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A new matheuristic approach for the multi-depot vehicle routing problem with inter-depot routes

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Abstract

The multi-depot vehicle routing problem with inter-depot routes is studied in this paper, where vehicles may reset their capacity at any depot during the working day. Due to the complexity of this problem, exact approaches are limited to small-size applications. In order to overcome this limitation, we propose a matheuristic which integrates a mixed integer linear programming formulation with a set of relax-and-fix strategies. This solution approach is shown to be very efficient, and for the first time, large-size benchmarking instances are solved.

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References

  • Angelelli E, Speranza MG (2002) The periodic vehicle routing problem with intermediate facilities. Eur J Oper Res 137(2):233–247

    Article  Google Scholar 

  • Baldacci R, Mingozzi A (2009) A unified exact method for solving different classes of vehicle routing problems. Math Program 120(2):347–380

    Article  Google Scholar 

  • Baldacci R, Hadjiconstantinou E, Mingozzi A (2004) An exact algorithm for the capacitated vehicle routing problem based on a two-commodity network flow formulation. Oper Res 52(5):723–738

    Article  Google Scholar 

  • Bard JF, Huang L, Dror M, Jaillet P (1998) A branch and cut algorithm for the VRP with satellite facilities. IIE Trans 30(9):821–834

    Google Scholar 

  • Benjamin AM, Beasley JE (2010) Metaheuristics for the waste collection vehicle routing problem with time windows, driver rest period and multiple disposal facilities. Comput Oper Res 37(12):2270–2280

    Article  Google Scholar 

  • Brandao J, Mercer A (1997) A tabu search algorithm for the multi-trip vehicle routing and scheduling problem. Eur J Oper Res 100(1):180–191

    Article  Google Scholar 

  • Cattaruzza D, Absi N, Feillet D, Vidal T (2014) A memetic algorithm for the multi trip vehicle routing problem. Eur J Oper Res 236(3):833–848

    Article  Google Scholar 

  • Chao I, Golden BL, Wasil E (1993) A new heuristic for the multi-depot vehicle routing problem that improves upon best-known solutions. Am J Math Manag Sci 13:371–406

    Google Scholar 

  • Clarke G, Wright JW (1964) Scheduling of vehicles from a central depot to a number of delivery points. Oper Res 12(4):568–581

    Article  Google Scholar 

  • Cordeau JF, Gendreau M, Laporte G (1997) A tabu search heuristic for periodic and multi-depot vehicle routing problems. Networks 30(2):105–119

    Article  Google Scholar 

  • Crevier B, Cordeau JF, Laporte G (2007) The multi-depot vehicle routing problem with inter-depot routes. Eur J Oper Res 176(2):756–773

    Article  Google Scholar 

  • Dantzig G, Fulkerson R, Johnson S (1954) Solution of a large-scale traveling-salesman problem. J Oper Res Soc Am 2:393–410

    Google Scholar 

  • Dondo RGDRG, Cerda J (2009) A hybrid local improvement algorithm for large-scale multi-depot vehicle routing problems with time windows. Comput Chem Eng 33(2):513–530

    Article  Google Scholar 

  • Gillet BE, Miller LR (1974) A Heuristic algorithm for the vehicle-dispatch problem. Oper Res 22:340–349

    Article  Google Scholar 

  • Hemmelmayr V, DoernerK F, Hartl RF, Rath S (2013) A heuristic solution method for node routing based solid waste collection problems. J Heuristics 19(2):129–156

    Article  Google Scholar 

  • Kim BI, Kim S, Sahoo S (2006) Waste collection vehicle routing problem with time windows. Comput Oper Res 33(12):3624–3642

    Article  Google Scholar 

  • Laporte G (2009) Fifty years of vehicle routing. Transp Sci 43(4):408–416

    Article  Google Scholar 

  • Laporte G, Semet F (2002) Classical heuristics for the capacitated VRP. In: Toth P, Vigo D (eds) The vehicle routing problem, monographs on discrete mathematical and applications. SIAM, Philadelphia, pp 109–128

    Chapter  Google Scholar 

  • Laporte G, Nobert Y, Arpin D (1984) Optimal solutions to capacitated multi-depot vehicle routing problems. Congressus Numerantium 44:283–292

    Google Scholar 

  • Laporte G, Nobert Y, Taillefer S (1988) Solving a family of multi-depot vehicle-routing and location-routing problems. Transp Sci 22(3):161–172

    Article  Google Scholar 

  • Lim A, Wang F (2005) Multi-depot vehicle routing problem: a one-stage approach. IEEE Trans Autom Sci Eng 2(4):397–402

