Robust multi-manned mixed-model assembly line balancing with dynamic task assignment considering product mix uncertainty

The manufacturing industry is facing rapid changes in customer preferences, short product life cycles, and demand fluctuations. As a result, manufacturers tend to adopt mixed-model assembly lines that produce multiple types of products, and they need these lines to be as flexible as possible to handle market changes and different product model sequences. Dynamic task assignments and walking workers enhance the flexibility of a mixed-model assembly line because the assignment of tasks and workers to stations can change in each takt depending on the product unit entering the line. In this study, we consider the design of a mixed-model assembly line with walking workers and dynamic task assignments. The objective is to minimize the sum of worker and equipment costs. We study the robust optimization problem where the line must meet the takt time for any mix of products entering the line. We formulate the problem as a scenario-based Mixed Integer Linear Programming (MILP). However, the number of scenarios grows exponentially with the length of the product sequence, and the MILP does not scale well. To circumvent this issue, we employ an adversarial approach that iteratively looks for a worse input product mix. The sub-problem that finds the worst sequence of products is NP-hard. Therefore, we rely on a local search approach to generate sequences. Computational experiments show that the proposed dynamic assignment reduces costs by 4.6% to 14% compared to the fixed and model-dependent assignments. The approach efficiently reassigns 20% to 30% of tasks, improving equipment use, especially in industries with an ample cycle time. The proposed robust approach outperforms the scenario-based MILP in terms of computational time and solution quality, especially for large-size instances.