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The fleet size and mix location-routing problem with time windows: Formulations and a heuristic algorithm

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  • Koç, Çağrı
  • Bektaş, Tolga
  • Jabali, Ola
  • Laporte, Gilbert

Abstract

This paper introduces the fleet size and mix location-routing problem with time windows (FSMLRPTW) which extends the location-routing problem by considering a heterogeneous fleet and time windows. The main objective is to minimize the sum of vehicle fixed cost, depot cost and routing cost. We present mixed integer programming formulations, a family of valid inequalities and we develop a powerful hybrid evolutionary search algorithm (HESA) to solve the problem. The HESA successfully combines several metaheuristics and offers a number of new advanced efficient procedures tailored to handle heterogeneous fleet dimensioning and location decisions. We evaluate the strengths of the proposed formulations with respect to their ability to find optimal solutions. We also investigate the performance of the HESA. Extensive computational experiments on new benchmark instances have shown that the HESA is highly effective on the FSMLRPTW.

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  • Koç, Çağrı & Bektaş, Tolga & Jabali, Ola & Laporte, Gilbert, 2016. "The fleet size and mix location-routing problem with time windows: Formulations and a heuristic algorithm," European Journal of Operational Research, Elsevier, vol. 248(1), pages 33-51.
    • Handle: RePEc:eee:ejores:v:248:y:2016:i:1:p:33-51
    DOI: 10.1016/j.ejor.2015.06.082
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    as
    1. Nagy, Gabor & Salhi, Said, 2007. "Location-routing: Issues, models and methods," European Journal of Operational Research, Elsevier, vol. 177(2), pages 649-672, March.
    2. G. Clarke & J. W. Wright, 1964. "Scheduling of Vehicles from a Central Depot to a Number of Delivery Points," Operations Research, INFORMS, vol. 12(4), pages 568-581, August.
    3. Karaoglan, Ismail & Altiparmak, Fulya & Kara, Imdat & Dengiz, Berna, 2011. "A branch and cut algorithm for the location-routing problem with simultaneous pickup and delivery," European Journal of Operational Research, Elsevier, vol. 211(2), pages 318-332, June.
    4. F-H Liu & S-Y Shen, 1999. "The fleet size and mix vehicle routing problem with time windows," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(7), pages 721-732, July.
    5. Karaoglan, Ismail & Altiparmak, Fulya & Kara, Imdat & Dengiz, Berna, 2012. "The location-routing problem with simultaneous pickup and delivery: Formulations and a heuristic approach," Omega, Elsevier, vol. 40(4), pages 465-477.
    6. Stefan Ropke & David Pisinger, 2006. "An Adaptive Large Neighborhood Search Heuristic for the Pickup and Delivery Problem with Time Windows," Transportation Science, INFORMS, vol. 40(4), pages 455-472, November.
    7. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(4), pages 1007-1017, August.
    8. Drexl, Michael & Schneider, Michael, 2015. "A survey of variants and extensions of the location-routing problem," European Journal of Operational Research, Elsevier, vol. 241(2), pages 283-308.
    9. Ropke, Stefan & Pisinger, David, 2006. "A unified heuristic for a large class of Vehicle Routing Problems with Backhauls," European Journal of Operational Research, Elsevier, vol. 171(3), pages 750-775, June.
    10. M. L. Balinski, 1965. "Integer Programming: Methods, Uses, Computations," Management Science, INFORMS, vol. 12(3), pages 253-313, November.
    11. Demir, Emrah & Bektaş, Tolga & Laporte, Gilbert, 2012. "An adaptive large neighborhood search heuristic for the Pollution-Routing Problem," European Journal of Operational Research, Elsevier, vol. 223(2), pages 346-359.
    12. G. Dantzig & R. Fulkerson & S. Johnson, 1954. "Solution of a Large-Scale Traveling-Salesman Problem," Operations Research, INFORMS, vol. 2(4), pages 393-410, November.
    13. Mauro Dell'Amico & Michele Monaci & Corrado Pagani & Daniele Vigo, 2007. "Heuristic Approaches for the Fleet Size and Mix Vehicle Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 41(4), pages 516-526, November.
    14. Prodhon, Caroline & Prins, Christian, 2014. "A survey of recent research on location-routing problems," European Journal of Operational Research, Elsevier, vol. 238(1), pages 1-17.
    15. Irnich, S. & Schneider, M. & Vigo, D., 2014. "Four Variants of the Vehicle Routing Problem," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 63514, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    16. Koç, Çağrı & Bektaş, Tolga & Jabali, Ola & Laporte, Gilbert, 2014. "The fleet size and mix pollution-routing problem," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 239-254.
    17. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1461-1465, December.
    18. N. R. Achuthan & L. Caccetta & S. P. Hill, 2003. "An Improved Branch-and-Cut Algorithm for the Capacitated Vehicle Routing Problem," Transportation Science, INFORMS, vol. 37(2), pages 153-169, May.
    19. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(1), pages 193-194, February.
    20. Vidal, Thibaut & Crainic, Teodor Gabriel & Gendreau, Michel & Prins, Christian, 2014. "A unified solution framework for multi-attribute vehicle routing problems," European Journal of Operational Research, Elsevier, vol. 234(3), pages 658-673.
    21. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(5), pages 1273-1289, October.
    22. Mina, Hokey & Jayaraman, Vaidyanathan & Srivastava, Rajesh, 1998. "Combined location-routing problems: A synthesis and future research directions," European Journal of Operational Research, Elsevier, vol. 108(1), pages 1-15, July.
    23. W Dullaert & G K Janssens & K Sörensen & B Vernimmen, 2002. "New heuristics for the Fleet Size and Mix Vehicle Routing Problem with Time Windows," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(11), pages 1232-1238, November.
    24. Maria Albareda-Sambola, 2015. "Location-Routing and Location-Arc Routing," Springer Books, in: Gilbert Laporte & Stefan Nickel & Francisco Saldanha da Gama (ed.), Location Science, edition 127, chapter 0, pages 399-418, Springer.
    25. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(3), pages 819-821, June.
    26. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(2), pages 541-545, April.
    27. Rosemary T. Berger & Collette R. Coullard & Mark S. Daskin, 2007. "Location-Routing Problems with Distance Constraints," Transportation Science, INFORMS, vol. 41(1), pages 29-43, February.
    28. Olli Bräysy & Wout Dullaert & Geir Hasle & David Mester & Michel Gendreau, 2008. "An Effective Multirestart Deterministic Annealing Metaheuristic for the Fleet Size and Mix Vehicle-Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 42(3), pages 371-386, August.
    29. Marius M. Solomon, 1987. "Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints," Operations Research, INFORMS, vol. 35(2), pages 254-265, April.
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