Robust assembly line balancing problem considering preventive maintenance scenarios with interval processing time

Considering preventive maintenance (PM) scenarios in the assembly line balancing problem (ALBP) have been proved effective and can be used to increase production efficiency. All these studies assumed that the processing time of tasks was fixed. However, many factors can affect the processing time in the actual production process and make the original task allocation plans infeasible. The robust method is introduced to solve the uncertain processing time, and the robust ALBP considering PM scenarios (RALBP_PMs) is studied in this paper. In this problem, three objectives are optimized: the cycle time under the regular scenario, the maximum cycle time, and the maximum task alteration under all PM scenarios. A robust mixed-integer optimization model is proposed to hedge against uncertainty, and then it is linearized by duality to make it solvable. A Q-learning-based variable neighborhood search (QVNS) algorithm with several improvements is designed to solve this problem. Several heuristic rules are designed to improve the performance of the initial population. Roulette wheel selection based on crowding distance is designed to select a solution with more potential. Eleven problem-specific neighborhood structures are designed to improve search efficiency. These structures are sorted by the Q-learning-based sorting method to find a good solution quickly. Experiment results demonstrate that considering PM scenarios in RALBP is necessary. The proposed mathematical model can obtain the Pareto solutions of small-scale instances, and the proposed QVNS algorithm is more suitable for solving large-scale instances.