IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i17p2165-d629373.html
   My bibliography  Save this article

On the Modelling of Emergency Ambulance Trips: The Case of the Žilina Region in Slovakia

Author

Listed:
  • Ľuboš Buzna

    (Department of International Research Projects—ERAdiate+, University of Žilina, 010 26 Žilina, Slovakia
    Department of Mathematical Methods and Operations Research, Faculty of Management Science and Informatics, University of Žilina, 010 26 Žilina, Slovakia)

  • Peter Czimmermann

    (Department of Mathematical Methods and Operations Research, Faculty of Management Science and Informatics, University of Žilina, 010 26 Žilina, Slovakia)

Abstract

The efficient operation of emergency medical services is critical for any society. Typically, optimisation and simulation models support decisions on emergency ambulance stations’ locations and ambulance management strategies. Essential inputs for such models are the spatiotemporal characteristics of ambulance trips. Access to data on the movements of ambulances is limited, and therefore modelling efforts often rely on assumptions (e.g., the Euclidean distance is used as a surrogate of the ambulance travel time; the closest available ambulance is dispatched to a call; or the travel time estimates, offered by application programming interfaces for ordinary vehicles, are applied to ambulances). These simplifying assumptions are often based on incomplete data or common sense without being fully supported by the evidence. Thus, data-driven research to model ambulance trips is required. We investigated a unique dataset of global positioning system-based measurements collected from seventeen emergency ambulances over three years. We enriched the data by exploring external sources and designed a rule-based procedure to extract ambulance trips for emergency cases. Trips were split into training and test sets. The training set was used to develop a series of statistical models that capture the spatiotemporal characteristics of emergency ambulance trips. The models were used to generate synthetic ambulance trips, and those were compared with the test set to decide which models are the most suitable and to evaluate degrees to which they fit the statistical properties of real-world trips. As confirmed by the low values of the Kullback–Leibler divergence ( 0.004 – 0.229 ) and by the Kolmogorov–Smirnov test at the significance level of 0.05 , we found a very good fit between the probability distributions of spatiotemporal properties of synthetic and real trips. A reasonable modelling choice is a model where the exponential dependency on the population density is used to locate emergency cases, emergency cases are allocated to hospitals following empirical probabilities, and ambulances are routed using the fastest paths. The models we developed can be used in optimisations and simulations to improve their validity.

