Optimal selection of cruise ship waste disposal ports

As cruise ships call at many ports and passengers come from all over the world, it is very easy to carry viruses on cruise ships. Under the control of the epidemic situation on board, the solid waste generated by them should be scientifically treated to prevent the spread of infectious diseases such as COVID-19 pneumonia. Therefore, Reasonable selection of waste disposal ports and formulation of unloading plans are directly related to the resumption of cruise operations. This study considers the cost and risk of waste disposal, uses robust optimization to deal with waste volume, increases the scenarios of port service interruption due to epidemics and other reasons, and proposes a variety of emergency strategies. Finally, the relevant strategies are selected according to the decision-maker's preference for cost and risk;By solving the relevant examples, the optimal choice of the cruise ship waste disposal port under the epidemic situation is given, which verifies the validity and feasibility of the model. The research helps to improve the management of cruise waste during the post-epidemic period, and has practical value and guiding significance for the normal operation and development of the global cruise market. © 2023 SPIE.

Decision-Dependent Distributionally Robust Markov Decision Process Method in Dynamic Epidemic Control

In this paper, we present a Distributionally Robust Markov Decision Process (DRMDP) approach for addressing the dynamic epidemic control problem. The Susceptible-Exposed-Infectious-Recovered (SEIR) model is widely used to represent the stochastic spread of infectious diseases, such as COVID-19. While Markov Decision Processes (MDP) offers a mathematical framework for identifying optimal actions, such as vaccination and transmission-reducing intervention, to combat disease spreading according to the SEIR model. However, uncertainties in these scenarios demand a more robust approach that is less reliant on error-prone assumptions. The primary objective of our study is to introduce a new DRMDP framework that allows for an ambiguous distribution of transition dynamics. Specifically, we consider the worst-case distribution of these transition probabilities within a decision-dependent ambiguity set. To overcome the computational complexities associated with policy determination, we propose an efficient Real-Time Dynamic Programming (RTDP) algorithm that is capable of computing optimal policies based on the reformulated DRMDP model in an accurate, timely, and scalable manner. Comparative analysis against the classic MDP model demonstrates that the DRMDP achieves a lower proportion of infections and susceptibilities at a reduced cost. [ FROM AUTHOR] Copyright of IISE Transactions is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)

A distributionally robust optimization approach for airline integrated recovery under in-flight pandemic transmission risks.

The COVID-19 pandemic has hit the airline industry hard, leading to heterogeneous epidemiological situations across markets, irregular flight bans, and increasing operational hurdles. Such a melange of irregularities has presented significant challenges to the airline industry, which typically relies on long-term planning. Given the growing risk of disruptions during epidemic and pandemic outbreaks, the role of airline recovery is becoming increasingly crucial for the aviation industry. This study proposes a novel model for airline integrated recovery problem under the risk of in-flight epidemic transmission risks. This model recovers the schedules of aircraft, crew, and passengers to eliminate possible epidemic dissemination while reducing airline operating costs. To account for the high uncertainty with respect to in-flight transmission rates and to prevent overfitting of the empirical distribution, a Wasserstein distance-based ambiguity set is utilized to formulate a distributionally robust optimization model. Aimed at tackling computation difficulties, a branch-and-cut solution method and a large neighborhood search heuristic are proposed in this study based on an epidemic propagation network. The computation results for real-world flight schedules and a probabilistic infection model suggest that the proposed model is capable of reducing the expected number of infected crew members and passengers by 45% with less than 4% increase in flight cancellation/delay rates. Furthermore, practical insights into the selection of critical parameters as well as their relationship with other common disruptions are provided. The integrated model is expected to enhance airline disruption management against major public health events while minimizing economic loss.

