Bilevel Programming Research Articles

Competitive pricing and seed node selection in a two-echelon supply chain

This paper presents a bi-level game model for pricing in a supply chain where the manufacturer (He) is the leader, and the retailer (She) is the follower. The leader decides on the wholesale price, and the follower decides on the selling price and selects seed nodes. The main idea of the model is that the marketing strategy used for promoting the product is focused on giving free samples to potential customers. Hence, the importance of analyzing a social network becomes evident. To maximize her profit, the retailer decides based on three factors: first, the leader's decision about wholesale price; second, the social network structure, which is critical for selecting the seed nodes; and third, people's valuation of the product. Therefore, a bi-level Mixed-Integer Nonlinear Programming model is developed to consider the social binds between potential customers. To solve this model, we employ a meta-heuristic algorithm. Finally, the effect of the model's parameters on decision variables and the objective functions is discussed. Based on the analysis and discussions, the production cost has a prominent impact on the players’ decisions and profits. Furthermore, instead of spending all the marketing budget on increasing seed nodes, it is suggested that they be spent on market research and improving good publicity. Moreover, deciding whether the players want to maximize the profit or market penetration is required before diving into decision-making.

Decarbonizing the inland container fleet with carbon cap-and-trade scheme

Market-based measures, like the carbon cap-and-trade (CCT) scheme, can effectively reduce emissions and promote green technology by internalizing the external costs in the shipping industry. Under the CCT scheme, the government sets the quantity commitment of carbon emissions for a unit of shipping work, and the excessive quantity must be traded from the inner shipping market. To cope with carbon regulation, carriers can adjust their ship deployment plan and adopt new engine technologies to support low-carbon fuels. This paper proposes a bi-level programming model to investigate the effects of the CCT scheme on the decisions of carriers in a competitive inland container shipping network. At the upper level, carriers adjust their own ship deployment plan and the choice of technology and fuel type. At the lower level, the shippers between different origins and destinations choose the shipping lines with the given ship deployment plans of carriers. Two kinds of equilibrium are considered in the proposed problem: the competitive equilibrium of carriers on freight shipment in the inland shipping network and the trading equilibrium of carbon quotas. The former equilibrium can be captured by a traffic assignment model in a similar transit transportation network, and the latter equilibrium follows the idea of the demand–supply equilibrium of carbon quotas in the traditional market. The two equilibria interact since the freight distribution affects the shipping revenue of each ship and the trading equilibrium is related to the total cost of the ship. The properties of the optimal choice of technology and fuel type are theoretically studied. We find that the optimal choice of fuel technology for each ship assigned to any shipping line at any given CCT must be Pareto optimal in the sense of cost-related and emission-relative measures. Based on the result, the optimal solution of the proposed model can be calculated by a sampling-based method. Numerical examples based on the Yangtze River are further adopted to illustrate the proposed model and conclusions.

Priority-based two-phase method for hierarchical service composition allocation in cloud manufacturing

Manufacturing service composition (MSC) is an essential issue in cloud manufacturing, which streamlines complex manufacturing tasks into manageable subtasks and integrates distributed services to enhance task completion. Existing studies allocate services for subtasks with maximizing quality of service (QoS) simultaneously, assuming that all subtasks are of equal importance. However, different subtasks hold varied significance and priorities. One rational method is to prioritize the allocation of premium or scarce services to important subtasks. Therefore, this study proposes a two-phase, subtask priority-based approach for the hierarchical allocation of the MSC. The initial phase applies a multi-attribute decision-making method based on complex networks, the Enhanced Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS-EK), to assess subtask importance. The TOPSIS-EK method ascertains subtask importance, delineating the subtasks into Key Manufacturing Subtasks (KMTs) and Ordinary Manufacturing Subtasks (OMTs). The second phase uses bilevel optimization for the hierarchical allocation of the MSC to KMTs and OMTs, respectively. A hybrid Particle Swarm Optimization and Genetic Algorithm with Chaos-sequence and Inheritance (PSOGA-CI) is developed to solve the model. The proposed approach is validated with a case on the production of an airplane engine turbine rotor blade.

