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Interest in integrating lot-sizing and cutting stock problems has been increasing over the years. This integrated problem has been applied in many industries, such as paper, textile and furniture. Yet, there are only a few studies that acknowledge the importance of uncertainty to optimise these integrated decisions. This work aims to address this gap by incorporating demand uncertainty through stochastic programming and robust optimisation approaches. Both robust and stochastic models were specifically conceived to be solved by a column generation method. In addition, both models are embedded in a rolling-horizon procedure in order to incorporate dynamic reaction to demand realisation and adapt the models to a multistage stochastic setting. Computational experiments are proposed to test the efficiency of the column generation method and include a Monte Carlo simulation to assess both stochastic programming and robust optimisation for the integrated problem. Results suggest that acknowledging uncertainty can cut costs by up to 39.7%, while maintaining or reducing variability at the same time. [ABSTRACT FROM AUTHOR]

Success of the UK's Spherical Tokamak for Energy Production (STEP) programme requires a robust plasma control system. This system has to guide the plasma from initiation to the burning phase, maintain it there, produce the desired fusion power for the desired duration and then terminate the plasma safely. This has to be done in a challenging environment with limited sensors and without overloading plasma-facing components. The plasma parameters and the operational regime in the STEP prototype will be very different from tokamaks, which are presently in operation. During fusion burn, the plasma regime in STEP will be self-organizing, adding further complications to the plasma control system design. This article describes the work to date on the design of individual controllers for plasma shape and position, magneto hydrodynamic instabilities, heat load and fusion power. Having studied 'normal' operation, the article discusses the philosophy of how the system will handle exceptions, when things do not go exactly as planned. This article is part of the theme issue 'Delivering Fusion Energy – The Spherical Tokamak for Energy Production (STEP)'. [ABSTRACT FROM AUTHOR]

This article focuses on the problem of robust adaptive safety control of a class of nonlinear systems with parametric uncertainties. Two novel definitions, that is, robust adaptive control Lyapunov function (RACLF) and robust adaptive control barrier function (RACBF) are introduced in this article. Also, an estimation of unknown parameters is obtained based on multiple identification models, state predictors and a logic switching mechanism. The switching mechanism plays a vital role in enhancing the transient properties of nonlinear systems. Meanwhile, a safe motion framework for differential robots is provided based on the existence of parametric uncertainties in RACLF and RACBF, and a safe and stable controller is obtained by solving quadratic programming. Finally, simulation results of differential robot capable of safe motion in space are presented to verify the validity of the design method. [ABSTRACT FROM AUTHOR]

The Chinese postman problem (CPP) is a widely recognized combinatorial optimization problem with numerous real-world applications. Modeling such real-world applications often involves considering uncertain variables. Robust optimization is one of the prominent approaches for solving optimization problems when uncertainties are present in the parameters of the optimization problem. In this paper, we delve into the realm of the uncertain multi-objective Chinese postman problem, incorporating budget constraints while simultaneously optimizing profit maximization and time minimization, all within the framework of robust optimization methodology. We formulate the deterministic form of uncertain multi-objective CPP for three different types of uncertainty sets: ellipsoidal, polyhedral, and budgeted. To tackle these formulations, we employ four established multi-objective solution strategies: the global criteria approach, the fuzzy programming method, ϵ -constraint, and the Genetic algorithm. Subsequently, we conduct numerical experiments to verify the proposed models. [ABSTRACT FROM AUTHOR]

We consider data-driven approaches that integrate a machine learning prediction model within distributionally robust optimization (DRO) given limited joint observations of uncertain parameters and covariates. Our framework is flexible in the sense that it can accommodate a variety of regression setups and DRO ambiguity sets. We investigate asymptotic and finite sample properties of solutions obtained using Wasserstein, sample robust optimization, and phi-divergence-based ambiguity sets within our DRO formulations, and explore cross-validation approaches for sizing these ambiguity sets. Through numerical experiments, we validate our theoretical results, study the effectiveness of our approaches for sizing ambiguity sets, and illustrate the benefits of our DRO formulations in the limited data regime even when the prediction model is misspecified. [ABSTRACT FROM AUTHOR]

Integrating inventory with production–distribution operations has critical importance realized by several companies' top management a long time before; however, challenging. The management has to decide where to shift products, which demand to fulfil, from which distribution centre (s), how much inventory to keep and a host of critical and complex decisions. As the organization increase in size and complexity, more robust optimization tools required to help analyze and comprehend these complex decisions. In this study, inventory, production and distribution problems with planned shortages, back-ordered quantity and delay in replenishment studied under uncertainty. A multi-objective multi-product model for minimizing the inventory, production and shipment costs and delivery time developed for the integrated system. The study considers the model's different input parameters under a fuzzy and stochastic environment. The fuzziness converted to deterministic using interval type-2 trapezoidal fuzzy number. The randomness follows the Maxwell–Boltzmann distribution in which the deterministic form obtained using chance-constrained programming. The developed integrated model illustrated a numerical example in a manufacturing firm and solved using three robust goal programming variants. The results indicated inventory, production and transshipment costs are 99% minimized with 100% delivery time achievement. [ABSTRACT FROM AUTHOR]

It is challenging for decision‐makers (DMs) to deal with uncertainties in multi‐level agricultural water resource systems, where DMs independently make decisions but have different levels of power. In this paper, we model the multi‐level agricultural water resources system under deep uncertainties as a Stackelberg game, use multi‐level programming to solve equilibrium water allocation problems, and introduce robustness metrics into multi‐level programming to balance solution feasibility and model optimality within uncertain environments. The approach is applied to a shallow groundwater area with three decision levels, pursuing, from the top level to the bottom one, high food production, fair water allocation, and increased economic benefit. The model generated a series of optimal equilibrium solutions with different robustness degrees. DMs can choose "rational" solutions according to their acceptable costs, oriented robustness degree, expected objective values, and advance risk assessment of uncertainties. Among these solutions, we capture a critical point with high objective values and strong robustness, where DMs can accomplish both objective optimality and solution robustness with a low cost. The proposed approach in this study provides a posterior decision support to consider solution robustness while designing policies in multi‐level agricultural water resource systems under deep uncertainties. Key Points: An introduction of robust measure into multi‐level programming balances solution robustness and model optimalityThere is a critical point that decision makers can achieve high objective values and strong robustness with low costs [ABSTRACT FROM AUTHOR]

