Solving the Capacitated Open Vehicle Routing Problem Algorithm, Based on Probability Distribution Modelling of Saving Matrix

Same day last-mile parcels delivery services are recently gaining a great deal of attention in the transportation science community. In the Tel Aviv metropolitan area, smart mobility companies provide delivery services for small parcels using scooter fleets. Scooter couriers deliver the parcels from the local post offices to the final customers. Since a scooter has a limited capacity and is paid with respect to the total travelling distance, the problem can be formulated as a Capacitated Open Vehicle Routing Problem (COVRP). The proposed approach is based on the high sparseness of the Clarke-Wright (CW) saving matrix for COVRP in case of parcels delivery from post offices. In this case the CW algorithm can be separated to construction of all feasible Hamiltonian paths at the first phase and its optimal combination by solving maximal weight clique problem (MWCP) at the second phase. Computational results show that the proposed algorithm is competitive, improves known benchmark results on some instances and saves 40–80% of delivery cost in the Tel Aviv metropolitan area.