Mitigating the COVID-19 pandemic through data-driven resource sharing

COVID-19 outbreaks in local communities can result in a drastic surge in demand for scarce resources such as mechanical ventilators. To deal with such demand surges, many hospitals (1) purchased large quantities of mechanical ventilators, and (2) canceled/postponed elective procedures to preserve care capacity for COVID-19 patients. These measures resulted in a substantial financial burden to the hospitals and poor outcomes for non-COVID-19 patients. Given that COVID-19 transmits at different rates across various regions, there is an opportunity to share portable healthcare resources to mitigate capacity shortages triggered by local outbreaks with fewer total resources. This paper develops a novel data-driven adaptive robust simulation-based optimization (DARSO) methodology for optimal allocation and relocation of mechanical ventilators over different states and regions. Our main methodological contributions lie in a new policy-guided approach and an efficient algorithmic framework that mitigates critical limitations of current robust and stochastic models and make resource-sharing decisions implementable in real-time. In collaboration with epidemiologists and infectious disease doctors, we give proof of concept for the DARSO methodology through a case study of sharing ventilators among regions in Ohio and Michigan. The results suggest that our optimal policy could satisfy ventilator demand during the first pandemic's peak in Ohio and Michigan with 14% (limited sharing) to 63% (full sharing) fewer ventilators compared to a no sharing strategy (status quo), thereby allowing hospitals to preserve more elective procedures. Furthermore, we demonstrate that sharing unused ventilators (rather than purchasing new machines) can result in 5% (limited sharing) to 44% (full sharing) lower expenditure, compared to no sharing, considering the transshipment and new ventilator costs.

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.

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.

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%.

Systematic Literature Review on Robust Optimization in Solving Sustainable Development Goals (SDGs) Problems during the COVID-19 Pandemic

Handling uncertainty is important in decision making, especially for SDGs problems. Robust Optimization (RO) is an applied optimization method that can be employed to handle optimization under uncertain data. With SDGs problems, many uncertain data have been considered in decision making. With RO, the data uncertainties are assumed to lay within a compact, convex continuous set. There are three special sets that can be used to represent the data, i.e., box, ellipsoidal, or polyhedral uncertainty sets. These special sets lead the SDGs problems to a computationally tractable optimization model, such that the global optimal solution is attained. However, literature reviews on the application of RO in SDGs decision-making is sparse, especially during the COVID-19 pandemic period. This paper examines the following topics: (1) the purposes of studies of RO and SDGs during the COVID-19 pandemic, (2) the state-of-the-art in RO-SDGs to determine the research objectives, and (3) the SDGs type of problems that have been modeled using RO. A systematic literature review is conducted in this paper, wherein discussion is based on a PRISMA (Preferred Reporting Items for Systematic Review and Meta-Analyses) flowchart. To this end, the database reference searching conducted on the Scopus, Science Direct, and SAGE databases, is completed using the help RStudio software. The analysis was carried out on two datasets, assisted by the output visualization using RStudio software with the "bibliometrix” package, and using the ‘biblioshiny()' command to create a link to the "shiny web interface”. In this paper, the research gap on application of RO to SDGs problems is analyzed in order to identify the research objectives, methods, and specific RO-SDGs problems. As a result, the application of RO to SDGs problems is rare;this finding provides a motivation to conduct a further study of RO and SDGs during the COVID-19 pandemic. An expansion is presented using the key phrase "Operations Research and Optimization Modeling”, or "OROM”. SDGs in Indonesia may be referenced as an example of the capacity building available through RO/OROM. © 2023 by the authors.

Resilience strategies in coping to disruptions of wheat supply chain caused by the Russia–Ukraine war crisis: case study from an emerging economy

