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The Multi-depot Periodic Vehicle Routing Problem

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Abstraction, Reformulation and Approximation (SARA 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3607))

Abstract

The Multi-Depot Periodic Vehicle Routing Problem (MDPVRP) is the problem of designing, for an homogeneous fleet of vehicles of capacity Q, a set of routes for each day of a given p-day period. The routes of day k must be executed by m k vehicles based at the depot assigned to day k. Each vehicle performs only one route per day and each vehicle route must start and finish at the same depot. Each customer i may require to be visited on f i (say) di.erent days during the period and these visits may only occur in one of a given number of allowable daycombinations. For example, a customer may require to be visited twice during a 5-day period imposing that these visits should take place on Monday-Thursday or Monday-Friday or Tuesday-Friday. The MDPVRP consists of simultaneously assigning a day-combination to each customer and designing the vehicle routes for each day of the planning period so that each customer is visited the required number of times, the number of routes on each day does not exceed the number of vehicles available at the depot assigned to that day and the total cost of the routes is minimized.

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References

  1. Augerat, P., Belenguer, J.M., Benavent, E., Corberan, A., Naddef, D., Rinaldi, G.: Computational results with a branch and cut code for the capacitated vehicle routing problem. Rapport de recherche 1 RR949-M, ARTEMIS-IMAG, Grenoble France (1995)

    Google Scholar 

  2. Baldacci, R., Bodin, L.D., Mingozzi, A.: The Multiple Disposal Facilities and Multiple Inventory Locations Rollon-Rolloff Vehicle Routing Problem. Computers and Operations Research (to appear)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  4. Beltrami, E.J., Bodin, L.D.: Networks and vehicle routing for municipal waste collection. Networks 4, 65–94 (1974)

    Article  MATH  Google Scholar 

  5. Carter, M.W., Farolden, J.M., Laporte, G., Xu, J.: Solving an integrated logistics problem arising in grocery distribution. INFOR 34, 290–306 (1996)

    MATH  Google Scholar 

  6. Chao, I.M., Golden, B.L., Wasil, E.A.: A new heuristic for the multi-depot vehicle routing problem that improves upon best-known results. Am. J. Math. Mgmt. Sci. 13, 371–406 (1993)

    MATH  Google Scholar 

  7. Chao, I.M., Golden, B.L., Wasil, E.A.: An improved heuristic for the period vehicle routing problem. Networks 26, 22–44 (1995)

    Article  MathSciNet  Google Scholar 

  8. Christofides, N., Beasley, J.E.: The period routing problem. Networks 14, 237–256 (1984)

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  10. Fukasawa, R., Lysgaard, J., Poggi de Aragao, M., Reis, M., Uchoa, E., Werneck, R.F.: Robust branch-and-cut-and-price for the capacitated vehicle routing problem. In: Bienstock, D., Nemhauser, G.L. (eds.) IPCO 2004. LNCS, vol. 3064, pp. 1–15. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  11. Gaudioso, M., Paletta, G.: A heuristic for the periodic vehicle routing problem. Trans. Sci. 26, 86–92 (1992)

    Article  MATH  Google Scholar 

  12. Gillet, B.E., Johnson, J.G.: Multi-terminal vehicle-dispatch algorithm. Omega 4, 711–718 (1976)

    Article  Google Scholar 

  13. Hadjiconstantinou, E., Christofides, N., Mingozzi, A.: A new exact algorithm for the vehicle routing problem based on q-paths and K-shortest paths relaxations. Annals of Operations Research 61, 21–43 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  14. Laporte, G., Nobert, Y., Arpin, D.: Optimal solutions to capacitated multi-depot vehicle routing problem. Congress. Num. 44, 283–292 (1984)

    MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  16. Lysgaard, J., Letchford, A.N., Eglese, R.W.: A new branch-and-cut algorithm for the capacitated vehicle routing problems. Mathematical Programming 100, 423–445 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  17. Naddef, D., Rinaldi, G.: Branch-and cut algorithms for the capacitated VRP. In: Toth, P., Vigo, D. (eds.) The Vehicle Routing Problem. SIAM, Philadelphia (2002)

    Google Scholar 

  18. Raft, O.M.: A modular algorithm for an extended vehicle scheduling problem. Eur. J. Oper. Res. 11, 67–76 (1982)

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  20. Russel, R.A., Gribbin, D.: A multiphase approach to the period routing problem. Networks 21, 747–765 (1991)

    Article  Google Scholar 

  21. Russel, R.A., Igo, W.: An assignment routing problem. Networks 9, 1–17 (1979)

    Article  Google Scholar 

  22. Tan, C.C.R., Beasley, J.E.: A heuristic algorithm for the period routing problem. Omega 12, 497–504 (1984)

    Article  Google Scholar 

  23. Tillman, F.A., Cain, T.M.: An upper bound algorithm for the single and multiple terminal delivery problem. Mgmt. Sci. 18, 664–682 (1972)

    Article  MATH  Google Scholar 

  24. Tillman, F.A., Hering, R.W.: A study for look-ahead procedure for solving the multiterminal delivery problem. Trans. Res. 5, 225–229 (1971)

    Article  Google Scholar 

  25. Toth, P., Vigo, D.: The vehicle routing problem. Monographs on Discrete Mathematics and Applications. SIAM, Philadelphia (2002)

    Book  MATH  Google Scholar 

  26. Toth, P., Vigo, D.: Branch-and-bound algorithms for the capacitated VRP. In: Toth, P., Vigo, D. (eds.) The vehicle routing problem, Philadelphia. SIAM Monographs on Discrete Mathematics and Applications (2002)

    Google Scholar 

  27. Wren, A., Holliday, A.: Computer scheduling of vehicles from one or more depots to a number of delivery points. Oper. Res. Q. 23, 333–344 (1972)

    Article  Google Scholar 

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Mingozzi, A. (2005). The Multi-depot Periodic Vehicle Routing Problem. In: Zucker, JD., Saitta, L. (eds) Abstraction, Reformulation and Approximation. SARA 2005. Lecture Notes in Computer Science(), vol 3607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11527862_27

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  • DOI: https://doi.org/10.1007/11527862_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-27872-6

  • Online ISBN: 978-3-540-31882-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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