A concurrent learning (CL) adaptive control is proposed for a class of nonlinear systems in the presence of dead-zone input nonlinearity to guarantee the exponential convergence of the tracking and the parameter estimation errors. The proposed method enriches and encompasses the conventional filtering-based CL by proposing robust and optimal terms. The optimal term is designed by solving a suitable quadratic programming optimization problem based on control Lyapunov function theory which also meets the need for prescribed control bounds. A suitable robust term is proposed to tackle the presence of the dead-zone input nonlinearity. Recent methods of adaptive CL tune the control parameters using trial and error, which is a tedious task. In this paper, by some analysis and proposing two nonlinear optimization problems, the values of the control parameters are derived. The nonlinear optimization problems are solved using the time-varying iteration particle swarm optimization algorithm. The simulation results indicate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Relief logistics is vital to disaster relief management. Herein, a risk-averse two-stage distributionally robust programming model is proposed to provide decision support for planning disaster relief logistics. It is distinct from the conventional disaster relief logistics planning problem in that (i) the facility location-inventory model and the multi-commodity network flow formulation are integrated; (ii) the probability distribution information of the supply, demand, and road link capacity is partially known, and (iii) the two-stage distributionally robust optimisation (DRO) method based on the worst-case mean-conditional value-at-risk criterion is developed. For tractability, we reformulate the proposed DRO model as equivalent mixed-integer linear programs for box and polyhedral ambiguity sets, which can be directly solved to optimality using the CPLEX software. To evaluate the validity of the proposed DRO model, we conduct numerical experiments based on a real-world case study addressing hurricane threats in the Gulf of Mexico region of the United States. Furthermore, we compare the performance of the proposed DRO model with that of the conventional two-stage stochastic programming model. Finally, we report the managerial implications and insights of using the risk-averse two-stage DRO approach for disaster relief management. [ABSTRACT FROM AUTHOR]

Hydrogel‐based engineered cardiac patches (ECP) hold great promise as potential treatment options for myocardial infarction (MI). However, optimizing the preparation of ECP with better biocompatibility, mechanical stability, and adaptation to MI repair remains a challenge. In this study, a chitosan (CS) hydrogel with good mechanical robustness through programmed control of hydrogen bonding is constructed to adapt to the continuous beating of myocardial tissue. With the synergistic effects of lipoic acid (TA), proanthocyanidins (PAs), and Eu3+, a functional platform capable of improving mitochondrial function, antioxidation, and pro‐vascularization is further constructed for the adaptive repair of the MI microenvironment. The fabricated functionalized chitosan hydrogel (CS/TA@PAs‐Eu) possessed good mechanical stability and ionic conductivity, showing the potential for long‐term adaptation to myocardial tissue pulsation. Also, the CS/TA@PAs‐Eu hydrogel promoted cardiomyocytes (CMs) maturation and functionalization, and effectively improved mitochondrial function, scavenged reactive oxygen species (ROS) as well as promoted angiogenesis. Animal studies indicated that the CS/TA@PAs‐Eu hydrogel can perform adaptive repair of MI to prevent left ventricular (LV) remodeling and restore cardiac function. This study highlights a functionalized hydrogel ECP with good biocompatibility and mechanical robustness for the adaptive repair of MI. [ABSTRACT FROM AUTHOR]

As diversity among patient populations continues to grow, racial and ethnic diversity in the neurology workforce is increasingly essential to the delivery of culturally competent care and for enabling inclusive, generalizable clinical research. Unfortunately, diversity in the workforce is an area in which the field of neurology has historically lagged and faces formidable challenges, including an inadequate number of trainees entering the field, bias experienced by trainees and faculty from minoritized racial and ethnic backgrounds, and 'diversity tax', the disproportionate burden of service work placed on minoritized people in many professions. Although neurology departments, professional organizations and relevant industry partners have come to realize the importance of diversity to the field and have taken steps to promote careers in neurology for people from minoritized backgrounds, additional steps are needed. Such steps include the continued creation of diversity leadership roles in neurology departments and organizations, the creation of robust pipeline programmes, aggressive recruitment and retention efforts, the elevation of health equity research and engagement with minoritized communities. Overall, what is needed is a shift in culture in which diversity is adopted as a core value in the field. In this Review, Hamilton dissects the importance of racial and ethnic diversity among the neurology workforce for providing inclusive and equitable care to diverse populations. The Review summarizes current barriers to achieving diversity in the field and presents strategic approaches to overcoming these. [ABSTRACT FROM AUTHOR]

Recently, the benefits of employing philosophical principles to optimize supply chains in the construction sector have been delved into by many researchers. This comprises three key segments: customers or employers, design, and construction. To address challenges and enhance the viability and competitiveness of the construction sector, the adoption of supply chain management has been proposed. This study develops a multi-objective mathematical model to design a construction supply chain, which includes a primary supplier and multiple customer projects. The primary goal is to ensure that the necessary materials are delivered at different intervals, considering each product's specific technical requirements and life cycles. It is crucial to prevent late deliveries, as they can lead to product wastage and substantially impact management decisions. Additionally, it is important to highlight that this study addresses the uncertainty in the supply chain, which further complicates the planning and decision-making processes. Accordingly, some related sensitivity analyses were done to reveal the profound influence of uncertainty on the proposed model, and its important uncertain parameters were specified. Next, the study employs the robust programming approach introduced by Bertsimas and Sim to tackle the uncertainty. To validate the proposed approach, it is implemented in a real-world case study. For small-size problems, the modified weighted Chebyshev method is used for solving the model. Then, the best–worst multi-criteria decision-making technique assesses the suggested model's ability to solve various problems in larger sizes. Subsequently, the study applies meta-heuristic algorithms like MOGA-II, MORDA, and MOSA to solve large-size problems. According to the outputs analysis, the MORDA algorithm executed better than the others. Ultimately, the study derives managerial insights based on the findings from the sensitivity analysis. [ABSTRACT FROM AUTHOR]

