Stochastic Optimization Model Research Articles

Towards optimal customized electricity pricing via iterative two-layer optimization for consumers and prosumers

Designing an electricity price mechanism that efficiently enables users to manage their self-production and consumption behavior to accommodate renewable energy and regulate peak load is a hard task with the emergence of prosumer with photovoltaic and energy storage. To address this issue, we propose an iterative two-layer optimization to investigate customized price of electricity for different types of users in the presence of photovoltaic uncertainty. By taking into account power flow restrictions, the model is used to explore the optimal time-of-use, demand, and on-grid prices for both electricity consumers and prosumers. The consumer and prosumer peak-flat-valley periods are initially divided in the upper layer. Then, a model for distribution system operator profit maximization is proposed to minimize operation cost, power loss, and peak–valley difference. A stochastic optimization model is presented in the lower layer for consumer and prosumer to hedge against the risk of uncertain photovoltaic with the aim of minimizing electricity tariff, demand tariff, and life cycle cost of energy storage. Numerical experiments conducted on modified 15-bus and 69-bus distribution systems with different types of users show the effectiveness of the iterative two-layer optimization for customized price of electricity in peak-shaving and valley-filling while ensuring the interests of distribution system operator and users. Results show that the total profit increases by more than 4% and the net load fluctuation variance reduces higher than 20% compared with the traditional pricing method.

Stochastic Optimal Operation of SOP-Assisted Active Distribution Networks with High Penetration of Renewable Energy Sources

This paper introduces a mixed-integer convex model for optimizing the scheduling of soft open points (SOPs) integrated with energy storage (ES) in active distribution networks (ADNs) with high proportions of photovoltaic sources, designed to ensure zero risk of constraint violations. A stochastic optimization model for ADNs is proposed to maximize the benefits of SOPs while simultaneously minimizing system power losses, SOP power losses, voltage deviations, PV power curtailment, battery energy storage system (BESS) operation cost, and utility power purchase. Uncertainties in PV generation and load demand are considered by Monte Carlo simulation and k-means technologies. Finally, simulation cases from a 21-bus distribution network show that the curtailment of PV sources is minimized and the power fluctuations of the BESS are reduced in comparison to the case without SOP. Constraints in the nodal voltages, power outputs, energy balance, and power flow are all satisfied.

Optimal day-ahead offering strategy for large producers based on market price response learning

In day-ahead electricity markets based on uniform marginal pricing, small variations in the offering and bidding curves may substantially modify the resulting market outcomes. In this work, we deal with the problem of finding the optimal offering curve for a risk-averse profit-maximizing generating company (GENCO) in a data-driven context. In particular, a large GENCO’s market share may imply that its offering strategy can alter the marginal price formation, which can be used to increase profit. We tackle this problem from a novel perspective. First, we propose an optimization-based methodology to summarize each GENCO’s step-wise supply curves into a subset of representative price-energy blocks. Then, the relationship between the resulting market price and the energy block offering prices is modeled through a probabilistic forecasting tool: a Distributional Neural Network, which also allows us to generate stochastic scenarios for the sensibility of the market towards the GENCO strategy via a set of linear constraints. Finally, this predictive model is embedded in the stochastic optimization model employing a constraint learning approach. Results show how allowing the GENCO to deviate from its true marginal costs renders significant changes in its profits and the marginal price of the market. Additionally, these results have also been tested in an out-of-sample validation setting, showing how this optimal offering strategy can effective in a real-world market context.

How to Conclude a Suspended Sports League?

Problem definition: Professional sports leagues may be suspended because of various reasons, such as the recent coronavirus disease 2019 pandemic. A critical question that the league must address when reopening is how to appropriately select a subset of the remaining games to conclude the season in a shortened time frame. Despite the rich literature on scheduling an entire season starting from a blank slate, concluding an existing season is quite different. Our approach attempts to achieve team rankings similar to those that would have resulted had the season been played out in full. Methodology/results: We propose a data-driven model that exploits predictive and prescriptive analytics to produce a schedule for the remainder of the season composed of a subset of originally scheduled games. Our model introduces novel rankings-based objectives within a stochastic optimization model, whose parameters are first estimated using a predictive model. We introduce a deterministic equivalent reformulation along with a tailored Frank–Wolfe algorithm to efficiently solve our problem as well as a robust counterpart based on min-max regret. We present simulation-based numerical experiments from previous National Basketball Association seasons 2004–2019, and we show that our models are computationally efficient, outperform a greedy benchmark that approximates a nonrankings-based scheduling policy, and produce interpretable results. Managerial implications: Our data-driven decision-making framework may be used to produce a shortened season with 25%–50% fewer games while still producing an end-of-season ranking similar to that of the full season, had it been played. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.0558 .