Purpose: The Russia–Ukraine war has disrupted the wheat supply worldwide. Given that wheat is one of the most important agri-food products in the world, it is necessary to pay attention to the wheat supply chain during the global crises. The use of resilience strategies is one of the solutions to face the supply chain disruptions. In addition, there is a possibility of multiple crises occurring in global societies simultaneously. Design/methodology/approach: In this research, the resilience strategies of backup suppliers (BS) and inventory pre-prepositioning (IP) were discussed in order to cope with the wheat supply chain disruptions. Furthermore, the p-Robust Scenario-based Stochastic Programming (PRSSP) approach was used to optimize the wheat supply chain under conditions of disruptions from two perspectives, feasibility and optimality. Findings: After implementing the problem of a real case in Iran, the results showed that the use of resilience strategy reduced costs by 9.33%. It was also found that if resilience strategies were used, system's flexibility and decision-making power increased. Besides, the results indicated that if resilience strategies were used and another crisis like the COVID-19 pandemic occurred, supply chain costs would increase less than when resilience strategies were not used. Originality/value: In this study, the design of the wheat supply chain was discussed according to the wheat supply disruptions due to the Russia–Ukraine war and its implementation on a real case. In the following, various resilience strategies were used to cope with the wheat supply chain disruptions. Finally, the effect of the COVID-19 pandemic on the wheat supply chain in the conditions of disruptions caused by the Russia–Ukraine war was investigated. © 2023, Emerald Publishing Limited.

A resilient inventory management of pharmaceutical supply chains under demand disruption

Inspired by the global supply chain disruptions caused by the COVID-19 pandemic, we study optimal procurement and inventory decisions for a pharmaceutical supply chain over a finite planning horizon. To model disruption, we assume that the demand for medical drugs is uncertain and shows spatiotemporal variability. To address demand uncertainty, we propose a two-stage optimization framework, where in the first stage, the total cost of pre-positioning drugs at distribution centers and its associated risk is minimized, while the second stage minimizes the cost of recourse decisions (e.g., reallocation, inventory management). To allow for different risk preferences, we propose to capture the risk of demand uncertainty through the expectation and worst-case measures, leading to two different models, namely (risk-neutral) stochastic programming and (risk-averse) robust optimization. We consider a finite number of scenarios to represent the demand uncertainty, and to solve the resulting models efficiently, we propose L-shaped decomposition-based algorithms. Through extensive numerical experiments, we illustrate the impact of various parameters, such as travel time, product's shelf life, and waste due to transportation and storage, on the supply chain resiliency and cost, under optimal risk-neutral and risk-averse policies. These insights can assist decision makers in making informed choices. © 2023 Elsevier Ltd

Service center location problems with decision dependent utilities and a pandemic case study

We study a service center location problem with ambiguous utility gains upon receiving service. The model is motivated by the problem of deciding medical clinic/service centers, possibly in rural communities, where residents need to visit the clinics to receive health services. A resident gains his utility based on travel distance, waiting time, and service features of the facility that depend on the clinic location. The elicited location-dependent utilities are assumed to be ambiguously described by an expected value and variance constraint. We show that despite a non-convex nonlinearity, given by a constraint specified by a maximum of two second-order conic functions, the model admits a mixed 0-1 second-order cone (MISOCP) formulation. We study the non-convex substructure of the problem, and present methods for developing its strengthened formulations by using valid tangent inequalities. Computational study shows the effectiveness of solving the strengthened formulations. Examples are used to illustrate the importance of including decision dependent ambiguity. An illustrative example to identify locations for Covid-19 testing and vaccination is used to further illustrate the model and its properties. © 2023 The Authors. Naval Research Logistics published by Wiley Periodicals LLC.

A reliable emergency logistics network for COVID-19 considering the uncertain time-varying demands.

The evolving COVID-19 epidemic pose significant threats and challenges to emergency response operations. This paper focuses on designing an emergency logistic network, including the deployment of emergency facilities and the allocation of supplies to satisfy the time-varying demands. A Demand prediction-Network optimization-Decision adjustment framework is proposed for the emergency logistic network design. We first present an improved short-term epidemic model to predict the evolutionary trajectory of the epidemic. Then, considering the uncertainty of the estimated demands, we construct a capacitated multi-period, multi-echelon facility deployment and resource allocation robust optimization model to improve the reliability of the decisions. To address the conservativeness of robust solutions during the evolution of the epidemic, an uncertainty budget adjustment strategy is proposed and integrated into the rolling horizon optimization approach. The results of the case study show that (i) the short-term prediction method has higher accuracy and the accuracy increases with the amount of observed data; (ii) considering the demand uncertainty, the proposed robust optimization model combined with uncertainty budget adjustment strategy can improve the performance of the emergency logistic network; (iii) the proposed solution method is more efficient than its benchmark, especially for large-scale cases. Moreover, some managerial insights related to the emergency logistics network design problem are presented.