This research suggests a Robust and Risk-Averse Medical Waste Chain Network Design by considering Viability requirements (RRMWCNDV). The aim is to locate a waste management facility that minimizes waste and promotes the recycling of materials like metal and plastic, contributing to environmental benefits. The proposed RRMWCNDV aims to be viable, robust and risk-averse. A two-stage robust stochastic programming model was utilized to develop this framework. It incorporates risk by employing the Weighted Value at Risk (WVaR) approach for the first time. The study reveals that incorporating risk and robustness scenarios results in a lower cost function. The degree of conservatism in decision-making can be adjusted between 0% and 100%, increasing the cost function. The confidence level in WVaR indicates risk aversion, with an increase in the cost function with a 4% increase. The agility coefficient, which indicates the percentage of waste demand production from HC transferred to another facility, also affects the cost function and population risk. A decrease in the sustainability coefficient results in a 53% rise in the cost function and a 12.82% increase in population risk. The model demonstrates NP-hard characteristics and becomes exponentially complex for larger scales. [ABSTRACT FROM AUTHOR]

The uncertainties of the power load, wind power, and photovoltaic power lead to errors between point prediction values and real values, which challenges the safe operation of distribution networks. In this paper, a robust reactive power scheduling (RRPS) model based on a modified bootstrap technique is proposed to consider the uncertainties of power loads and renewable energy sources. Firstly, a deterministic reactive power scheduling (DRPS) model and an RRPS model are formulated. Secondly, a modified bootstrap technique is proposed to estimate prediction errors of power loads and renewable energy sources without artificially assuming the probability density function of prediction errors. To represent all possible scenarios, point prediction values and prediction errors are combined to construct two worst-case scenarios in the RRPS model. Finally, the RRPS model is solved to find a scheduling scheme, which ensures the security of distribution networks for all possible scenarios in theory. Simulation results show that the worstcase scenarios constructed by the modified bootstrap technique outperform popular baselines. Besides, the RRPS model based on the modified bootstrap technique balances economics and security well.

Supply Chain Production Planning (SCPP) is a core value of operation management that affects organization performance and market competitiveness. In the presence of increasing competitive market pressure, firms need to look for a surviving way to improve themselves by attacking several goals simultaneously to gain competitive advantages. Therefore, a practical approach that can handle two main obstacles, i.e. conflicting objectives and an uncertain environment, is needed to assist Decision Makers (DMs) in planning an efficient SCPP. To tackle SCPP problems, a five-phase combinatorial approach is proposed to overcome not only these two main obstacles but also several weak points of traditional Fuzzy Linear Programming (FLP). The five-phase combinatorial approach is developed by integrating the application of Intuitionistic Fuzzy Linear Programming (IFLP), Realistic Robust Programming (RRP), Chance-Constrained Programming (CCP), and Augmented Epsilon Constraint (AUGMECON). Then, a case study of SCPP is performed using this approach by aiming to minimize total supply chain costs, minimize shortages of products, and maximize total values of purchasing where operating costs, customer demand, defective rate, and service level are imprecise. The performance of the proposed approach shows to outperform the traditional FLP approach in terms of hesitation allowance, robust modeling, satisfaction and non-satisfaction levels consideration, and providing a set of strong Pareto optimal solutions. These benefits help DMs to obtain the best compromise solution that is more robust and concrete as well as reflects more intention of DMs. [ABSTRACT FROM AUTHOR]

Flexible and rapidly adaptable automated production processes, e.g. with collaborative lightweight robots, are key aspects for the competitiveness of companies in globalised markets. However, software adaptation of the robot still requires specific programming skills. We have developed a human-centred programming by demonstration approach based on augmented reality to enable operators to intuitively adapt the robot programme. The developed hand-interaction model overcomes the challenge of object tracking during the assembly demonstration phase. This allows quick programme modifications by the operator using the head-mounted augmented reality device. The human-in-the-loop concept ensures a highly reliable and robust programming process. [ABSTRACT FROM AUTHOR]

The low efficiency and high cost of fresh agricultural product terminal distribution directly restrict the operation of the entire supply network. To reduce costs and optimize the distribution network, we construct a mixed integer programming model that comprehensively considers to minimize fixed, transportation, fresh-keeping, time, carbon emissions, and performance incentive costs. We analyzed the performance of traditional rider distribution and robot distribution modes in detail. In addition, the uncertainty of the actual market demand poses a huge threat to the stability of the terminal distribution network. In order to resist uncertain interference, we further extend the model to a robust counterpart form. The results of the simulation show that the instability of random parameters will lead to an increase in the cost. Compared with the traditional rider distribution mode, the robot distribution mode can save 12.7% on logistics costs, and the distribution efficiency is higher. Our research can provide support for the design of planning schemes for transportation enterprise managers. [ABSTRACT FROM AUTHOR]

This paper converts the robust linear programming under the polyhedral uncertainty set to standard linear programming. After eliminating the parameter uncertainty, we design a projection neural network to address the problem. The equilibrium point of the neural network model is theoretically proved to be stable in the Lyapunov sense and globally convergent to the optimal solution to robust linear programming. Two numerical examples are provided to illustrate the validity and performance of the proposed approach. [ABSTRACT FROM AUTHOR]

Defanging equipment layout in multi-floor satellites consists of two primary tasks: (i) allocating the equipment to the satellite's layers and (ii) placing the equipment in each layer individually. In reviewing the previous literature in this field, firstly, the issue of assigning equipment to layers is observed in a few articles, and regarding the layout, the non-overlapping constraint has always been a challenge, particularly for components that do not have a circular cross-section. In addition to presenting a heuristic method for allocating equipment to different layers of the satellite, this article presents a robust flexible programming model (RFPM) for the placement of equipment at different layers, taking into account the inherent flexibility of the equipment in terms of placement and the subject of uncertainty. This model is based on the existing uncertainty between the distances between pieces of cuboid equipment, which has not been addressed in any of the previous research, and by comparing its outputs with cases from past studies, we demonstrate a significantly higher efficiency related to placing the equipment and meeting the limit of non-overlapping constraints between the equipment. Finally, it would be possible to reduce the design time in the conceptual and preparatory stages, as well as the satellite's overall size, while still satisfying other constraints such as stability and thermal limitations, moments of inertia and center of gravity. [ABSTRACT FROM AUTHOR]

