In dynamic smart manufacturing environments, disruptions such as Autonomous Mobile Robot (AMR) failures, machine breakdowns, and volatile demand pose significant challenges to real-time coordination for AMR fleet management. This paper proposes a novel Digital Twin (DT)-enabled fleet management framework for AMRs that integrates incident detection, surrogate-based multiobjective optimisation, and high-fidelity simulation to enable agile and efficient incident response. The system leverages a hybrid digital architecture composed of Digital Models (DMs) and Digital Shadows (DSs) to abstract real-time shop-floor data and support adaptive scheduling decisions under uncertainty. A lightweight surrogate model embedded in the Incident Response Module (IRM) facilitates rapid rescheduling, while the DT enables in-depth scenario validation and continuous system refinement. The framework is instantiated on a battery-module assembly line and evaluated across four scenarios (Machine Breakdown, AMR Breakdown, Demand Change). The surrogate delivers deployable “Best Combined” schedules near the Pareto knee within 3-10 s, achieving >98% faster decision latency than high-fidelity evaluations while closely reproducing reference outcomes (MAPE 1.03% for makespan, 0.49% for energy; NRMSE 1.17% and 0.62%, respectively; Wilcoxon tests indicate no significant differences). Against classical dispatch rules (FCFS, SPT, LPT), the surrogate consistently improves both objectives-typically 2-10% shorter makespan and 3-6% lower energy-while maintaining balanced behaviour in cross-scenario KPIs (moderated utilisation, fewer charging events, and controlled collisions per task). The results demonstrate that a prescriptive, multi-fidelity DT can provide accurate, incident-aware schedules at real-time speed, offering a scalable path to resilient AMR coordination that preserves throughput and energy efficiency under diverse shop-floor disruptions.