Bi-objective optimization of human-robot collaborative mixed-model multiple assembly lines considering model assignment and energy consumption

A critical yet often overlooked challenge in mixed-model and multi-line production environments is the model-line assignment problem–deciding which product models should be allocated to which assembly lines. This decision has a profound effect on overall production efficiency, as it directly influences subsequent balancing and scheduling decisions. The integration of collaborative robots (cobots) into these environments further complicates this task. Despite its significance, the joint consideration of model-line assignment and robotic line balancing has received limited attention in the literature. This study addresses this gap by formulating the robotic mixed-model multiple assembly line balancing problem with simultaneous model-line assignment (MLA-RMMALB) and proposing a multi-objective mixed-integer programming model. The model aims to minimize total production costs and $P{M}_{2.5}$ emissions resulting from cobots’ energy consumption. To handle the complexity of the problem, a Non-dominated Sorting Genetic Algorithm II (NSGA-II) is developed as a solution approach. The model's effectiveness is demonstrated through a numerical example involving 21 tasks and benchmark problems from the literature. Solutions obtained under integrated model-line assignment are compared with random assignment scenarios, revealing significant performance gains in both objectives. NSGA-II proves capable of delivering optimal or near-optimal solutions efficiently for small- and medium-sized instances, and high-quality results for larger problems. This study contributes to literature by addressing critical challenges in multi-line mixed-model production by jointly considering model-line assignment, cobot heterogeneity, and the parallel operation of cobots and human workers. It proposes NSGA-II as an effective solution method for this complex problem. Practically, the study provides a decision-support tool for manufacturers aiming to optimize both cost-efficiency and environmental performance in robotic assembly systems. The findings are especially relevant for industries adopting cobots in high-variety production environments where these factors must be simultaneously managed.