A Bilevel Approach for Compensation and Routing Decisions in Last-Mile Delivery

In last-mile delivery logistics, peer-to-peer logistic platforms play an important role in connecting senders, customers, and independent carriers to fulfill delivery requests. As the carriers are not under the platform’s control, the platform has to anticipate their reactions while deciding how to allocate the delivery operations. Indeed, carriers’ decisions largely affect the platform’s revenue. In this paper, we model this problem using bilevel programming. At the upper level, the platform decides how to assign the orders to the carriers; at the lower level, each carrier solves a profitable tour problem to determine which offered requests to accept, based on her own profit maximization. Possibly, the platform can influence carriers’ decisions by determining also the compensation paid for each accepted request. The two considered settings result in two different formulations: the bilevel profitable tour problem with fixed compensation margins and with margin decisions, respectively. For each of them, we propose single-level reformulations and alternative formulations where the lower-level routing variables are projected out. A branch-and-cut algorithm is proposed to solve the bilevel models, with a tailored warm-start heuristic used to speed up the solution process. Extensive computational tests are performed to compare the proposed formulations and analyze solution characteristics. Funding: The research of E. Fernandez was partially funded through the Spanish Ministerio de Ciencia y Tecnología and European Regional Development Funds (ERDF) [Grant MTM2019-105824GB-I00]. The research of C. Archetti, M. Cerulli, and I. Ljubić was partially funded by CY Initiative of Excellence, France [Grant “Investissements d’Avenir ANR-16-IDEX-0008”]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.0129 .

Multitasking optimization for the imaging problem in electrical capacitance tomography

Electrical capacitance tomography excels in measuring multiphase flows, but it faces challenges in reconstructing high-accuracy images. To tap into the potential of this measurement technique, we model the image reconstruction problem as a bilevel multitasking optimization problem, aiming to enhance imaging quality via effective knowledge transfer and integration across various tasks. This new imaging model consists of a target optimization problem and an auxiliary optimization problem, facilitating knowledge transfer and fusion between tasks. We design a new algorithm to solve the target optimization problem and integrate it with an autoencoder used for the cross-task knowledge transfer, forming a new multitasking optimizer to solve this proposed bilevel multitasking optimization imaging model. The extreme learning machine is developed for the prediction of learnable prior images by introducing a novel bilevel optimization framework that enables concurrent parameter selection and model training. A novel nested algorithm, designed to efficiently address optimization problems structured hierarchically, is developed to solve the training model. Evaluation results show that the new imaging algorithm outperforms popular imaging methods in terms of reconstruction accuracy and robustness, while also demonstrating stable performance. This proposed imaging algorithm achieves cross-task knowledge transfer and fusion, integrates measurement physics and machine learning, mines and integrates effective image priors, adaptively learns model parameters, alleviates the ill-posed property of the image reconstruction problem, increase the automation of the model, and improves imaging quality, robustness and performance stability, which provides a comprehensive solution to mitigate challenges in imaging.

Strategic operation of electric vehicle in residential microgrid with vehicle-to-home features

The urgent need for innovative energy solutions to facilitate the transition to renewable energy and electric vehicles (EVs) is particularly critical in developing countries, where high emissions and grid reliability challenges persist. This study investigates an off-grid residential renewable energy system with stationary storage like battery and hydrogen, alongside an EV as mobile storage. A bi-level optimization framework is established considering stationary and mobile energy storage options and a strategy is proposed to implement Vehicle-to-Home (V2H) in off-gird settings. Three cases are studied, with optimal component sizing determined using an optimization tool integrated with MATLAB. Firstly, to determine the most cost-effective stationary storage alternative, Case 1 uses hydrogen and Case 2 employs a battery as storage. Then Case 3 integrates the optimal stationary storage with mobile storage using V2H technology enabling the EV to support household energy needs during peak times. Results highlight that combining stationary and mobile storage (Case 3) offers a 15.92% reduction in Total Net Present Cost (TNPC) and a 13.9% reduction in Levelized Cost of Energy (LCOE) compared with stationary storage alone. This off-grid system (Case 3) also outperforms the conventional grid economically and environmentally, offering 2.13× TNPC reduction and 7,813 kg/yr carbon emissions mitigation.

