Bi-objective optimization for a multi-period COVID-19 vaccination planning problem

Optimizing the Selection of Mass Vaccination Sites: Access and Equity Consideration

In the early phases of the COVID-19 pandemic, vaccine accessibility was limited, impacting large metropolitan areas such as Los Angeles County, which has over 10 million residents but only nine initial vaccination sites, which resulted in people experiencing long travel times to get vaccinated. We developed a mixed-integer linear model to optimize site selection, considering equitable access for vulnerable populations. Analyzing 277 zip codes between December 2020 and May 2021, our model incorporated factors such as car ownership, ethnic group disease vulnerability, and the Healthy Places Index, alongside travel times by car and public transit. Our optimized model significantly outperformed actual site allocations for all ethnic groups. We observed that White populations faced longer travel times, likely due to their residences being in more remote, less densely populated areas. Conversely, areas with higher Latino and Black populations, often closer to the city center, benefited from shorter travel times in our model. However, those without cars experienced greater disadvantages. While having many vaccination sites might improve access for those dependent on public transit, that advantage is diminished if people must search among many sites to find a location with available vaccines.

Determining optimal COVID-19 testing center locations and capacities

We study the problem of determining the locations and capacities of COVID-19 specimen collection centers to efficiently improve accessibility to polymerase chain reaction testing during surges in testing demand. We develop a two-echelon multi-period location and capacity allocation model that determines optimal number and locations of pop-up testing centers, capacities of the existing centers as well as assignments of demand regions to these centers, and centers to labs. The objective is to minimize the total number of delayed appointments and specimens subject to budget, capacity, and turnaround time constraints, which will in turn improve the accessibility to testing. We apply our model to a case study for locating COVID-19 testing centers in the Region of Waterloo, Canada using data from the Ontario Ministry of Health, public health databases, and medical literature. We also test the performance of the model under uncertain demand and analyze its outputs under various scenarios. Our analyses provide practical insights to the public health decision-makers on the timing of capacity expansions and the locations for the new pop-up centers. According to our results, the optimal strategy is to dynamically expand the existing specimen collection center capacities and prevent bottlenecks by locating pop-up facilities. The optimal locations of pop-ups are among the densely populated areas that are in proximity to the lab and a subset of those locations are selected with the changes in demand. A comparison with a static approach promises up to 39% cost savings under high demand using the developed multi-period model.

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

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.

Equitable and effective vaccine access considering vaccine hesitancy and capacity constraints

The COVID-19 pandemic continues to have an unprecedented impact on people's lives and the economy worldwide. Vaccines are the strongest evidence-based defense against the spread of the disease. The release of COVID-19 vaccines to the general public created policy challenges associated with how to best allocate vaccines among different sub-regions. In the United States, after vaccines became widely available for all eligible adults, policymakers faced objectives such as (i) achieving an equitable allocation to reduce populations' travel times to get vaccinated and (ii) effectively allocating vaccine doses to minimize waste and unmet need. This problem was further exacerbated by the underlying factors of population vaccine hesitancy and sub-regions' varying capacity levels to administer vaccines to eligible and willing populations. Although simple to implement, commonly used pro rata policies do not capture the complexities of this problem. We propose two alternatives to simple pro rata policies. The first alternative is based on a Mixed-Integer Linear Programming Model that minimizes the maximum travel duration of patients and aims to achieve an equitable and effective allocation of vaccines to sub-regions while considering capacity and vaccine hesitancy. A second alternative is a heuristic approach that may be more palatable for policymakers who (i) are not familiar with mathematical modeling, (ii) are reluctant to use black-box models, and (iii) prefer algorithms that are easy to understand and implement. We demonstrate the results of our model through a case study based on real data from the state of Alabama and show that substantial improvements in travel time-based equity are achievable through capacity improvements in a small subset of counties. We perform additional computational experiments that compare the proposed methods in terms of several metrics and demonstrate the promising performance of our model and proposed heuristic. We find that while our mathematical model can achieve equitable and effective vaccine allocation, the proposed heuristic performs better if the goal is to minimize average travel duration. Finally, we explore two model extensions that aim to (i) lower vaccine hesitancy by allocating vaccines, and (ii) prioritize vaccine access for certain high-risk sub-populations.

