Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2023 Nov 1;310(3):1249-1272.
doi: 10.1016/j.ejor.2023.03.032. Epub 2023 Apr 20.

Fair-split distribution of multi-dose vaccines with prioritized age groups and dynamic demand: The case study of COVID-19

Behnam Vahdani  1 , Mehrdad Mohammadi  1   2 , Simon Thevenin  3 , Michel Gendreau  4 , Alexandre Dolgui  3 , Patrick Meyer  1
Affiliations

Fair-split distribution of multi-dose vaccines with prioritized age groups and dynamic demand: The case study of COVID-19

Behnam Vahdani et al. Eur J Oper Res. .

Abstract

The emergence of the SARS-CoV-2 virus and new viral variations with higher transmission and mortality rates have highlighted the urgency to accelerate vaccination to mitigate the morbidity and mortality of the COVID-19 pandemic. For this purpose, this paper formulates a new multi-vaccine, multi-depot location-inventory-routing problem for vaccine distribution. The proposed model addresses a wide variety of vaccination concerns: prioritizing age groups, fair distribution, multi-dose injection, dynamic demand, etc. To solve large-size instances of the model, we employ a Benders decomposition algorithm with a number of acceleration techniques. To monitor the dynamic demand of vaccines, we propose a new adjusted susceptible-infectious-recovered (SIR) epidemiological model, where infected individuals are tested and quarantined. The solution to the optimal control problem dynamically allocates the vaccine demand to reach the endemic equilibrium point. Finally, to illustrate the applicability and performance of the proposed model and solution approach, the paper reports extensive numerical experiments on a real case study of the vaccination campaign in France. The computational results show that the proposed Benders decomposition algorithm is 12 times faster, and its solutions are, on average, 16% better in terms of quality than the Gurobi solver under a limited CPU time. In terms of vaccination strategies, our results suggest that delaying the recommended time interval between doses of injection by a factor of 1.5 reduces the unmet demand up to 50%. Furthermore, we observed that the mortality is a convex function of fairness and an appropriate level of fairness should be adapted through the vaccination.

Keywords: Benders decomposition; Distribution; Dynamic demand; Fairness; Vaccine distribution.

PubMed Disclaimer

Figures

Fig. 1
Fig. 1
The SIR model.
Fig. 2
Fig. 2
BD’s flowchart.
Fig. 3
Fig. 3
The case study representing different regions with corresponding population indices.
Fig. 4
Fig. 4
The outcomes of the dynamic optimization model.
Fig. 5
Fig. 5
Comparison between ABD and GRB.
Fig. 6
Fig. 6
Impact of minimum percentage of demand to be met on total cost, inventory, and unmet demand.
Fig. 7
Fig. 7
Impact of the maximum supply of vaccines on total cost, inventory, and unmet demand.
Fig. 8
Fig. 8
Impact of inventory holding capacity on total cost, inventory, and unmet demand.
Fig. 9
Fig. 9
Impact of inventory holding cost on total cost, inventory, and unmet demand.
Fig. 10
Fig. 10
Impact of demand on total cost, inventory, and unmet demand.
Fig. 11
Fig. 11
Impact of the time interval between two doses injection on total cost, inventory, and unmet demand.
Fig. 12
Fig. 12
Impact of fairness service level gap on the unmet demand.
Fig. 13
Fig. 13
Impact of unmet cost on the objective function and the amount of unmet demand.
See this image and copyright information in PMC

References

    1. Abbasi, B., Fadaki, M., Kokshagina, O., Saeed, N., & Chhetri, P. (2020). Modeling vaccine allocations in the COVID-19 pandemic: A case study in Australia. Available at SSRN 3744520.
    1. Abou-Ismail A. Compartmental models of the COVID-19 pandemic for physicians and physician-scientists. SN Comprehensive Clinical Medicine. 2020;2:852–858. - PMC - PubMed
    1. Ahmadzadeh E., Vahdani B. A location-inventory-pricing model in a closed loop supply chain network with correlated demands and shortages under a periodic review system. Computers and Chemical Engineering. 2017;101:148–166.
    1. Alam S.T., Ahmed S., Ali S.M., Sarker S., Kabir G., et al. Challenges to COVID-19 vaccine supply chain: Implications for sustainable development goals. International Journal of Production Economics. 2021;239:108193. - PMC - PubMed
    1. Alcaraz G.G., Vargas-De-León C. Modeling control strategies for influenza a H1N1 epidemics: SIR models. Revista Mexicana de Física. 2012;58(1):37–43.

LinkOut - more resources