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A two-stage heuristic method for vehicle routing problem with split deliveries and pickups

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Abstract

The vehicle routing problem (VRP) is a well-known combinatorial optimization issue in transportation and logistics network systems. There exist several limitations associated with the traditional VRP. Releasing the restricted conditions of traditional VRP has become a research focus in the past few decades. The vehicle routing problem with split deliveries and pickups (VRPSPDP) is particularly proposed to release the constraints on the visiting times per customer and vehicle capacity, that is, to allow the deliveries and pickups for each customer to be simultaneously split more than once. Few studies have focused on the VRPSPDP problem. In this paper we propose a two-stage heuristic method integrating the initial heuristic algorithm and hybrid heuristic algorithm to study the VRPSPDP problem. To validate the proposed algorithm, Solomon benchmark datasets and extended Solomon benchmark datasets were modified to compare with three other popular algorithms. A total of 18 datasets were used to evaluate the effectiveness of the proposed method. The computational results indicated that the proposed algorithm is superior to these three algorithms for VRPSPDP in terms of total travel cost and average loading rate.

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References

  • Ai, T.J., Kachitvichyanukul, V., 2009. A particle swarm optimization for the vehicle routing problem with simultaneous pickup and delivery. Comput. Oper. Res., 36(5):1693–1702. [doi:10.1016/j.cor.2008.04.003]

    Article  MATH  Google Scholar 

  • Archetti, C., Savelsbergh, M.W.P., Speranza, M.G., 2008. To split or not to split: that is the question. Transp. Res. PT E-Logist. Transp., 44(1):114–123. [doi:10.1016/j.tre.2006. 04.003]

    Article  Google Scholar 

  • Baldacci, R., Toth, P., Vigo, D., 2010. Exact algorithms for routing problems under vehicle capacity constraints. Ann. Oper. Res., 175(1):213–245. [doi:10.1007/s10479-009-0650-0]

    Article  MATH  MathSciNet  Google Scholar 

  • Çatay, B., 2010. A new saving-based ant algorithm for the vehicle routing problem with simultaneous pickup and delivery. Expert Syst. Appl., 37(10):6809–6817. [doi:10. 1016/j.eswa.2010.03.045]

    Article  Google Scholar 

  • Chen, A.L., Yang, G.K., Wu, Z.M., 2006. Hybrid discrete particle swarm optimization algorithm for capacitated vehicle routing problem. J. Zhejiang Univ.-Sci. A, 7(4):607–614. [doi:10.1631/jzus.2006.A0607]

    Article  MATH  Google Scholar 

  • Chen, J.F., Wu, T.H., 2006. Vehicle routing problem with simultaneous deliveries and pickups. J. Oper. Res. Soc., 57(5):579–587. [doi:10.1057/palgrave.jors.2602028]

    Article  MATH  Google Scholar 

  • Chepuri, K., Homem-de-Mello, T., 2005. Solving the vehicle routing problem with stochastic demands using the cross-entropy method. Ann. Oper. Res., 134(1):153–181. [doi:10. 1007/s10479-005-5729-7]

    Article  MATH  MathSciNet  Google Scholar 

  • de Oliveira, H.C.B., Vasconcelos, G.C., 2010. A hybrid search method for the vehicle routing problem with time windows. Ann. Oper. Res., 180(1):125–144. [doi:10.1007/s10479-008-0487-y]

    Article  MATH  Google Scholar 

  • Dror, M., Trudeau, P., 1989. Savings by split delivery routing. Transp. Sci., 23(2):141–145.

    Article  MATH  MathSciNet  Google Scholar 

  • Gajpal, Y., Abad, P., 2009. An ant colony system (ACS) for vehicle routing problem with simultaneous delivery and pickup. Comput. Oper. Res., 36(12):3215–3223. [doi:10. 1016/j.cor.2009.02.017]

    Article  MATH  Google Scholar 

  • Gulczynski, D., Golden, B., Wasil, E., 2010. The split delivery vehicle routing problem with minimum delivery amounts. Transp. Res. PT E-Logist. Transp., 46(5):612–626. [doi:10.1016/j.tre.2009.12.007]

