Vaccine and Test Kit Distribution
Vaccine and Test Kit Distribution
Embedded Files
● Full paper on arXiv (PDF) [1]
● Full paper on arXiv (PDF) [1]
Problem Definition
Problem Definition
Speeding up testing and vaccination is essential to controlling the coronavirus disease 2019 (COVID-19) pandemic that has became a global health crisis. In this paper, we develop mathematical frameworks for optimizing locations of distribution centers and plans for distributing resources such as test kits and vaccines under spatiotemporal uncertainties of infection and demand trends. We aim to balance between operational cost (including costs of deploying facilities, shipping and storage) and quality of service (reflected by delivery speed and demand coverage), while ensuring equity and fairness of resource distribution based on historical infection data and demographics of estimated demand.
Speeding up testing and vaccination is essential to controlling the coronavirus disease 2019 (COVID-19) pandemic that has became a global health crisis. In this paper, we develop mathematical frameworks for optimizing locations of distribution centers and plans for distributing resources such as test kits and vaccines under spatiotemporal uncertainties of infection and demand trends. We aim to balance between operational cost (including costs of deploying facilities, shipping and storage) and quality of service (reflected by delivery speed and demand coverage), while ensuring equity and fairness of resource distribution based on historical infection data and demographics of estimated demand.
Methodology and Results
Methodology and Results
Using weighted multiple objectives, we formulate a stochastic integer program and also seek robust solutions against the distributional ambiguity of demand. For the latter, we propose a distributionally robust optimization model using a moment ambiguity set, and derive monolithic reformulations depending on specific forms of this set. We compare different approaches by solving instances generated using real COVID-19 infection data for distributing vaccines and test kits over the United States and the state of Michigan, respectively. We demonstrate results over distinct phases of the pandemic to estimate cost and speed of resource distribution depending on the scales and coverage.
Using weighted multiple objectives, we formulate a stochastic integer program and also seek robust solutions against the distributional ambiguity of demand. For the latter, we propose a distributionally robust optimization model using a moment ambiguity set, and derive monolithic reformulations depending on specific forms of this set. We compare different approaches by solving instances generated using real COVID-19 infection data for distributing vaccines and test kits over the United States and the state of Michigan, respectively. We demonstrate results over distinct phases of the pandemic to estimate cost and speed of resource distribution depending on the scales and coverage.
A Two-Stage Mixed-Integer Linear Program (TS-MILP)
A Two-Stage Mixed-Integer Linear Program (TS-MILP)
A Distributionally Robust Optimization Model (DRO)
A Distributionally Robust Optimization Model (DRO)
Data Preparation -- Vaccine Distribution in the United States
Data Preparation -- Vaccine Distribution in the United States
We divide the United States into 10 Department of Health and Human Services (DHHS) regions and present the confidence intervals of COVID-19 vaccines' acceptance rates and mean values of the estimated demand during the three phases for each DHHS region below.
We divide the United States into 10 Department of Health and Human Services (DHHS) regions and present the confidence intervals of COVID-19 vaccines' acceptance rates and mean values of the estimated demand during the three phases for each DHHS region below.
Results -- Vaccine Distribution in the United States
Results -- Vaccine Distribution in the United States
To summarize the out-of-sample performance of optimal solutions given by the three approaches, we provide Table 4, where we rank the models from the most preferred (= 1) to the least preferred (= 3) in terms of the resultant amounts of unsatisfied demand and overall cost, respectively. The DRO approach cannot solve the problem to optimality or even obtain feasible solutions within the computational time limit (being 2 hours) for Phases 2 and 3. As a result, we only compare DT and SP for these two phases. (DT = deterministic model, SP = stochastic model, DRO = distributionally robust optimization model)
To summarize the out-of-sample performance of optimal solutions given by the three approaches, we provide Table 4, where we rank the models from the most preferred (= 1) to the least preferred (= 3) in terms of the resultant amounts of unsatisfied demand and overall cost, respectively. The DRO approach cannot solve the problem to optimality or even obtain feasible solutions within the computational time limit (being 2 hours) for Phases 2 and 3. As a result, we only compare DT and SP for these two phases. (DT = deterministic model, SP = stochastic model, DRO = distributionally robust optimization model)
The average shipments in the optimal solutions of SP and DRO for Phase 1's vaccine distribution are presented in Figures 1 and 2, respectively.
