Reconciling the EU forest, biodiversity, and climate strategies.

Forests provide important ecosystem services (ESs), including climate change mitigation, local climate regulation, habitat for biodiversity, wood and non-wood products, energy, and recreation. Simultaneously, forests are increasingly affected by climate change and need to be adapted to future environmental conditions. Current legislation, including the European Union (EU) Biodiversity Strategy, EU Forest Strategy, and national laws, aims to protect forest landscapes, enhance ESs, adapt forests to climate change, and leverage forest products for climate change mitigation and the bioeconomy. However, reconciling all these competing demands poses a tremendous task for policymakers, forest managers, conservation agencies, and other stakeholders, especially given the uncertainty associated with future climate impacts. Here, we used process-based ecosystem modeling and robust multi-criteria optimization to develop forest management portfolios that provide multiple ESs across a wide range of climate scenarios. We included constraints to strictly protect 10% of Europe's land area and to provide stable harvest levels under every climate scenario. The optimization showed only limited options to improve ES provision within these constraints. Consequently, management portfolios suffered from low diversity, which contradicts the goal of multi-functionality and exposes regions to significant risk due to a lack of risk diversification. Additionally, certain regions, especially those in the north, would need to prioritize timber provision to compensate for reduced harvests elsewhere. This conflicts with EU LULUCF targets for increased forest carbon sinks in all member states and prevents an equal distribution of strictly protected areas, introducing a bias as to which forest ecosystems are more protected than others. Thus, coordinated strategies at the European level are imperative to address these challenges effectively. We suggest that the implementation of the EU Biodiversity Strategy, EU Forest Strategy, and targets for forest carbon sinks require complementary measures to alleviate the conflicting demands on forests.

Effect of breathing phase number on the 4D robust optimization for pancreatic cancer intensity modulated proton therapy.

PURPOSE: Respiratory movement, as one of the main challenges in proton therapy for pancreatic cancer patients, could not only lead to harm to normal tissues but also lead to failure of the tumor control, resulting in irreversible consequences. Including respiratory movements into the plan optimization, i.e. 4D robust optimization, may mitigate the interplay effect. However, 4D robust optimization considering images of all breathing phases is time-consuming and less efficient. This work aims to investigate the effect of the breathing phase number on the 4D robust optimization for pancreatic cancer intensity modulated proton therapy (IMPT) by examining plan quality and computational efficiency. METHODS: A total of 15 pancreatic cancer patients were retrospectively analyzed. In this study, both anterior-fields and posterior-fields plans were created for each patient. For each plan, six four-dimensional (4D) robust treatment planning strategies with different numbers of respiratory phases and one three-dimensional (3D) treatment plan were created. Optimization of the plans were performed on all ten phases (10phase plan), two extreme phases (2phase plan), two extreme phases plus an intermediate state (3phase plan), two extreme phases plus the 3D CT (3Aphase plan), six phases during the exhalation stage (6Exphase plan), six phases during the inhalation stage (6Inphase plan) and 3D Computed Tomography (CT) scan image (3D plan), respectively. 4D dynamic dose (4DDD) was then calculated to access the interplay effect by considering respiratory motion and dynamic beam delivery. Plan quality and dosimetric parameters for the target and organs at risk (OARs) were then analyzed. RESULTS: Compared to the 4D plans, 3D plan performed terribly in terms of target coverage and organs at risk. Target dose in anterior-fields plan varied slightly among all six 4D treatment planning strategies. Both the 6Exphase and 6Inphase plans demonstrated performance that was comparable to the 10phase plan in target coverage, outperforming the other five plans for anterior-fields plan. It's basically the same for the posterior-fields plan. The six strategies showed similar OARs sparing effect for both anterior-fields and posterior-fields plan. Compared with the 10phase plan, the average decline rates of the optimization time of the six plans of 2phase, 3phase, 3Aphase, 6Exphase, 6Inphase, and 3D were 73.26 ± 6.54% vs. 74.48 ± 6.63%, 65.80 ± 7.89% vs. 65.81 ± 9.58%, 54.67 ± 11.52% vs. 65.75 ± 9.58%, 42.14 ± 13.57% vs. 39.63 ± 16.93%, 37.72 ± 11.70% vs. 40.79 ± 13.62% and 75.52 ± 8.21% vs. 80.67 ± 5.62%, respectively (anterior vs. posterior). With the decrease of the number of phases selected for optimization, the decline rates increased, while the other dosimetry parameters generally showed a deterioration trend. CONCLUSION: In this study, a comprehensive evaluation of six 4D robust treatment planning strategies and one 3D treatment planning strategy for pancreatic cancer patients receiving IMPT was performed. The results showed that six 4D robust optimization strategies were comparable in common posterior field therapy. 2phase and 3phase (including 3Aphase) treatment planning strategies could replace the 10phase treatment planning strategy. It should be noted that patients with large motion amplitudes should receive special attention. The dosimetric performance of the 6Exphase and 6Inphase plans closely aligned with that of the 10phase plan in anterior fields. These plans offered a feasible alternative to 10phase treatment planning strategy by reducing optimization time while maintaining dose coverage of the target and protection of OARs. This research provides guidelines to reduce optimization time and improve clinical efficiency for pancreatic cancer IMPT.

