Minimizing the average arriving distance in carpooling

The massive use of cars in cities brings several problems such as traffic congestion and air pollution. Carpooling is an effective way to reduce the use of cars on the premise of meeting passenger transport needs. However, route planning will influence the efficiency of carpooling. By now, most researches on the route planning of carpooling mainly pay attention to minimizing the total driving distance of cars, but for passengers, the most crucial thing is to get to the destination as soon as possible. And in most cases, the minimum total driving distance of cars does not mean the minimal average arriving distance of all passengers. To address this issue, in this article, we formulate a novel carpooling route calculation problem with the objective of minimizing the average arriving distance of all passengers in carpooling. Then, we prove that this problem is NP-hard. To solve this problem, for the situation that the vehicle capacity is sufficient to deliver all passengers, we propose a heuristic algorithm named SimilarDirection with 2 c approximation ratio in delivery order calculation phase, where c is the capacity of each vehicle. For the situation that the vehicle capacity is insufficient, we provide three algorithms named DelFar, Unchanged, and DelRan. Experimental results show that our SimilarDirection algorithm can produce less average arriving distance of all passengers than other three contrast algorithms in both the real-world dataset experiments and the synthetic dataset experiments, and DelFar has the best performance in producing less average arriving distance when the vehicle capacity is insufficient.