The average shipments in the optimal solutions of SP and DRO for Phase 1's vaccine distribution are presented in Figures 1 and 2, respectively.
Lastly, we compare the vaccine allocation results in the SP approach with the current Pfizer-BioNTech and Moderna's status reported by CDC [2, 3].
Lastly, we compare the vaccine allocation results in the SP approach with the current Pfizer-BioNTech and Moderna's status reported by CDC [2, 3].
Data Preparation -- COVID-19 Test Kit Allocation in Michigan, USA
Data Preparation -- COVID-19 Test Kit Allocation in Michigan, USA
We divide Michigan into 8 regions and present the projected demand median during different phases and population above 65 for each region below.
We divide Michigan into 8 regions and present the projected demand median during different phases and population above 65 for each region below.
Results -- COVID-19 Test Kit Allocation in Michigan, USA
Results -- COVID-19 Test Kit Allocation in Michigan, USA
We summarize out-of-sample performance given by solutions of the three approaches under different resource settings in Table 7, where we rank the approaches from the most preferred (= 1) to the least preferred (= 3) in terms of unsatisfied demand and overall cost, respectively.
We summarize out-of-sample performance given by solutions of the three approaches under different resource settings in Table 7, where we rank the approaches from the most preferred (= 1) to the least preferred (= 3) in terms of unsatisfied demand and overall cost, respectively.
Next, we present the cost breakdown over different phases in Figure 8.
Next, we present the cost breakdown over different phases in Figure 8.
Managerial Implications
Managerial Implications
Our results indicate the importance of incorporating demand uncertainty in resource distribution as the stochastic and robust approaches always outperform the deterministic one. If we prioritize the worst-case performance in terms of unmet demand (i.e., untested or unvaccinated people who qualify), then the distributionally robust approach is preferred despite of its higher overall cost. Nevertheless, the stochastic programming approach can provide an intermediate plan under budgetary restrictions without significant compromises in demand coverage.
Our results indicate the importance of incorporating demand uncertainty in resource distribution as the stochastic and robust approaches always outperform the deterministic one. If we prioritize the worst-case performance in terms of unmet demand (i.e., untested or unvaccinated people who qualify), then the distributionally robust approach is preferred despite of its higher overall cost. Nevertheless, the stochastic programming approach can provide an intermediate plan under budgetary restrictions without significant compromises in demand coverage.
References:
References:
[1] Basciftci, B., Yu, X., Shen, S., “Resource Distribution Under Spatiotemporal Uncertainty of Disease Spread: Stochastic versus Robust Approaches,” 2021, Available at arXiv [link].
[1] Basciftci, B., Yu, X., Shen, S., “Resource Distribution Under Spatiotemporal Uncertainty of Disease Spread: Stochastic versus Robust Approaches,” 2021, Available at arXiv [link].
[2] Center for Disease Control and Prevention (2021a) COVID-19 Vaccine Distribution Allocations by Jurisdiction-Moderna. https://data.cdc.gov/Vaccinations/COVID-19-Vaccine-Distribution-Allocations-by-Juris/b7pe-5nws.
[2] Center for Disease Control and Prevention (2021a) COVID-19 Vaccine Distribution Allocations by Jurisdiction-Moderna. https://data.cdc.gov/Vaccinations/COVID-19-Vaccine-Distribution-Allocations-by-Juris/b7pe-5nws.
[3] Center for Disease Control and Prevention (2021b) COVID-19 Vaccine Distribution Allocations by Jurisdiction-Pfizer. https://data.cdc.gov/Vaccinations/COVID-19-Vaccine-Distribution-Allocations-by-Juris/saz5-9hgg.
[3] Center for Disease Control and Prevention (2021b) COVID-19 Vaccine Distribution Allocations by Jurisdiction-Pfizer. https://data.cdc.gov/Vaccinations/COVID-19-Vaccine-Distribution-Allocations-by-Juris/saz5-9hgg.
Contributors:
Contributors:
Beste Basciftci
Beste Basciftci
Assistant Professor, Industrial Engineering Program
Assistant Professor, Industrial Engineering Program
Sabanci University
Sabanci University
Xian Yu
Xian Yu
PhD Candidate, Department of Industrial and Operations Engineering
PhD Candidate, Department of Industrial and Operations Engineering
University of Michigan
University of Michigan
Page updated
Report abuse