Partial linear recharging strategy for the electric fleet size and mix vehicle routing problem with time windows and recharging stations

The electric fleet size and mix vehicle routing problem with time windows and recharging stations (E-FSMFTW) is an extension of the well-known electric vehicle routing problem with time windows (EVRPTW). The fleet consists of heterogeneous electric vehicles that differ in their fixed cost, transport capacity and battery size. In this paper, we introduce the electric fleet size and mix vehicle routing problem with a partial linear recharging strategy (E-FSMFTW-PR). To solve this problem, we formulate a path-based mixed-integer linear model without replicating any recharging stations. Then, we propose a tailored hybrid heuristic that combines a large neighborhood search algorithm with a set partitioning component. Our methods are tested on the public E-FSMFTW benchmark instances. The results show that our model can be used in a commercial solver to solve 88 out of 108 small-scale E-FSMFTW-PR instances. Allowing partial linear recharging can significantly reduce the logistical cost of large-scale E-FSMFTW instances compared to the best-known solutions with full recharging strategy. We also use the heuristic algorithm to solve a newly designed instance set from a real-world dataset, and investigate the benefit of the partial linear recharging strategy. Finally, our heuristic is benchmarked against state-of-the-art algorithms on benchmark instances of related problems. Our algorithm finds 38 new best solutions on large-scale E-FSMFTW-FR instances, finds 11 new best solutions on large-scale EVRPTW-PR instances, and obtains a high-quality local optimal solution on a real-world dataset.