The pickup and delivery problem with synchronized en-route transfers for microtransit planning

TL;DR

This paper introduces a MILP model and heuristic for optimizing microtransit routes with synchronized en-route transfers, significantly reducing costs and improving efficiency in large-scale networks.

Contribution

It develops a novel MILP model that determines transfer locations dynamically and a heuristic that efficiently solves large-scale instances with high accuracy.

Findings

Adding synchronized en-route transfers reduces total costs by up to 19.6%.

The heuristic achieves less than 1.5% optimality gap with much faster computation.

Over 50% of vehicle routes can be improved with synchronized transfers in large networks.

Abstract

Microtransit and other flexible transit fleet services can reduce costs by incorporating transfers. However, transfers are costly to users if they must get off a vehicle and wait at a stop for another pickup. A mixed integer linear programming model (MILP) is proposed to solve pickup and delivery problems with vehicle-synchronized en-route transfers (PDPSET). The transfer location is determined by the model and can be located at any candidate node in the network rather than a static facility defined in advance. The transfer operation is strictly synchronized between vehicles within a hard time window. A heuristic algorithm is proposed to solve the problem with an acceptable solution in a much shorter computation time than commercial software. Two sets of synthetic numerical experiments are tested: small-scale instances based on a 5x5 grid network, and large-scale instances of varying network sizes up to 250x250 grids to test scalability. The results show that adding synchronized en-route transfers in microtransit can further reduce the total cost by 10% on average and maximum savings can reach up to 19.6% in our small-scale test instances. The heuristic on average has an optimality gap less than 1.5% while having a fraction of the run time and can scale up to 250x250 grids with run times within 1 minute. Two large-scale examples demonstrate that over 50% of vehicle routes can be further improved by synchronized en-route transfers and the maximum savings in vehicle travel distance that can reach up to 20.37% for the instance with 100 vehicles and 300 requests on a 200x200 network.