IDEAS home Printed from https://ideas.repec.org/a/eee/jomega/v40y2012i4p465-477.html
   My bibliography  Save this article

The location-routing problem with simultaneous pickup and delivery: Formulations and a heuristic approach

Author

Listed:
  • Karaoglan, Ismail
  • Altiparmak, Fulya
  • Kara, Imdat
  • Dengiz, Berna

Abstract

In this paper, we consider a variant of the Location-Routing Problem (LRP), namely the LRP with simultaneous pickup and delivery (LRPSPD). The LRPSPD seeks to minimize total cost by simultaneously locating the depots and designing the vehicle routes that satisfy pickup and delivery demand of each customer at the same time. We propose two polynomial-size mixed integer linear programming formulations for the problem and a family of valid inequalities to strengthen the formulations. While the first formulation is a node-based formulation, the second one is a flow-based formulation. Furthermore, we propose a two-phase heuristic approach based on simulated annealing, tp_SA, to solve the large-size LRPSPD and two initialization heuristics to generate an initial solution for the tp_SA. We then empirically evaluate the strengths of the proposed formulations with respect to their ability to find optimal solutions or strong lower bounds, and investigate the performance of the proposed heuristic approach. Computational results show that the flow-based formulation performs better than the node-based formulation in terms of the solution quality and the computation time on small-size problems. However, the node-based formulation can yield competitive lower bounds in a reasonable amount of time on medium-size problems. Meantime, the proposed heuristic approach is computationally efficient in finding good quality solutions for the LRPSPD.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:jomega:v:40:y:2012:i:4:p:465-477 DOI: 10.1016/j.omega.2011.09.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0305048311001393
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    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. Perl, Jossef & Daskin, Mark S., 1985. "A warehouse location-routing problem," Transportation Research Part B: Methodological, Elsevier, vol. 19(5), pages 381-396, October.
    3. Kulkarni, R. V. & Bhave, P. R., 1985. "Integer programming formulations of vehicle routing problems," European Journal of Operational Research, Elsevier, vol. 20(1), pages 58-67, April.
    4. Wasner, Michael & Zapfel, Gunther, 2004. "An integrated multi-depot hub-location vehicle routing model for network planning of parcel service," International Journal of Production Economics, Elsevier, vol. 90(3), pages 403-419, August.
    5. Gerardo Berbeglia & Jean-François Cordeau & Irina Gribkovskaia & Gilbert Laporte, 2007. "Rejoinder on: Static pickup and delivery problems: a classification scheme and survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 45-47, July.
    6. Salhi, Said & Rand, Graham K., 1989. "The effect of ignoring routes when locating depots," European Journal of Operational Research, Elsevier, vol. 39(2), pages 150-156, March.
    7. Costa, Alysson M. & França, Paulo M. & Lyra Filho, Christiano, 2011. "Two-level network design with intermediate facilities: An application to electrical distribution systems," Omega, Elsevier, vol. 39(1), pages 3-13, January.
    8. Anken, F. & Beasley, J.E., 2012. "Corporate structure optimisation for multinational companies," Omega, Elsevier, vol. 40(2), pages 230-243, April.
    9. Srivastava, R, 1993. "Alternate solution procedures for the location-routing problem," Omega, Elsevier, vol. 21(4), pages 497-506, July.
    10. Jacobsen, S. K. & Madsen, O. B. G., 1980. "A comparative study of heuristics for a two-level routing-location problem," European Journal of Operational Research, Elsevier, vol. 5(6), pages 378-387, December.
    11. Laporte, Gilbert & Nobert, Yves, 1981. "An exact algorithm for minimizing routing and operating costs in depot location," European Journal of Operational Research, Elsevier, vol. 6(2), pages 224-226, February.
    12. Watson-Gandy, CDT & Dohrn, PJ, 1973. "Depot location with van salesmen -- A practical approach," Omega, Elsevier, vol. 1(3), pages 321-329, June.
    13. Kara, Imdat & Laporte, Gilbert & Bektas, Tolga, 2004. "A note on the lifted Miller-Tucker-Zemlin subtour elimination constraints for the capacitated vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 158(3), pages 793-795, November.
    14. Laporte, Gilbert & Nobert, Yves & Pelletier, Paul, 1983. "Hamiltonian location problems," European Journal of Operational Research, Elsevier, vol. 12(1), pages 82-89, January.
    15. 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.
    16. Mosheiov, Gur, 1994. "The Travelling Salesman Problem with pick-up and delivery," European Journal of Operational Research, Elsevier, vol. 79(2), pages 299-310, December.
    17. Gerardo Berbeglia & Jean-François Cordeau & Irina Gribkovskaia & Gilbert Laporte, 2007. "Static pickup and delivery problems: a classification scheme and survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 1-31, July.
