A data-driven robust optimization model by cutting hyperplanes on vaccine access uncertainty in COVID-19 vaccine supply chain

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.

Optimizing the COVID-19 cold chain vaccine distribution network with medical waste management: A robust optimization approach

This paper investigates the distribution problem of the COVID-19 vaccine at the provincial level in Turkey and the management of medical waste, considering the cold chain requirements and the perishable nature of vaccines. In this context, a novel multi-period multi-objective mixed-integer linear programming model is initially presented over a 12-month planning horizon for solving the deterministic distribution problem. The model includes newly structured constraints due to the feature of COVID-19 vaccines, which must be administered in two doses at specified intervals. Then, the presented model is tested for the province of Izmir with deterministic data, and the results show that the demand can be satisfied and community immunity can be achieved in the specified planning horizon. Moreover, for the first time, a robust model is created using polyhedral uncertainty sets to manage uncertainties related to supply and demand quantities, storage capacity, and deterioration rate, and it has been analyzed under different uncertainty levels. Accordingly, as the level of uncertainty increases, the percentage of meeting the demand gradually decreases. It is observed that the biggest effect here is the uncertainty in supply, and in the worst case, approximately 30% of the demand cannot be met.

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.

Robust optimization and strategic analysis for agri-food supply chain under pandemic crisis: Case study from an emerging economy

Pandemic crises like the coronavirus disease 2019 (COVID-19) have severely influenced companies working in the Agri-food industry in different countries. Some companies could overcome this crisis by their elite managers, while many experienced massive financial losses due to a lack of the appropriate strategic planning. On the other hand, governments sought to provide food security to the people during the pandemic crisis, putting extreme pressure on companies operating in this field. Therefore, the aim of this study is to develop a model of the canned food supply chain under uncertain conditions in order to analyze it strategically during the COVID-19 pandemic. The problem uncertainty is addressed using robust optimization, and also the necessity of using a robust optimization approach compared to the nominal approach to the problem is indicated. Finally, to face the COVID-19 pandemic, after determining the strategies for the canned food supply chain, by solving a multi-criteria decision-making (MCDM) problem, the best strategy is specified considering the criteria of the company under study and its equivalent values are presented ​​as optimal values of a mathematical model of canned food supply chain network. The results demonstrated that "expanding the export of canned food to neighboring countries with economic justification" was the best strategy for the company under study during the COVID-19 pandemic. According to the quantitative results, implementing this strategy reduced by 8.03% supply chain costs and increased by 3.65% the human resources employed. Finally, the utilization of available vehicle capacity was 96%, and the utilization of available production throughput was 75.8% when using this strategy.

Robust design of a logistics system using FePIA procedure and analysis of trade-offs between CO2 emissions and net present value

The problems of flexible planning of the design of logistics systems for the collection of food products such as raw milk can result in a decrease in the performance of critical indicators for their performance. This paper proposes a new efficient methodology for robustly designing a first-mile logistics system for storing and refrigerating milk as a perishable product considering decisions related to open facilities and the flow of products, including sustainability indices. The proposed approach is modeled as a bi-objective problem by considering the minimization of greenhouse gas emissions (CO2) produced by milk transportation canteens and the maximization of the system configuration's net present value (NPV). We have analyzed and determined the most robust configuration for the first time and explained the robustness-NPV and robustness-CO2 relationships. The proposed mathematical model is solved by the Epsilon constraints method, and the robustness is calculated considering an extension of the FePIA methodology for multiobjective problems. A novel contribution is a balance in the possible future values generated by the company related to its cash flows and the generation of CO2 emissions when using a motorized transport frequently used in the shipment of raw milk considering a new important aspect such as the volume of product transported and the slope of the path between the production farm and the storage cooling tanks.

A data-driven optimization model to response to COVID-19 pandemic: a case study

COVID-19 is a highly prevalent disease that has led to numerous predicaments for healthcare systems worldwide. Owing to the significant influx of patients and limited resources of health services, there have been several limitations associated with patients' hospitalization. These limitations can cause an increment in the COVID-19-related mortality due to the lack of appropriate medical services. They can also elevate the risk of infection in the rest of the population. The present study aims to investigate a two-phase approach to designing a supply chain network for hospitalizing patients in the existing and temporary hospitals, efficiently distributing medications and medical items needed by patients, and managing the waste created in hospitals. Since the number of future patients is uncertain, in the first phase, trained Artificial Neural Networks with historical data forecast the number of patients in future periods and generate scenarios. Through the use of the K-Means method, these scenarios are reduced. In the second phase, a multi-objective, multi-period, data-driven two-stage stochastic programming is developed using the acquired scenarios in the previous phase concerning the uncertainty and disruption in facilities. The objectives of the proposed model include maximizing the minimum allocation-to-demand ratio, minimizing the total risk of disease spread, and minimizing the total transportation time. Furthermore, a real case study is investigated in Tehran, the capital of Iran. The results showed that the areas with the highest population density and no facilities near them have been selected for the location of temporary facilities. Among temporary facilities, temporary hospitals can allocate up to 2.6% of the total demand, which puts pressure on the existing hospitals to be removed. Furthermore, the results indicated that the allocation-to-demand ratio can remain at an ideal level when disruptions occur by considering temporary facilities. Our analyses focus on: (1) Examining demand forecasting error and generated scenarios in the first phase, (2) exploring the impact of demand parameters on the allocation-to-demand ratio, total time and total risk, (3) investigating the strategy of utilizing temporary hospitals to address sudden changes in demand, (4) evaluating the effect of disruption to facilities on the supply chain network.

