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An adaptive memory algorithm for the split delivery vehicle routing problem

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Abstract

The split delivery vehicle routing problem (SDVRP) relaxes routing restrictions forcing unique deliveries to customers and allows multiple vehicles to satisfy customer demand. Split deliveries are used to reduce total fleet cost to meet those customer demands. We provide a detailed survey of the SDVRP literature and define a new constructive algorithm for the SDVRP based on a novel concept called the route angle control measure. We extend this constructive approach to an iterative approach using adaptive memory concepts, and then add a variable neighborhood descent process. These three new approaches are compared to exact and heuristic approaches by solving the available SDVRP benchmark problem sets. Our approaches are found to compare favorably with existing approaches and we find 16 new best solutions for a recent 21 problem benchmark set.

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References

  • Ambrosino, D., Sciomachen, A.: A food distribution network problem: a case study. IMA J. Manag. Math. 18(1), 33–53 (2007)

    Article  MATH  Google Scholar 

  • Archetti, C., Mansini, R., Speranza, M.G.: Complexity and reducibility of the skip delivery problem. Transp. Sci. 39(2), 182–187 (2005)

    Article  Google Scholar 

  • Archetti, C., Hertz, A., Speranza, M.G.: A tabu search algorithm for the split delivery vehicle routing problem. Transp. Sci. 40(1), 64–73 (2006a)

    Article  Google Scholar 

  • Archetti, C., Savelsbergh, M.W.P., Speranza, M.G.: Worst-case analysis for split delivery vehicle routing problems. Transp. Sci. 40(2), 226–234 (2006b)

    Article  Google Scholar 

  • Archetti, C., Savelsbergh, M.W.P., Speranza, M.G.: To split or not to split: That is the question. Transp. Res. Part E 44(1), 114–123 (2008)

    Article  Google Scholar 

  • Belenguer, J., Martinez, M., Mota, E.: A lower bound for the split delivery vehicle routing problem. Oper. Res. 48(5), 801–810 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  • Belfiore, P.P., Yoshizaki, H.T.Y.: Scatter search for heterogeneous fleet vehicle routing problems with time windows and split deliveries. Prod. Publ. Assoc. Bras. Engenh. Prod. 16(3), 455–469 (2006)

    Google Scholar 

  • Boudia, M., Prins, C., Reghioui, M.: An effective memetic algorithm with population management for the split delivery vehicle routing problem. In: Hybrid Metaheuristics. Lecture Notes in Computer Science, vol. 4771, pp. 16–30. Springer, Berlin (2007)

    Chapter  Google Scholar 

  • Bouzaiene-Ayari, B., Dror, M., Laporte, G.: Vehicle routing with stochastic demands and split deliveries. Found. Comput. Decis. Sci. 18(2), 63–69 (1993)

    MATH  Google Scholar 

  • Bräysy, O.: A reactive variable neighborhood search for the vehicle-routing problem with time windows. INFORMS J. Comput. 15(4), 347–368 (2003)

    Article  MathSciNet  Google Scholar 

  • Chen, S., Golden, B., Wasil, E.: The split delivery vehicle routing problem: Applications, algorithms, test problems, and computational results. Networks 49(4), 318–329 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  • Christofides, N., Eilon, S.: An algorithm for the vehicle-dispatching problem. Oper. Res. Q. 20(3), 309–318 (1969)

    Article  Google Scholar 

  • Christofides, N., Mingozzi, A., Toth, P.: The vehicle routing problem. In: Christofides, N., Mingozzi, A., Toth, P., Sandi, C. (eds.) Combinatorial optimization, pp. 315–338. Wiley, Chichester (1979). Chap. 11

    Google Scholar 

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

    Article  Google Scholar 

  • Dantzig, G., Ramser, J.: The truck dispatching problem. Manag. Sci. 6(1), 80–91 (1959)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  • Dror, M., Trudeau, P.: Split delivery routing. Nav. Res. Logist. 37(3), 383–402 (1990)

    MATH  MathSciNet  Google Scholar 

  • Dror, M., Laporte, G., Trudeau, P.: Vehicle routing with split deliveries. Discrete Appl. Math. 50(3), 239–254 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  • Foster, B.A., Ryan, D.M.: An integer programming approach to the vehicle scheduling problem. Oper. Res. Q. 27(2), 367–384 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  • Frizzell, P., Giffin, J.: The bounded split delivery vehicle routing problem with grid network distances. Asia-Pac. J. Oper. Res. 9, 101–116 (1992)

