Distributionally Robust Optimization Research Articles

Multi-objective planning of distribution network based on distributionally robust model predictive control

The uncoordinated integration of numerous distributed resources poses significant challenges to the safe and stable operation of distribution networks. To address the uncertainties associated with the intermittent output of distributed power sources, we propose a multi-objective planning strategy for distribution networks based on distributionally robust model predictive control (MPC). Initially, an error fuzzy set is established on a Wasserstein sphere using historical data to enhance out-of-sample performance. Next, a multi-objective optimization framework is constructed, balancing returns and risks, and is subsequently converted into a single-objective solution using value-at-risk conditions. This is followed by the implementation of multi-step rolling optimization within the model predictive control framework. We have linearized the proposed model using the linearized power flow method and conducted a thorough validation on an enhanced IEEE 37-node test system. Distributionally robust optimization (DRO) has been shown to reduce costs by a significant 29.16% when compared to an RO method. Moreover, the energy storage capacity required has been notably reduced by 33.33% on the 29-node system and by 20% on the 35-node system. These quantified results not only demonstrate the substantial economic efficiency gains but also the enhanced robustness of our proposed planning under the uncertainties associated with renewable energy integration.

Cooperative energy and reserve trading strategies for multiple integrated energy systems based on asymmetric nash bargaining theory

To tackle the issues of cooperative energy and reserve trading as well as fair cooperative benefit allocation among multiple integrated energy systems (IESs), this paper proposes a two-stage cooperative energy and reserve trading model for multiple integrated energy systems (MIESs). Specifically, at day-ahead stage, MIESs aim to maximize their overall profit through cooperative electricity and heat trading. At real-time stage, MIESs trade demand response (DR) reserve to minimize the overall wind power deviation compensation cost. To reduce the complexity in model solution, we transform the model into two sub-problems. In sub-problem 1, we determine the energy and DR reserve trading volumes. Here, distributionally robust optimization (DRO) is utilized to manage the severe uncertainties in wind power distribution. In sub-problem 2, based on the outcomes from sub-problem 1, we settle the energy and DR reserve trading prices. To ensure the fairness of benefit allocation, asymmetric Nash bargaining theory is applied to assess each IES's contributions in trading volumes and profit growth. Interval adaptive alternating direction method of multipliers (IA-ADMM) is used to preserve each IES's privacy. Finally, simulation results demonstrate that, compared with independent operation, cooperative trading among MIESs increases profits for all IESs, thereby motivating their participation in cooperative trading.

Distributionally robust hospital capacity expansion planning under stochastic and correlated patient demand

This paper investigates the optimal locations and capacities of hospital expansion facilities under uncertain future patient demands, considering both spatial and temporal correlations. We propose a novel two-stage distributionally robust optimization (DRO) model that integrates a Spatio-Temporal Neural Network (STNN). Specifically, we develop an STNN model that predicts future hospital occupancy levels considering spatial and temporal patterns in time-series datasets over a network of hospitals. The predictions of the STNN model are then used in the construction of the ambiguity set of the DRO model. To address computational challenges associated with two-stage DRO, we employ the linear-decision-rules technique to derive a tractable mixed-integer linear programming approximation. Extensive computational experiments conducted on real-world data demonstrate the superiority of the STNN model in minimizing forecast errors. Compared to neural network models built for each individual hospital, the proposed STNN model achieves a 53% improvement in average root mean square error. Furthermore, the results demonstrate the value of incorporating spatiotemporal dependencies of demand uncertainty in the DRO model, as evidenced by out-of-sample analysis conducted with both ground truth data and under perfect information scenarios.

FairDRO: Group fairness regularization via classwise robust optimization

Existing group fairness-aware training methods fall into two categories: re-weighting underrepresented groups according to certain rules, or using regularization terms such as smoothed approximations of fairness metrics or surrogate statistical quantities. While each category has its own strength in applicability or performance when compared to each other, their successful performances are typically limited to specific cases. To that end, we propose a new approach called FairDRO, which takes advantage of both categories through a classwise group distributionally robust optimization (DRO) framework. Our method unifies re-weighting and regularization by incorporating a well-justified group fairness metric into the objective as regularization, but solving it through a principled re-weighting strategy. To optimize our resulting objective efficiently, we adopt an iterative algorithm and consequently develop two variants of FairDRO algorithm depending on the choice of surrogate loss. For in-depth understanding, we derive three theoretical results: (i) a closed-form solution for the correct re-weights; (ii) justifications for using the surrogate losses; and (iii) a convergence analysis of our method. Experimental results show that our algorithms consistently achieve state-of-the-art performance in accuracy-fairness trade-offs across multiple benchmarks, demonstrating scalability and broad applicability compared to existing methods.

