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Distributionally robust optimization with multivariate second-order stochastic dominance constraints with applications in portfolio optimization

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OPTIMIZATION 2023年第7期72卷 1839-1862页

作者： Wang, Shuang Pang, Liping Guo, Hua Zhang, Hongwei Dalian Univ Technol Sch Math Sci Dalian Peoples R China Key Lab Computat Math & Data Intelligence Liaonin Dalian Peoples R China

In this paper, we study the stochastic optimization problem with multivariate second-order stochastic dominance (MSSD) constraints where the distribution of uncertain parameters is unknown. Instead, only some historical data are available. Using the Wasserstein metric, we construct an ambiguity set and develop a data-driven distributionally robust optimization model with multivariate second-order stochastic dominance constraints (DROMSSD). By utilizing the linear scalarization function, we transform MSSD constraints into univariate constraints. We present a stability analysis focusing on the impact of the variation of the ambiguity set on the optimal value and optimal solutions. Moreover, we carry out quantitative stability analysis for the DROMSSD problems as the sample size increases. Specially, in the context of the portfolio, we propose a convex lower reformulation of the corresponding DROMSSD models under some mild conditions. Finally, some preliminary numerical test results are reported. We compare the DROMSSD model with the sample average approximation model through out-of-sample performance, certificate and reliability. We also use real stock data to verify the effectiveness of the DROSSM model.

关键词： stochastic programming distributionally robust optimization multivariate second-order stochastic dominance Wasserstein metric

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Risk aversion and flexibility options in electricity markets

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ENERGY ECONOMICS 2023年第1期126卷

作者： Moebius, Thomas Riepin, Iegor Muesgens, Felix van der Weijde, Adriaan H. Brandenburg Univ Technol Cottbus Senftenberg Siemens Halske Ring 13 D-03046 Cottbus Germany Tech Univ Berlin Einsteinufer 25 D-10587 Berlin Germany Netherlands Org Appl Sci Res TNO Anna van Buerenpl 1 NL-2595 DA The Hague Netherlands

Flexibility options, such as demand response, energy storage and interconnection, have the potential to reduce variation in electricity prices between different future scenarios, thereby reducing investment risk. Investing in flexibility options can also lower the need for generation capacity. However, there are complex interactions between different flexibility options. In this paper, we investigate the interactions between flexibility and investment risk in electricity markets. In particular, we focus on the investment strategies of risk-averse decision-makers. We employ a large-scale stochastic transmission and generation expansion model of the European electricity system, providing it with uncertain future scenarios based on ENTSOs' Ten-Year Network Development Plan. Using this model, we first investigate the effect of risk aversion on investment decisions. We find that the interplay of parameters leads to (i) more investment in a less emission-intensive energy system if planners are risk averse (hedging against CO2 price uncertainty), (ii) constant total installed capacity, regardless of the level of risk aversion (i.e. planners do not hedge against demand and uncertainties when deploying renewable energy sources) and (iii) an allocation of investments that disregards cost differences for load shedding across Europe. Second, we examine the individual effects of three flexibility elements on optimal investment levels at different levels of risk aversion: demand response, investment in additional interconnection capacity and investment in additional energy storage. We show that flexible technologies have a higher value for risk-averse decision-makers, although the effects are nonlinear. Finally, we investigate the interactions between the flexibility elements. We find that risk-averse decision-makers show a strong preference for transmission-grid expansion once flexibility is available at a low cost.

关键词： Flexibility Storage Demand response Generation and transmission expansion Investment Risk aversion stochastic programming

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An integrated chance constraints approach for optimal vaccination strategies under uncertainty for COVID-19

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SOCIO-ECONOMIC PLANNING SCIENCES 2023年第PartA期87卷 101547页

作者： Gong, Jiangyue Gujjula, Krishna Reddy Ntaimo, Lewis Texas A&M Univ Wm Michael Barnes Dept Ind & Syst Engn 64 3131 TAMU College Stn TX 78743 USA

Despite concerted efforts by health authorities worldwide to contain COVID-19, the SARS-CoV-2 virus has continued to spread and mutate into new variants with uncertain transmission characteristics. Therefore, there is a need for new data-driven models for determining optimal vaccination strategies that adapt to the new variants with their uncertain transmission characteristics. Motivated by this challenge, we derive an integrated chance constraints stochastic programming (ICC-SP) approach for finding vaccination strategies for epidemics that incorporates population demographics for any region of the world, uncertain disease transmission and vaccine efficacy. An optimal vaccination strategy specifies the proportion of individuals in a given household-type to vaccinate to bring the reproduction number to below one. The ICC-SP approach provides a quantitative method that allows to bound the expected excess of the reproduction number above one by an acceptable amount according to the decision-maker's level of risk. This new methodology involves a multi-community household based epidemiology model that uses census demographics data, vaccination status, age-related heterogeneity in disease susceptibility and infectivity, virus variants, and vaccine efficacy. The new methodology was tested on real data for seven neighboring counties in the United States state of Texas. The results are promising and show, among other findings, that vaccination strategies for controlling an outbreak should prioritize vaccinating certain household sizes as well as age groups with relatively high combined susceptibility and infectivity.

