Fuel distribution is a critical bottleneck in open-pit mining operations, where unplanned equipment downtime due to fuel depletion directly increases operational costs and disrupts production continuity. Optimizing fuel truck routing under real-time, dynamic conditions, accounting for equipment locations, fuel levels, and refueling priorities, remains an insufficiently addressed problem in the existing vehicle routing literature. This study evaluates and compares three algorithmic approaches for solving the priority-constrained fuel truck routing problem in open-pit mining: Brute Force (BF), Branch and Bound with a Reduced Matrix Approach (B & B), and Ant Colony Optimization (ACO). The algorithms are tested on two datasets from a North American coal mine, a primary dataset of 14 equipment units and a supplementary dataset of 38 units, using geodesic distances and a three-tier priority structure based on real-time fuel levels. A modified B & B formulation employing matrix reduction and dummy variables is applied to enforce priority group constraints without premature depot returns. ACO parameters are tuned for the priority-constrained routing environment with a fixed depot start. On the primary dataset, BF yields the optimal path of 54.39 km in 1.68 seconds, B & B produces a near-optimal path of 55.01 km in 1.41 seconds, and ACO achieves a heuristic path of 55.01 km in 0.22 seconds. Scalability analysis shows that BF becomes computationally infeasible beyond 17 equipment units, B & B beyond 29 units, while ACO consistently delivers near-optimal solutions across all tested scales within approximately 1 second. ACO is identified as the most suitable algorithm for real-time fuel truck routing in large-scale open-pit mining operations, offering the best balance between solution quality and computational efficiency, with a deviation of 1.13% from the optimal path.