A negative-carbon planning method for agricultural rural industrial park integrated energy system considering biomass energy and modern agricultural facilities

Biomass energy, recognized as a “zero-carbon” energy, has gradually become a crucial approach to promoting the low-carbon transformation of agricultural rural industrial parks (ARIP). Meanwhile, modern agricultural facilities (MAF) can play a significant role in adjusting agricultural load. Therefore, this paper proposes a negative-carbon planning method for the ARIP integrated energy system (IES). Firstly, carbon activities occurring during the operation of ARIP are sorted out and modeled based on the life cycle assessment (LCA) method, especially modeling the “zero-carbon” and “negative-carbon” benefits of biomass energy. At the same time, the models of both agricultural irrigation systems and straw bundling direct combustion heating are constructed in the ARIP planning. Then, a negative-carbon planning model for ARIP IES is established with the goal of minimizing the annualized total cost, where carbon emission reduction is integrated into the optimization objectives through carbon trading. On this basis, a two-stage distributionally robust optimization (DRO) planning model is constructed, where a box-like set and comprehensive norm constraints are used to model the seasonal differences of agricultural industry loads and the uncertainty of probability distribution in photovoltaic (PV) scenarios. Especially, a box set with adjustable uncertainty coefficients is introduced to simulate fluctuations of output in PV scenario. Finally, the CPLEX solver is used to solve the planning model. verify the effectiveness of the proposed planning method in enhancing the economic and environmental effects of ARIP. Results indicate that the proposed planning model can reduce the total cost by 49.584 × 104 $. Besides, the annual carbon emissions can be reduced from 37533.98 t CO2-eq to −15834.5 t CO2-eq. Especially, the carbon sequestration effect of biochar is the key link in achieving “negative carbon” in ARIP.

Reformulation and Enhancement of Distributed Robust Optimization Framework Incorporating Decision-Adaptive Uncertainty Sets

Distributionally robust optimization (DRO) is an advanced framework within the realm of optimization theory that addresses scenarios where the underlying probability distribution governing the data is uncertain or ambiguous. In this paper, we introduce a novel class of DRO challenges where the probability distribution of random variables is contingent upon the decision variables, and the ambiguity set is defined through parameterization involving the mean and a covariance matrix, which also depend on the decision variables. This dependency makes DRO difficult to solve directly; therefore, first, we demonstrate that under the condition of a full-space support set, the original problem can be reduced to a second-order cone programming (SOCP) problem. Subsequently, we solve this second-order cone programming problem using a projection differential equation approach. Compared with the traditional methods, the differential equation method offers advantages in providing continuous and smooth solutions, offering inherent stability analysis, and possessing a rich mathematical toolbox, which make the differential equation a powerful and versatile tool for addressing complex optimization challenges.

EXPRESS: Distributionally Robust Appointment Scheduling That Can Deal with Independent Service Times

Consider a single server that should serve a given number of customers during a fixed period. The Appointment Scheduling Problem (ASP) determines the schedule of planned appointments that minimizes some cost function that accounts for both the cost of idle times and the cost of waiting. When service time distributions are fully specified, the ASP presents a much investigated computationally challenging stochastic program. When service time distributions are only partially specified, one can apply distributionally robust optimization (DRO) to find the schedule that minimizes costs in worst-case circumstances. We assume that only the mean, mean absolute deviation and range of the service times are known, and develop a DRO method that finds the optimal (minimax) schedule. For independent service times, the minmax problem becomes nonlinear and difficult, if not impossible, to solve exactly. Existing DRO methods for ASP with partial information (such as mean and variance) therefore consider relaxations that allow correlations between service times. Such relaxations have major repercussions, as the worst-case scenario will then be highly correlated. Our method thus deals with independent service times and finds the robust schedule as the solution to a linear program. We identify several new structural features of optimal robust schedules. We also apply the method to model extensions including sequencing and alternative objective functions.