    Article  Google Scholar 

  • Lin S (1965) Computer solutions of the traveling salesman problem. Bell Syst Tech J 44(10):2245–2269

    Article  Google Scholar 

  • Lin S, Kernighan BW (1973) An effective heuristic algorithm for the traveling-salesman problem. Oper Res 21:498–516

    Article  Google Scholar 

  • Maniezzo V, Stützle T, Voß S (eds) (2009) Matheuristics: hybridizing metaheuristics and mathematical programming. Annals of information system. Springer, Berlin

    Google Scholar 

  • Markov I, Varone S, Bierlaire M (2016) Integrating a heterogeneous fixed fleet and a flexible assignment of destination depots in the waste collection VRP with intermediate facilities. Transp Res B 84:256–273

    Article  Google Scholar 

  • Mingozzi A, Roberti R, Toth P (2013) An exact algorithm for the multitrip vehicle routing problem. Inf J Comput 25(2):193–207

    Article  Google Scholar 

  • Muter I, Cordeau JF, Laporte G (2014) A branch-and-price algorithm for the multidepot vehicle routing problem with interdepot routes. Transp Sci 48(3):425–441

    Article  Google Scholar 

  • Petch RJ, Salhi S (2003) A multi-phase constructive heuristic for the vehicle routing problem with multiple trips. Discrete Appl Math 133:69–92

    Article  Google Scholar 

  • Renaud J, Boctor FF, Laporte G (1996a) An improved petal heuristic for the vehicle routing problem. J Oper Res Soc 47:329–336

    Article  Google Scholar 

  • Renaud J, Laporte G, Boctor FF (1996b) A tabu search heuristic for the multi-depot vehicle routing problem. Comput Oper Res 23(3):229–235

    Article  Google Scholar 

  • Schneider M, Stenger A, Hof J (2015) An adaptive VNS algorithm for vehicle routing problems with intermediate stops. OR Spectr 37:353–387

    Article  Google Scholar 

  • Tarantilis CD, Zachariadis EE, Kiranoudis CT (2008) A hybrid guided local search for the vehicle-routing problem with intermediate replenishment facilities. Inf J Comput 20(1):154–168

    Article  Google Scholar 

  • Toth P, Vigo D (eds) (2014) Vehicle routing: problems, methods, and applications, second edition. MOS-SIAM series on optimization, no. 18. SIAM, Philadelphia

    Google Scholar 

  • Tu W, Fang Z, Li Q, Shaw S-L, Chen B (2014) A bi-level Voronoi diagram-based metaheuristic for a large-scale multi-depot vehicle routing problem. Transp Res E 61:84–97

    Article  Google Scholar 

  • Van Breedam A (2001) Comparing descent heuristics and metaheuristics for the vehicle routing problem. Comput Oper Res 28(4):289–315

    Article  Google Scholar 

  • Vidal T, Crainic T, Gendreau M, Lahrichi N, Rei W (2012) A hybrid genetic algorithm for multidepot and periodic vehicle routing problems. Oper Res 60(3):611–624

    Article  Google Scholar 

Download references

Acknowledgements

Tânia Ramos and Ana Barbosa-Póvoa acknowledge the support provided by FCT and P2020 under the project PTDC/EGE-OGE/28071/2017, Lisboa-01.0145-Feder-28071. Maria Isabel Gomes acknowledges the support provided by FCT under the project UID/MAT/00297/2019 (Centro de Matemática e Aplicações).

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Authors and Affiliations

  1. Centre for Management Studies, Instituto Superior Técnico (CEG-IST), Universidade de Lisboa, Av. Rovisco Pais, 1049-001, Lisbon, Portugal

    Tânia Rodrigues Pereira Ramos & Ana Paula Barbosa-Póvoa

  2. Business Research Unit, ISCTE (BRU-ISCTE), Instituto Universitário de Lisboa, Lisbon, Portugal

    Tânia Rodrigues Pereira Ramos

  3. Centre for Mathematics and Applications, Faculdade de Ciências e Tecnologia (CMA-FCT), Universidade Nova de Lisboa, Lisbon, Portugal

    Maria Isabel Gomes

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  1. Tânia Rodrigues Pereira Ramos
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  2. Maria Isabel Gomes
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  3. Ana Paula Barbosa-Póvoa
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Correspondence to Tânia Rodrigues Pereira Ramos.

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Ramos, T.R.P., Gomes, M.I. & Barbosa-Póvoa, A.P. A new matheuristic approach for the multi-depot vehicle routing problem with inter-depot routes. OR Spectrum 42, 75–110 (2020). https://doi.org/10.1007/s00291-019-00568-7

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