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Mathematical optimization models for reallocating and sharing health equipment in pandemic situations

Author

Listed:
  • Víctor Blanco

    (Universidad de Granada
    Universidad de Granada)

  • Ricardo Gázquez

    (Universidad de Granada
    Universidad de Granada)

  • Marina Leal

    (Universidad Miguel Hernández
    Universidad Miguel Hernández)

Abstract

In this paper we provide a mathematical programming based decision tool to optimally reallocate and share equipment between different units to efficiently equip hospitals in pandemic emergency situations under lack of resources. The approach is motivated by the COVID-19 pandemic in which many Heath National Systems were not able to satisfy the demand of ventilators, sanitary individual protection equipment or different human resources. Our tool is based in two main principles: (1) Part of the stock of equipment at a unit that is not needed (in near future) could be shared to other units; and (2) extra stock to be shared among the units in a region can be efficiently distributed taking into account the demand of the units. The decisions are taken with the aim of minimizing certain measures of the non-covered demand in a region where units are structured in a given network. The mathematical programming models that we provide are stochastic and multiperiod with different robust objective functions. Since the proposed models are computationally hard to solve, we provide a divide-et-conquer math-heuristic approach. We report the results of applying our approach to the COVID-19 case in different regions of Spain, highlighting some interesting conclusions of our analysis, such as the great increase of treated patients if the proposed redistribution tool is applied.

Suggested Citation

  • Víctor Blanco & Ricardo Gázquez & Marina Leal, 2023. "Mathematical optimization models for reallocating and sharing health equipment in pandemic situations," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 355-390, July.
    • Handle: RePEc:spr:topjnl:v:31:y:2023:i:2:d:10.1007_s11750-022-00643-3
    DOI: 10.1007/s11750-022-00643-3
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    1. Pun, Chi Seng & Wong, Hoi Ying, 2019. "A linear programming model for selection of sparse high-dimensional multiperiod portfolios," European Journal of Operational Research, Elsevier, vol. 273(2), pages 754-771.
    2. Conde, Eduardo & Leal, Marina & Puerto, Justo, 2018. "A minmax regret version of the time-dependent shortest path problem," European Journal of Operational Research, Elsevier, vol. 270(3), pages 968-981.
    3. Justo Puerto & Federica Ricca & Andrea Scozzari, 2018. "Extensive facility location problems on networks: an updated review," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 187-226, July.
    4. Michaud, Richard O. & Michaud, Robert O., 2008. "Efficient Asset Management: A Practical Guide to Stock Portfolio Optimization and Asset Allocation," OUP Catalogue, Oxford University Press, edition 2, number 9780195331912.
    5. Dimitris Bertsimas & Leonard Boussioux & Ryan Cory-Wright & Arthur Delarue & Vassilis Digalakis & Alexandre Jacquillat & Driss Lahlou Kitane & Galit Lukin & Michael Li & Luca Mingardi & Omid Nohadani , 2021. "From predictions to prescriptions: A data-driven response to COVID-19," Health Care Management Science, Springer, vol. 24(2), pages 253-272, June.
    6. Conde, Eduardo, 2007. "Minmax regret location-allocation problem on a network under uncertainty," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1025-1039, June.
    7. Daniel Garcia-Vicuña & Laida Esparza & Fermin Mallor, 2022. "Hospital preparedness during epidemics using simulation: the case of COVID-19," 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. 30(1), pages 213-249, March.
    8. Chowdhury, Priyabrata & Paul, Sanjoy Kumar & Kaisar, Shahriar & Moktadir, Md. Abdul, 2021. "COVID-19 pandemic related supply chain studies: A systematic review," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 148(C).
    9. Ann Melissa Campbell & Dieter Vandenbussche & William Hermann, 2008. "Routing for Relief Efforts," Transportation Science, INFORMS, vol. 42(2), pages 127-145, May.
    10. Victor Blanco & Justo Puerto & Safae El Haj Ben Ali, 2014. "Revisiting several problems and algorithms in continuous location with $$\ell _\tau $$ ℓ τ norms," Computational Optimization and Applications, Springer, vol. 58(3), pages 563-595, July.
    11. P. Baricelli & C. Lucas & E. Messina & G. Mitra, 1996. "A model for strategic planning under uncertainty," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 4(2), pages 361-384, December.
    12. Mahmoudi, Mohammad Reza & Baleanu, Dumitru & Mansor, Zulkefli & Tuan, Bui Anh & Pho, Kim-Hung, 2020. "Fuzzy clustering method to compare the spread rate of Covid-19 in the high risks countries," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    13. Benítez-Peña, Sandra & Carrizosa, Emilio & Guerrero, Vanesa & Jiménez-Gamero, M. Dolores & Martín-Barragán, Belén & Molero-Río, Cristina & Ramírez-Cobo, Pepa & Romero Morales, Dolores & Sillero-Denami, 2021. "On sparse ensemble methods: An application to short-term predictions of the evolution of COVID-19," European Journal of Operational Research, Elsevier, vol. 295(2), pages 648-663.
    14. Ye, Qing Chuan & Zhang, Yingqian & Dekker, Rommert, 2017. "Fair task allocation in transportation," Omega, Elsevier, vol. 68(C), pages 1-16.
    15. Aissi, Hassene & Bazgan, Cristina & Vanderpooten, Daniel, 2009. "Min-max and min-max regret versions of combinatorial optimization problems: A survey," European Journal of Operational Research, Elsevier, vol. 197(2), pages 427-438, September.
    16. Maleki, Mohsen & Mahmoudi, Mohammad Reza & Heydari, Mohammad Hossein & Pho, Kim-Hung, 2020. "Modeling and forecasting the spread and death rate of coronavirus (COVID-19) in the world using time series models," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    17. Ogryczak, Wlodzimierz, 2000. "Inequality measures and equitable approaches to location problems," European Journal of Operational Research, Elsevier, vol. 122(2), pages 374-391, April.
    18. Maria Albareda-Sambola & Antonio Alonso-Ayuso & Laureano Escudero & Elena Fernández & Yolanda Hinojosa & Celeste Pizarro-Romero, 2010. "A computational comparison of several formulations for the multi-period incremental service facility location problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 62-80, July.
    19. Sanjay Mehrotra & Hamed Rahimian & Masoud Barah & Fengqiao Luo & Karolina Schantz, 2020. "A model of supply‐chain decisions for resource sharing with an application to ventilator allocation to combat COVID‐19," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(5), pages 303-320, August.
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