Extended matrix modeling of integrated energy systems considering network dynamic characteristics and source–load uncertainty

A refined and efficient modeling approach is indispensable for enhancing the timeliness of scheduling strategies for the integrated energy system (IES). Non-flowing variables such as pressure and temperature introduced by energy devices, however, worsen the complexity while improving the completeness for models. Nonlinear and uncertain variables associated with network dynamic characteristics and source–load uncertainty in the systems seriously postpone the modeling processes. An extended matrix modeling approach is proposed in this paper to tackle such issues. New nodes, branches, definition rules and topological matrices are first presented to create an extended matrix model that is compatible with both flowing and non-flowing variables. To boost the modeling efficiency, adaptive piecewise linearization (APL) with extended matrix form and modified Taylor expansion are applied to approximate various nonlinear characteristics. The convex approximation based on Kullback–Leibler (KL) divergence and the strong duality theory characterized by Wasserstein distance are adopted to deal with uncertain variables, which adapt to combine with the above matrix model. A linearized matrix modeling framework applicable to highly automated by computers is thus established. The distributionally robust optimization (DRO) scheduling strategy is verified in a standard test system with the proposed modeling. The effect of dynamic characteristics and uncertain factors on the strategy is discussed. The results show that the extended matrix model simulates the response for real physical systems more effectively, which exhibits the better performances in modeling, objectives and scheduling strategies.

An integrated distributionally robust model for two-echelon patient appointment scheduling

We develop a distributionally robust optimization (DRO) model for the outpatient appointment scheduling problem of a set of patients served in two serial stages, consultation and examination. The arrival sequence of patients is known, and the problem of scheduling is to assign appointment time for each patient to minimize total cost with random service time for two serial stages. A max–min problem is formulated for the two-stage appointment scheduling as a whole, in which the waiting time exhibits a high degree of coupling due to the continuous two-stage process. To address this, we devise a two-stage network maximum flow model that provides an equivalent linear expression for the waiting time. For the inner maximum problem, we employ a conic programming approach for equivalent representation, incorporate the scheduling decision of the outer minimum problem, and convert the model to its equivalent copositive programming by taking the conic duality. We conduct numerical experiments and sensitivity analysis using real and simulated data, and the results verify the effectiveness of our proposed DRO model.

Two-stage multi-objective distributionally robust operation optimization and benefits equalization of an off-grid type electric-hydrogen-ammonia-methanol coupling system

As the proportion of renewable energy has increased significantly, electric-hydrogen coupling technology has emerged as a pivotal strategy for optimizing the utilization of renewable energy resources. In particular, within the power and chemical sectors, the preparation of ammonia and methanol using electric-hydrogen coupling technology has emerged as the two principal avenues for the utilization of hydrogen energy. However, as a nascent technology, the preparation of ammonia and methanol by electric-hydrogen coupling is confronted with a multitude of challenges, including the considerable uncertainty surrounding the generation of renewable energy, the dearth of economic benefits, and the need to ensure a fair allocation of benefits among the various stakeholders. To enhance the risk resistance of the electric-hydrogen-ammonia-methanol coupling system (EHAMCS), improve the economic benefits, ensure the environmentality and stability of the system, and realize the fair distribution of benefits among the energy participants, this paper constructs a multi-objective distributionally robust optimization (DRO) and multi-dimensional benefits equilibrium model for the EHAMCS and performs a numerical analysis with an off-grid type EHAMCS as an example. The results demonstrate that: 1) The cooperative operation of the EHAMCS offers notable economic advantages. When compared with only pursuing economic benefits, under multi-objective optimization, the economic benefits of the coupling system can be reduced by 1.49 %, but the carbon emission can be reduced by 10.06 %, and the instability is reduced by 0.02, which can create derivative benefits. 2) The two-stage DRO model is an effective means of addressing the impact of system operation uncertainty and the affine strategy enables the rapid adjustment of the day-ahead dispatching plan, thereby balancing the power deviation. 3) The multi-dimensional factor benefit balancing scheme is more conducive to the participation of clean energy and downstream ammonia and methanol energy subsystems in cooperative operation and promotes the consumption of clean energy while improving the energy conversion value of the EHAMCS to increase economic benefits. 4) EHAMCS operators should adjust their operational strategies in time with market and policy signals, and select historical samples reasonably, so as to realize the balance of the DRO model in terms of economy, robustness, and practicality. The effectiveness of the model and the superiority of the EHAMCS are thus verified.