Resilient and social health service network design to reduce the effect of COVID-19 outbreak

With the severe outbreak of the novel coronavirus (COVID-19), researchers are motivated to develop efficient methods to face related issues. The present study aims to design a resilient health system to offer medical services to COVID-19 patients and prevent further disease outbreaks by social distancing, resiliency, cost, and commuting distance as decisive factors. It incorporated three novel resiliency measures (i.e., health facility criticality, patient dissatisfaction level, and dispersion of suspicious people) to promote the designed health network against potential infectious disease threats. Also, it introduced a novel hybrid uncertainty programming to resolve a mixed degree of the inherent uncertainty in the multi-objective problem, and it adopted an interactive fuzzy approach to address it. The actual data obtained from a case study in Tehran province in Iran proved the strong performance of the presented model. The findings show that the optimum use of medical centers' potential and the corresponding decisions result in a more resilient health system and cost reduction. A further outbreak of the COVID-19 pandemic is also prevented by shortening the commuting distance for patients and avoiding the increasing congestion in the medical centers. Also, the managerial insights show that establishing and evenly distributing camps and quarantine stations within the community and designing an efficient network for patients with different symptoms result in the optimum use of the potential capacity of medical centers and a decrease in the rate of bed shortage in the hospitals. Another insight drawn is that an efficient allocation of the suspect and definite cases to the nearest screening and care centers makes it possible to prevent the disease carriers from commuting within the community and increase the coronavirus transmission rate.

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%.

Analysis of performance of Covid-19 vaccine supply chain in India

Purpose

This study aims to analyse the structure of the Indian vaccine supply chain (SC) during the Covid-19 crisis and explore the underlying challenges at each stage in the network. It also brings out the difference in performance of various constituent states.

Design/methodology/approach

This study relied on both primary and secondary data for the analyses. For the primary data, the study gathered experts’ opinions to validate the authors’ inferences. For the secondary data, it relies on government data provided in websites.

Findings

Based on the quartile analysis and cluster analysis of the secondary data, the authors find that the constituent states responded differently during the first and second waves. This was due to the differences in SC characteristics attributed to varied demographics and administrative efficiency.

Research limitations/implications

This paper’s analyses is primarily limited to secondary information and inferences are based on them. The study has important implications for implementing the large-scale vaccination drives by government and constituent states for better coordination and last-mile delivery.

Originality/value

The contribution is unique in studying the performance of constituent states using statistical techniques, with secondary data from authentic sources. It is also unique in combining this observation with validation from experts.

Designing a sustainable reverse supply chain network for COVID-19 vaccine waste under uncertainty

The vast nationwide COVID-19 vaccination programs are implemented in many countries worldwide. Mass vaccination is causing a rapid increase in infectious and non-infectious vaccine wastes, potentially posing a severe threat if there is no well-organized management plan. This paper develops a mixed-integer mathematical programming model to design a COVID-19 vaccine waste reverse supply chain (CVWRSC) for the first time. The presented problem is based on minimizing the system's total cost and carbon emission. The uncertainty in the tendency rate of vaccination is considered, and a robust optimization approach is used to deal with it, where an interactive fuzzy approach converts the model into a single objective problem. Additionally, a Lagrangian relaxation (LR) algorithm is utilized to deal with the computational difficulty of the large-scale CVWRSC network. The model's practicality is investigated by solving a real-life case study. The results show the gain of the developed integrated network, where the presented framework performs better than the disintegrated vaccine and waste supply chain models. According to the results, vaccination operations and transportation of non-infectious wastes are responsible for a large portion of total cost and emission, respectively. Autoclaving technology plays a vital role in treating infectious wastes. Moreover, the sensitivity analyses demonstrate that the vaccination tendency rate significantly impacts both objective functions. The case study results prove the model's robustness under different realization scenarios, where the average objective function of the robust model is less than the deterministic model ones' in all scenarios. Finally, some insights are given based on the obtained results.

A humanitarian cold supply chain distribution model with equity consideration: The case of COVID-19 vaccine distribution in the European Union

This research develops a humanitarian cold supply chain model with equity consideration for COVID-19 vaccine distribution during a pandemic, considering deprivation cost and an important social concept named equity. The proposed comprehensive plan minimizes all incurred costs, including transportation costs, shortage costs, deprivation costs, and holding costs, while aiming at eliminating infection and mortality rates. The proposed three-echelon supply chain model includes suppliers, distributors, and affected regions (ARs), as destinations. We apply the proposed model to the actual vaccine distribution data during the COVID-19 outbreak in Europe. A mixed integer programming (MIP) model is developed to minimize the costs and satisfy the demand goals in the vaccine distribution plan. A sensitivity analysis demonstrates how total and deprivation costs affect each other, helping the managers establish a trade-off between them. The results show that appropriate supply chain planning can minimize logistics and social costs. The proposed model can help policymakers, and decision-makers better understand the importance of equity and implement a fair distribution of vaccines, considering the deprivation cost as a social cost.