Decisions made for designing and operating a warehouse system are of great significance. These operational decisions are strongly affected by total logistics costs, including investment and direct operating costs. The number of orders made by customers in the logistics section of warehouse management is very high because the number, type of products and items ordered by different customers vary broadly. However, machines layout for picking up products at logistics centres is minimal, inflexible, and, in some cases, inconclusive. In this study, we address joint order batching procedures of orders considering picker routing problem as a mixed-integer programming model. Extensive numerical experiments were generated in small, medium, and large sizes. In order to consider the uncertainty of parameters, we applied robust possibilistic programming for this problem. Three different meta-heuristic algorithms; genetic algorithm, particle swarm optimisation algorithm, and honey artificial bee colony algorithms are used as solution approaches to solve the formulated model. The performance of solution approaches over the problem was analysed using several test indexes. In all three group examples, there was no significant difference among mean values of the objective function, while there was a remarkable difference among computing times. [ABSTRACT FROM AUTHOR]

Malawi has a population of around 20 million people and is one of the world's most economically deprived nations. Severe mental illness (largely comprising psychoses and severe mood disorders) is managed by a very small number of staff in four tertiary facilities, aided by clinical officers and nurses in general hospitals and clinics. Given these constraints, psychosis is largely undetected and untreated, with a median duration of untreated psychosis (DUP) of around six years. Our aim is to work with people with lived experience (PWLE), caregivers, local communities and health leaders to develop acceptable and sustainable psychosis detection and management systems to increase psychosis awareness, reduce DUP, and to improve the health and lives of people with psychosis in Malawi. We will use the UK Medical Research Council guidance for developing and evaluating complex interventions, including qualitative work to explore diverse perspectives around psychosis detection, management, and outcomes, augmented by co-design with PWLE, and underpinned by a Theory of Change. Planned deliverables include a readily usable management blueprint encompassing education and community supports, with an integrated care pathway that includes Primary Health Centre clinics and District Mental Health Teams. PWLE and caregivers will be closely involved throughout to ensure that the interventions are shaped by the communities concerned. The effect of the interventions will be assessed with a quasi-experimental sequential implementation in three regions, in terms of DUP reduction, symptom remission, functional recovery and PWLE / caregiver impact, with quality of life as the primary outcome. As the study team is focused on long-term impact, we recognise the importance of having embedded, robust evaluation of the programme as a whole. We will therefore evaluate implementation processes and outcomes, and cost-effectiveness, to demonstrate the value of this approach to the Ministry of Health, and to encourage longer-term adoption across Malawi. [ABSTRACT FROM AUTHOR]

In this paper, we deal with second-order conic programming (SOCP) duals for a robust convex quadratic optimization problem with uncertain data in the constraints. We first introduce a SOCP dual problem for this robust convex quadratic optimization problem with polytopic uncertain sets. Then, we obtain a zero duality gap result between this robust convex quadratic optimization problem and its dual problem in terms of a new robust type characteristic cone constraint qualification. We also construct a SOCP dual problem for this robust convex quadratic optimization problem with norm-constrained uncertain sets and obtain the corresponding zero duality gap result between them. Moreover, some numerical examples are given to explain the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, a bi-objective mixed-integer linear programming model is constructed to manage the pharmaceutical supply chain of a hospital. The proposed model aims to concurrently reduce the overall cost of obtaining drugs from several vendors and choose the best suitable source. The suggested model takes into account supplier distance, inventory management, and multi-product and multi-period. The major assumptions of the proposed model are product storage for future periods of decreased demand and supplier capacity. The results indicate that the ideal approach can minimize hospital supply and pharmaceutical planning expenses. The Best-Worst and TOPSIS methods determine which pharmaceutical supplier should be selected for future orders. The suggested model identifies human resource capability as an essential factor that might significantly affect the system's total cost. The results of applying the model and the sensitivity analysis validate the efficacy and validity of the suggested mathematical model and solution strategy. [ABSTRACT FROM AUTHOR]

Bedside point-of-care ultrasound scans are a cheap, quick and safe diagnostic tool. There is increasing evidence for the use of point-of-care surgeon-performed ultrasound scans in adults, however there are fewer studies of its use in children. This systematic review aims to provide an up-to-date summary of the evidence behind surgeon-performed ultrasound scans in paediatric surgery. The PubMed database was used to conduct this systematic review between the dates 1 Jan 1980 to 1 June 2020 (last search: 1 June 2020). Seven primary research studies were included in this review. There is good evidence for the use of ultrasound scans in appendicitis and hypertrophic pyloric stenosis. Training times are easily achievable and transferable within a surgical department. Although the use of surgeon-performed bedside ultrasound scans has been described in appendicitis and hypertrophic pyloric stenosis, more research is required to embed this into clinical practice, particularly in low volume centres such as district general hospitals. A robust training programme is also recommended to incorporate ultrasound scans into clinical practice. • Evidence for ultrasound scans in appendicitis and hypertrophic pyloric stenosis. • More research needed to implement in hospitals, especially small volume centres. • Robust ultrasound training programme recommended for clinical practice. [ABSTRACT FROM AUTHOR]