Optimal planning of integrated electricity-natural gas distribution systems with hydrogen enriched compressed natural gas operation

In future integrated electricity-natural gas distribution systems (IEGDS), hydrogen and methane converted from excessive renewable generation will be mixed with natural gas to form hydrogen enriched compressed natural gas (HCNG) for fewer carbon emissions. Consequently, optimal planning of the HCNG-integrated IEGDS plays an essential role in increasing the economy and technical benefits. However, integrating HCNG operation into the planning of IEGDS still has many challenges, such as unrealistic modeling, nonlinear constraints, and the potential risk of voltage violations. The purpose of this paper is to develop a tractable optimization model for planning and operation of the HCNG-integrated IEGDS, aiming to minimize the investment and operating cost, reduce the voltage violation, and improve the renewable power penetration rate. To achieve this, a bilevel optimization model is developed for optimal planning of wind turbines and soft open points (SOPs) in the IEGDS considering comprehensive HCNG operation, in which both hydrogen and methane injection are considered and optimized for different system operation scenarios. Furthermore, the proposed nonlinear model is reformulated to a tractable bilevel mixed-integer second-order cone model using several reformulation techniques and solved by the reformulation and decomposition algorithm. Case studies, performed using the publicly available datasets, are conducted to demonstrate the economic and technical improvement by implementing the proposed planning model. The annual planning results show that incorporating the coordination between SOPs and methane injection results in a 6.77% reduction in investment cost, a 22.64% reduction in operating cost, a 62.69% decrease in voltage violation, and a 23.58% increase in the wind power penetration rate. Moreover, SOPs are more applicable to the safe operation of the IEGDS under high energy load conditions.

Security constrained unit commitment in smart energy systems: A flexibility-driven approach considering false data injection attacks in electric vehicle parking lots

In this paper, a new structure, the so-called FBSCUCFDIP-P/EV is proposed as flexibility-based security constrained unit commitment (SCUC) in the presence of false data injection (FDI) attack into the communication infrastructure of electric vehicle parking lot (EVPL). Herein, the uncertain EVPLs are integrated into the SCUC problem with the aim of reducing the operation cost. It is notable that growing integration of unspecified EVPLs can introduce novel challenges to the power system, significantly impacting its flexibility. In this study, electric vehicles are leveraged as a means to enhance system flexibility. Meanwhile, the FDI attacks in EVPLs can distort the system’s flexibility and lead to inaccurate assessments of the power system’s ability to adapt to changing conditions. In order to model the FDI attack, a bi-level optimization problem based on mixed integer linear programming is formulated. At the upper level, the impact of EVPLs on the flexibility indices of the SCUC is evaluated, and the false data injected into the EVPL is calculated at the lower level. Since both levels of the proposed FBSCUCFDIP-P/EV include discrete variables, a reformulation and decomposition technique is utilized to achieve the optimal solution. Instead, an extreme gradient boosting (XGBoost)-based machine learning method is considered to detection and correction of FDI attack. The proposed approach is tested on the IEEE 24-bus system. The simulation results initially indicate the improvement of the flexibility of the power system in proposed structure. Further, injecting false data into all available EVPLs causes to increase the system operation cost. Besides, false data leads to distorted charging and discharging scheduling of EVPLs; likewise, scheduling and commitment of power generation units also changes. Subsequently, the application of the XGBoost algorithm effectively mitigates the impact of FDI attacks, achieving a maximum accuracy of 85.41%.

Bi-level programming for joint order acceptance and production planning in industrial robot manufacturing enterprise

Effectively addressing the Order Acceptance and Production Planning (OAP) problem is crucial for industrial robot manufacturers, particularly considering the rapid expansion of the industrial robot market. A bi-level programming model is structured to enhance synergies in response to department reformation within an industrial robot manufacturer. The upper-level model focuses on order acceptance, considering rejection and delay penalty costs, aiming to maximize enterprise profit. The lower-level model concentrates on product production, aiming to minimize the total sum of production costs and Work-In-Progress (WIP) holding costs. Detailed constraints related to material readiness, including inventory levels and procurement lead times, are comprehensively examined. Given the NP-hard complexity of this multi-objective problem, a meta-heuristic algorithm Whale Optimization Algorithm (WOA) is implemented. To enhance WOA’s optimization capabilities, two heuristic algorithms, Solution Improvement policy (I-algorithm) and Heuristic-based acceleration strategy (H-algorithm), are introduced, resulting in the development of WOA-IH. The experimental evidence suggests that the proposed model facilitates decision coordination for manufacturers, particularly in order management, production planning, and material procurement. Furthermore, this study contributes to applying bi-level programming theory in managing supply chains for industrial robotics.