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.

Integrated supplier selection, scheduling, and routing problem for perishable product supply chain: A distributionally robust approach

Due to the global outbreak of COVID-19, the perishable product supply chains have been impacted in different ways, and consequently, the risks of food insecurity have been increased in many affected countries. The uncertainty in supply and demand of perishable products, are among the most influential factors impacting the supply chain networks. Accordingly, the provision and distribution of food and other perishable commodities have become much more important than in the past. In this study, a bi-objective optimization model is proposed for a three-echelon perishable food supply chain (PFSC) network with multiple products to formulate an integrated supplier selection, production scheduling, and vehicle routing problem. The proposed model aims to mitigate the risks of demand and supply uncertainties and reinforce the distribution-related decisions by simultaneously optimizing the total network costs and suppliers' reliability. Using the distributionally robust modeling paradigm, the probability distribution of uncertain demand is assumed to belong to an ambiguity set with given moment information. Accordingly, distributionally robust chance-constrained approach is applied to ensure that the demands of retailers and capacity of vehicles are satisfied with high probability. Leveraging duality and linearization techniques, the proposed model is reformulated as a mixed-integer linear program. Then, the weighted goal programming approach is adopted to address the multi-objectiveness of the proposed optimization model. To certify the performance and applicability of the model, a real-world case study in the poultry industry is investigated. Finally, the sensitivity analysis is conducted to evaluate the impacts of influential parameters on the objective functions and optimal decisions, and then some managerial insights are provided based on the obtained results. © 2022 Elsevier Ltd

Resource distribution under spatiotemporal uncertainty of disease spread: Stochastic versus robust approaches

We consider the problem of optimizing locations of distribution centers (DCs) and plans for distributing resources such as test kits and vaccines, under spatiotemporal uncertainties of disease spread and demand for the resources. We aim to balance the operational cost (including costs of deploying facilities, shipping, and storage) and quality of service (reflected by demand coverage), while ensuring equity and fairness of resource distribution across multiple populations. We compare a sample-based stochastic programming (SP) approach with a distributionally robust optimization (DRO) approach using a moment-based ambiguity set. Numerical studies are conducted on instances of distributing COVID-19 vaccines in the United States and test kits, to compare SP and DRO models with a deterministic formulation using estimated demand and with the current resource distribution plans implemented in the US. We demonstrate the results over distinct phases of the pandemic to estimate the cost and speed of resource distribution depending on scale and coverage, and show the "demand-driven” properties of the SP and DRO solutions. Our results further indicate that if the worst-case unmet demand is prioritized, then the DRO approach is preferred despite of its higher overall cost. Nevertheless, the SP approach can provide an intermediate plan under budgetary restrictions without significant compromises in demand coverage. © 2022 Elsevier Ltd

A multi-objective optimization modelling for design and planning a robust closed-loop supply chain network under supplying disruption due to crises

Global crises such as COVID-19 pandemic and the Russian-Ukrainian war pose many challenges for closed-loop supply chain networks (CLSCN) due to the lack of supplies of raw materials and returned products. Therefore, this research focused on developing a multi-objective MILP mathematical model for the design and planning of CLSCN to help overcome these challenges considering the uncertainty in both the supplying capacity of the raw materials and the return rate of the used products.The developed models aim to maximize total profit, minimize total cost, and maximize overall cus-tomer service level (OCSL) using the e-lexicographic procedure.The effect of variation in both the supply capacity and return rate of the used products on the design and performance of the CLSCN have been studied. It is recommended to optimize the profit then the total cost with a maximum allowable deviation of 5%, and finally optimize the OCSL.(c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Ain Shams Uni-versity. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/ by-nc-nd/4.0/).