• An original centrality metric objective function for the LMRNP is introduced. • A new data-driven adaptive distributionally robust equilibrium programming method. • The DBSCAN algorithm is newly adopted to construct a data-driven ambiguity set. • The proposed model is theoretically derived into a computationally solvable form. • The performance of the deduced model is validated by two real data sets. This paper studies a variant of the two-stage last mile relief network problem by introducing a centrality metric objective including the distance centrality metric, the demand centrality value-at-risk and the residual supplies centrality metric. Under the scenario-based design, the demand in each scenario is described as a random fuzzy variable whose probability distribution is ambiguous. In order to characterize its ambiguousness, this paper designs a Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm based on sample data to construct a data-driven ambiguity set containing the support and mean, which not only realizes the visualization of the ambiguous probability distribution, but also provides a finite set of scenarios for the uncertain demand. Given the constructed data-driven ambiguity set, this paper proposes a data-driven adaptive distributionally robust equilibrium programming (DDADREP) method for the last mile relief network problem (LMRNP). In view of its computational difficulty, the safe approximation, duality technique and credibility measure theory are used to approximate it as a mixed integer second-order cone programming with significant computational advantages. Finally, the proposed model is validated with two real-world cases, and its effectiveness as well as advantages is demonstrated by comparison with the classical robust optimization and the nominal equilibrium optimization, respectively. [ABSTRACT FROM AUTHOR]

Maritime emergency materials distribution is a key aspect of maritime emergency responses. To effectively deal with the challenges brought by the uncertainty of the maritime transport environment, the multi-agent joint decision-making location-routing problem of maritime emergency materials distribution (MEMD-LRP) under an uncertain decision-making environment is studied. First, two robust bi-level optimization models of MEMD-LRP are constructed based on the effect of the uncertainty of the ship's sailing time and demand of emergency materials at the accident point, respectively, on the premise of considering the rescue time window and priority of emergency materials distribution. Secondly, with the help of robust optimization theory and duality theory, the robust optimization models are transformed into robust equivalent models that are easy to solve. Finally, a hybrid algorithm based on the ant colony and tabu search (ACO-TS) algorithm solves multiple sets of numerical cases based on the case design of the Bohai Sea area, and analyzes the influence of uncertain parameters on the decision making of MEMD-LRP. The study of MEMD-LRP under uncertain decision-making environments using bi-level programming and robust optimization methods can help decision makers at different levels of the maritime emergency logistics system formulate emergency material reserve locations and emergency material distribution schemes that can effectively deal with the uncertainty in maritime emergencies. [ABSTRACT FROM AUTHOR]

This research addresses the problem regarding the efficient operation of photovoltaic (PV) plants in monopolar direct current (DC) distribution networks from a perspective of convex optimization. PV plant operation is formulated as a nonlinear programming (NLP) problem while considering two single-objective functions: the minimization of the expected daily energy losses and the reduction in the expected CO2 emissions at the terminals of conventional generation systems. The NLP model that represents the energy management system (EMS) design is transformed into a convex optimization problem via the second-order cone equivalent of the product between two positive variables. The main contribution of this research is that it considers the uncertain nature of solar generation and expected demand curves through robust convex optimization. Numerical results in the monopolar DC version of the IEEE 33-bus grid demonstrate the effectiveness and robustness of the proposed second-order cone programming model in defining an EMS for a monopolar DC distribution network. A comparative analysis with four different combinatorial optimizers is carried out, i.e., multiverse optimization (MVO), the salp swarm algorithm (SSA), the particle swarm optimizer (PSO), and the crow search algorithm (CSA). All this is achieved while including an iterative convex method (ICM). This analysis shows that the proposed robust model can find the global optimum for two single-objective functions. The daily energy losses are reduced by 44.0082% with respect to the benchmark case, while the CO2 emissions (kg) are reduced by 27.3771%. As for the inclusion of uncertainties, during daily operation, the energy losses increase by 22.8157%, 0.2023%, and 23.7893% with respect to the benchmark case when considering demand uncertainty, PV generation uncertainty, and both. Similarly, CO2 emissions increase by 11.1854%, 0.9102%, and 12.1198% with regard to the benchmark case. All simulations were carried out using the Mosek solver in the Yalmip tool of the MATLAB software. [ABSTRACT FROM AUTHOR]

The southern Appalachian region is a hotspot of ecological biodiversity that is under increasing threat from climate change and rapid population growth. We posit that informal science education is uniquely adapted to foster environmental stewardship in the region, but the current state of informal science education within the southern Appalachians is poorly understood. We reviewed current informal science education centers (ISECs), which we define as centers for science learning outside of structured curriculum (n = 166). For each of these centers, we compiled information on geographical location, programs offered, and funding sources. We found large geographic gaps in ISEC coverage that often aligned with low-population, low-income counties. The most common program type in our dataset was field trips, followed by public programming, while research and virtual programming were the least often offered. ISECs that had funding from multiple organizations generally had the most diverse and robust programming. [ABSTRACT FROM AUTHOR]

Reconfiguring the structure of the supply chain network is one of the most strategic and vital decisions in designing a supply chain network. In this study, a Closed-Loop Blood Supply Chain Network (CLBSCN) considering blood group compatibility, ABO-Rh(D), and blood product shelf life has been studied to determine the best strategic and tactical decisions simultaneously considering lateral resupply/transshipment and service-level maximization. Several vital parameters, including supply and demand, are considered fuzzy numbers to approximate reality due to the nature of the world. Furthermore, two crucial factors include ABO-Rh(D) and blood product shelf life considered, while the concept of lateral resupply governs the interconnections of hospitals' excess blood units. We propose a fuzzy multi-objective Mixed-Integer Non-Linear Programming (MINLP) model to consider two critical objective functions: minimizing the total costs of the network and maximizing the minimum service level to the patients at each Hospital. The fuzzy multi-objective MINLP model is converted to a deterministic multi-objective model using the equivalent auxiliary crisp model to deal with uncertainty. Then, by utilizing two interactive fuzzy solution approaches, the results have been compared based on a real case study to suggest the best solution for the proposed model. Also, we conduct sensitivity analysis on essential parameters such as demand, supply, and capacity to understand how these parameter variations impact two proposed objective functions. Then, the proposed model is tested on a real case study for model validation. The results confirmed that considering the lateral resupply could significantly save the costs of the designed network by a total of $343,000. Interestingly, maximizing the minimum service level at hospitals increased the service level from 58% to 68%. [ABSTRACT FROM AUTHOR]

