty

In the assembly line production dominated by manual assembly, the uncertainty of task time is an important factor affecting the cycle time. Considering that stochastic optimization requires precise probability distribution information and high conservatism in robust optimization. In this paper, we focuse on the balance problems of a mixed-model U-shaped assembly line under uncertain task time. A fuzzy set centered on empirical distribution and with Wasserstein distance as the radius is used to describe the uncertainty of working hours. The optimization goal is to minimize production time, and a distributed robust optimization model for the assembly line balance problem is established. In order to reduce the complexity of the model, the strong duality theory is used to transform the model into a form that is easy to solve. To guarantee the robustness of the solution, a robustness metric is designed and used as a constraint condition for the model. Based on the above model, an improved genetic algorithm is presented by designing a decoding method based on interval number and introducing adaptive crossover and mutation probabilities. Finally, numerical simulation experiments are carried out through standard examples and production examples of circuit breaker chassis. Compared to stochastic optimization and robust optimization methods, the established model reduces the conservatism of results while maintaining high robustness, and the improved genetic algorithm proposed for the problem has good optimization ability.