Pre-disaster allocation and post-disaster dispatch strategies of power emergency resources for resilience enhancement of distribution networks

With the frequent occurrence of large-scale power outages caused by extreme disasters, coordinated dispatch of power emergency resources (PERs) and repair crews (RCs) has gradually become an essential method to enhance the resilience of distribution networks (DNs). Previous works solve this coordinated dispatch problem in a risk-neutral approach with the assumption that the supply of power repair materials (PRMs) is still fully available after the disaster. However, growing evidence indicates that certain extreme disasters may lead to limited availability of PERs in the DN, rendering risk-neutral decision making impractical. To fill this gap, this paper proposes a resilience-oriented PERs pre-disaster allocation and post-disaster dispatch strategy in a risk-averse manner. In the pre-disaster prevention process, a two-stage distributionally robust optimization (DRO) model based on mean-CVaR is developed, considering the uncertainties of both system damage and PERs demands, along with the decision maker's preference for risk. In the post-disaster restoration process, a collaborative spatio-temporal dispatching model for PERs and RCs with the goal of minimizing outage losses is established. To tackle the computational challenges associated with PRMs allocation based on DRO, robust counterpart transformation and dual theory are utilized. Case studies are conducted using a real world modified 118-bus distribution network. In comparative analysis, five control groups are established to validate the necessity to consider the limited supply of PRMs and the risk-averse attitude of decision makers in enhancing DNs resilience.

A reliable ensemble forecasting modeling approach for complex time series with distributionally robust optimization

Accurate ensemble forecast results provide strong support for management decisions. While the existing ensemble forecasting model ignores the requirement of directional accuracy making its prediction direction is usually error-prone. To address this issue, we develop a convex directional prediction error measure and subsequently construct a reliable ensemble forecasting model that minimizes the horizontal prediction error with the bounded directional prediction error. Mathematically, we provided the proper range of the required directional error level. Furthermore, we find the classical ensemble forecasting model is a special case of our study when the directional error level is larger than the upper bound we gave in this study. To deal with the possible deterioration of the individual model over time, we also considered its worst possible prediction performance by introducing the distributionally robust optimization (DRO) technique into the proposed reliable ensemble forecasting model. Technically, we showed that the DRO-based reliable ensemble forecasting model is convex and can be reformulated into a second-order cone problem which can be readily solved by off-the-shelf solvers. Finally, the effectiveness of the proposed reliable ensemble forecasting model and the DRO-based reliable ensemble forecasting model were validated on three different datasets, e.g., the exchange rate, the oil price, and the country risk index. To sum up, we construct a reliable ensemble forecasting model to simultaneously control the horizontal prediction error and directional prediction error of ensemble forecasting, and thus enhance the reliability of ensemble forecasting.

Global supply chain flow planning for Chinese manufacturing under the BRI: An SFG-DRO method

The Belt and Road Initiative (BRI) has fostered the free flow of commodities and optimal distribution of resources for the global manufacturing supply chain (GMSC), meanwhile confronted with risks and uncertainties. This paper proposes the SFG-DRO method, which can well solve the flow distribution problem of GMSC under the BRI with uncertainties. The proposed method combines trend prediction from the stochastic frontier gravity (SFG) model with 1-Wasserstein fuzzy set-based distributionally robust optimization (DRO). Additionally, this paper integrates the principles of the column and constraint generation (C&CG) algorithm with the particle swarm optimization (PSO) algorithm to handle the above two-stage nonlinear problems efficiently. The results show that the SFG-DRO distribution method significantly reduces transportation costs by 25% and enhances security. By examining flow distribution across three key BRI channels, this paper identifies underexploited markets along the southward channel and substantial market potential with security risks along the northeast sea-land channel, proposing relevant improvement suggestions.

