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.

[1]  Temel Öncan,et al.  A new enhancement of the Clarke and Wright savings heuristic for the capacitated vehicle routing problem , 2005, J. Oper. Res. Soc..

[2]  Nicos Christofides,et al.  An Algorithm for the Vehicle-dispatching Problem , 1969 .

[3]  Samuel J. Raff,et al.  Routing and scheduling of vehicles and crews : The state of the art , 1983, Comput. Oper. Res..

[4]  Marshall L. Fisher,et al.  Optimal Solution of Vehicle Routing Problems Using Minimum K-Trees , 1994, Oper. Res..

[5]  Ulrich Derigs,et al.  A simple and efficient tabu search heuristic for solving the open vehicle routing problem , 2009, J. Oper. Res. Soc..

[6]  Sean R Eddy,et al.  What is dynamic programming? , 2004, Nature Biotechnology.

[7]  S. A. MirHassani,et al.  A particle swarm optimization algorithm for open vehicle routing problem , 2011, Expert Syst. Appl..

[8]  Christos D. Tarantilis,et al.  Solving the open vehicle routeing problem via a single parameter metaheuristic algorithm , 2005, J. Oper. Res. Soc..

[9]  Krzysztof Fleszar,et al.  A variable neighbourhood search algorithm for the open vehicle routing problem , 2009, Eur. J. Oper. Res..

[10]  Simona Ronchi Della Rocca,et al.  λ Δ -Models , 2004 .

[11]  Samy Bengio,et al.  Neural Combinatorial Optimization with Reinforcement Learning , 2016, ICLR.

[12]  Zhiwen Fang.  Exact Algorithms for the Maximum Clique Problem , 2016 .

[13]  Majid Yousefikhoshbakht,et al.  Solving the open vehicle routing problem by a hybrid ant colony optimization , 2014 .

[14]  Paolo Toth,et al.  Models, relaxations and exact approaches for the capacitated vehicle routing problem , 2002, Discret. Appl. Math..

[15]  Adam N. Letchford,et al.  A branch-and-cut algorithm for the capacitated open vehicle routing problem , 2007, J. Oper. Res. Soc..

[16]  Hua Jiang,et al.  An Exact Algorithm for the Maximum Weight Clique Problem in Large Graphs , 2017, AAAI.

[17]  José Brandão,et al.  A tabu search algorithm for the open vehicle routing problem , 2004, Eur. J. Oper. Res..

[18]  Richard W. Eglese,et al.  A new tabu search heuristic for the open vehicle routing problem , 2005, J. Oper. Res. Soc..

[19]  D Sariklis,et al.  A heuristic method for the open vehicle routing problem , 2000, J. Oper. Res. Soc..

[20]  Kejun Zhu,et al.  A hybrid GA-TS algorithm for open vehicle routing optimization of coal mines material , 2011, Expert Syst. Appl..

[21]  George B. Dantzig,et al.  The Truck Dispatching Problem , 1959 .

[22]  Christos D. Tarantilis,et al.  Combination of geographical information system and efficient routing algorithms for real life distribution operations , 2004, Eur. J. Oper. Res..

[23]  G. Clarke,et al.  Scheduling of Vehicles from a Central Depot to a Number of Delivery Points , 1964 .

[24]  James P. Kelly,et al.  A Network Flow-Based Tabu Search Heuristic for the Vehicle Routing Problem , 1996, Transp. Sci..

[25]  R. Kawtummachai,et al.  A Heuristic Approach Based on Clarke-Wright Algorithm for Open Vehicle Routing Problem , 2013, TheScientificWorldJournal.