Organ transplantation is a crucial task in the healthcare supply chain, which organizes the supply and demand for various vital organs. In this regard, dealing with uncertainty is one of the main challengings in designing an organ transplant supply chain. To address this gap, in the present research, a mathematical formulation and solution method is proposed to optimize the organ transplants supply chain under shipment time uncertainty. A possibilistic programming model and simulation-based solution method are developed for organ transplant center location, allocation, and distribution. The proposed mathematical model optimizes the overall cost by considering the fuzzy uncertainty of organ demands and transportation time. Moreover, a novel simulation-based optimization is applied using the credibility theory to deal with the uncertainty in the optimization of this mathematical model. In addition, the proposed model and solution method are evaluated by implementing different test problems. The numerical results demonstrate that the optimal credibility level is between 0.2 and 0.6 in all tested cases. Moreover, the patient's satisfaction rate is higher than the viability rate in the designed organ supply chain. [ABSTRACT FROM AUTHOR]

Recent literature highlights the value of applying theories of change in the design of projects and programmes preventing/countering violent extremism (P/CVE). Theories of change are tools that explain how the results of an intervention are expected to happen. As such, they add further layers of understanding to traditional results hierarchies, thereby strengthening their quality and reducing risk. This is because, when made explicit, assumptions about how change occurs can be tested and validated or disproved provided that sufficient and accurate data about them is collected and analysed. When fed back into programming, and implementation, the results will strengthen the basis for stronger and more effective responses to violent extremism. Conversely, the absence of a clear theory of change may obscure critical understandings concerning the intervention logic and weaken the basis for expected results. [ABSTRACT FROM AUTHOR]

The randomness and fluctuation of wind power output will cause certain waste in capacity allocation of integrated energy system. Therefore, a robust chance constrained optimization model is proposed to solve the shortcomings of the traditional model in wind power output analysis, such as weak reliability and conservative results. First, the uncertainty of wind power output is analyzed. Second, a robust chance constrained optimization model combining stochastic programming and robust optimization is established to deal with the uncertainty of the output power of the integrated energy system objectively. Finally, the results are compared with the existing integrated energy system capacity configuration, and the validity of the model is verified. The results show that the robust chance constrained optimization model proposed in this paper can effectively reduce the capacity cost by 38.2% while ensuring the robustness of the system in wind power uncertainty analysis. [ABSTRACT FROM AUTHOR]

After a natural disaster, medical supplies will be in high demand in the disaster-affected communities. Providing prompt and high-quality rescue resources is critical to the emergency relief network's overall quality. This study presents a mathematical optimization model for constructing a multi-period emergency relief system that minimizes the system's overall expected costs. The model considers location, allocation, and distribution decisions as well as flow of medical supplies and injured people. Medical supply distribution centers and roads are vulnerable to failure in the suggested model. Since certain parameters in the real world are unknown, the model parameters' uncertainty is explored. There are four sources of uncertainty regarding the number of injured people, demand, costs, and the probability of failure. To cope these uncertainties, a robust-stochastic optimization approach is used. Also, a case study focused on an earthquake in southern and western cities of Fars province is discussed to assess the efficacy of the suggested model. The findings demonstrate that the robust-stochastic approach is capable of effectively controlling cost and demand uncertainty, and that failing to account for uncertainty when planning relief logistics would be extremely deceptive. The planned relief system has the highest cost at the highest level of uncertainty, but it will offer a better protected solution to uncertainty with a greater level of robustness. The stochastic model has the lowest cost, but it is unable to produce the most conservative solution with the best uncertainty protection when there is a great deal of uncertainty in the system. [ABSTRACT FROM AUTHOR]

Purpose: This paper aimed to design a robust blood supply chain model that includes the stages of collection, processing and distribution of blood and blood products taking into account the lifespan and age of demand, which seeks to reduce supply chain costs and reduce the shortage and waste of blood products. Methodology: In this paper, MINLP method is used to model the research problem and in order to face the uncertainty in the problem parameters, the MPFRP method based on fuzzy data is proposed. The designed model was first evaluated for validation with numerical examples in small and large size and using real data in a case study in GAMS software? Findings: Using numerical examples and real data, the output indicates the performance of the proposed model. The output also had acceptable flexibility in the face of uncertainty in the parameters of the research model. Originality/Value: In this study, in order to reduce the shortage of blood products in situations where blood product is not available in the same group as the requested blood product, the ABO-RH adaptability principle has been used to replace the received demand with a compatible inventory. And also, to deal with uncertainty in uncertain parameters in the supply chain a solution based onmixed possibilistic-flexible robust programming is proposed. [ABSTRACT FROM AUTHOR]

As the United Kingdom reduces its CO2 emissions in order to meet its 2050 net zero greenhouse gas targets, there will be a significant evolution of the UK's energy mix. The reliance on hydrocarbons will decrease while there is predicted to be an increase in low carbon energy sources such as renewables and nuclear. In order to decarbonise and achieve the net zero emissions targets while concurrently producing enough energy to provide for national energy needs, large‐scale, low carbon energy generation projects need to be developed alongside energy storage facilities to provide flexibility within a low carbon energy supply. Robust CCUS programmes will need be developed in order to capture and store unavoidable carbon dioxide emissions. The subsurface geology of the UK provides opportunities for the development of low carbon energy generation, energy storage and CCS, and the Upper Permian Zechstein Supergroup deposited in eastern England and offshore in the Southern North Sea is a potential host for these new developments. In NE England, salt cavern gas storage sites have been developed in thick Zechstein evaporites since the mid 20th centrury. In this paper we present new isopach maps and well correlation panels which will help to outline optimal locations for the development of additional salt caverns for gas storage. A review of the Zechstein Supergroup indicates that it does not exhibit great potential for the development of CCS, due both to its complex reservoir characteristics and to difficulties with both subsurface imaging and monitoring. However thick Zechstein evaporites could provide an excellent seal for CO2 storage in the underlying Lower Permian Rotliegend Group. [ABSTRACT FROM AUTHOR]