A robust optimization problem for drone-based equitable pandemic vaccine distribution with uncertain supply

Widespread vaccination is the only way to overcome the COVID-19 global crisis. However, given the vaccine scarcity during the early outbreak of the pandemic, ensuring efficient and equitable distribution of vaccines, particularly in rural areas, has become a significant challenge. To this end, this study develops a two-stage robust vaccine distribution model that addresses the supply uncertainty incurred by vaccine shortages. The model aims to optimize the social and economic benefits by jointly deciding vaccination facility location, transportation capacity, and reservation plan in the first stage, and rescheduling vaccinations in the second stage after the confirmation of uncertainty. To hedge vaccine storage and transportation difficulties in remote areas, we consider using drones to deliver vaccines in appropriate and small quantities to vaccination points. Two tailored column-and-constraint generation algorithms are proposed to exactly solve the robust model, in which the subproblems are solved via the vertex traversal and the dual methods, respectively. The superiority of the dual method is further verified. Finally, we use real-world data to demonstrate the necessity to account for uncertain supply and equitable distribution, and analyze the impacts of several key parameters. Some managerial insights are also produced for decision-makers.

Facility planning and schedule design in the pandemic: Eliminating contacts at construction workplace

The construction industry has been severely affected by the COVID-19 pandemic and the associated restrictions on person-to-person contacts issued by the government. A construction site usually has a high number of workers working at the same time; therefore, the question of how to ensure their safety during the pandemic-that is, how to protect them from getting infected-has become an urgent problem. In this study, we propose a bi-objective integer programming model to establish the optimal schedule plan under COVID-19 regulations. We develop a solution method and conduct numerical experiments to solve and validate our model. The optimal schedule plan can avoid contacts between workers of different groups while minimizing the total costs of complying with government policy. Our proposed model can be applied in practice to help project managers establish a reasonable and cost-effective schedule plan. This study contributes to reducing the operating costs of contractors and protecting the health of construction workers.

Dynamic fair balancing of COVID-19 patients over hospitals based on forecasts of bed occupancy

This paper introduces mathematical models that support dynamic fair balancing of COVID-19 patients over hospitals in a region and across regions. Patient flow is captured in an infinite server queueing network. The dynamic fair balancing model within a region is a load balancing model incorporating a forecast of the bed occupancy, while across regions, it is a stochastic program taking into account scenarios of the future bed surpluses or shortages. Our dynamic fair balancing models yield decision rules for patient allocation to hospitals within the region and reallocation across regions based on safety levels and forecast bed surplus or bed shortage for each hospital or region. Input for the model is an accurate real-time forecast of the number of COVID-19 patients hospitalised in the ward and the Intensive Care Unit (ICU) of the hospitals based on the predicted inflow of patients, their Length of Stay and patient transfer probabilities among ward and ICU. The required data is obtained from the hospitals' data warehouses and regional infection data as recorded in the Netherlands. The algorithm is evaluated in Dutch regions for allocation of COVID-19 patients to hospitals within the region and reallocation across regions using data from the second COVID-19 peak.

A decision support system for scheduling a vaccination campaign during a pandemic emergency: The COVID-19 case

This paper considers the organization and scheduling of a vaccination campaign during a pandemic emergency. We describe the decision process and introduce an optimization model, which showed a powerful multi-scenario tool for scheduling a campaign in detail within a dynamic and uncertain context. The solution of the model gave the decision maker the possibility to test different settings and have a configurable solution within few seconds, compared with the man-days of effort that would have required a manual schedule. Analysis of a real case study on COVID-19 vaccination campaign in northern Italy showed that the use of such optimized solution allowed to cover the target population within a much shorter time interval, compared to a manual approach.

Large-scale emergency medical services scheduling during the outbreak of epidemics

This paper studies a new large-scale emergency medical services scheduling (EMSS) problem during the outbreak of epidemics like COVID-19, which aims to determine an optimal scheduling scheme of emergency medical services to minimize the completion time of nucleic acid testing to achieve rapid epidemic interruption. We first analyze the impact of the epidemic spread and assign different priorities to different emergency medical services demand points according to the degree of urgency. Then, we formulate the EMSS as a mixed-integer linear program (MILP) model and analyze its complexity. Given the NP-hardness of the problem, we develop two fast and effective improved discrete artificial bee colony algorithms (IDABC) based on problem properties. Experimental results for a real case and practical-sized instances with up to 100 demand points demonstrate that the IDABC significantly outperforms MILP solver CPLEX and two state-of-the-art metaheuristic algorithms in both solution quality and computational efficiency. In addition, we also propose some managerial implications to support emergency management decision-making.

