Aiming at the inefficiency caused by an unbalanced workstation load in the mixed-model assembly line (MMAL), we study the assembly line (AL) design and load balancing problem under parallel tasks. Considering the task configuration cost, workstation opening cost and penalty cost of unbalanced load on the assembly line, a mixed integer programming model with the workstation’s space capacity constraint is established to formulate the mixed-model assembly line load balancing problem (MMALLBP), which is aiming at minimizing the total cost. In addition, the simulated annealing algorithm with an improvement strategy is proposed. Numerical experiments using the improved simulated annealing algorithm are superior to the solver in terms of solving time and stability, and the solving accuracy is higher than that of the traditional simulated annealing algorithm. Allowing parallel tasks can flexibly allocate tasks to the workstations, effectively use the idle time of the workstations, reduce the number of opened workstations, improve the production efficiency, reduce construction costs and the risk caused by the unbalanced load of AL.

The mixed-model assembly line balancing problem (MMALBP) in multi-demand scenarios is investigated, which addresses demand fluctuations for each product in each scenario. The objective is to minimize the sum of costs associated with tasks allocation, workstation activation, and penalty costs for unbalanced workloads. A mixed integer programming model is developed to consider the constraint of workstation space capacity. A phased heuristic algorithm is designed to solve the problem. The computational results show that considering demand fluctuations in multiple demand scenarios leads to more balanced workstation loads and improved assembly line production efficiency. Finally, sensitivity analysis of important parameters is conducted to summarize the impact of parameter changes on the results and provide practical management insights.