The Virtual Power Plant Bidding Strategy Model based on Multi-stage Semi-anticipativity Distributionally Robust Optimization

For virtual power plants (VPPs), the strength of their market competitiveness largely depends on their ability to dispatch various distributed resources. An efficient bidding strategy model that can provide superior decision-making solutions is the key to enhancing this competitiveness. This paper focuses on price-making VPP and constructs an efficient three-period VPP bidding strategy model (3P-VPP) with a bi-level optimization framework for the day-ahead energy market by introducing three-period generator output constraints and generator ramping constraints. Furthermore, to address the uncertainty of renewable resources, we introduce the theory of distributionally robust optimization (DRO) and the concept of semi-anticipativity, refining the 3P-VPP model into a multi-stage DRO VPP bidding strategy model based semi-anticipativity (SADRO-VPP). The model possesses dynamic adaptation capabilities, tailoring the optimal decision-making solutions based on the accuracy of the forecast data. When faced with unreliable prediction data, the model will offer a more robust decision-making plan to guard against potential extreme scenarios. Conversely, when the forecast data is credible, the model adeptly utilizes this information to provide more economical decision-making strategies. The experimental results demonstrate that the 3P-VPP model exhibits higher computational efficiency compared to traditional model, while the SADRO-VPP model provides effective scheduling solutions and bidding strategies for VPP.

Robust Distributed Learning Against Both Distributional Shifts and Byzantine Attacks.

In distributed learning systems, robustness threat may arise from two major sources. On the one hand, due to distributional shifts between training data and test data, the trained model could exhibit poor out-of-sample performance. On the other hand, a portion of working nodes might be subject to Byzantine attacks, which could invalidate the learning result. In this article, we propose a new research direction that jointly considers distributional shifts and Byzantine attacks. We illuminate the major challenges in addressing these two issues simultaneously. Accordingly, we design a new algorithm that equips distributed learning with both distributional robustness and Byzantine robustness. Our algorithm is built on recent advances in distributionally robust optimization (DRO) as well as norm-based screening (NBS), a robust aggregation scheme against Byzantine attacks. We provide convergence proofs in three cases of the learning model being nonconvex, convex, and strongly convex for the proposed algorithm, shedding light on its convergence behaviors and endurability against Byzantine attacks. In particular, we deduce that any algorithm employing NBS (including ours) cannot converge when the percentage of Byzantine nodes is [Formula: see text] or higher, instead of [Formula: see text] , which is the common belief in current literature. The experimental results verify our theoretical findings (on the breakpoint of NBS and others) and also demonstrate the effectiveness of our algorithm against both robustness issues, justifying our choice of NBS over other widely used robust aggregation schemes. To the best of our knowledge, this is the first work to address distributional shifts and Byzantine attacks simultaneously.

Comprehensive review of energy management strategies: Considering battery energy storage system and renewable energy sources

AbstractThe transformation of power system networks is slowly taking shape, the advent of interruptive technological platforms dealing with digitalization and real‐time trading of power has gained attention based on incorporation of more renewables into the grid. The stochastic nature of renewables pauses security of supply challenges and other related stability concerns, and for this reason efficient methods are investigated in this review to build an understanding of microgrid energy management system (MG‐EMS) and distribution‐based energy management strategies aimed at transforming the conventional grid network into smart grid network. In essence, propagating a technological shift to microgrids which have proven to be ideal distribution networks for residential and commercial loads, have become indispensable in handling distributed energy resources (DER), such as solar, PV, wind, battery energy storage systems (BESS) and small‐scale microgrids, for example in case of excess supply, energy storage system (ESS) has been formulated as a solution to curb excess supply and can offer ancillary services to the grid network. Within the perspective of electricity generation and distribution, microgrid control methodologies, distribution network (DN) management approaches and incumbent optimization strategies used to coordinate and manage grid‐level uncertainties are investigated. In addition, this study proposes distributionally robust optimization (DRO), to manage and mitigate risks associated to shortage or oversupply of power from RESs.

Uncertain Scheduling of the Power System Based on Wasserstein Distributionally Robust Optimization and Improved Differential Evolution Algorithm

The rapid development of renewable energy presents challenges to the security and stability of power systems. Aiming at addressing the power system scheduling problem with load demand and wind power uncertainty, this paper proposes the establishment of different error fuzzy sets based on the Wasserstein probability distance to describe the uncertainties of load and wind power separately. Based on these Wasserstein fuzzy sets, a distributed robust chance-constrained scheduling model was established. In addition, the scheduling model was transformed into a linear programming problem through affine transformation and CVaR approximation. The simplex method and an improved differential evolution algorithm were used to solve the model. Finally, the model and algorithm proposed in this paper were applied to model and solve the economic scheduling problem for the IEEE 6-node system with a wind farm. The results show that the proposed method has better optimization performance than the traditional method.

