IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v247y2015i1p27-36.html
   My bibliography  Save this article

A minimum cost network flow model for the maximum covering and patrol routing problem

Author

Listed:
  • Dewil, R.
  • Vansteenwegen, P.
  • Cattrysse, D.
  • Van Oudheusden, D.

Abstract

This paper shows how the maximum covering and patrol routing problem (MCPRP) can be modeled as a minimum cost network flow problem (MCNFP). Based on the MCNFP model, all available benchmark instances of the MCPRP can be solved to optimality in less than 0.4s per instance. It is furthermore shown that several practical additions to the MCPRP, such as different start and end locations of patrol cars and overlapping shift durations can be modeled by a multi-commodity minimum cost network flow model and solved to optimality in acceptable computational times given the sizes of practical instances.

Suggested Citation

  • Dewil, R. & Vansteenwegen, P. & Cattrysse, D. & Van Oudheusden, D., 2015. "A minimum cost network flow model for the maximum covering and patrol routing problem," European Journal of Operational Research, Elsevier, vol. 247(1), pages 27-36.
    • Handle: RePEc:eee:ejores:v:247:y:2015:i:1:p:27-36
    DOI: 10.1016/j.ejor.2015.05.067
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221715004798
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2015.05.067?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Richard D. McBride, 1998. "Advances in Solving the Multicommodity-Flow Problem," Interfaces, INFORMS, vol. 28(2), pages 32-41, April.
    2. Divsalar, A. & Vansteenwegen, P. & Sörensen, K. & Cattrysse, D., 2014. "A memetic algorithm for the orienteering problem with hotel selection," European Journal of Operational Research, Elsevier, vol. 237(1), pages 29-49.
    3. H. A. Eiselt & Michel Gendreau & Gilbert Laporte, 1995. "Arc Routing Problems, Part II: The Rural Postman Problem," Operations Research, INFORMS, vol. 43(3), pages 399-414, June.
    4. Keskin, Burcu B. & Li, Shirley (Rong) & Steil, Dana & Spiller, Sarah, 2012. "Analysis of an integrated maximum covering and patrol routing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(1), pages 215-232.
    5. H. A. Eiselt & Michel Gendreau & Gilbert Laporte, 1995. "Arc Routing Problems, Part I: The Chinese Postman Problem," Operations Research, INFORMS, vol. 43(2), pages 231-242, April.
    6. Fred Glover & Darwin Klingman & Nancy Phillips, 1990. "Netform Modeling and Applications," Interfaces, INFORMS, vol. 20(4), pages 7-27, August.
    7. J. A. Tomlin, 1966. "Minimum-Cost Multicommodity Network Flows," Operations Research, INFORMS, vol. 14(1), pages 45-51, February.
    8. Divsalar, A. & Vansteenwegen, P. & Cattrysse, D., 2013. "A variable neighborhood search method for the orienteering problem with hotel selection," International Journal of Production Economics, Elsevier, vol. 145(1), pages 150-160.
    9. Vansteenwegen, Pieter & Souffriau, Wouter & Oudheusden, Dirk Van, 2011. "The orienteering problem: A survey," European Journal of Operational Research, Elsevier, vol. 209(1), pages 1-10, February.
    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. Paul A. Chircop & Timothy J. Surendonk & Menkes H. L. van den Briel & Toby Walsh, 2022. "On routing and scheduling a fleet of resource-constrained vessels to provide ongoing continuous patrol coverage," Annals of Operations Research, Springer, vol. 312(2), pages 723-760, May.
    2. Sukanya Samanta & Goutam Sen & Soumya Kanti Ghosh, 2022. "A literature review on police patrolling problems," Annals of Operations Research, Springer, vol. 316(2), pages 1063-1106, September.
    3. Xiuqiao Sun & Jian Wang & Weitiao Wu & Wenjia Liu, 2018. "Genetic Algorithm for Optimizing Routing Design and Fleet Allocation of Freeway Service Overlapping Patrol," Sustainability, MDPI, vol. 10(11), pages 1-15, November.
    4. Chen, Xinyuan & Wu, Shining & Liu, Yannick & Wu, Weiwei & Wang, Shuaian, 2022. "A patrol routing problem for maritime Crime-Fighting," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 168(C).
    5. Yuchen Luo & Bruce Golden & Rui Zhang, 2023. "The Hot Spot Coverage Patrol Problem: Formulations and Solution Approaches," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1286-1307, November.