A robust treatment planning approach for chest motion in postmastectomy chest wall intensity modulated radiation therapy.

PURPOSE: Chest wall postmastectomy radiation therapy (PMRT) should consider the effects of chest wall respiratory motion. The purpose of this study is to evaluate the effectiveness of robustness planning intensity modulated radiation therapy (IMRT) for respiratory movement, considering respiratory motion as a setup error. MATERIAL AND METHODS: This study analyzed 20 patients who underwent PMRT (10 left and 10 right chest walls). The following three treatment plans were created for each case and compared. The treatment plans are a planning target volume (PTV) plan (PP) that covers the PTV within the body contour with the prescribed dose, a virtual bolus plan (VP) that sets a virtual bolus in contact with the body surface and prescribing the dose that includes the PTV outside the body contour, and a robust plan (RP) that considers respiratory movement as a setup uncertainty and performs robust optimization. The isocenter was shifted to reproduce the chest wall motion pattern and the doses were recalculated for comparison for each treatment plan. RESULT: No significant difference was found between the PP and the RP in terms of the tumor dose in the treatment plan. In contrast, VP had 3.5% higher PTV Dmax and 5.5% lower PTV V95% than RP (p < 0.001). The RP demonstrated significantly higher lung V20Gy and Dmean by 1.4% and 0.4 Gy, respectively, than the PP. The RP showed smaller changes in dose distribution affected by chest wall motion and significantly higher tumor dose coverage than the PP and VP. CONCLUSION: We revealed that the RP demonstrated comparable tumor doses to the PP in treatment planning and was robust for respiratory motion compared to both the PP and the VP. However, the organ at risk dose in the RP was slightly higher; therefore, its clinical use should be carefully considered.

The end-of-life power battery recycling & remanufacturing center location-adjustment problem considering battery capacity and quantity uncertainty.

The booming electric vehicle market has led to an increasing number of end-of-life power batteries. In order to reduce environmental pollution and promote the realization of circular economy, how to fully and effectively recycle the end-of-life power batteries has become an urgent challenge to be solved today. The recycling & remanufacturing center is an extremely important and key facility in the recycling process of used batteries, which ensures that the recycled batteries can be handled in a standardized manner under the conditions of professional facilities. In reality, different adjustment options for existing recycling & remanufacturing centers have a huge impact on the planning of new sites. This paper proposes a mixed-integer linear programming model for the siting problem of battery recycling & remanufacturing centers considering site location-adjustment. The model allows for demolition, renewal, and new construction options in planning for recycling & remanufacturing centers. By adjusting existing sites, this paper provides an efficient allocation of resources under the condition of meeting the demand for recycling of used batteries. Next, under the new model proposed in this paper, the uncertainty of the quantity and capacity of recycled used batteries is considered. By establishing different capacity conditions of batteries under multiple scenarios, a robust model was developed to determine the number and location of recycling & remanufacturing centers, which promotes sustainable development, reduces environmental pollution and effectively copes with the risk of the future quantity of used batteries exceeding expectations. In the final results of the case analysis, our proposed model considering the existing sites adjustment reduces the cost by 3.14% compared to the traditional model, and the average site utilization rate is 15.38% higher than the traditional model. The results show that the model has an effective effect in reducing costs, allocating resources, and improving efficiency, which could provide important support for decision-making in the recycling of used power batteries.