    18. Amiri, Ali, 2006. "Designing a distribution network in a supply chain system: Formulation and efficient solution procedure," European Journal of Operational Research, Elsevier, vol. 171(2), pages 567-576, June.
    19. Hansen, P. H. & Hegedahl, B. & Hjortkjaer, S. & Obel, B., 1994. "A heuristic solution to the warehouse location-routing problem," European Journal of Operational Research, Elsevier, vol. 76(1), pages 111-127, July.
    20. Melo, M.T. & Nickel, S. & Saldanha-da-Gama, F., 2009. "Facility location and supply chain management - A review," European Journal of Operational Research, Elsevier, vol. 196(2), pages 401-412, July.
    21. ReVelle, C.S. & Eiselt, H.A. & Daskin, M.S., 2008. "A bibliography for some fundamental problem categories in discrete location science," European Journal of Operational Research, Elsevier, vol. 184(3), pages 817-848, February.
    22. G. Nagy & S. Salhi, 1998. "The many-to-many location-routing problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 6(2), pages 261-275, December.
    23. Ambrosino, Daniela & Grazia Scutella, Maria, 2005. "Distribution network design: New problems and related models," European Journal of Operational Research, Elsevier, vol. 165(3), pages 610-624, September.
    24. Albareda-Sambola, Maria & Fernández, Elena & Saldanha-da-Gama, Francisco, 2011. "The facility location problem with Bernoulli demands," Omega, Elsevier, vol. 39(3), pages 335-345, June.
    25. Tuzun, Dilek & Burke, Laura I., 1999. "A two-phase tabu search approach to the location routing problem," European Journal of Operational Research, Elsevier, vol. 116(1), pages 87-99, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Allahyari, Somayeh & Salari, Majid & Vigo, Daniele, 2015. "A hybrid metaheuristic algorithm for the multi-depot covering tour vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 242(3), pages 756-768.
    2. Zhang, Zhenzhen & Liu, Mengyang & Lim, Andrew, 2015. "A memetic algorithm for the patient transportation problem," Omega, Elsevier, vol. 54(C), pages 60-71.
    3. Günther Zäpfel & Michael Bögl, 2016. "An adaptive structure of a hub-and-spoke system with direct and depot shipments in the case of volatile demand over time," Journal of Business Economics, Springer, vol. 86(7), pages 697-721, October.
    4. Sun, Li & Zhao, Lindu & Hou, Jing, 2015. "Optimization of postal express line network under mixed driving pattern of trucks," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 77(C), pages 147-169.
    5. 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.
    6. He, Yan & Wu, Tao & Zhang, Canrong & Liang, Zhe, 2015. "An improved MIP heuristic for the intermodal hub location problem," Omega, Elsevier, vol. 57(PB), pages 203-211.
    7. 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.
    8. Validi, Sahar & Bhattacharya, Arijit & Byrne, P.J., 2014. "A case analysis of a sustainable food supply chain distribution system—A multi-objective approach," International Journal of Production Economics, Elsevier, vol. 152(C), pages 71-87.
    9. Bieniek, Milena, 2015. "A note on the facility location problem with stochastic demands," Omega, Elsevier, vol. 55(C), pages 53-60.
    10. Gribkovskaia, Irina & Halskau, Oyvind & Kovalyov, Mikhail Y., 2015. "Minimizing takeoff and landing risk in helicopter pickup and delivery operations," Omega, Elsevier, vol. 55(C), pages 73-80.
    11. Qian, Fubin & Strusevich, Vitaly & Gribkovskaia, Irina & Halskau, Øyvind, 2015. "Minimization of passenger takeoff and landing risk in offshore helicopter transportation: Models, approaches and analysis," Omega, Elsevier, vol. 51(C), pages 93-106.
    12. Lin Zhou & Xu Wang & Lin Ni & Yun Lin, 2016. "Location-Routing Problem with Simultaneous Home Delivery and Customer’s Pickup for City Distribution of Online Shopping Purchases," Sustainability, MDPI, Open Access Journal, vol. 8(8), pages 1-20, August.
    13. Zare Mehrjerdi, Yahia & Nadizadeh, Ali, 2013. "Using greedy clustering method to solve capacitated location-routing problem with fuzzy demands," European Journal of Operational Research, Elsevier, vol. 229(1), pages 75-84.
    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. Klibi, Walid & Martel, Alain & Guitouni, Adel, 2016. "The impact of operations anticipations on the quality of stochastic location-allocation models," Omega, Elsevier, vol. 62(C), pages 19-33.
    16. Nadizadeh, Ali & Hosseini Nasab, Hasan, 2014. "Solving the dynamic capacitated location-routing problem with fuzzy demands by hybrid heuristic algorithm," European Journal of Operational Research, Elsevier, vol. 238(2), pages 458-470.
    17. repec:eee:transb:v:104:y:2017:i:c:p:17-35 is not listed on IDEAS
    18. Huang, Shan-Huen & Lin, Pei-Chun, 2015. "Vehicle routing–scheduling for municipal waste collection system under the “Keep Trash off the Ground” policy," Omega, Elsevier, vol. 55(C), pages 24-37.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jomega:v:40:y:2012:i:4:p:465-477. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/375/description#description .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.