IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v222y2012i1p17-30.html
   My bibliography  Save this article

Integer linear programming models for grid-based light post location problem

Author

Listed:
  • Noor-E-Alam, Md.
  • Mah, Andrew
  • Doucette, John

Abstract

Selecting optimal location is a key decision problem in business and engineering. This research focuses to develop mathematical models for a special type of location problems called grid-based location problems. It uses a real-world problem of placing lights in a park to minimize the amount of darkness and excess supply. The non-linear nature of the supply function (arising from the light physics) and heterogeneous demand distribution make this decision problem truly intractable to solve. We develop ILP models that are designed to provide the optimal solution for the light post problem: the total number of light posts, the location of each light post, and their capacities (i.e., brightness). Finally, the ILP models are implemented within a standard modeling language and solved with the CPLEX solver. Results show that the ILP models are quite efficient in solving moderately sized problems with a very small optimality gap.

Suggested Citation

  • Noor-E-Alam, Md. & Mah, Andrew & Doucette, John, 2012. "Integer linear programming models for grid-based light post location problem," European Journal of Operational Research, Elsevier, vol. 222(1), pages 17-30.
    • Handle: RePEc:eee:ejores:v:222:y:2012:i:1:p:17-30
    DOI: 10.1016/j.ejor.2012.04.032
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221712003402
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2012.04.032?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. Armann Ingolfsson & Susan Budge & Erhan Erkut, 2008. "Optimal ambulance location with random delays and travel times," Health Care Management Science, Springer, vol. 11(3), pages 262-274, September.
    2. Domschke, Wolfgang & Krispin, Gabriela, 1997. "Location and layout planning: a survey," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 8164, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    3. Canbolat, Mustafa S. & Wesolowsky, George O., 2010. "The rectilinear distance Weber problem in the presence of a probabilistic line barrier," European Journal of Operational Research, Elsevier, vol. 202(1), pages 114-121, April.
    4. Taniguchi, Eiichi & Noritake, Michihiko & Yamada, Tadashi & Izumitani, Toru, 1999. "Optimal size and location planning of public logistics terminals," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 35(3), pages 207-222, September.
    5. Bernard Gendron & Jean-Yves Potvin & Patrick Soriano, 2003. "A Tabu Search with Slope Scaling for the Multicommodity Capacitated Location Problem with Balancing Requirements," Annals of Operations Research, Springer, vol. 122(1), pages 193-217, September.
    6. Aytug, Haldun & Saydam, Cem, 2002. "Solving large-scale maximum expected covering location problems by genetic algorithms: A comparative study," European Journal of Operational Research, Elsevier, vol. 141(3), pages 480-494, September.
    7. Teixeira, Joao C. & Antunes, Antonio P., 2008. "A hierarchical location model for public facility planning," European Journal of Operational Research, Elsevier, vol. 185(1), pages 92-104, February.
    8. George O. Wesolowsky, 1972. "Rectangular Distance Location under the Minimax Optimality Criterion," Transportation Science, INFORMS, vol. 6(2), pages 103-113, May.
    9. Sue Abdinnour-Helm & M.A. Venkataramanan, 1998. "Solution approaches to hub location problems," Annals of Operations Research, Springer, vol. 78(0), pages 31-50, January.
    10. AltInel, I. Kuban & Durmaz, Engin & Aras, Necati & ÖzkIsacIk, Kerem Can, 2009. "A location-allocation heuristic for the capacitated multi-facility Weber problem with probabilistic customer locations," European Journal of Operational Research, Elsevier, vol. 198(3), pages 790-799, November.
    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. Zhang, Ce & Dong, Huijie & Xu, Yuanlu & Nick, Lucky, 2024. "Balancing Cost and Economic Efficiency: Consider the multi-purpose optimization of green energy market's function in Green energy interactive infrastructure," Energy, Elsevier, vol. 309(C).
    2. Zhang, Fan & Lv, Huitao & Xing, Qiang & Ji, Yanjie, 2024. "Deployment of battery-swapping stations: Integrating travel chain simulation and multi-objective optimization for delivery electric micromobility vehicles," Energy, Elsevier, vol. 290(C).
    3. Faiz, Tasnim Ibn & Noor-E-Alam, Md, 2019. "Data center supply chain configuration design: A two-stage decision approach," Socio-Economic Planning Sciences, Elsevier, vol. 66(C), pages 119-135.