关键词： OR in health services COVID-19 Vaccination strategies stochastic programming Integrated chance-constraints

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Distributionally Robust Optimization Using Cost-Aware Ambiguity Sets

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IEEE CONTROL SYSTEMS LETTERS 2023年 7卷 1855-1860页

作者： Schuurmans, Mathijs Patrinos, Panagiotis Katholieke Univ Leuven Dept Elect Engn ESAT STADIUS Leuven 3001 Belgium

We present a novel framework for distributionally robust optimization (DRO), called cost-aware DRO (Cadro). The key idea of Cadro is to exploit the cost structure in the design of the ambiguity set to reduce conservatism. Particularly, the set specifically constrains the worst-case distribution along the direction in which the expected cost of an approximate solution increases most rapidly. We prove that Cadro provides both a high-confidence upper bound and a consistent estimator of the out-of-sample expected cost, and show empirically that it produces solutions that are substantially less conservative than existing DRO methods, while providing the same guarantees.

关键词： Costs TV stochastic processes Machine learning Upper bound Training Standards stochastic programming constrained optimization

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Backtesting coordinated hydropower bidding using neural network forecasting

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ENERGY SYSTEMS-OPTIMIZATION MODELING SIMULATION AND ECONOMIC ASPECTS 2023年第3期14卷 847-867页

作者： Bringedal, Amanda Saebo Sovikhagen, Anne-Marthe Liaklev Aasgard, Ellen Krohn Fleten, Stein-Erik Norwegian Univ Sci & Technol Alfred Getz Vei 3 N-7034 Trondheim Norway SINTEF Energy Res Sem Saelands Vei 11 N-7034 Trondheim Norway

A stochastic programming model for a price-taking, profit-maximizing hydropower producer participating in the Nordic day-ahead and balancing market is developed and evaluated by backtesting over 200 historical days. We find that the producer may gain 0.07% by coordinating its trades in the day-ahead and balancing market, compared to considering the two markets sequentially. It is thus questionable whether a coordinated bidding strategy is worthwhile. However, the gain from coordinating trades is dependent on the quality of the forecasts for the balancing market. The limited gain of 0.07% comes from using an artificial neural network prediction model that is trained on historical data on seasonal effects, day-ahead market price, wind and temperature forecasts. To quantify the effect of the forecasting model on the gain of coordination, we therefore develop a benchmarking framework for two additional prediction models: a naive forecast predicting zero imbalance in expectation, and a perfect information forecast. Using the naive method, we estimate the lower bound of coordination to be 0.0% which coincides with theory. When having perfect information, we find that the upper bound for the gain is 3.8% which indicates that a substantial gain in profits can be obtained by coordinated bidding if accurate prediction methods could be developed.

关键词： Electricity markets Hydropower Neural network stochastic programming

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Practicable robust stochastic optimization under divergence measures with an application to equitable humanitarian response planning

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OR SPECTRUM 2023年第3期45卷 759-806页

作者： Caunhye, Aakil M. Alem, Douglas Univ Edinburgh Business Sch 29 Buccleuch Pl Edinburgh EH8 9JU Scotland

We seek to provide practicable approximations of the two-stage robust stochastic optimization model when its ambiguity set is constructed with an f-divergence radius. These models are known to be numerically challenging to various degrees, depending on the choice of the f-divergence function. The numerical challenges are even more pronounced under mixed-integer first-stage decisions. In this paper, we propose novel divergence functions that produce practicable robust counterparts, while maintaining versatility in modeling diverse ambiguity aversions. Our functions yield robust counterparts that have comparable numerical difficulties to their nominal problems. We also propose ways to use our divergences to mimic existing f-divergences without affecting the practicability. We implement our models in a realistic location-allocation model for humanitarian operations in Brazil. Our humanitarian model optimizes an effectiveness-equity trade-off, defined with a new utility function and a Gini mean difference coefficient. With the case study, we showcase (1) the significant improvement in practicability of the robust stochastic optimization counterparts with our proposed divergence functions compared to existing f-divergences, (2) the greater equity of humanitarian response that the objective function enforces and (3) the greater robustness to variations in probability estimations of the resulting plans when ambiguity is considered.