Robust optimization of the energy concept of an industrial process w.r.t. uncertain energy costs and environmental conditions.

In order to limit the global warming to 1.5 °C as decided by the Paris Agreement, the greenhouse gas emissions have to be dramatically reduced within the next couple of years. In order to realize this in industrial sectors with low to medium temperature requirements, such as food or pulp and paper industry, fossil fuels must be replaced by renewable energy sources to generate electricity, steam and process heat. To realize this in a most economical way, a deterministic multi-objective optimization and a robust scalar optimization of the renewable energy concept of an industrial process are carried out, whereby the robust optimization takes uncertainties in the assumptions of the price for purchasing natural gas and the solar radiation into account. To set up the automated optimization processes, suitable mathematical descriptions of generation units (e.g. photovoltaic systems, wind turbines, solar thermal systems), conversion units (e.g. heat pumps, boilers) and storages (e.g. thermal, electrical) are described first. The comparison of both optimization approaches shows that deterministic optimization is able to find very good solutions, but that the spread of the objectives is significantly larger than with robust optimization when there are uncertainties in the assumptions. The robust optimization thus expands the portfolio for selecting suitable energy concepts and enables future scenarios and developments to be considered, which is particularly necessary in dynamic and heavily changing environments. Furthermore, considering the typically long operating times of industrial plants, economically well-founded decisions can be made, which can have a positive effect on the current restraint to make necessary investments..

Transformation scenarios towards multifunctional landscapes: A multi-criteria land-use allocation model applied to Jambi Province, Indonesia.

In tropical regions, shifting from forests and traditional agroforestry to intensive plantations generates conflicts between human welfare (farmers' demands and societal needs) and environmental protection. Achieving sustainability in this transformation will inevitably involve trade-offs between multiple ecological and socioeconomic functions. To address these trade-offs, our study used a new methodological approach allowing the identification of transformation scenarios, including theoretical landscape compositions that satisfy multiple ecological functions (i.e., structural complexity, microclimatic conditions, organic carbon in plant biomass, soil organic carbon and nutrient leaching losses), and farmers needs (i.e., labor and input requirements, total income to land, and return to land and labor) while accounting for the uncertain provision of these functions and having an actual potential for adoption by farmers. We combined a robust, multi-objective optimization approach with an iterative search algorithm allowing the identification of ecological and socioeconomic functions that best explain current land-use decisions. The model then optimized the theoretical land-use composition that satisfied multiple ecological and socioeconomic functions. Between these ends, we simulated transformation scenarios reflecting the transition from current land-use composition towards a normative multifunctional optimum. These transformation scenarios involve increasing the number of optimized socioeconomic or ecological functions, leading to higher functional richness (i.e., number of functions). We applied this method to smallholder farms in the Jambi Province, Indonesia, where traditional rubber agroforestry, rubber plantations, and oil palm plantations are the main land-use systems. Given the currently practiced land-use systems, our study revealed short-term returns to land as the principal factor in explaining current land-use decisions. Fostering an alternative composition that satisfies additional socioeconomic functions would require minor changes ("low-hanging fruits"). However, satisfying even a single ecological indicator (e.g., reduction of nutrient leaching losses) would demand substantial changes in the current land-use composition ("moonshot"). This would inevitably lead to a profit decline, underscoring the need for incentives if the societal goal is to establish multifunctional agricultural landscapes. With many oil palm plantations nearing the end of their production cycles in the Jambi province, there is a unique window of opportunity to transform agricultural landscapes.

Mechanisms for Robust Local Differential Privacy.

