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Location-Routing Problems with Distance Constraints

Author

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  • Rosemary T. Berger

    (Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, Pennsylvania 18015)

  • Collette R. Coullard

    (School of Mathematics and Computer Science, Lake Superior State University, Sault Sainte Marie, Michigan 49783)

  • Mark S. Daskin

    (Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208)

Abstract

An important aspect of designing a distribution system is determining the locations of the facilities. For systems in which deliveries are made along multiple stop routes, the routing problem and location problem must be considered simultaneously. In this paper, a set-partitioning-based formulation of an uncapacitated location-routing model with distance constraints is presented. An alternate set of constraints is identified that significantly reduces the total number of constraints and dramatically improves the linear programming relaxation bound. A branch and price algorithm is developed to solve instances of the model. The algorithm provides optimal solutions in reasonable computation time for problems involving as many as 10 candidate facilities and 100 customers with various distance constraints.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ortrsc:v:41:y:2007:i:1:p:29-43
    DOI: 10.1287/trsc.1060.0156
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    References listed on IDEAS

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    1. Maria Rossana D. de Veluz & Anak Agung Ngurah Perwira Redi & Renato R. Maaliw & Satria Fadil Persada & Yogi Tri Prasetyo & Michael Nayat Young, 2023. "Scenario-Based Multi-Objective Location-Routing Model for Pre-Disaster Planning: A Philippine Case Study," Sustainability, MDPI, vol. 15(6), pages 1-33, March.
    2. 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.
    3. Sahar Validi & Arijit Bhattacharya & P. J. Byrne, 2020. "Sustainable distribution system design: a two-phase DoE-guided meta-heuristic solution approach for a three-echelon bi-objective AHP-integrated location-routing model," Annals of Operations Research, Springer, vol. 290(1), pages 191-222, July.
    4. 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.
    5. Capelle, Thomas & Cortés, Cristián E. & Gendreau, Michel & Rey, Pablo A. & Rousseau, Louis-Martin, 2019. "A column generation approach for location-routing problems with pickup and delivery," European Journal of Operational Research, Elsevier, vol. 272(1), pages 121-131.
    6. Arslan, Okan, 2021. "The location-or-routing problem," Transportation Research Part B: Methodological, Elsevier, vol. 147(C), pages 1-21.
    7. Michael Schneider & Michael Drexl, 2017. "A survey of the standard location-routing problem," Annals of Operations Research, Springer, vol. 259(1), pages 389-414, December.
    8. Zhi-Hai Zhang & Gemma Berenguer & Zuo-Jun (Max) Shen, 2015. "A Capacitated Facility Location Model with Bidirectional Flows," Transportation Science, INFORMS, vol. 49(1), pages 114-129, February.
    9. Drexl, M. & Schneider, M., 2014. "A Survey of the Standard Location-Routing Problem," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 65940, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    10. Paolo Gianessi & Laurent Alfandari & Lucas Létocart & Roberto Wolfler Calvo, 2016. "The Multicommodity-Ring Location Routing Problem," Transportation Science, INFORMS, vol. 50(2), pages 541-558, May.
    11. 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.
    12. Menezes, Mozart B.C. & Ruiz-Hernández, Diego & Verter, Vedat, 2016. "A rough-cut approach for evaluating location-routing decisions via approximation algorithms," Transportation Research Part B: Methodological, Elsevier, vol. 87(C), pages 89-106.
    13. Hyoshin (John) Park & Ali Haghani & Song Gao & Michael A. Knodler & Siby Samuel, 2018. "Anticipatory Dynamic Traffic Sensor Location Problems with Connected Vehicle Technologies," Service Science, INFORMS, vol. 52(6), pages 1299-1326, December.
    14. Ponboon, Sattrawut & Qureshi, Ali Gul & Taniguchi, Eiichi, 2016. "Branch-and-price algorithm for the location-routing problem with time windows," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 86(C), pages 1-19.
    15. Hunkar Toyoglu & Oya Ekin Karasan & Bahar Yetis Kara, 2011. "Distribution network design on the battlefield," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(3), pages 188-209, April.
    16. 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.
    17. Ahn, Jaemyung & de Weck, Olivier & Geng, Yue & Klabjan, Diego, 2012. "Column generation based heuristics for a generalized location routing problem with profits arising in space exploration," European Journal of Operational Research, Elsevier, vol. 223(1), pages 47-59.
    18. Walid Klibi & Francis Lasalle & Alain Martel & Soumia Ichoua, 2010. "The Stochastic Multiperiod Location Transportation Problem," Transportation Science, INFORMS, vol. 44(2), pages 221-237, May.

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