Blockchain-enabled framework for transactive home energy management with cloud energy storage under uncertainties

In modern paradigm of smart grid, prosumers can trade energy peer-to-peer in a transactive energy market to reduce energy costs and improve energy efficiency. In addition, cloud energy storage (CES) is a type of shared energy storage systems with high economic efficiency that can provide energy storage services for prosumers and become an active player in energy trading. However, transactive energy implementation in power systems has several challenges such as data privacy and security. In existing researches, energy trading mechanisms rely on central authorities, where security and privacy cannot be maintained. Therefore, this paper presents a decentralized stochastic optimization model of transactive energy management based on blockchain in the presence of CES. In this framework, the smart contract based on Alternating Direction Method of Multipliers technique is deployed on the Ganache and Ethereum blockchains, and the YALMIP toolbox along with CPLEX solver handle decentralized optimization in the MATLAB software. The numerical results demonstrate that not only the capacity of distributed generations is fully utilized, but also total costs of smart homes are reduced by more than 27%, and the total grid’s delivery power to smart homes is decreased by more than 24% compared to the inflexible scheduling.

Robust trajectory planning for non-cooperative target rendezvous based on closed-loop uncertainty analysis

A robust trajectory planning method for non-cooperative target rendezvous is investigated based on closed-loop uncertainty analysis. The proposed method addresses the issue that uncertainties affect the optimality of objective functions and the reliability of constraints. Considering multiple uncertainties, a stochastic optimal rendezvous model with a robustness performance index and chance constraints is presented with line-of-sight dynamics. The guidance model, angles-only navigation model and control model are derived, and uncertainty propagation equations for closed-loop GN&C system is proposed by using linear covariance analysis. The stochastic optimal rendezvous model is transformed into a robust optimal rendezvous model by using 3-σ of the random variables. The genetic algorithm is used to solve the robust trajectory planning problem, and a series of examples demonstrate that the robust maneuver solution can be significantly better than the solution corresponding to deterministic trajectory optimization problem.

Solving Contextual Stochastic Optimization Problems through Contextual Distribution Estimation

Stochastic optimization models always assume known probability distributions about uncertain parameters. However, it is unrealistic to know the true distributions. In the era of big data, with the knowledge of informative features related to uncertain parameters, this study aims to estimate the conditional distributions of uncertain parameters directly and solve the resulting contextual stochastic optimization problem by using a set of realizations drawn from estimated distributions, which is called the contextual distribution estimation method. We use an energy scheduling problem as the case study and conduct numerical experiments with real-world data. The results demonstrate that the proposed contextual distribution estimation method offers specific benefits in particular scenarios, resulting in improved decisions. This study contributes to the literature on contextual stochastic optimization problems by introducing the contextual distribution estimation method, which holds practical significance for addressing data-driven uncertain decision problems.

A stochastic optimization model for patient evacuation from health care facilities during hurricanes

We propose a rigorous modeling and methodological effort that integrates statistical implementation of hydrology models in predicting inland and coastal flood scenarios due to hurricanes and a scenario-based stochastic integer programming model which suggests resource and staging area decisions in the first stage and the evacuation decisions in the second stage. This novel study combines physics-based flood prediction models and stochastic optimization for large-scale multi-facility coordination of hospital and nursing home evacuations before impending hurricanes. The optimization model considers scenario-dependent evacuation demand, transport vehicles with varying capacities, and both critical and non-critical patients. Utilizing Hurricane Harvey of 2017 as a case study and actual healthcare facility locations in southeast Texas, we explore various evacuation policies, demonstrating the impact of routing strategies, staging area decisions, flood thresholds, and receiving facility capacities on evacuation outcomes. One of the findings is that choosing staging area(s) and deploying evacuation vehicles optimally considering the uncertainty of the hurricane’s path at the time of decision making could have significant effect on the total cost of the operation and evacuation time experienced by the evacuees. We also show the non-negligible value of the scenario-based staging and routing solution conservatively calculated in relation to a single scenario solution using the concept of value of stochastic solution.

