Agile optimization of a two-echelon vehicle routing problem with pickup and delivery

In this paper, we consider a vehicle routing problem in which a fleet of homogeneous vehicles, initially located at a depot, has to satisfy customers' demands in a two-echelon network: first, the vehicles have to visit intermediate nodes (e.g., a retail center or a consolidation center), where they deliver raw materials or bulk products and collect a number of processed items requested by the customers in their route; then, the vehicles proceed to complete their assigned routes, thus delivering the processed items to the final customers before returning to the depot. During this stage, vehicles might visit other intermediate nodes for reloading new items. In some real-life scenarios, this problem needs to be solved in just a few seconds or even milliseconds, which leads to the concept of "agile optimization." This might be the case in some rescue operations using drones in humanitarian logistics, where every second can be decisive to save lives. In order to deal with this real-time two-echelon vehicle routing problem with pickup and delivery, an original constructive heuristic is proposed. This heuristic is able to provide a feasible and reasonably good solution in just a few milliseconds. The constructive heuristic is extended into a biased-randomized algorithm using a skewed probability distribution to modify its greedy behavior. This way, parallel runs of the algorithm are able to generate even better results without violating the real-time constraint. Results show that the proposed methodology generates competitive results in milliseconds, being able to outperform other heuristics from the literature.