    MATH  MathSciNet  Google Scholar 

  • Frizzell, P., Giffin, J.: The split delivery vehicle scheduling problem with time windows and grid network distances. Comput. Oper. Res. 22(6), 655–667 (1995)

    Article  MATH  Google Scholar 

  • Ho, S., Haugland, D.: A tabu search heuristic for the vehicle routing problem with time windows and split deliveries. Comput. Oper. Res. 31(12), 1947–1964 (2004)

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  • Jin, M., Liu, K., Eksioglu, B.: A column generation algorithm for the vehicle routing problem with split delivery. Oper. Res. Lett. 36(2), 265–270 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  • Kytöjoki, J., Nuortio, T., Bräysy, O., Gendreau, M.: An efficient variable neighborhood search heuristic for very large scale vehicle routing problems. Comput. Oper. Res. 34(9), 2743–2757 (2007)

    Article  MATH  Google Scholar 

  • Lee, C.-G., Epelman, M.A., White, C.C., Bozer, Y.: A shortest path approach to the multiple-vehicle routing problem with split pick-ups. Transp. Res. Part B 40(4), 265–284 (2006)

    Article  Google Scholar 

  • Liu, K.: A study on the split delivery vehicle routing problem. Ph.D. thesis, Mississippi State University (2005)

  • Mladenović, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24(11), 1097–1100 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  • Mota, E., Campos, V., Corberan, A.: A new metaheuristic for the vehicle routing problem with split demands. In: Evolutionary Computation in Combinatorial Optimization. Lecture Notes in Computer Science, vol. 4446, pp. 121–129. Springer, Berlin (2007)

    Chapter  Google Scholar 

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

    MATH  Google Scholar 

  • Nowak, M.: The pickup and delivery problem with split loads. Ph.D. thesis, Georgia Institute of Technology (2005)

  • Polacek, M., Hartl, R.F., Doerner, K., Reimann, M.: A variable neighborhood search for the multi depot vehicle routing problem with time windows. J. Heur. 105(6), 613–627 (2004)

    Article  Google Scholar 

  • Sierksma, G., Tijssen, G.: Routing helicopters for crew exchanges on off-shores locations. Ann. Oper. Res. 76(1–4), 261–286 (1998)

    Article  MATH  Google Scholar 

  • Song, S.H., Lee, K.S., Kim, G.S.: A practical approach to solving a newspaper logistics problem using a digital map. Comput. Ind. Eng. 43(1–2), 315–330 (2002)

    Article  Google Scholar 

  • Tavakkoli-Moghaddam, R., Safaei, N., Kah, M., Rabbani, M.: A new capacitated vehicle routing problem with split service for minimizing fleet cost by simulated annealing. J. Franklin Inst. 344(5), 406–425 (2007)

    Article  MathSciNet  Google Scholar 

  • Wilck, J., Cavalier, T.: Solving the split delivery vehicle routing problem with a loaded travel cost objective. In: G. Bayraksan, W. Lin, Y. Son, R. Wysk (eds.) Proceedings 2007 Industrial Engineering Research Conference, Nashville, TN. Institute of Industrial Engineers (2007)

  • Yu, Y., Chen, H., Chu, F.: Large scale inventory routing problem with split delivery: a new model and Lagrangian relaxation approach. Int. J. Serv. Oper. Inform. 1(3), 304–320 (2006)

    Article  Google Scholar 

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Authors and Affiliations

  1. BIE Department, Wright State University, 3640 Colonel Glenn Hwy, Dayton, OH, 45435, USA

    Rafael E. Aleman & Xinhui Zhang

  2. Air Force Institute of Technology, Wright-Patterson AFB, Dayton, OH, 45433, USA

    Raymond R. Hill

Authors
  1. Rafael E. Aleman
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  2. Xinhui Zhang
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  3. Raymond R. Hill
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Correspondence to Raymond R. Hill.

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Aleman, R.E., Zhang, X. & Hill, R.R. An adaptive memory algorithm for the split delivery vehicle routing problem. J Heuristics 16, 441–473 (2010). https://doi.org/10.1007/s10732-008-9101-3

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  • DOI: https://doi.org/10.1007/s10732-008-9101-3

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