Optimizing Customized Bus Lines Considering Users' Transfer Willingness under Cooperative and Competitive Relationship between Metro and Online Car-hailing

In the context of ‘carbon peak’ and ‘carbon neutrality’, coordinating individual travel demand through multi-modal transportation and guiding travelers towards new shared public transportation (PT) modes is increasingly important. In this paper, we analyze the competitive and cooperative relationship between online car-hailing (OCH) services and metro systems in Nanning, China, and conduct aquestionnaire survey among different types of OCH users. A mixed choice model that considers psychological latent variables is constructed to investigate OCH users’ attitudes and cognitions toward customized buses (CBs). An improved adaptive Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm is proposed to identify potential carpooling station sets, and a hybrid genetic-ant colony algorithm (GACA) is designed to solve bi-level programming model for CB line optimization. Case study results indicate an 83.8% overall transfer rate from OCH users to CBs, with the optimized scheme achieving a 69.68% reduction in carbon emissions.

A neurodynamic approach for a class of pseudoconvex semivectorial bilevel optimization problems

The article proposes an exact approach to finding the global solution of a nonconvex semivectorial bilevel optimization problem, where the objective functions at each level are pseudoconvex, and the constraints are quasiconvex. Due to its non-convexity, this problem is challenging, but it attracts more and more interest because of its practical applications. The algorithm is developed based on monotonic optimization combined with a recent neurodynamic approach, where the solution set of the lower-level problem is inner approximated by copolyblocks in outcome space. From that, the upper-level problem is solved using the branch-and-bound method. Finding the bounds is converted to pseudoconvex programming problems, which are solved using the neurodynamic method. The algorithm's convergence is proved, and computational experiments are implemented to demonstrate the accuracy of the proposed approach.

Stochastic Optimization and Uncertainty Quantification of Natrium-based Nuclear-Renewable Energy Systems for Flexible Power Applications in Deregulated Markets

Rapid integration of variable renewable energy sources (VRES) has made modeling and stochastic optimization of hybrid energy systems crucial for studying their long-term performance and viability. However, most studies have focused on just historical data, which may be unreliable for capturing short-term fluctuations, rare events, and long-term patterns of energy demand, price, and the variability of renewable energy sources. For this study, optimal synthetic time series models were developed using Wasserstein distance. The models were validated by comparing the key statistical measures against those of the historical data. They were then used to optimize the integrated Natrium-style advanced energy systems and their long-term (30 years) economics. The stochastic model performs bi-level optimization to find the optimal sizes for the balance of plant and thermal energy storage, while also optimizing energy dispatch to achieve the maximum net present value.In studies of two deregulated markets (California ISO and the Electric Reliability Council of Texas), the integrated Natrium-style system performed better in CAISO than in ERCOT, given higher and more consistent electricity prices during peak-demand periods. The potentially enlarged cost associated with the variable operation and maintenance of the TES system also plays a significant role in driving the system sizing, thus its impacts on the system are investigated in detail through comparison against a baseline case. The study also finds that the bi-level optimization results based on stochastic gradient descent closely match the grid search results. The uncertainty quantification of the stochastic signals provides further NPV-related insights and probability distributions for the case studies. The normal standard error of the mean of NPV for the case with and without TES VOM for CAISO were found to be 7.73M ± 1.09M USD and 104.99M ± 1.25M USD, respectively based on a 95% confidence. Given the relatively small NPV variance based on 150 samples, the analysis affords the most robust possible prediction of the techno-economic performance of the integrated Natrium-style energy systems.

From Curtailed Renewable Energy to Green Hydrogen: Infrastructure Planning for Hydrogen Fuel-Cell Vehicles

Problem definition: Hydrogen fuel-cell vehicles (HFVs) have been proposed as a promising green transportation alternative. For regions experiencing renewable energy curtailment, promoting HFVs can achieve the dual benefit of reducing curtailment and developing sustainable transportation. However, promoting HFVs faces several major hurdles, including uncertain vehicle adoption, the lack of refueling infrastructure, the spatial mismatch between hydrogen demand and renewable sources for hydrogen production, and the strained power transmission infrastructure. In this paper, we address these challenges and study how to promote HFV adoption by deploying HFV infrastructure and utilizing renewable resources. Methodology/results: We formulate a planning model that jointly determines the location and capacities of hydrogen refueling stations (HRSs) and hydrogen plants as well as electricity transmission and grid upgrade. Despite the complexity of explicitly considering drivers’ HFV adoption behavior, the bilevel optimization model can be reformulated as a tractable mixed-integer second-order cone program. We apply our model calibrated with real data to the case of Sichuan, a province in China with abundant hydro resources and a vast amount of hydropower curtailment. Managerial implications: We obtain the following findings. (i) The optimal deployment of HRSs displays vastly different spatial patterns depending on the HFV adoption target. The capital city, a transportation hub, is excluded from the plan under a low target and only emerges as the center of HFV adoption under a high target. (ii) Promoting the HFV adoption can overall help reduce hydropower curtailment, but the effectiveness depends on factors such as the adoption target and the grid upgrade cost. (iii) Being a versatile energy carrier, hydrogen can be transported to various locations, which allows for strategic placement of HRSs in locations distinct from hydrogen plant sites. This flexibility offers HFVs greater potential cost savings and curtailment reduction compared with other alternative fuel vehicles (e.g., electric vehicles) under current cost estimates. Funding: W. Qi acknowledges the support from the National Natural Science Foundation of China [Grants 72242106 and 72188101] and the Natural Sciences and Engineering Research Council of Canada [Grant RGPIN-2019-04769]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.0381 .

