Reward-Density Heuristic for Dynamic Multi-Vehicle Routing: Performance and Computational Efficiency

The Vehicle Routing Problem (VRP) and its variants represent some of the most practically consequential optimization challenges in modern logistics and urban mobility. In this study, we address a dynamic, online variant combining elements of the VRP and the Orienteering Problem (OP), in which a fleet of vehicles must maximise cumulative reward collected within a fixed time horizon while continuously replanning as new tasks arrive. We propose and evaluate a reward-density heuristic for dynamic multi-vehicle assignment, referred to as the Efficiency heuristic. We evaluate this formulation across two application domains: autonomous drone task allocation and urban taxi dispatch, across multiple fleet sizes and task scales. The proposed method is compared with four classical construction heuristics and three metaheuristic algorithms (Adaptive Large Neighbourhood Search, Genetic Algorithm, and Simulated Annealing), all evaluated under identical conditions. Across all tested configurations, the Efficiency heuristic matches the solution quality of the best metaheuristic algorithms while requiring two to three orders of magnitude less planning time, establishing Pareto dominance over all competing methods on the reward-versus-compute frontier. These findings suggest a practical design principle for real-time allocation and dispatch systems: in dynamic, time-constrained routing environments, carefully designed greedy heuristics can match the output of sophisticated search procedures at a fraction of the computational cost, making them preferable for online deployment.