A Revisit to Sunk Cost Fallacy for Two-Stage Stochastic Binary Decision Making

This paper undertakes a revisit of the sunk cost fallacy, which refers to the tendency of people to persist investing resources into something, even if it is destined to have no good outcome. We emphasize that the utilities associated with different alternatives are not static for decision makers, which is exactly opposite to the traditional perspective. This paper argues that the utility of an option may change due to the choice of another option, suggesting that decisions considered irrational by the traditional analytical method, i.e., sunk cost fallacy, may be rational. We propose a novel analytical method for decision making with sunk cost when considering the utility change and validate the effectiveness of this method through mathematical modeling and computational experiments. This paper mathematically describes such decision-making problems, analyzing the impact of changes in the utilities across different alternatives on decision making with a real-world example. Furthermore, we develop a two-stage stochastic optimization model for such decision-making problems and employ the sample average approximation (SAA) method to solve them. The results from computational experiments indicate that some decisions traditionally considered irrational are, in fact, rational when the utility of an option changes as a result of choosing another option. This paper, therefore, highlights the significance of incorporating utility changes into the decision-making process and stands as a valuable addition to the literature, offering a refreshed and effective decision-making method for improved decision making.

Online Learning for Constrained Assortment Optimization Under Markov Chain Choice Model

Assortment optimization finds many important applications in both brick-and-mortar and online retailing. Decision makers select a subset of products to offer to customers from a universe of substitutable products, based on the assumption that customers purchase according to a Markov chain choice model, which is a very general choice model encompassing many popular models. The existing literature predominantly assumes that the customer arrival process and the Markov chain choice model parameters are given as input to the stochastic optimization model. However, in practice, decision makers may not have this information and must learn them while maximizing the total expected revenue on the fly. In “Online Learning for Constrained Assortment Optimization under the Markov Chain Choice Model,” S. Li, Q. Luo, Z. Huang, and C. Shi developed a series of online learning algorithms for Markov chain choice-based assortment optimization problems with efficiency, as well as provable performance guarantees.

BM-RCWTSG: An integrated matching framework for electric vehicle ride-hailing services under stochastic guidance

Electric vehicles (EVs) are playing an increasingly vital role in sustainable ride-hailing services, primarily due to their potential to reduce carbon emissions and enhance environmental well-being. A core service of ride-hailing platforms is to match riders with nearby drivers within a short time window. In this mandate, it is crucial to ensure a high matching rate and low rider waiting time since these are key indicators of customer satisfaction and the platform’s operational effectiveness. However, existing matching mechanisms in the literature failed to consider important aspects related to EVs, including the range limit, charging detour time, and charging waiting time. These factors can significantly affect the system matching rate, rider waiting time, and vehicle utilization rate. To address the new challenges of the increased adoption of EVs in ride-hailing services, we propose a data-driven stochastic optimization framework for EV ride-hailing matching. The proposed framework integrates two stochastic optimization models, namely the stochastic guidance (SG) model and the EV matching (EVM) model. The SG model optimizes EV relocation and improves the system matching rate by proactively guiding idle EVs to the designated regions based on probabilistic rider demand forecasting. The EVM model utilizes the relocated EVs and current rider demands to provide the optimal matching solution that minimizes the overall cost associated with rider waiting time, EV charging waiting time, and charging detours. We conduct experimental validation of this approach using two real-world data sets from New York City. Comparative results suggest that by utilizing the proposed framework, the matching rate can be increased up to 22.9%, and the rider and EV waiting times can be reduced up to 14.9% and 73.6%, respectively, compared to the benchmark models.

AI‐Based Ensemble Flood Forecasts and Its Implementation in Multi‐Objective Robust Optimization Operation for Reservoir Flood Control

AbstractInforming reservoirs with forecasts is highly important for real‐time flood control. This study proposed a forecast‐informed methodology framework for reservoir flood control operation under uncertainty. A new combination of two post‐processing methods, that is, the Cloud model and error‐based copula functions, were developed to merge individual AI‐based forecasts to ensemble flood forecasts, so called stochastic errors‐based Cloud (SE‐Cloud). A multi‐objective robust optimization model (MRO) integrating the risk, resilience, and vulnerability was then proposed to tackle flood control problems under ensemble forecasts; for comparison, a two‐objective stochastic optimization model (TSO) was developed to minimize the expected highest reservoir level and peak release. The proposed methodology was applied to the Lishimen reservoir in the Shifeng River subbasin, China, aiming to comprehensively verify the relationships among deterministic forecasts, ensemble forecasts, and flood control performance. Results showed that the Cloud model could effectively integrate different models and improve forecast accuracy. But a higher deterministic forecast quality did not consistently result in improved flood control performance. SE‐Cloud could capture the peak flow and effectively characterize forecast uncertainties and increased hypervolume values by 13.14%–39.65% compared to the Cloud model, indicating the superiority of ensemble forecasts in generating robust solutions over individual deterministic forecasts. MRO released more inflow than TSO, decreasing the expected highest water level by 0.05 m and incrementing the expected peak release by 4.29%. However, with downstream resilience value remaining at zero, it is demonstrated that MRO improving upstream vulnerability did not necessarily diminish resilience. The enhanced robustness highlights the potential of AI‐based ensemble forecasts in flood control.