Hybrid energy storage systems (HESSs) have gradually been viewed as essential energy/ power buffers to balance the generation and load sides of fully electrified ships. To resolve the balance issue of HESS under multiple power resources, that is, shipboard diesel generators and fuel cells (FCs), this study proposes a robust sizing method implemented with a power allocation strategy. The proposed method is hierarchically formulated as two sequential sub‐problems: (1) a robust programming to determine the power/energy capacities of HESS under the maximal power demand scenario and (2) a control framework to fulfil the power allocation under multiple power resources. A ship case with one diesel engine and one FC is studied to show the validity of the proposed method. The simulation results show that the integration of HESS facilitates the power supply of critical propulsion loads. Compared with no HESS, HESS integration can reduce the deviation of direct current bus voltage sag by 56% and reduce the power fluctuations of the main engine and FC by 7.3% and 55.9%, respectively. [ABSTRACT FROM AUTHOR]

• Comprehensive optimization model is proposed for healthcare network design incorporates a robust goal programming approach. • Uncertainties of distribution of healthcare demand and facility capacity are captured. • Healthcare products have a limited shelf-life. • An option contract is applied for supply coordination with pre-determined supports before and after disruption occurrence. • Risk mitigation strategies are regarded to enhance the efficiency and effectiveness of design decisions under disruption. In this paper, a robust goal programming model for a healthcare network design problem under disruption is developed. The objective of the proposed multi-period, multi-echelon model is to simultaneously optimize the total deviation from the considered three goals, including minimizing network cost, maximizing network coverage, and maximizing network reliability. Distribution uncertainty of healthcare demand and facility capacity is captured. The perishability of healthcare products is regarded with limited shelf-life. Using an option contract ensures appropriate coordination with suppliers during pre and post-disaster periods. Via handling the tractable robust budget-based counterpart model, suitable strategies are proposed to present the designed network's efficiency and effectiveness. Risk mitigation strategies deal with disrupted demand and supply in the healthcare network with specific impacts on coverage, cost, and reliability of the services. The proposed cooperate coverage mechanism provides appropriate service coverage under disruption propagation. Finally, the option contract has achieved cost-efficient coordination under demand uncertainty. Furthermore, practical managerial insights are demonstrated by investigating a real-life case study and conducting extensive sensitivity analyses. [ABSTRACT FROM AUTHOR]

This paper presents a fully-decentralized peer-to-peer (P2P) electricity and gas market for retailers and prosumers with coupled energy units, considering the uncertainties of wholesale electricity market price and prosumers' demand. The goal is to improve the overall economy of the proposed market while increasing its flexibility. In this market, the retailers are equipped with self-generation and energy storage units and can bilaterally negotiate for electricity and gas transactions with prosumers to maximize their profit. Furthermore, they can sell power to the upstream market in addition to prosumers. The prosumers have access to several retailers to supply their required electricity and gas and can freely provide their energy needs from every retailer, contributing to dynamicity in the proposed market. Given that they have an energy hub consisting of boiler units, combined heat and electricity (CHP) units, and electric pumps, they can switch their energy supply source from electricity to gas and vice versa. A robust possibilistic programming approach is applied to address the uncertainties. A fully-decentralized approach called the alternating direction method of multipliers (ADMM) is utilized to solve the presented decentralized robust problem. The proposed decentralized algorithm finds an optimum solution by establishing a smart balance between the average expected value, optimality robustness, and feasibility robustness. The feasibility and competitiveness of the proposed approach are evaluated through numerical studies on a distribution system with two retailers and three prosumers. The data analysis of the simulation results verifies the effectiveness of the proposed decentralized robust framework as well as the proposed decentralized solution. According to the maximum deviation, the expected optimal value in the robust case, the retailer's profit has decreased by 12.1 percent, and the prosumers' cost has increased by 27.4 percent due to the feasibility penalty term. [ABSTRACT FROM AUTHOR]

In this study, we consider the robust knapsack problem defined by the model of Bertsimas and Sim (Operations Research 52(1):35–53, 2004) where each item weight is uncertain and is defined with an interval. The problem is to choose a subset of items that is feasible for all of the cases in which up to a pre-specified number of items are allowed to take maximum weights simultaneously while maximizing the sum of profits of chosen items. Several integer optimization formulations for the problem have been proposed, however the strength of the upper bounds obtained from their LP-relaxations have not been theoretically analyzed and compared. In this paper, we establish a theoretical relationship among those formulations in terms of their LP-relaxations. Especially, we theoretically prove that previously proposed strong formulations (two extended formulations and a formulation using submodularity) yield the same LP-relaxation bound. In addition, through computational tests with benchmark instances, we analyze the trade-off between the strength of the lower bounds and the required computation time to solve the LP-relaxations. The results show that the formulation using submodularity shows competitive theoretical and computational performance. [ABSTRACT FROM AUTHOR]

Robust bi-level programming problems are a newborn branch of optimization theory. In this study, we have considered a bi-level model with constraint-wise uncertainty at the upper-level, and the lower-level problem is fully convex. We use the optimal value reformulation to transform the given bi-level problem into a single-level mathematical problem and the concept of robust counterpart optimization to deal with uncertainty in the upper-level problem. Necessary optimality conditions are beneficial because any local minimum must satisfy these conditions. As a result, one can only look for local (or global) minima among points that hold the necessary optimality conditions. Here we have introduced an extended non-smooth robust constraint qualification (RCQ) and developed the KKT type necessary optimality conditions in terms of convexifactors and subdifferentials for the considered uncertain two-level problem. Further, we establish as an application the robust bi-level Mond-Weir dual (MWD) for the considered problem and produce the duality results. Moreover, an example is proposed to show the applicability of necessary optimality conditions. [ABSTRACT FROM AUTHOR]