Distributionally Robust Newsvendor Under Stochastic Dominance with a Feature-Based Application

Problem definition: In this paper, we study the newsvendor problem under some distributional ambiguity sets and explore their relations. Additionally, we explore the benefits of implementing this robust solution in the feature-based newsvendor problem. Methodology and results: We propose a new type of discrepancy-based ambiguity set, the JW ambiguity set, and analyze it within the framework of first-order stochastic dominance. We show that the distributionally robust optimization (DRO) problem with this ambiguity set admits a closed-form solution for the newsvendor loss. This result also implies that the newsvendor problem under the well-known infinity-Wasserstein ambiguity set and Lévy ball ambiguity set admit closed-form inventory levels as a by-product. In the application of feature-based newsvendor, we adopt general kernel methods to estimate the conditional demand distribution and apply our proposed DRO solutions to account for the estimation error. Managerial implications: The closed-form solutions enable an efficient computation of optimal inventory levels. In addition, we explore the property of optimal robust inventory levels with respect to the nonrobust version via concepts of perceived critical ratio and mean repulsion. The results of numerical experiments and the case study indicate that the proposed model outperforms other state-of-the-art approaches, particularly in environments where demand is influenced by covariates and difficult to estimate. Funding: X. Li is supported by the Singapore Ministry of Education [Tier 1 Grant 23-0619-P0001, 24-0500-A0001] and National Natural Science Foundation of China [Grant 72331004]. L. Zhang is partially supported by the National Natural Science Foundation of China [Grants 72171156 and 72231002] and the Hong Kong Research Grants Council [Grant 16212419]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.0159 .

A distributionally robust approach for the parallel machine scheduling problem with optional machines and job tardiness

This paper investigates a parallel machine scheduling problem with uncertain job processing time, where the job tardiness and optional machines are considered. To address the factor of energy saving, only a subset of all available machines are turned on, which is referred to as not-all-machine (NAM). To depict the uncertain processing time, a mean–mean absolute deviation (MAD) ambiguity set is utilized, and the cost of job tardiness is minimized under the worst-case distribution scenario over the ambiguity set. After building a distributionally robust optimization (DRO) model, theoretical bounds of the optimal number of machines are obtained. Since the model is not computationally scalable, an upper bound on its inner minimization problem is employed, and a mixed integer linear programming (MILP) approximation is obtained based on McCormick inequalities. For the DRO model, tailored speedup techniques are employed, significantly enhancing the computational performance. To evaluate the validity of the proposed DRO model, we compare it with its stochastic programming (SP) counterpart under various parameter settings. Numerical experiments demonstrate that the DRO model exhibits strong performance in the worst-case scenarios. As the problem size increases, the DRO model casts clear advantages over the SP model in terms of computational efficiency and reliability. It is observed that the performance of the DRO model is more stable than that of the nominal sequence, especially with loose due dates. Furthermore, the out-of-sample performance under various decision making preferences shed new lights into the trade-off between energy saving and production efficiency.

Optimal planning and operation of integrated energy systems in South Korea: Introducing a Novel ambiguity set based distributionally robust optimization

In this paper, we address the increasing focus on Renewable Energy Sources (RES) and energy policies in S. Korea, advocating for a shift from large, centralized power systems to decentralized Local Power Systems (LPS). This transition emphasizes the integration of Integrated Energy Systems (IES), which significantly enhances the target benefits for stakeholders in the power system. We have also adopted a Distributionally Robust Optimization (DRO) approach to account for the output uncertainty of RES and developed and applied new ambiguity sets tailored to each RES, enhancing the extensive robust design previously utilized with DRO. By applying our proposed ambiguity set-based DRO, we avoid excessive robustness and achieve superior optimal outcomes compared to the general DRO methodology, potentially making a significant contribution to business investment decisions. We have categorized the main stakeholders of the power system as Independent Systems Operators (ISO), Renewable Energy Providers (REP), Energy Exchange Aggregators (EXA), and End-users. The integration of IES leads to a benefit improvement rate of up to 34.8 %, 23.0 %, and 24.2 % for ISOs, REPs, and End-users, respectively, on a global scale. EXAs can secure an annual economic profit of up to $191,362.