IDEAS home Printed from https://ideas.repec.org/a/kap/netspa/v23y2023i3d10.1007_s11067-023-09589-w.html
   My bibliography  Save this article

Equilibrium-based Workload Balancing for Robust Emergency Response Operation

Author

Listed:
  • Khaled Abdelghany

    (Southern Methodist University)

  • Parya Roustaee

    (Southern Methodist University)

  • Ahmed Hassan

    (Cairo University)

  • Aline Karak

    (Southern Methodist University)

  • Mohammad Khodayar

    (Southern Methodist University)

Abstract

This paper presents an equilibrium-based modeling framework for emergency response (ER) workload balancing for robust operations in metropolitan areas. The problem is formulated as a non-linear mathematical program (NLP), which determines the optimal maximum workload for each ER station such that the weighted sum of the area-wide expected response time and its variation is minimized. The concept of Marginal Cost of Uncertainty (MCU) is introduced to measure the impact of a station's workload increase on the robustness of the area-wide service performance. The solution of the NLP is proved to be equivalent to a state of equilibrium in which all stations have a minimum MCU. An iterative solution methodology is developed, which adopts a modified version of the Frank-Wolfe decomposition algorithm for convex optimization. The workload is iteratively balanced among adjacent stations until the state of equilibrium is achieved. At equilibrium, no station can reduce its MCU value by unilaterally shifting a part of its workload to any other station(s) in the area. The developed framework is applied to determine the optimal workload balancing strategy for 58 fire stations serving the City of Dallas. The framework is shown to enhance the robustness of the ER service performance especially in situations with imbalanced workloads.

Suggested Citation

  • Khaled Abdelghany & Parya Roustaee & Ahmed Hassan & Aline Karak & Mohammad Khodayar, 2023. "Equilibrium-based Workload Balancing for Robust Emergency Response Operation," Networks and Spatial Economics, Springer, vol. 23(3), pages 715-753, September.
    • Handle: RePEc:kap:netspa:v:23:y:2023:i:3:d:10.1007_s11067-023-09589-w
    DOI: 10.1007/s11067-023-09589-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11067-023-09589-w
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11067-023-09589-w?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. 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. Current, John & Min, Hokey & Schilling, David, 1990. "Multiobjective analysis of facility location decisions," European Journal of Operational Research, Elsevier, vol. 49(3), pages 295-307, December.
    3. Beraldi, P. & Bruni, M. E. & Conforti, D., 2004. "Designing robust emergency medical service via stochastic programming," European Journal of Operational Research, Elsevier, vol. 158(1), pages 183-193, October.
    4. Xueping Li & Zhaoxia Zhao & Xiaoyan Zhu & Tami Wyatt, 2011. "Covering models and optimization techniques for emergency response facility location and planning: a review," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(3), pages 281-310, December.
    5. Ming Liu & Dapeng Yang & Fengxia Hao, 2017. "Optimization for the Locations of Ambulances under Two-Stage Life Rescue in the Emergency Medical Service: A Case Study in Shanghai, China," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-14, August.
    6. Dimitris Bertsimas & Aurélie Thiele, 2006. "A Robust Optimization Approach to Inventory Theory," Operations Research, INFORMS, vol. 54(1), pages 150-168, February.
    7. Matthew S. Maxwell & Eric Cao Ni & Chaoxu Tong & Shane G. Henderson & Huseyin Topaloglu & Susan R. Hunter, 2014. "A Bound on the Performance of an Optimal Ambulance Redeployment Policy," Operations Research, INFORMS, vol. 62(5), pages 1014-1027, October.
    8. Marsh, Michael T. & Schilling, David A., 1994. "Equity measurement in facility location analysis: A review and framework," European Journal of Operational Research, Elsevier, vol. 74(1), pages 1-17, April.
    9. G Barbarosoǧlu & Y Arda, 2004. "A two-stage stochastic programming framework for transportation planning in disaster response," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(1), pages 43-53, January.
    10. John M. Mulvey & Robert J. Vanderbei & Stavros A. Zenios, 1995. "Robust Optimization of Large-Scale Systems," Operations Research, INFORMS, vol. 43(2), pages 264-281, April.
    11. Huang, Yongxi & Fan, Yueyue & Cheu, Ruey Long, 2008. "Optimal Allocation of Multiple Emergency Service Resources for Protection of Critical Transportation Infrastructure," Institute of Transportation Studies, Working Paper Series qt83m87669, Institute of Transportation Studies, UC Davis.
    12. Leknes, Håkon & Aartun, Eirik Skorge & Andersson, Henrik & Christiansen, Marielle & Granberg, Tobias Andersson, 2017. "Strategic ambulance location for heterogeneous regions," European Journal of Operational Research, Elsevier, vol. 260(1), pages 122-133.
    13. van Barneveld, T.C. & Bhulai, S. & van der Mei, R.D., 2016. "The effect of ambulance relocations on the performance of ambulance service providers," European Journal of Operational Research, Elsevier, vol. 252(1), pages 257-269.
    14. Schmid, Verena, 2012. "Solving the dynamic ambulance relocation and dispatching problem using approximate dynamic programming," European Journal of Operational Research, Elsevier, vol. 219(3), pages 611-621.
    Full references (including those not matched with items on IDEAS)

