Sustainable Mixed-Model Assembly Line Balancing with an Analytical Lower Bound and Adaptive Large Neighborhood Search

The growing emphasis on sustainable manufacturing has motivated the integration of environmental and social factors into traditional assembly line balancing problems (ALBPs). This study introduces a Sustainable Mixed-Model Assembly Line Balancing Problem (S-MMALBP) that jointly considers task precedence, machine selection, worker allocation, carbon-emission control, and green-rating incentives. An exact optimization model is formulated to minimize total operating cost while satisfying sustainability and capacity constraints. To address the problem’s combinatorial complexity, an Adaptive Large Neighborhood Search (ALNS) metaheuristic is developed, incorporating customized destroy and repair operators, adaptive penalty updating, and a simulated-annealing-based acceptance criterion. An analytical lower bound is derived to evaluate the algorithm’s performance, and an enhanced constructive method, Precedence-Driven Task Grouping (PDTG), is proposed to generate high-quality initial solutions. Computational experiments on benchmark instances confirm that the ALNS achieves near-optimal solutions with deviations below 5% from the lower bound, while solving large instances within seconds. A real-world case study on aircraft assembly involving 166 tasks further validates the model’s applicability, achieving a cost deviation below 4% from the theoretical bound under realistic sustainability constraints. The results demonstrate that the proposed model provides an effective and scalable decision-support tool for designing environmentally and socially responsible production systems. The study is the first to incorporate sustainability and worker–machine decisions into a mixed-model ALB framework solved by a tailored ALNS and lower bound.