Dynamic UAV-based traffic monitoring under uncertainty as a stochastic arc-inventory routing policy

Given the rapid advances in unmanned aerial vehicles, or drones, and increasing need to monitor traffic at a city level, one of the current research gaps is how to systematically deploy drones over multiple periods. We propose a real-time data-driven approach: we formulate the first deterministic arc-inventory routing problem and derive its stochastic dynamic policy. The policy is expected to be of greatest value in scenarios where uncertainty is highest and costliest, such as city traffic monitoring during major events. The Bellman equation for an approximation of the proposed inventory routing policy is formulated as a selective vehicle routing problem. We propose an approximate dynamic programming algorithm based on Least Squares Monte Carlo simulation to find that policy. The algorithm has been modified so that the least squares dependent variable is defined to be the "expected stock out cost upon the next replenishment". The new algorithm is tested on 30 simulated instances of real time trajectories over 5 time periods of the selective VRP to evaluate the proposed policy and algorithm. Computational results on the selected instances show that the algorithm can outperform the myopic policy by 23% to 28% over those tests, depending on the parametric design. Further tests are conducted on classic benchmark arc routing problem instances. The 11-link instance gdb19 is expanded into a sequential 15-period stochastic dynamic example and used to demonstrate why a naive static multi-period deployment plan would not be effective in real networks.