Optimizing Large-Scale COVID-19 Nucleic Acid Testing with a Dynamic Testing Site Deployment Strategy

The COVID-19 epidemic has spread worldwide, infected more than 0.6 billion people, and led to about 6 million deaths. Conducting large-scale COVID-19 nucleic acid testing is an effective measure to cut off the transmission chain of the COVID-19 epidemic, but it calls for deploying numerous nucleic acid testing sites effectively. In this study, we aim to optimize the large-scale nucleic acid testing with a dynamic testing site deployment strategy, and we propose a multiperiod location-allocation model, which explicitly considers the spatial-temporal distribution of the testing population and the time-varied availability of various testing resources. Several comparison models, which implement static site deployment strategies, are also developed to show the benefits of our proposed model. The effectiveness and benefits of our model are verified with a real-world case study on the Chenghua district of Chengdu, China, which indicates that the optimal total cost of the dynamic site deployment strategy can be 15% less than that of a real plan implemented in practice and about 2% less than those of the other comparison strategies. Moreover, we conduct sensitivity analysis to obtain managerial insights and suggestions for better testing site deployment in field practices. This study highlights the importance of dynamically deploying testing sites based on the target population's spatial-temporal distribution, which can help reduce the testing cost and increase the robustness of producing feasible plans with limited medical resources.

A resilient, robust transformation of healthcare systems to cope with COVID-19 through alternative resources

The COVID-19 pandemic - as a massive disruption - has significantly increased the need for medical services putting an unprecedented strain on health systems. This study presents a robust location-allocation model under uncertainty to increase the resiliency of health systems by applying alternative resources, such as backup and field hospitals and student nurses. A multi-objective optimization model is developed to minimize the system's costs and maximize the satisfaction rate among medical staff and COVID-19 patients. A robust approach is provided to face the data uncertainty, and a new mathematical model is extended to linearize a nonlinear constraint. The ICU beds, ward beds, ventilators, and nurses are considered the four main capacity limitations of hospitals for admitting different types of COVID-19 patients. The sensitivity analysis is performed on a real-world case study to investigate the applicability of the proposed model. The results demonstrate the contribution of student nurses and backup and field hospitals in treating COVID-19 patients and provide more flexible decisions with lower risks in the system by managing the fluctuations in both the number of patients and available nurses. The results showed that a reduction in the number of available nurses incurs higher costs for the system and lower satisfaction among patients and nurses. Moreover, the backup and field hospitals and the medical staff elevated the system's resiliency. By allocating backup hospitals to COVID-19 patients, only 37% of severe patients were lost, and this rate fell to less than 5% after establishing field hospitals. Moreover, medical students and field hospitals curbed the costs and increased the satisfaction rate of nurses by 75%. Finally, the system was protected from failure by increasing the conservatism level. With a 2% growth in the price of robustness, the system saved 13%.

Bi-objective optimization of a stochastic resilient vaccine distribution network in the context of the COVID-19 pandemic

This paper develops an approach to optimize a vaccine distribution network design through a mixed-integer nonlinear programming model with two objectives: minimizing the total expected number of deaths among the population and minimizing the total distribution cost of the vaccination campaign. Additionally, we assume that a set of input parameters (e.g., death rate, social contacts, vaccine supply, etc.) is uncertain, and the distribution network is exposed to disruptions. We then investigate the resilience of the distribution network through a scenario-based robust-stochastic optimization approach. The proposed model is linearized and finally validated through a real case study of the COVID-19 vaccination campaign in France. We show that the current vaccination strategies are not optimal, and vaccination prioritization among the population and the equity of vaccine distribution depend on other factors than those conceived by health policymakers. Furthermore, we demonstrate that a vaccination strategy mixing the population prioritization and the quarantine restrictions leads to an 8.5% decrease in the total number of deaths.

Determining locations and layouts for parcel lockers to support supply chain viability at the last mile

The pandemic caused by the corona virus SARS-CoV-2 raised many new challenges for humanity. For instance, governments imposed regulations such as lockdowns, resulting in supply chain shocks at different tiers. Additionally, delivery services reached their capacity limits because the demand for mail orders soared temporarily during the lockdowns. We argue that one option to support supply chain viability at the last-mile delivery tier is to use (outdoor) parcel lockers through which customers can collect their orderings 24/7 while ensuring physical distancing. The location planning of such lockers is known to be of utmost importance for their success. Another important topic to address is that the design of the compartment structure of the parcel lockers should meet the (uncertain) customer demand for different commodities. Both of the latter planning issues are combined into one optimization problem in this article. The objective is to maximize a linear function (e.g., expected profits) of the covered demand, given a budget an operator is willing to invest. An integer linear programming formulation is proposed, and a reformulation based on Benders decomposition is derived. It is shown that the Benders cuts can be separated in linear time. The developed algorithms enable solving of large-scale problem instances demonstrated by a performance analysis of computational experiments. The impact of different problem parameters on the obtained solutions is demonstrated by a sensitivity analysis. A case study based on real-world data from Austria is presented. The results show that using parcel lockers can support supply chain viability at the last-mile delivery tier. Moreover, the relatively small investment cost yields promising returns. The results further indicate that small-sized and medium-sized compartments should be preferred over large and x-large ones in the parcel locker compartment design.

