Intelligent fuzzy queueing optimisation of uncertain maintenance systems using hybrid successive over-relaxation and reinforcement learning for smart manufacturing

This paper presents a fuzzy queueing system that simultaneously incorporates F-policy admission control, differentiated working vacations, server breakdowns, and state-dependent customer impatience to optimise maintenance management policies in complex manufacturing systems. To address the inherent imprecision of operational data, the system parameters are modelled using fuzzy numbers. We solve the steady-state equations using a hybrid successive over-relaxation (SOR) method to ensure high numerical stability and fast convergence within the computational procedure used to propagate fuzzy uncertainties. Further, to overcome computational bottlenecks, a Neural Network (NN) surrogate model is developed to approximate the system's behaviour, which is then optimised using Proximal Policy Optimisation (PPO) within a fuzzy decision-making framework. Validation through an automotive powertrain case study calibrated to representative operating conditions demonstrates that this integrated approach achieves an 12.3% reduction in total operating costs compared to baseline configurations. The PPO algorithm also identifies optimal control thresholds, leading to significant improvements in machine availability.