    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. McCormack, Richard & Coates, Graham, 2015. "A simulation model to enable the optimization of ambulance fleet allocation and base station location for increased patient survival," European Journal of Operational Research, Elsevier, vol. 247(1), pages 294-309.
    2. Sagarkumar Hirpara & Monit Vaishnav & Pratik J. Parikh & Nan Kong & Priti Parikh, 2022. "Locating trauma centers considering patient safety," Health Care Management Science, Springer, vol. 25(2), pages 291-310, June.
    3. Rajagopalan, Hari K. & Saydam, Cem, 2009. "A minimum expected response model: Formulation, heuristic solution, and application," Socio-Economic Planning Sciences, Elsevier, vol. 43(4), pages 253-262, December.
    4. Farahani, Reza Zanjirani & Fallah, Samira & Ruiz, Rubén & Hosseini, Sara & Asgari, Nasrin, 2019. "OR models in urban service facility location: A critical review of applications and future developments," European Journal of Operational Research, Elsevier, vol. 276(1), pages 1-27.
    5. Pradhananga, Rojee & Taniguchi, Eiichi & Yamada, Tadashi & Qureshi, Ali Gul, 2014. "Bi-objective decision support system for routing and scheduling of hazardous materials," Socio-Economic Planning Sciences, Elsevier, vol. 48(2), pages 135-148.
    6. Ran Wei & Alan Murray, 2015. "Spatial uncertainty in harvest scheduling," Annals of Operations Research, Springer, vol. 232(1), pages 275-289, September.
    7. Srinivas, Sharan & Ramachandiran, Surya & Rajendran, Suchithra, 2022. "Autonomous robot-driven deliveries: A review of recent developments and future directions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 165(C).
    8. Canbolat, Mustafa S. & Wesolowsky, George O., 2012. "On the use of the Varignon frame for single facility Weber problems in the presence of convex barriers," European Journal of Operational Research, Elsevier, vol. 217(2), pages 241-247.
    9. Marco Migliore & Salvatore Amoroso & Valeria Cardaci & Mario Catalano, 2011. "The role of passenger modal shift nodes in the interaction between land use and transport system," ERSA conference papers ersa10p1606, European Regional Science Association.
    10. Nelas, José & Dias, Joana, 2020. "Optimal Emergency Vehicles Location: An approach considering the hierarchy and substitutability of resources," European Journal of Operational Research, Elsevier, vol. 287(2), pages 583-599.
    11. Jayaswal, Sachin & Vidyarthi, Navneet, 2013. "Capacitated Multiple Allocation Hub Location with Service Level Constraints for Multiple Consignment Classes," IIMA Working Papers WP2013-11-02, Indian Institute of Management Ahmedabad, Research and Publication Department.
    12. Soovin Yoon & Laura A. Albert, 2018. "An expected coverage model with a cutoff priority queue," Health Care Management Science, Springer, vol. 21(4), pages 517-533, December.
    13. Mark Horner & Michael Widener, 2011. "The effects of transportation network failure on people’s accessibility to hurricane disaster relief goods: a modeling approach and application to a Florida case study," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 59(3), pages 1619-1634, December.
    14. Wajid, Shayesta & Nezamuddin, N., 2023. "Capturing delays in response of emergency services in Delhi," Socio-Economic Planning Sciences, Elsevier, vol. 87(PA).
    15. Eric Delmelle & Jean-Claude Thill & Dominique Peeters & Isabelle Thomas, 2014. "A multi-period capacitated school location problem with modular equipment and closest assignment considerations," Journal of Geographical Systems, Springer, vol. 16(3), pages 263-286, July.
    16. Tammy Drezner & Zvi Drezner & Pawel Kalczynski, 2019. "A directional approach to gradual cover," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 70-93, April.
    17. Zvi Drezner & Vladimir Marianov & George O. Wesolowsky, 2016. "Maximizing the minimum cover probability by emergency facilities," Annals of Operations Research, Springer, vol. 246(1), pages 349-362, November.
    18. Kratica, Jozef & Stanimirovic, Zorica & Tosic, Dusan & Filipovic, Vladimir, 2007. "Two genetic algorithms for solving the uncapacitated single allocation p-hub median problem," European Journal of Operational Research, Elsevier, vol. 182(1), pages 15-28, October.
    19. Nilay Noyan, 2010. "Alternate risk measures for emergency medical service system design," Annals of Operations Research, Springer, vol. 181(1), pages 559-589, December.
    20. Westgate, Bradford S. & Woodard, Dawn B. & Matteson, David S. & Henderson, Shane G., 2016. "Large-network travel time distribution estimation for ambulances," European Journal of Operational Research, Elsevier, vol. 252(1), pages 322-333.

    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:222:y:2012:i:1:p:17-30. 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.