The occurrence of natural and artificial disasters due to their unexpected nature requires precise planning and management in the relief supply chain. A major measure in times of crisis is to assist the damaged points. Due to the limitations in the relief process at the time of the accident, relief centers should be opened in appropriate locations that cover the needs of the damaged points in the shortest possible time. Initially, a nonlinear two-level cooperative gradual maximal covering model in relief supply chain is proposed first. The chain includes supply centers, relief, and damaged points under uncertainty of some key parameters. The major goal is to locate the relief centers and determine the allocations and transfer of goods between the two levels. The bi-objective model minimizes the high logistical costs and maximizes damaged points' coverages with uncertain costs. Different robust possibilistic programming approaches have utilized the given approaches' performances, and some suitable recommendations are given. The robust possibilistic model provides the best results among all models. The results show that the robust possibilistic programming model outperforms the possibilistic programming model. [ABSTRACT FROM AUTHOR]

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This paper studies a location and sizing problem for an emergency medical service system using distributionally robust chance-constrained programming approach. The medical demands are uncertain and described in an ambiguity set, which is constructed based on Wasserstein-metric. The location problem is modelled through minimising the total expected costs, including construction costs of facilities, purchase of ambulances and maintenance costs. The chance constraints are introduced to guarantee the service level of geographical areas. For the chance constraints, three reformulations such as CVaR-approximation, the mixed integer linear programme exact reformulation and the physically bounded bilinear reformulation are studied. A numerical study is conducted to illustrate the computational performance and objective values. [ABSTRACT FROM AUTHOR]

We obtain a large number of degree and distance-based topological indices, graph and Laplacian spectra and the corresponding polynomials, entropies and matching polynomials of n-dimensional hypercubes through the use of Hadamard symmetry and recursive dynamic computational techniques. Moreover, computations are used to provide independent numerical values for the topological indices of the 11- and 12-cubes. We invoke symmetry-based recursive Hadamard transforms to obtain the graph and Laplacian spectra of nD-hypercubes and the computed numerical results are constructed for up to 23-dimensional hypercubes. The symmetries of these hypercubes constitute the hyperoctahedral wreath product groups which also pave the way for the symmetry-based elegant computations. These results are used to independently validate the exact analytical expressions that we have obtained for the topological indices as well as graph, Laplacian spectra and their polynomials. We invoke a robust dynamic programming technique to handle the computationally intensive generation of matching polynomials of hypercubes and compute all matching polynomials up to the 6-cube. The distance degree sequence vectors have been obtained numerically for up to 108-dimensional cubes and their frequencies are found to be in binomial distributions akin to the spectra of n-cubes. [ABSTRACT FROM AUTHOR]

In this paper, we investigate an integrated procurement and capacitated vehicle routing problem for the distribution of multiple relief goods after the disaster, to determine the best tour for vehicles as well as the best selection of multiple relief goods and their quantity to be loaded on vehicles. Due to the uncertain nature of the parameters, the demand distribution and cost parameters are considered as fuzzy parameters. Furthermore, this paper examines the impact of information and communication technology in the affected areas so that instant information, communicate between the affected areas and the disaster coordination center due to new events caused by the disaster. We have examined the impact of information and communication technology on reducing demand uncertainty such that with consideration of the cost of equipping GPS in affected areas, as well as its impact on reducing demand uncertainty and the cost of dissatisfaction as a result; the best affected areas are selected to be equipped with GPS. To have robust solutions, a robust possibilistic programming model is proposed. The results of the model are shown in a real case study in district 7 of Tehran which acclaim that the proposed model achieves a better result than the traditional models without considering ICT. [ABSTRACT FROM AUTHOR]

Despite the fact that medical responses are crucial for saving precious lives during any humanitarian crisis (e.g., the COVID-19 pandemic), healthcare infrastructure in many communities are partially covered or are not covered yet. In order to strengthen the health system response to such crisis, especially in low- to middle-income communities, this paper extends a novel multi-objective model for designing a health service network under uncertainty which simultaneously considers efficiency, social responsibility, and network cost. For efficiency, a modified data envelopment analysis model is introduced and inserted into the proposed model to decrease the inefficiency of healthcare facilities belonging to the different tiers of the health system. For social responsibility, two measures of job creation and balanced development are incorporated into the extended model. This is not only considered to cope with the increased numbers of patients and disaster victims to healthcare facilities but also to deal with the challenge of the economy and the livelihoods of people during the crisis. Moreover, a novel mixed possibilistic-flexible robust programming (MPFRP) approach is developed to protect the considered network against uncertainty. To show the applicability of the extended model, a real-world case study is presented. The results reveal that contrary to fuzzy programming models, the MPFRP performs well in terms of social responsibility (72%), cost (8%), and efficiency (28%) and is able to make a trade-off between these three measures. In this study, the resilience level of the designed network is not addressed while disregarding any short-term stoppage owing to internal or external sources of disruption in designing may bring about a considerable loss. [ABSTRACT FROM AUTHOR]

Uncertainties from hydrological and meteorological environments constantly pose disturbances to water sustainability. Programming under such uncertainties aims at finding solutions to this risky condition. From the sight of uncertain water availability, this paper builds a water life cycle model to reduce the risks of inappropriate estimations of water availability within a river basin and incorporates the results in robust programming. Then, a policy-driven scenario analysis is conducted to provide managerial implications in terms of ongoing water-saving policies. With Min–Tuo river basin as the case, we finally reach the conclusions that: (1) Equity is a necessity when considering the water allocation in a river basin, which enables a more sustainable mode of local water use. (2) Local citizens' willingness to follow the policies is a key to relieve the water pressure, while the progress of water-saving techniques could add to its effectiveness. [ABSTRACT FROM AUTHOR]

The development of cell sites as part of the infrastructure of telecommunication technology is playing a unique role in emerging businesses at present. Natural disasters and crises can disrupt communication equipment and create severe challenges in service provisions, especially health and security, by damaging sites. This might lead to traffic congestion in certain network sections, causing chaos and social crises and increasing the commissioning and equipping costs of backup sites for operators. This study developed an integrated location-coverage-allocation model to improve sustainability through maximum coverage, enhanced flexibility, and minimized overhead expense by determining the position of backup sites and mitigating environmental pollution resulting from the establishment of sites. The stochastic robust optimization model was employed to control the effect of nonparametric uncertainty, while acceptable solutions were generated using the Lagrangian relaxation to address complicated model constraints. [ABSTRACT FROM AUTHOR]