    Article  Google Scholar 

  • Hennig, F., Nygreen, B., Christiansen, M., et al., 2012. Maritime crude oil transportation-a split pickup and split delivery problem. Eur. J. Oper. Res., 218(3):764–774. [doi:10.1016/j.ejor.2011.09.046]

    Article  Google Scholar 

  • Ho, S.C., Haugland, D., 2004. A tabu search heuristic for vehicle routing problem with time windows and split deliveries. Comput. Oper. Res., 31(12):1947–1964. [doi:10.1016/S0305-0548(03)00155-2]

    Article  MATH  Google Scholar 

  • Hoff, A., Gribkovskaia, I., Laporte, G., et al., 2009. Lasso solution strategies for the vehicle routing problem with pickups and deliveries. Eur. J. Oper. Res., 192(3):755–766. [doi:10.1016/j.ejor.2007.10.021]

    Article  MATH  Google Scholar 

  • Jin, M.Z., Liu, K., Bowden, R.O., 2007. A two-stage algorithm with valid inequalities for the split delivery vehicle routing problem. Int. J. Prod. Econ., 105(1):228–242. [doi:10.1016/j.ijpe.2006.04.014]

    Article  Google Scholar 

  • Lambert, S., Riopel, D., Abdul-Kader, W., 2011. A reverse logistics decisions conceptual framework. Comput. Ind. Eng., 61(3):561–581. [doi:10.1016/j.cie.2011.04.012]

    Article  Google Scholar 

  • Lee, C.G., Epelman, M.A., White, C.C.III, et al., 2006. A shortest path approach to the multiple-vehicle routing problem with pick-ups. Transp. Res. PT B-Method., 40(4):265–284. [doi:10.1016/j.trb.2004.11.004]

    Article  Google Scholar 

  • Li, J.X., Chu, F., Chen, H.X., 2011. Coordination of split deliveries in one-warehouse multi-retailer distribution systems. Comput. Ind. Eng., 60(2):291–301. [doi:10. 1016/j.cie.2010.11.012]

    Article  Google Scholar 

  • Liu, R., Xie, X.L., Augusto, V., et al., 2013. Heuristic algorithms for a vehicle routing problem with simultaneous delivery and pickup and time windows in home health care. Eur. J. Oper. Res., 230(3):475–486. [doi:10.1016/j.ejor.2013.04.044]

    Article  MathSciNet  Google Scholar 

  • Mitra, S., 2005. An algorithm for the generalized vehicle routing problem with backhauling. Asia Pac. J. Oper. Res., 22(2):153–169. [doi:10.1142/S0217595905000522]

    Article  MATH  MathSciNet  Google Scholar 

  • Mitra, S., 2008. A parallel clustering technique for the vehicle routing problem with split deliveries and pickups. J. Oper. Res. Soc., 59(11):1532–1546. [doi:10.1057/palgrave.jors. 2602500]

    Article  MATH  Google Scholar 

  • Montané, F.A.T., Galvão, R.D., 2006. A tabu search algorithm for the vehicle routing problem with simultaneous pick-up and delivery service. Comput. Oper. Res., 33(3):595–619. [doi:10.1016/j.cor.2004.07.009]

    Article  MATH  MathSciNet  Google Scholar 

  • Moreno, L., de Aragão, M.P., Uchoa, E., 2010. Improved lower bounds for the split delivery vehicle routing problem. Oper. Res. Lett., 38(4):302–306. [doi:10.1016/j.orl.2010. 04.008]

    Article  MATH  MathSciNet  Google Scholar 

  • Mullaseril, P.A., Dror, M., Leung, J., 1997. Split-delivery routing heuristics in livestock feed distribution. J. Oper. Res. Soc., 48(2):107–116.

    MATH  Google Scholar 

  • Nanry, W.P., Barnes, J.W., 2000. Solving the pickup and delivery problem with time windows using reactive tabu search. Transp. Res. PT B-Method., 34(2):107–121. [doi:10.1016/S0191-2615(99)00016-8]

    Article  Google Scholar 

  • Nowak, M., Ergun, O., White, C.C.III, 2009. An empirical study on the benefit of split loads with the pickup and delivery problem. Eur. J. Oper. Res., 198(3):734–740. [doi:10.1016/j.ejor.2008.09.041]