Suggested Citation

  • Ľuboš Buzna & Peter Czimmermann, 2021. "On the Modelling of Emergency Ambulance Trips: The Case of the Žilina Region in Slovakia," Mathematics, MDPI, vol. 9(17), pages 1-30, September.
  • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2165-:d:629373
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/17/2165/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/9/17/2165/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Alan T. Murray, 2015. "Fire Station Siting," International Series in Operations Research & Management Science, in: H. A. Eiselt & Vladimir Marianov (ed.), Applications of Location Analysis, edition 1, chapter 12, pages 293-306, Springer.
    2. Brotcorne, Luce & Laporte, Gilbert & Semet, Frederic, 2003. "Ambulance location and relocation models," European Journal of Operational Research, Elsevier, vol. 147(3), pages 451-463, June.
    3. Susan Budge & Armann Ingolfsson & Dawit Zerom, 2010. "Empirical Analysis of Ambulance Travel Times: The Case of Calgary Emergency Medical Services," Management Science, INFORMS, vol. 56(4), pages 716-723, April.
    4. Peter Kolesar & Warren Walker & Jack Hausner, 1975. "Determining the Relation between Fire Engine Travel Times and Travel Distances in New York City," Operations Research, INFORMS, vol. 23(4), pages 614-627, August.
    5. 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.
    6. C. J. Jagtenberg & S. Bhulai & R. D. Mei, 2017. "Optimal Ambulance Dispatching," International Series in Operations Research & Management Science, in: Richard J. Boucherie & Nico M. van Dijk (ed.), Markov Decision Processes in Practice, chapter 0, pages 269-291, Springer.
    7. C. J. Jagtenberg & S. Bhulai & R. D. Mei, 2017. "Dynamic ambulance dispatching: is the closest-idle policy always optimal?," Health Care Management Science, Springer, vol. 20(4), pages 517-531, December.
    8. Knight, V.A. & Harper, P.R. & Smith, L., 2012. "Ambulance allocation for maximal survival with heterogeneous outcome measures," Omega, Elsevier, vol. 40(6), pages 918-926.
    9. McLay, Laura A. & Boone, Edward L. & Brooks, J. Paul, 2012. "Analyzing the volume and nature of emergency medical calls during severe weather events using regression methodologies," Socio-Economic Planning Sciences, Elsevier, vol. 46(1), pages 55-66.
    10. Dirk Degel & Lara Wiesche & Sebastian Rachuba & Brigitte Werners, 2015. "Time-dependent ambulance allocation considering data-driven empirically required coverage," Health Care Management Science, Springer, vol. 18(4), pages 444-458, December.
    11. Laura McLay & Maria Mayorga, 2010. "Evaluating emergency medical service performance measures," Health Care Management Science, Springer, vol. 13(2), pages 124-136, June.
    12. Ľudmila Jánošíková & Marek Kvet & Peter Jankovič & Lýdia Gábrišová, 2019. "An optimization and simulation approach to emergency stations relocation," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(3), pages 737-758, September.
    13. Erhan Erkut & Armann Ingolfsson & Güneş Erdoğan, 2008. "Ambulance location for maximum survival," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(1), pages 42-58, February.
    14. T. C. Barneveld & S. Bhulai & R. D. Mei, 2017. "A dynamic ambulance management model for rural areas," Health Care Management Science, Springer, vol. 20(2), pages 165-186, June.
    15. 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.
    16. Degel, Dirk & Wiesche, Lara & Rachuba, Sebastian & Werners, Brigitte, 2014. "Reorganizing an existing volunteer fire station network in Germany," Socio-Economic Planning Sciences, Elsevier, vol. 48(2), pages 149-157.
    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. Yoon, Soovin & Albert, Laura A., 2021. "Dynamic dispatch policies for emergency response with multiple types of vehicles," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).
    3. Dmitrii Usanov & G.A. Guido Legemaate & Peter M. van de Ven & Rob D. van der Mei, 2019. "Fire truck relocation during major incidents," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(2), pages 105-122, March.
    4. 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.
    5. 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.
    6. Wang, Wei & Wang, Shuaian & Zhen, Lu & Qu, Xiaobo, 2022. "EMS location-allocation problem under uncertainties," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 168(C).
    7. Thije van Barneveld, 2016. "The Minimum Expected Penalty Relocation Problem for the Computation of Compliance Tables for Ambulance Vehicles," INFORMS Journal on Computing, INFORMS, vol. 28(2), pages 370-384, May.
    8. Wang, Wei & Wu, Shining & Wang, Shuaian & Zhen, Lu & Qu, Xiaobo, 2021. "Emergency facility location problems in logistics: Status and perspectives," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 154(C).
    9. Shayesta Wajid & N. Nezamuddin, 2023. "Optimizing emergency services for road safety using a decomposition method: a case study of Delhi," OPSEARCH, Springer;Operational Research Society of India, vol. 60(1), pages 155-173, March.
    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. Amir Ardestani-Jaafari & Beste Kucukyazici, 2022. "Improving Patient Transfer Protocols for Regional Stroke Networks," Management Science, INFORMS, vol. 68(9), pages 6610-6633, September.
    12. Wajid, Shayesta & Nezamuddin, N., 2023. "Capturing delays in response of emergency services in Delhi," Socio-Economic Planning Sciences, Elsevier, vol. 87(PA).
    13. 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.
    14. Nilay Noyan, 2010. "Alternate risk measures for emergency medical service system design," Annals of Operations Research, Springer, vol. 181(1), pages 559-589, December.
    15. Wajid, Shayesta & Nezamuddin, N., 2022. "A robust survival model for emergency medical services in Delhi, India," Socio-Economic Planning Sciences, Elsevier, vol. 83(C).
    16. Bélanger, V. & Lanzarone, E. & Nicoletta, V. & Ruiz, A. & Soriano, P., 2020. "A recursive simulation-optimization framework for the ambulance location and dispatching problem," European Journal of Operational Research, Elsevier, vol. 286(2), pages 713-725.
    17. Jenkins, Phillip R. & Lunday, Brian J. & Robbins, Matthew J., 2020. "Robust, multi-objective optimization for the military medical evacuation location-allocation problem," Omega, Elsevier, vol. 97(C).
    18. 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.
    19. 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.
    20. Ibrahim Çapar & Sharif H Melouk & Burcu B Keskin, 2017. "Alternative metrics to measure EMS system performance," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(7), pages 792-808, July.

    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:gam:jmathe:v:9:y:2021:i:17:p:2165-:d:629373. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.