    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. Bélanger, V. & Ruiz, A. & Soriano, P., 2019. "Recent optimization models and trends in location, relocation, and dispatching of emergency medical vehicles," European Journal of Operational Research, Elsevier, vol. 272(1), pages 1-23.
    2. Enayati, Shakiba & Mayorga, Maria E. & Rajagopalan, Hari K. & Saydam, Cem, 2018. "Real-time ambulance redeployment approach to improve service coverage with fair and restricted workload for EMS providers," Omega, Elsevier, vol. 79(C), pages 67-80.
    3. Amir Ali Nasrollahzadeh & Amin Khademi & Maria E. Mayorga, 2018. "Real-Time Ambulance Dispatching and Relocation," Manufacturing & Service Operations Management, INFORMS, vol. 20(3), pages 467-480, July.
    4. Martin van Buuren & Caroline Jagtenberg & Thije van Barneveld & Rob van der Mei & Sandjai Bhulai, 2018. "Ambulance Dispatch Center Pilots Proactive Relocation Policies to Enhance Effectiveness," Interfaces, INFORMS, vol. 48(3), pages 235-246, June.
    5. Carvalho, A.S. & Captivo, M.E. & Marques, I., 2020. "Integrating the ambulance dispatching and relocation problems to maximize system’s preparedness," European Journal of Operational Research, Elsevier, vol. 283(3), pages 1064-1080.
    6. Areej Alhothali & Budoor Alwated & Kamil Faisal & Sultanah Alshammari & Reem Alotaibi & Nusaybah Alghanmi & Omaimah Bamasag & Manal Bin Yamin, 2022. "Location-Allocation Model to Improve the Distribution of COVID-19 Vaccine Centers in Jeddah City, Saudi Arabia," IJERPH, MDPI, vol. 19(14), pages 1-21, July.
    7. Yanyan Wang & Baiqing Sun, 2022. "Multiperiod optimal emergency material allocation considering road network damage and risk under uncertain conditions," Operational Research, Springer, vol. 22(3), pages 2173-2208, July.
    8. van Barneveld, Thije & Jagtenberg, Caroline & Bhulai, Sandjai & van der Mei, Rob, 2018. "Real-time ambulance relocation: Assessing real-time redeployment strategies for ambulance relocation," Socio-Economic Planning Sciences, Elsevier, vol. 62(C), pages 129-142.
    9. Bertsimas, Dimitris & Ng, Yeesian, 2019. "Robust and stochastic formulations for ambulance deployment and dispatch," European Journal of Operational Research, Elsevier, vol. 279(2), pages 557-571.
    10. Drent, Collin & Keizer, Minou Olde & Houtum, Geert-Jan van, 2020. "Dynamic dispatching and repositioning policies for fast-response service networks," European Journal of Operational Research, Elsevier, vol. 285(2), pages 583-598.
    11. Jian Wang & Yin Wang & Mingzhu Yu, 2022. "A multi-period ambulance location and allocation problem in the disaster," Journal of Combinatorial Optimization, Springer, vol. 43(5), pages 909-932, July.
    12. Luo, Weicong & Yao, Jing & Mitchell, Richard & Zhang, Xiaoxiang & Li, Wenqiang, 2022. "Locating emergency medical services to reduce urban-rural inequalities," Socio-Economic Planning Sciences, Elsevier, vol. 84(C).
    13. Shishebori, Davood & Yousefi Babadi, Abolghasem, 2015. "Robust and reliable medical services network design under uncertain environment and system disruptions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 77(C), pages 268-288.
    14. Jian Wang & Yin Wang & Mingzhu Yu, 0. "A multi-period ambulance location and allocation problem in the disaster," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-24.
    15. Minjiao Zhang & Simge Küçükyavuz & Saumya Goel, 2014. "A Branch-and-Cut Method for Dynamic Decision Making Under Joint Chance Constraints," Management Science, INFORMS, vol. 60(5), pages 1317-1333, May.
    16. Alem, Douglas & Clark, Alistair & Moreno, Alfredo, 2016. "Stochastic network models for logistics planning in disaster relief," European Journal of Operational Research, Elsevier, vol. 255(1), pages 187-206.
    17. Li, Lingfeng & Jin, Mingzhou & Zhang, Li, 2011. "Sheltering network planning and management with a case in the Gulf Coast region," International Journal of Production Economics, Elsevier, vol. 131(2), pages 431-440, June.
    18. Seyed Babak Ebrahimi & Ehsan Bagheri, 2022. "A multi-objective formulation for the closed-loop plastic supply chain under uncertainty," Operational Research, Springer, vol. 22(5), pages 4725-4768, November.
    19. 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.
    20. Jagtenberg, C.J. & van den Berg, P.L. & van der Mei, R.D., 2017. "Benchmarking online dispatch algorithms for Emergency Medical Services," European Journal of Operational Research, Elsevier, vol. 258(2), pages 715-725.

    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:kap:netspa:v:23:y:2023:i:3:d:10.1007_s11067-023-09589-w. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.