Integrated Supplier Selection, Scheduling, and Routing Problem for Perishable Product Supply Chain: A Distributionally Robust Approach

Due to the global outbreak of COVID-19, the perishable product supply chains have been impacted in different ways, and consequently, the risks of food insecurity have been increased in many affected countries. The uncertainty in supply and demand of perishable products, are among the most influential factors impacting the supply chain networks. Accordingly, the provision and distribution of food and other perishable commodities have become much more important than in the past. In this study, a bi-objective optimization model is proposed for a three-echelon perishable food supply chain (PFSC) network with multiple products to formulate an integrated supplier selection, production scheduling, and vehicle routing problem. The proposed model aims to mitigate the risks of demand and supply uncertainties and reinforce the distribution-related decisions by simultaneously optimizing the total network costs and suppliers’ reliability. Using the distributionally robust modeling paradigm, the probability distribution of uncertain demand is assumed to belong to an ambiguity set with given moment information. Accordingly, distributionally robust chance-constrained approach is applied to ensure that the demands of retailers and capacity of vehicles are satisfied with high probability. Leveraging duality and linearization techniques, the proposed model is reformulated as a mixed-integer linear program. Then, the weighted goal programming approach is adopted to address the multi-objectiveness of the proposed optimization model. To certify the performance and applicability of the model, a real-world case study in the poultry industry is investigated. Finally, the sensitivity analysis is conducted to evaluate the impacts of influential parameters on the objective functions and optimal decisions, and then some managerial insights are provided based on the obtained results.

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.

Resource distribution under spatiotemporal uncertainty of disease spread: Stochastic versus robust approaches

We consider the problem of optimizing locations of distribution centers (DCs) and plans for distributing resources such as test kits and vaccines, under spatiotemporal uncertainties of disease spread and demand for the resources. We aim to balance the operational cost (including costs of deploying facilities, shipping, and storage) and quality of service (reflected by demand coverage), while ensuring equity and fairness of resource distribution across multiple populations. We compare a sample-based stochastic programming (SP) approach with a distributionally robust optimization (DRO) approach using a moment-based ambiguity set. Numerical studies are conducted on instances of distributing COVID-19 vaccines in the United States and test kits, to compare SP and DRO models with a deterministic formulation using estimated demand and with the current resource distribution plans implemented in the US. We demonstrate the results over distinct phases of the pandemic to estimate the cost and speed of resource distribution depending on scale and coverage, and show the “demand-driven” properties of the SP and DRO solutions. Our results further indicate that if the worst-case unmet demand is prioritized, then the DRO approach is preferred despite of its higher overall cost. Nevertheless, the SP approach can provide an intermediate plan under budgetary restrictions without significant compromises in demand coverage.

Originating multiple-objective portfolio selection by counter-COVID measures and analytically instigating robust optimization by mean-parameterized nondominated paths

The COVID-19 pandemic is unleashing crises of humanity, economy, and finance. Portfolio selection is widely recognized as the foundation of modern financial economics. Therefore, it is naturally crucial and inviting to utilize portfolio selection in order to counter COVID-19 in stock markets. We originate a counter-COVID measure for stocks, extend portfolio selection, and construct multiple-objective portfolio selection. Because of the uncertainty in measuring counter-COVID, we perform robust optimization. Specifically, we analytically compute the optimal solutions as a trail of an optimal portfolio due to the change of counter-COVID. We call the trail as mean-parameterized nondominated path. Moreover, the path is a continuous function of the change, so the portfolio relatively mildly varies for the change. In contrast, researchers typically still focus on 2-objective robust illustrations and infrequently explicitly compute the optimal solutions for multiple-objective portfolio optimization. To the best of our knowledge, there is limited research for multiple-objective portfolio selection of COVID and for the robust optimization of multiple-objective portfolio selection. In such an area, this paper contributes to the literature. The implications to fight COVID are that investors minimize risk, maximize return, and maximize counter-COVID in stock markets and that investors ascertain the multiple-objective portfolio selection as relatively robust.