Robust two‐level market coordinated transaction optimal model and benefit allocation strategy for a novel shared‐energy aggregator

AbstractShared‐energy storage (SES) can break the energy interaction barrier between the demand side and the supply side, which is becoming an option for improving the flexibility of energy systems. This study designed a novel structure for the shared‐energy aggregator (SEA), incorporating a microgrid (MG), prosumer and SES. Then, a two‐level market transaction optimization model for SEA, considering the robust stochastic optimization method, is proposed; namely, at the day‐ahead stage, a robust stochastic operation optimization model is constructed to achieve the dispatching plan from the demand side under the objective of achieving the minimum energy consumption cost for the prosumer, and at the real‐time market stage, a robust stochastic operation optimization model from the supply side is constructed to arrange the optimal dispatching strategy under the objective of the maximum aggregator benefits of MG and SES. Finally, an industrial park micro‐grid in Qinghai Province, China, is selected as an example for analysis.

Operational Robustness Assessment of the Hydro-Based Hybrid Generation System under Deep Uncertainties

The renewable-dominant hybrid generation systems (HGSs) are increasingly important to the electric power system worldwide. However, influenced by uncertain meteorological factors, the operational robustness of HGSs must be evaluated to inform the associated decision-making. Additionally, the main factors affecting the HGS’s robustness should be urgently identified under deep uncertainties, as this provides valuable guidance for HGS capacity configuration. In this paper, a multivariate stochastic simulation method is developed and used to generate uncertain resource scenarios of runoff, photovoltaic power, and wind power. Subsequently, a long-term stochastic optimization model of the HGS is employed to derive the optimal operating rules. Finally, these operating rules are used to simulate the long-term operation of an HGS, and the results are used to evaluate the HGS’s robustness and identify its main sensitivities. A clean energy base located in the Upper Yellow River Basin, China, is selected as a case study. The results show that the HGS achieves greater operational robustness than an individual hydropower system, and the robustness becomes weaker as the total capacity of photovoltaic and wind power increases. Additionally, the operational robustness of the HGS is found to be more sensitive to the total capacity than to the capacity ratio between photovoltaic and wind power.

Environmental Regulation and Stormwater Management Strategies for an Urban River in Northwest China: A Sustainable Approach

Low-impact developments (LIDs) have emerged as effective strategies for mitigating the adverse impacts of urbanization on river environments. This study aims to enhance river environment quality by examining the effects of LIDs and land use/cover change (LUCC) in the context of river environment and hydrological conditions. Using the Stormwater Management Model (SWMM) in an urban river setting, the study investigates the impact of LIDs on urban river water volume. An analysis of river runoff quality and quantity is conducted, followed by the development of an optimal river water regulation scheme through a multi-objective ecological scheduling model. The results reveal that the incorporation of LIDs can substantially decrease river runoff yield for varying recurrence periods of design rainstorms. Consequently, the flood peak reduction rate ranged from 10% to 18%, and the flood volume experienced a reduction of 10–29% in the study area. The combination of river water regulation, LIDs and LUCC leads to a decrease in river water volume within the lower river channel by up to 47% especially in a typical dry year and dry season, accompanied by a decline in river flow velocity and water self-purification capacity. A risk-based multi-objective stochastic optimization model is employed to ensure sustainable management of urban river runoff in terms of both quantity and quality. This research contributes to the advancement of knowledge in sustainable basin management practices and offers practical insights for policymakers involved in the management of water resources and environmental conservation in semi-arid basins.

Optimal Prosumer Operation with Consideration for Bounded Rationality in Peer-to-Peer Energy Trading Systems

With the large-scale development of distributed energy on the demand side, the trend of “supply exceeding demand” has gradually become prominent, and regional peer-to-peer (P2P) energy trading has become an important measure to improve the local consumption of distributed energy. However, most existing studies usually assume that prosumers behave entirely rationally with the goal of maximum benefit, which has been proved to deviate from the observed actual behaviors. Aiming at the optimal energy of prosumers participating in the P2P market, a prospect theory-based two-stage stochastic optimization model considering the bounded rationality was proposed to accurately simulate the decision-making behavior. Then, a benefit maximization model for the energy trading service provider (ETSP) was constructed considering the power flow constraint to ensure the safe operation of the system. Finally, an improved R-ADMM algorithm considering timeout was proposed to solve the above model and improve the convergence speed. The effectiveness of the proposed model and algorithm was verified via simulation.