We consider privacy mechanisms for releasing data X=(S,U), where S is sensitive and U is non-sensitive. We introduce the robust local differential privacy (RLDP) framework, which provides strong privacy guarantees, while preserving utility. This is achieved by providing robust privacy: our mechanisms do not only provide privacy with respect to a publicly available estimate of the unknown true distribution, but also with respect to similar distributions. Such robustness mitigates the potential privacy leaks that might arise from the difference between the true distribution and the estimated one. At the same time, we mitigate the utility penalties that come with ordinary differential privacy, which involves making worst-case assumptions and dealing with extreme cases. We achieve robustness in privacy by constructing an uncertainty set based on a Rényi divergence. By analyzing the structure of this set and approximating it with a polytope, we can use robust optimization to find mechanisms with high utility. However, this relies on vertex enumeration and becomes computationally inaccessible for large input spaces. Therefore, we also introduce two low-complexity algorithms that build on existing LDP mechanisms. We evaluate the utility and robustness of the mechanisms using numerical experiments and demonstrate that our mechanisms provide robust privacy, while achieving a utility that is close to optimal.

Robust Optimization Research of Cyber-Physical Power System Considering Wind Power Uncertainty and Coupled Relationship.

To mitigate the impact of wind power uncertainty and power-communication coupling on the robustness of a new power system, a bi-level mixed-integer robust optimization strategy is proposed. Firstly, a coupled network model is constructed based on complex network theory, taking into account the coupled relationship of energy supply and control dependencies between the power and communication networks. Next, a bi-level mixed-integer robust optimization model is developed to improve power system resilience, incorporating constraints related to the coupling strength, electrical characteristics, and traffic characteristics of the information network. The upper-level model seeks to minimize load shedding by optimizing DC power flow using fuzzy chance constraints, thereby reducing the risk of power imbalances caused by random fluctuations in wind power generation. Furthermore, the deterministic power balance constraints are relaxed into inequality constraints that account for wind power forecasting errors through fuzzy variables. The lower-level model focuses on minimizing traffic load shedding by establishing a topology-function-constrained information network traffic model based on the maximum flow principle in graph theory, thereby improving the efficiency of network flow transmission. Finally, a modified IEEE 39-bus test system with intermittent wind power is used as a case study. Random attack simulations demonstrate that, under the highest link failure rate and wind power penetration, Model 2 outperforms Model 1 by reducing the load loss ratio by 23.6% and improving the node survival ratio by 5.3%.

Solving the waste bin location problem with uncertain waste generation rate: A bi-objective robust optimization approach.

An efficient municipal solid waste (MSW) system is critical to modern cities in order to enhance sustainability and liveability of urban life. With this aim, the planning phase of the MSW system should be carefully addressed by decision makers. However, planning success is dependent on many sources of uncertainty that can affect key parameters of the system, for example, the waste generation rate in an urban area. With this in mind, this article contributes with a robust optimization model to design the network of collection points (i.e. location and storage capacity), which are the first points of contact with the MSW system. A central feature of the model is a bi-objective function that aims at simultaneously minimizing the network costs of collection points and the required collection frequency to gather the accumulated waste (as a proxy of the collection cost). The value of the model is demonstrated by comparing its solutions with those obtained from its deterministic counterpart over a set of realistic instances considering different scenarios defined by different waste generation rates. The results show that the robust model finds competitive solutions in almost all cases investigated. An additional benefit of the model is that it allows the user to explore trade-offs between the two objectives.

Improving robustness of water supply system using a multi-objective robust optimization framework.

Due to the uncertainty of rainfall and water demand, the water supply of various participants has been challenged in such a way that this challenge has accelerated the failure of water supply system. Thus, this study proposes a multi-stage Adjustable Robust Optimization integrated to the multi-objective programming framework to drive water supply system to the failure safety zone and thereby improve robustness of system under different scenarios. Indeed, Adjustable Robust Optimization framework is applied to investigate the two uncertain factors of rainfall and water demand. A real arid area of Sistan basin in southeastern Iran is considered to analyze the proposed multi-objective programming model. Next, various comparative feasibilities under different levels of uncertainty are carried out to examine the robustness status in more detail. In the following, due to the deterioration of climatic patterns in the coming years, some managerial insights are highlighted. According to the final outputs, the domestic sector has reached more optimal value compared to that of the agricultural and industrial participants in all objectives due to less water intake, and as a result, it has a significant impact on the robustness of water supply system.

Optimal policy of ordering blood units in the hospital according to compatibility and priority transfers between blood groups under uncertainty conditions: A case study.