    Article  MATH  Google Scholar 

  • Özdamar, L., Demir, O., 2012. A hierarchical clustering and routing procedure for large scale disaster relief logistics planning. Transp. Res. PT E-Logist. Transp., 48(3):591–602. [doi:10.1016/j.tre.2011.11.003]

    Article  Google Scholar 

  • Rieck, J., Zimmermann, J., 2010. A new mixed integer linear model for a rich vehicle routing problem with docking constraints. Ann. Oper. Res., 181(1):337–358. [doi:10. 1007/s10479-010-0748-4]

    Article  MATH  MathSciNet  Google Scholar 

  • Saberi, M., Verbas, İÖ., 2012. Continuous approximation model for the vehicle routing problem for emissions minimization at the strategic level. J. Transp. Eng., 138(11):1368–1376. [doi:10.1061/(ASCE)TE.1943-5436. 0000442]

    Article  Google Scholar 

  • Sheu, J.B., 2006. A novel dynamic resource allocation model for demand-responsive city logistics distribution operations. Transp. Res. PT E-Logist. Transp., 42(6):445–472. [doi:10.1016/j.tre.2005.05.004]

    Article  Google Scholar 

  • Sheu, J.B., 2008. Green supply chain management, reverse logistics and nuclear power generation. Transp. Res. PT E-Logist. Transp., 44(1):19–46. [doi:10.1016/j.tre.2006. 06.001]

    Article  MathSciNet  Google Scholar 

  • Solomon, M.M., 1987. Algorithms for the vehicle routing and scheduling problems with time window constraints. Oper. Res., 35(2):254–265.

    Article  MATH  MathSciNet  Google Scholar 

  • Subramanian, A., Drummond, L.M.A., Bentes, C., et al., 2010. A parallel heuristic for the vehicle routing problem with simultaneous pickup and delivery. Comput. Oper. Res., 37(11):1899–1911. [doi:10.1016/j.cor.2009.10.011]

    Article  MATH  Google Scholar 

  • Subramanian, A., Uchoa, E., Pessoa, A.A., et al., 2011. Branch-and-cut with lazy separation for the vehicle routing problem with simultaneous pickup and delivery. Oper. Res. Lett., 39(5):338–341. [doi:10.1016/j.orl.2011. 06.012]

    Article  MATH  MathSciNet  Google Scholar 

  • Wang, H.F., Chen, Y.Y., 2012. A genetic algorithm for the simultaneous delivery and pickup problems with time window. Comput. Ind. Eng., 62(1):84–95. [doi:10.1016/j.cie.2011.08.018]

    Article  Google Scholar 

  • Wang, Y., Ma, X.L., Wang, Y.H., et al., 2012. Location optimization of multiple distribution centers under fuzzy environment. J. Zhejiang Univ.-Sci. A (Appl. Phys. & Eng.), 13(10):782–798. [doi:10.1631/jzus.A1200137]

    Article  Google Scholar 

  • Wang, Y., Ma, X.L., Lao, Y.T., et al., 2013. Vehicle routing problem: simultaneous deliveries and pickups with split loads and time windows. J. Transp. Res. Board, 2378: 120–128. [doi:10.3141/2378-13]

    Article  Google Scholar 

  • Wang, Y., Ma, X.L., Lao, Y.T., et al., 2014. A fuzzy-based customer clustering approach with hierarchical structure for logistics network optimization. Expert Syst. Appl., 41(2):521–534. [doi:10.1016/j.eswa.2013.07.078]

    Article  Google Scholar 

  • Zhang, T., Chaovalitwongse, W.A., Zhang, Y.J., 2012. Scatter search for the stochastic travel-time vehicle routing problem with simultaneous pick-ups and deliveries. Comput. Oper. Res., 39(10):2277–2290. [doi:10.1016/j. cor.2011.11.021]

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Xiao-lei Ma.

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Project supported by the National Natural Science Foundation of China (No. 51138003) and the National Social Science Foundation of Chongqing of China (No. 2013YBJJ035)

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Wang, Y., Ma, Xl., Lao, Yt. et al. A two-stage heuristic method for vehicle routing problem with split deliveries and pickups. J. Zhejiang Univ. - Sci. C 15, 200–210 (2014). https://doi.org/10.1631/jzus.C1300177

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  • DOI: https://doi.org/10.1631/jzus.C1300177

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