Meta Learning With Graph Attention Networks for Low-Data Drug Discovery.

Finding candidate molecules with favorable pharmacological activity, low toxicity, and proper pharmacokinetic properties is an important task in drug discovery. Deep neural networks have made impressive progress in accelerating and improving drug discovery. However, these techniques rely on a large amount of label data to form accurate predictions of molecular properties. At each stage of the drug discovery pipeline, usually, only a few biological data of candidate molecules and derivatives are available, indicating that the application of deep neural networks for low-data drug discovery is still a formidable challenge. Here, we propose a meta learning architecture with graph attention network, Meta-GAT, to predict molecular properties in low-data drug discovery. The GAT captures the local effects of atomic groups at the atom level through the triple attentional mechanism and implicitly captures the interactions between different atomic groups at the molecular level. GAT is used to perceive molecular chemical environment and connectivity, thereby effectively reducing sample complexity. Meta-GAT further develops a meta learning strategy based on bilevel optimization, which transfers meta knowledge from other attribute prediction tasks to low-data target tasks. In summary, our work demonstrates how meta learning can reduce the amount of data required to make meaningful predictions of molecules in low-data scenarios. Meta learning is likely to become the new learning paradigm in low-data drug discovery. The source code is publicly available at: https://github.com/lol88/Meta-GAT.

A new bi-level TOPSIS based neutrosophic programming technique for land allocation to medium farm holders

Agriculture impacts a country's social and economic growth. Crop allocation, crop combinations, and crop production processes are all necessary to achieve optimal results during various growing seasons. To maximize farm earnings, proper farm planning and resource allocations are necessary. In agriculture, land allocation problems involve several uncertainties and unpredictable variables, includes water supply, labour demands, fertility use, and food requirements. The objective of this study is to propose novel bi-level programming approaches to overcome such issues and obtain optimal land allocation for medium-sized farmers. The current study examines a bi-level, TOPSIS-based neutrosophic programming approaches in two cases, including non-interactive and interactive approaches with linear, exponential, and hyperbolic membership functions to maximize net profit and minimize the expenditure. The proposed methods are compared to other approaches, such as the Torabi & Hassini approach, the Fuzzy Optimization Technique (FOT), and the Intuitionistic Fuzzy Optimization Technique (IFOT) and are found to be more effective than the existing ones.

The AI circular hydrogen economist: Hydrogen supply chain design via hierarchical deep multi-agent reinforcement learning

Hydrogen supply chain (HSC) consists of various production, conditioning, transportation, storage, and distribution processes, all of which require extensive computational resources for precise modelling. In this context, artificial intelligence (AI) is emerging as a pivotal tool for addressing model-based decision-making challenges, courtesy of its rapid and efficient computational capabilities. This paper proposes a comprehensive HSC model consisting of an economic policy planner, a wholesale hydrogen market, a power supply system, a hydrogen distribution system (HDS), and hydrogen refueling stations (HRSs). It leverages an AI circular hydrogen economist approach based on a hierarchical deep multi-agent reinforcement learning (MARL) algorithm, offering a new alternative to traditional multi-objective bi-level optimization platforms. The model incorporates green, blue, and gray hydrogen production processes as viable hydrogen production pathways, with the hierarchical MARL’s agents representing the HDS and HRSs at two decision-making levels. Energy requirements are met through a combination of on-site renewable energy sources, the main power grid, or distributed power generation systems. Several HSC scenarios are examined with respect to various combinations of green hydrogen supply rates and carbon credits granted to them under optimum conditions. The results showed that the developed hierarchical MARL has the potential to replace mathematical programming (MP), uncovering a new economic-environmental trade-off between profit of HDS and operational costs of HRSs. Notably, green hydrogen transactions exponentially increase within the supply chain as the carbon credits exceed $1 per kilogram of hydrogen. While this research focuses on optimizing daily operations within the HSC, future efforts can aim to extend this optimization to forecasted annual operations.