In spite of significant advancements in medicine, there is still a shortage of human blood in the world. At present, there is no alternative chemical process or product that can produce blood, and only humans are capable of doing so. It is for this reason that blood is such an important component of our healthcare system. Due to the perishability of blood, managing blood inventories can be challenging. The challenge is to maintain a high level of supply while minimizing loss due to expiration. The purpose of this study is to present a mathematical model that reduces inventory costs, determines the optimal ordering policy in hospitals, and prevents the loss of blood units. To determine the optimal inventory level and order volume, a mixed integer programming model is presented in both deterministic and non-deterministic conditions. In order to address the uncertainty in the problem, a robust optimization approach is used. This model minimizes the transfer of blood groups and transmission between hospitals by considering compatibility and priority. A sensitivity analysis has also been conducted on the model. Based on a case study, it is demonstrated that the costs of buying, storing, ordering, and wasting two important RBCs and platelets can be reduced.

Improving the resilience of power grids against typhoons with data-driven spatial distributionally robust optimization.

In recent years, the increased frequency of natural hazards has led to more disruptions in power grids, potentially causing severe infrastructural damages and cascading failures. Therefore, it is important that the power system resilience be improved by implementing new technology and utilizing optimization methods. This paper proposes a data-driven spatial distributionally robust optimization (DS-DRO) model to provide an optimal plan to install and dispatch distributed energy resources (DERs) against the uncertain impact of natural hazards such as typhoons. We adopt an accurate spatial model to evaluate the failure probability with regard to system components based on wind speed. We construct a moment-based ambiguity set of the failure distribution based on historical typhoon data. A two-stage DS-DRO model is then formulated to obtain an optimal resilience enhancement strategy. We employ the combination of dual reformulation and a column-and-constraints generation algorithm, and showcase the effectiveness of the proposed approach with a modified IEEE 13-node reliability test system projected in the Hong Kong region.

Effectiveness of robust optimization against geometric uncertainties in TomoHelical planning for prostate cancer.

BACKGROUND: Geometrical uncertainties in patients can severely affect the quality of radiotherapy. PURPOSE: We evaluated the dosimetric efficacy of robust optimization for helical intensity-modulated radiotherapy (IMRT) planning in the presence of patient setup uncertainty and anatomical changes. METHODS: Two helical IMRT plans for 10 patients with localized prostate cancer were created using either minimax robust optimization (robust plan) or a conventional planning target volume (PTV) margin approach (PTV plan). Plan robustness was evaluated by creating perturbed dose plans with setup uncertainty from isocenter shifts and anatomical changes due to organ variation. The magnitudes of the geometrical uncertainties were based on the patient setup uncertainty considered during robust optimization, which was identical to the PTV margin. The homogeneity index, and target coverage (TC, defined as the V100% of the clinical target volume), and organs at risk (OAR; rectum and bladder) doses were analyzed for all nominal and perturbed plans. A statistical t-test was performed to evaluate the differences between the robust and PTV plans. RESULTS: Comparison of the nominal plans showed that the robust plans had lower OAR doses and a worse homogeneity index and TC than the PTV plans. The evaluations of robustness that considered setup errors more than the PTV margin demonstrated that the worst-case perturbed scenarios for robust plans had significantly higher TC while maintaining lower OAR doses. However, when anatomical changes were considered, improvement in TC from robust optimization was not observed in the worst-case perturbed plans. CONCLUSIONS: For helical IMRT planning in localized prostate cancer, robust optimization provides benefits over PTV margin-based planning, including better OAR sparing, and increased robustness against systematic patient-setup errors.

A Low-Carbon and Economic Dispatch Strategy for a Multi-Microgrid Based on a Meteorological Classification to Handle the Uncertainty of Wind Power.