Optimal selection of COVID-19 vaccination sites in the Philippines at the municipal level

In this work, we present an approach to determine the optimal location of coronavirus disease 2019 (COVID-19) vaccination sites at the municipal level. We assume that each municipality is subdivided into smaller administrative units, which we refer to as barangays. The proposed method solves a minimization problem arising from a facility location problem, which is formulated based on the proximity of the vaccination sites to the barangays, the number of COVID-19 cases, and the population densities of the barangays. These objectives are formulated as a single optimization problem. As an alternative decision support tool, we develop a bi-objective optimization problem that considers distance and population coverage. Lastly, we propose a dynamic optimization approach that recalculates the optimal vaccination sites to account for the changes in the population of the barangays that have completed their vaccination program. A numerical scheme that solves the optimization problems is presented and the detailed description of the algorithms, which are coded in Python and MATLAB, are uploaded to a public repository. As an illustration, we apply our method to determine the optimal location of vaccination sites in San Juan, a municipality in the province of Batangas, in the Philippines. We hope that this study may guide the local government units in coming up with strategic and accessible plans for vaccine administration.

An Improved Genetic Algorithm for Location Allocation Problem with Grey Theory in Public Health Emergencies

The demand for emergency medical facilities (EMFs) has witnessed an explosive growth recently due to the COVID-19 pandemic and the rapid spread of the virus. To expedite the location of EMFs and the allocation of patients to these facilities at times of disaster, a location-allocation problem (LAP) model that can help EMFs cope with major public health emergencies was proposed in this study. Given the influence of the number of COVID-19-infected persons on the demand for EMFs, a grey forecasting model was also utilized to predict the accumulative COVID-19 cases during the pandemic and to calculate the demand for EMFs. A serial-number-coded genetic algorithm (SNCGA) was proposed, and dynamic variation was used to accelerate the convergence. This algorithm was programmed using MATLAB, and the emergency medical facility LAP (EMFLAP) model was solved using the simple (standard) genetic algorithm (SGA) and SNCGA. Results show that the EMFLAP plan based on SNCGA consumes 8.34% less time than that based on SGA, and the calculation time of SNCGA is 20.25% shorter than that of SGA. Therefore, SNCGA is proven convenient for processing the model constraint conditions, for naturally describing the available solutions to a problem, for improving the complexity of algorithms, and for reducing the total time consumed by EMFLAP plans. The proposed method can guide emergency management personnel in designing an EMFLAP decision scheme.

Adapting supply chain operations in anticipation of and during the COVID-19 pandemic

This article investigates the impacts of the COVID-19 pandemic and their proactive mediation by adaptive operational decisions in different network design structures in anticipation of and during the pandemic. In generalized terms, we contribute to the understanding of the effect of preparedness and recovery decisions in a pandemic setting on supply chain operations and performance. In particular, we examine the impact of inventory pre-positioning in anticipation of a pandemic and the adaptation of production-ordering policy during the pandemic. Our model combines three levels, which is not often seen jointly in operations management literature, i.e., pandemic dynamics, supply chain design, and operational production-inventory control policies. The analysis is performed for both two- and three-stage supply chains and different scenarios for pandemic dynamics (i.e., uncontrolled propagation or controlled dispersal with lockdowns). Our findings suggest that two-stage supply chains exhibit a higher vulnerability in disruption cases. However, they are exposed to a lower system inertia and show positive effects at the recovery stage. Supply chain adaptation ahead of a pandemic is more advantageous than during the pandemic when specific operational recovery policies are deployed. We show that it is instructive to avoid simultaneous changes in structural network design and operational policies since that can destabilize the production-inventory system and result in higher product shortages.

Optimal selection of COVID-19 vaccination sites in the Philippines at the municipal level

In this work, we present an approach to determine the optimal location of coronavirus disease 2019 (COVID-19) vaccination sites at the municipal level. We assume that each municipality is subdivided into smaller administrative units, which we refer to as barangays. The proposed method solves a minimization problem arising from a facility location problem, which is formulated based on the proximity of the vaccination sites to the barangays, the number of COVID-19 cases, and the population densities of the barangays. These objectives are formulated as a single optimization problem. As an alternative decision support tool, we develop a bi-objective optimization problem that considers distance and population coverage. Lastly, we propose a dynamic optimization approach that recalculates the optimal vaccination sites to account for the changes in the population of the barangays that have completed their vaccination program. A numerical scheme that solves the optimization problems is presented and the detailed description of the algorithms, which are coded in Python and MATLAB, are uploaded to a public repository. As an illustration, we apply our method to determine the optimal location of vaccination sites in San Juan, a municipality in the province of Batangas, in the Philippines. We hope that this study may guide the local government units in coming up with strategic and accessible plans for vaccine administration.