Optimal Operation and Market Integration of a Hybrid Farm with Green Hydrogen and Energy Storage: A Stochastic Approach Considering Wind and Electricity Price Uncertainties

In recent years, growing interest has emerged in investigating the integration of energy storage and green hydrogen production systems with renewable energy generators. These integrated systems address uncertainties related to renewable resource availability and electricity prices, mitigating profit loss caused by forecasting errors. This paper focuses on the operation of a hybrid farm (HF), combining an alkaline electrolyzer (AEL) and a battery energy storage system (BESS) with a wind turbine to form a comprehensive HF. The HF operates in both hydrogen and day-ahead electricity markets. A linear mathematical model is proposed to optimize energy management, considering electrolyzer operation at partial loads and accounting for degradation costs while maintaining a straightforward formulation for power system optimization. Day-ahead market scheduling and real-time operation are formulated as a progressive mixed-integer linear program (MILP), extended to address uncertainties in wind speed and electricity prices through a two-stage stochastic optimization model. A bootstrap sampling strategy is introduced to enhance the stochastic model’s performance using the same sampled data. Results demonstrate how the strategies outperform traditional Monte Carlo and deterministic approaches in handling uncertainties, increasing profits up to 4% per year. Additionally, a simulation framework has been developed for validating this approach and conducting different case studies.

Optimal scheduling of a microgrid based on renewable resources and demand response program using stochastic and IGDT-based approach

Optimal economic scheduling of microgrids with photovoltaic (PV) and wind generation has gained increased attention during recent years. Integration of renewable energy resources in microgrids requires increasingly active control and management of energy storages and demand response (DR). In this paper, a risk-based stochastic optimal energy management model is developed for microgrid with renewables, energy storage and load control by time-of-use-based DR programs. Microgrid includes PV system, wind system, micro-turbine, fuel cell, electric vehicle (EV), and energy storage. Information-gap decision theory (IGDT) is employed to address the uncertainty of loads and to provide the operating strategies for the microgrid controllable energy resources. This proposed model has been solved as a mixed-integer non-linear programming (MINLP) in General Algebraic Modeling System (GAMS) software and simulation results in different conditions are studied and discussed. Three different risk management strategies have been studied such as risk-averse, risk-neutral and risk-seeker mode. The simulation results indicate that the impacts of risk-averseness or risk-seeker of the decision maker affect the system operation. For instance, the results showed the DR program's role in risk-averse and risk-taking strategies, impacting consumption and costs. The proposed model ensures the risk-averse decision-maker that if the uncertain parameter deviates within the optimum robustness region, the final cost will not exceed the critical cost. On the other hand, the risk-seeking decision-maker can reach lower final costs by accepting the risks if the uncertain parameter deviates favorably within the opportunity region. Decision-makers can manage risks by adjusting consumption. Thus, considering the cost of risk management is crucial, as it increases with robust or opportunistic approaches.

Farm debt and the over-exploitation of natural capital

This paper uses a stochastic optimal control model to show how standard loan contracts create incentives for farmers to focus on short-term financial performance at the expense of farms’ long-term natural capital. These incentives are a manifestation of the debt overhang problem. Extending this model shows how sustainability-linked loans can be used to weaken these incentives in a way that potentially benefits farmers and their bankers. The magnitude of the economic benefits generated by these loans depends on farm characteristics. The paper investigates the optimal design of sustainability-linked loans.

Virtual Power Plant’s Optimal Scheduling Strategy in Day-Ahead and Balancing Markets Considering Reserve Provision Model of Energy Storage System

In recent years, with the rapid increase in renewable energy sources (RESs), a Virtual Power Plant (VPP) concept has been developed to integrate many small-scale RESs, energy storage systems (ESSs), and customers into a unified agent in the electricity market. Optimal coordination among resources within the VPP will overcome their disadvantages and enable them to participate in both energy and balancing markets. This study considers a VPP as an active agent in reserve provision with an upward reserve capacity contract pre-signed in the balancing capacity (BC) market. Based on the BC contract’s requirements and the forecasted data of RESs and demand, a two-stage stochastic optimization model is presented to determine the VPP’s optimal scheduling in the day-ahead (DA) and balancing energy (BE) markets. The probability of reserve activation in the BE market is considered in this model. The ESS’s reserve provision model is proposed so as not to affect its schedule in the DA market. The proposed optimal scheduling model is applied to a test VPP system; then, the effects of the BC contract and the probability of reserve activation on the VPP’s trading schedule are analyzed. The results show that the proposed model has practical significance.