Our work aims to investigate methods for solving the mixed-model assembly line balancing problem (MALBP) under uncertainty with the objective of minimizing the number of workstations. Specifically, we model task processing time as fuzzy stochastic variables (FRVs) due to the inherent uncertainties and variations in the manufacturing environment. Additionally, we introduce a ranking method for FRVs and propose a mathematical model to address MALBP. The recently developed Red Fox Optimization (RFO) algorithm is also discretized for the first time to support solving this problem. Finally, matheuristic algorithms combine a metaheuristic such as the popular Genetic Algorithm (GA), Particle Swarm Optimization (PSO), or the Discretized Red Fox Optimization (DRFO) algorithm with the Mixed-Integer Programming (MIP) model to generate the best solution in a reasonable time. Our comparative results demonstrate that the GA-MIP combination outperforms the others in both objective value and computational time. •We are the first to consider the Assembly Line Balancing Problem with fuzzy random processing time.•a new method to rank fuzzy stochastic processing times is introduced by comparing interval values.•The problem is formulated as chance-constrained programming model.•The recently developed Red Fox Optimization (RFO) algorithm is also discretized for the first time to support solution process.•A matheuristic combines a metaheuristic and the MIP model to search for better solutions for large-sized problems.•The metaheuristic algorithm to generate the starting solution for the MIP model to shorten finding the optimal solution.•Our results are nearly the same quality as the exact solution of the MIP model in a much shorter time for small-sized instances. MGA matheuristic yields significantly better performance than others in both terms of objective value and computational time for large-sized problems.