Peak-Hour Vehicle Routing for First-Mile Transportation: Problem Formulation and Algorithms

The first-mile transportation provides a transit service using ridesharing-based vehicles, e.g., feeder buses, for passengers to travel from their homes, workplaces, or public institutions to the nearest public transportation depots (rapid-transit metro or appropriated bus stations) which are located beyond comfortable walking distance. This paper studies the vehicle routing problem (VRP) for the first-mile transportation, which aims at finding the optimal travel routes for a vehicle fleet to deliver passengers from their doorstep to the depots, where the passengers can continue their journeys using fixed-route buses or trains. We focus on the Peak-Hour VRP (PHVRP) for a limited vehicle fleet capacity to serve a large volume of travel requests, with the aim of maximizing the number of served passengers. The PHVRP generalizes the VRP with time window by considering multiple alternative depots for each travel request, such that a request is satisfied if the passenger is taken to one of his/her nearest depots. We formally formulate the PHVRP with constraints on vehicle capacity, pickup time windows, and quality of service regarding riding time, where a novel trip-based constraint model is used. We proposed an ant-colony optimization algorithm for the PHVRP, which is initialized with pheromone information that jointly considers the temporal-spatial distance as well as depot similarity among different travel requests. We introduced a novel scheme (called trip-by-trip scheme) to construct the travel routes by repeatedly forming a single trip for the vehicle with earliest end time until no vehicle can accept any more trips. In constructing a single trip, the algorithm intelligently decides whether or not to end the trip instead of taking more passengers. The effectiveness of the proposed methods is evaluated by comparing with optimal solutions on small size instances and with heuristic solutions on large-size instances, using road network in Singapore and synthetic travel requests that are generated based on real bus travel demands.