    6. Timothy J. Surendonk & Paul A. Chircop, 2020. "On the computational complexity of the patrol boat scheduling problem with complete coverage," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(4), pages 289-299, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kotiloglu, S. & Lappas, T. & Pelechrinis, K. & Repoussis, P.P., 2017. "Personalized multi-period tour recommendations," Tourism Management, Elsevier, vol. 62(C), pages 76-88.
    2. Gunawan, Aldy & Lau, Hoong Chuin & Vansteenwegen, Pieter, 2016. "Orienteering Problem: A survey of recent variants, solution approaches and applications," European Journal of Operational Research, Elsevier, vol. 255(2), pages 315-332.
    3. Maryam Ataei & Ali Divsalar & Morteza Saberi, 2024. "The bi-objective orienteering problem with hotel selection: an integrated text mining optimisation approach," Information Technology and Management, Springer, vol. 25(3), pages 247-275, September.
    4. Ruiz-Meza, José & Montoya-Torres, Jairo R., 2022. "A systematic literature review for the tourist trip design problem: Extensions, solution techniques and future research lines," Operations Research Perspectives, Elsevier, vol. 9(C).
    5. Archetti, Claudia & Bertazzi, Luca & Laganà, Demetrio & Vocaturo, Francesca, 2017. "The Undirected Capacitated General Routing Problem with Profits," European Journal of Operational Research, Elsevier, vol. 257(3), pages 822-833.
    6. Colombi, Marco & Mansini, Renata, 2014. "New results for the Directed Profitable Rural Postman Problem," European Journal of Operational Research, Elsevier, vol. 238(3), pages 760-773.
    7. Arbib, Claudio & Servilio, Mara & Archetti, Claudia & Speranza, M. Grazia, 2014. "The directed profitable location Rural Postman Problem," European Journal of Operational Research, Elsevier, vol. 236(3), pages 811-819.
    8. Akbari, Vahid & Salman, F. Sibel, 2017. "Multi-vehicle synchronized arc routing problem to restore post-disaster network connectivity," European Journal of Operational Research, Elsevier, vol. 257(2), pages 625-640.
    9. Barbara De Rosa & Gennaro Improta & Gianpaolo Ghiani & Roberto Musmanno, 2002. "The Arc Routing and Scheduling Problem with Transshipment," Transportation Science, INFORMS, vol. 36(3), pages 301-313, August.
    10. Ghiani, Gianpaolo & Improta, Gennaro, 2000. "An efficient transformation of the generalized vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 122(1), pages 11-17, April.
    11. Angel Corberán & Gustavo Mejía & José M. Sanchis, 2005. "New Results on the Mixed General Routing Problem," Operations Research, INFORMS, vol. 53(2), pages 363-376, April.
    12. Lin, Jun & Qian, Yanjun & Cui, Wentian & Goh, Thong Ngee, 2015. "An effective approach for scheduling coupled activities in development projects," European Journal of Operational Research, Elsevier, vol. 243(1), pages 97-108.
    13. Jesica Armas & Peter Keenan & Angel A. Juan & Seán McGarraghy, 2019. "Solving large-scale time capacitated arc routing problems: from real-time heuristics to metaheuristics," Annals of Operations Research, Springer, vol. 273(1), pages 135-162, February.
    14. Chefi Triki, 2017. "Solving the Periodic Edge Routing Problem in the Municipal Waste Collection," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(03), pages 1-13, June.
    15. Luc Muyldermans & Patrick Beullens & Dirk Cattrysse & Dirk Van Oudheusden, 2005. "Exploring Variants of 2-Opt and 3-Opt for the General Routing Problem," Operations Research, INFORMS, vol. 53(6), pages 982-995, December.
    16. Fung, Richard Y.K. & Liu, Ran & Jiang, Zhibin, 2013. "A memetic algorithm for the open capacitated arc routing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 50(C), pages 53-67.
    17. Yuhui Sun & Wei Yu & Zhaohui Liu, 2023. "Approximation algorithms for some min–max and minimum stacker crane cover problems," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-25, January.
    18. Li, Jiliu & Qin, Hu & Shen, Huaxiao & Tsui, Kwok Leung, 2019. "The unilateral transportation problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 132(C), pages 1-29.
    19. Muyldermans, L. & Cattrysse, D. & Van Oudheusden, D. & Lotan, T., 2002. "Districting for salt spreading operations," European Journal of Operational Research, Elsevier, vol. 139(3), pages 521-532, June.
    20. Freeman, Nickolas K. & Keskin, Burcu B. & Çapar, İbrahim, 2018. "Attractive orienteering problem with proximity and timing interactions," European Journal of Operational Research, Elsevier, vol. 266(1), pages 354-370.

    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:ejores:v:247:y:2015:i:1:p:27-36. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.