Robust bilevel optimization for near-optimal lower-level solutions

Bilevel optimization problems embed the optimality of a subproblem as a constraint of another optimization problem. We introduce the concept of near-optimality robustness for bilevel optimization, protecting the upper-level solution feasibility from limited deviations from the optimal solution at the lower level. General properties and necessary conditions for the existence of solutions are derived for near-optimal robust versions of general bilevel optimization problems. A duality-based solution method is defined when the lower level is convex, leveraging the methodology from the robust and bilevel literature. Numerical results assess the efficiency of exact and heuristic methods and the impact of valid inequalities on the solution time.

Optimal scheduling model using the IGDT method for park integrated energy systems considering P2G–CCS and cloud energy storage

To enhance the energy efficiency and financial gains of the park integrated energy system (PIES). This paper constructs a bi-level optimization model of PIES-cloud energy storage (CES) based on source-load uncertainty. Firstly, the scheduling framework of PIES with refined power-to-gas (P2G), carbon capture and storage (CCS) and CES coupling is constructed. Moreover, a bi-level optimization model with the upper tier subject being the PIES operator and the lower tier subject being the CES operator is established under the ladder-type carbon price mechanism with reward and punishment (LCPMRP). Then a proposed entropy weight adaptive information gap decision theory method (EAIGDT) is proposed to eliminate the subjectivity factor and retain its non-probabilistic features while dealing with multiple source-load uncertainties, and according to the operator’s risk preference to build risk-averse (RA) and risk-seeking (RS) strategies, respectively. Finally, the measured data in a certain area of Xinjiang verifies the proposed optimal scheduling method. The results show that the method can effectively take into account the interests of various subjects and realise PIES low-carbon economic operation.

Service product codesign with digital platform operators based on hierarchical interactive optimization

This paper proposes a novel approach to address the evolving landscape of service product design, particularly in collaboration with digital platform operators. By formulating a nonlinear hierarchical interactive optimization model (HIO) based on bilevel programming (BLP), the paper tackles the complexities of joint decision-making between service providers and digital platforms. At the upper level, the model optimizes digital platform selection, product attribute configuration, and pricing to maximize provider profit, while the lower level determines platform participation in codesign to maximize their own profits. Furthermore, a codesign incentive mechanism, encompassing revenue-sharing proportions and platform promotion efforts, is designed to incentivize collaboration.Applied to the tourism industry, the HIO model is solved using a nested genetic algorithm (NGA), allowing for sensitivity analyses on platform contribution and promotion efforts. Results indicate that increased platform participation in codesign may raise configuration complexity and costs for the service agency, potentially impacting profitability. Additionally, higher platform promotion efforts can drive profit growth for both parties, supporting long-term development. Ultimately, the HIO model demonstrates superior performance compared to traditional two-stage method (TSM), underscoring its applicability and effectiveness in addressing codesign challenges between service agencies and digital platforms.

Solar–Hydrogen-Storage Integrated Electric Vehicle Charging Stations with Demand-Side Management and Social Welfare Maximization

The reliable operation of a power system requires a real-time balance between supply and demand. However, it is difficult to achieve this balance solely by relying on supply-side regulation. Therefore, it is necessary to cooperate with effective demand-side management, which is a key strategy within smart grid systems, encouraging end-users to actively engage and optimize their electricity usage. This paper proposes a novel bi-level optimization model for integrating solar, hydrogen, and battery storage systems with charging stations (SHS-EVCSs) to maximize social welfare. The first level employs a non-cooperative game theory model for each individual EVCS to minimize capital and operational costs. The second level uses a cooperative game framework with an internal management system to optimize energy transactions among multiple EVCSs while considering EV owners’ economic interests. A Markov decision process models uncertainties in EV charging times, and Monte Carlo simulations predict charging demand. Real-time electricity pricing based on the dual theory enables demand-side management strategies like peak shaving and valley filling. Case studies demonstrate the model’s effectiveness in reducing peak loads, balancing energy utilization, and enhancing overall system efficiency and sustainability through optimized renewable integration, energy storage, EV charging coordination, social welfare maximization, and cost minimization. The proposed approach offers a promising pathway toward sustainable energy infrastructure by harmonizing renewable sources, storage technologies, EV charging demands, and societal benefits.