In a modern power system, reducing carbon emissions has become a significant goal in mitigating the impact of global warming. Therefore, renewable energy sources, particularly wind-power generation, have been extensively implemented in the system. Despite the advantages of wind power, its uncertainty and randomness lead to critical security, stability, and economic issues in the power system. Recently, multi-microgrid systems (MMGSs) have been considered as a suitable wind-power deployment candidate. Although wind power can be efficiently utilized by MMGSs, uncertainty and randomness still have a significant impact on the dispatching and operation of the system. Therefore, to address the wind power uncertainty issue and achieve an optimal dispatching strategy for MMGSs, this paper presents an adjustable robust optimization (ARO) model based on meteorological clustering. Firstly, the maximum relevance minimum redundancy (MRMR) method and the CURE clustering algorithm are employed for meteorological classification in order to better identify wind patterns. Secondly, a conditional generative adversarial network (CGAN) is adopted to enrich the wind-power datasets with different meteorological patterns, resulting in the construction of ambiguity sets. Thirdly, the uncertainty sets that are finally employed by the ARO framework to establish a two-stage cooperative dispatching model for MMGS can be derived from the ambiguity sets. Additionally, stepped carbon trading is introduced to control the carbon emissions of MMGSs. Finally, the alternative direction method of multipliers (ADMM) and the column and constraint generation (C&CG) algorithm are adopted to achieve a decentralized solution for the dispatching model of MMGSs. Case studies indicate that the presented model has a great performance in improving the wind-power description accuracy, increasing cost efficiency, and reducing system carbon emissions. However, the case studies also report that the approach consumes a relative long running time. Therefore, in future research, the solution algorithm will be further improved for the purpose of raising the efficiency of the solution.

Risk-Aware Distributionally Robust Optimization for Mobile Edge Computation Task Offloading in the Space-Air-Ground Integrated Network.

As an emerging network paradigm, the space-air-ground integrated network (SAGIN) has garnered attention from academia and industry. That is because SAGIN can implement seamless global coverage and connections among electronic devices in space, air, and ground spaces. Additionally, the shortage of computing and storage resources in mobile devices greatly impacts the quality of experiences for intelligent applications. Hence, we plan to integrate SAGIN as an abundant resource pool into mobile edge computing environments (MECs). To facilitate efficient processing, we need to solve the optimal task offloading decisions. In contrast to existing MEC task offloading solutions, we have to face some new challenges, such as the fluctuation of processing capabilities for edge computing nodes, the uncertainty of transmission latency caused by heterogeneous network protocols, the uncertain amount of uploaded tasks during a period, and so on. In this paper, we first describe the task offloading decision problem in environments characterized by these new challenges. However, we cannot use standard robust optimization and stochastic optimization methods to obtain optimal results under uncertain network environments. In this paper, we propose the 'condition value at risk-aware distributionally robust optimization' algorithm for task offloading, denoted as RADROO, to solve the task offloading decision problem. RADROO combines the distributionally robust optimization and the condition value at risk model to achieve optimal results. We evaluated our approach in simulated SAGIN environments, considering confidence intervals, the number of mobile task offloading instances, and various parameters. We compare our proposed RADROO algorithm with state-of-the-art algorithms, such as the standard robust optimization algorithm, the stochastic optimization algorithm, the DRO algorithm, and the Brute algorithm. The experimental results show that RADROO can achieve a sub-optimal mobile task offloading decision. Overall, RADROO is more robust than others to the new challenges mentioned above in SAGIN.

Research on Real-Time Robust Optimization of Perishable Supply-Chain Systems Based on Digital Twins.

Aiming at the real-time robust optimization problem of perishable supply-chain systems in complex environments, a real-time robust optimization scheme based on supply-chain digital twins is proposed. Firstly, based on the quantitative logical relationship between production and sales of single-chain series supply-chain system products, the state space equation of the supply-chain system with logical characteristics, structural characteristics, and quantitative characteristics was constructed, and twin data were introduced to construct the digital twins of supply chains based on the state-space equation. Secondly, the perishable supply-chain system in complex environments was regarded as an uncertain closed-loop system from the perspective of the state space equation, and then a robust H∞ controller design strategy was proposed, and the supply-chain digital twins was used to update and correct the relevant parameters of the supply-chain system in real-time, to implement the real-time robust optimization based on the supply-chain digital twins. Finally, the simulation experiment was carried out with a cake supply-chain production as an example. The experimental results show that the real-time updating of relevant parameters through the digital twins can help enterprise managers to formulate reasonable management plans, effectively avoid the shortage problem of enterprises in the cake supply-chain system, and reduce the maximum inventory movement standard deviation of each link by 12.65%, 6.50%, and 14.87%, and the maximum production movement standard deviation by 70.21%, 56.84%, and 45.19%.

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.

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.

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%.

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.