关键词： stochastic programming Ambiguity Robust stochastic optimization Moreau-Yosida regularization f-divergence Equitable humanitarian logistics

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Supply chain planning of vaccine and pharmaceutical clusters under uncertainty: The case of COVID-19

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SOCIO-ECONOMIC PLANNING SCIENCES 2023年第PartB期87卷 101602页

作者： Kochakkashani, Farid Kayvanfar, Vahid Haji, Alireza George Washington Univ Dept Elect & Comp Engn Washington DC USA Hamad Bin Khalifa Univ Qatar Fdn Coll Sci & Engn Div Engn Management & Decis Sci Doha Qatar Sharif Univ Technol Dept Ind Engn Tehran Iran

As an abrupt epidemic occurs, healthcare systems are shocked by the surge in the number of susceptible patients' demands, and decision-makers mostly rely on their frame of reference for urgent decision-making. Many reports have declared the COVID-19 impediments to trading and global economic growth. This study aims to provide a mathematical model to support pharmaceutical supply chain planning during the COVID-19 epidemic. Additionally, it aims to offer new insights into hospital supply chain problems by unifying cold and non-cold chains and considering a wide range of pharmaceuticals and vaccines. This approach is unprecedented and includes an analysis of various pharmaceutical features such as temperature, shelf life, priority, and clustering. To propose a model for planning the pharmaceutical supply chains, a mixed-integer linear programming (MILP) model is used for a four-echelon supply chain design. This model aims to minimize the costs involved in the pharmaceutical supply chain by maintaining an acceptable service level. Also, this paper considers uncertainty as an intrinsic part of the problem and addresses it through the wait-and-see method. Furthermore, an unexplored unsupervised learning method in the realm of supply chain planning has been used to cluster the pharmaceuticals and the vaccines and its merits and drawbacks are proposed. A case of Tehran hospitals with real data has been used to show the model's capabilities, as well. Based on the obtained results, the proposed approach is able to reach the optimum service level in the COVID conditions while maintaining a reduced cost. The experiment illustrates that the hospitals' adjacency and emergency orders alleviated the service level significantly. The proposed MILP model has proven to be efficient in providing a practical intuition for decision-makers. The clustering technique reduced the size of the problem and the time required to solve the model considerably.

关键词： Pharmaceutical supply chain Vaccine supply chain Mathematical optimization stochastic programming K-means clustering COVID-19 epidemic Cold chain

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Optimal operation of virtual power plants with shared energy storage

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IET SMART GRID 2023年第2期6卷 147-157页

作者： Chen, Wenxule Xiang, Yue Liu, Junyong Sichuan Univ Coll Elect Engn 24 South Sect 1Yihuan Rd Chengdu 610065 Peoples R China

The emergence of the shared energy storage mode provides a solution for promoting renewable energy utilization. However, how establishing a multi-agent optimal operation model in dealing with benefit distribution under the shared energy storage is still a challenge. Considering the multi-agent integrated virtual power plant (VPP) taking part in the electricity market, an energy trading model based on the sharing mechanism is proposed to explore the effect of the shared energy storage on multiple virtual power plants (MVPPs). To analyse the relationship among MVPPs in the shared energy storage system (SESS), a game-theoretic method is introduced to simulate the bidding behaviour of VPP. Furthermore, the benefit distribution problem of the virtual power plant operator (VPPO) is formulated based on the Nash bargaining theory. In the case study, the proposed method is conducted in four VPPs with different resource endowments in terms of techno-economic and operation efficiency. Results verify that the multiple virtual power plants with a shared energy storage system interconnection system based on the sharing mechanism not only can achieve a win-win situation between the VPPO and the SESS on an operation cost but also obtain the optimal allocation scheme and improves the operation efficiency of the VPPs.

关键词： Optimisation techniques Power system management, operation and economics Knowledge based systems renewable energy sources multi-agent systems power markets operation efficiency energy storage energy management systems multiagent integrated virtual power plant shared energy storage mode Game theory power generation economics game theory multiagent optimal operation model virtual power plant operator shared energy storage system interconnection system renewable energy utilization energy trading model Power engineering computing power engineering computing virtual power plants Distributed power generation multiple virtual power plants stochastic programming sharing mechanism

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stochastic Unit Commitment: Model Reduction via Learning

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Current Sustainable/Renewable Energy Reports 2023年第2期10卷 36-44页

作者： Liu, Xuan Conejo, Antonio J. Constante Flores, Gonzalo E. Department of Electrical and Computer Engineering The Ohio State University ColumbusOH43210 United States Department of Integrated Systems Engineering The Ohio State University ColumbusOH43210 United States Davidson School of Chemical Engineering Purdue University West LafayetteIN47907 United States

Purpose of Review: As weather-dependent renewable generation increases its share in the generation mix of most electric energy systems, a stochastic unit commitment becomes the natural day-ahead scheduling tool. However, such a tool is generally computationally intractable if a detailed uncertainty description is considered. Taking this into account, we proposed a learning method to make the stochastic unit commitment problem tractable. Recent Findings: Recent advances in statistical learning and machine learning to address optimization problems can be advantageously applied to the rather intractable stochastic unit commitment problem. Considering these advances, we explore simple learning techniques to drastically reduce the size of a stochastic unit commitment problem without significantly altering its optimal solution. Summary: The considered stochastic unit commitment problem is formulated as a two-stage stochastic programming problem. The first stage represents commitment decisions, while the second one represents the operation conditions under different scenarios. Taking into account historical solved instances (or proxies for them), we reduce the size (measured by numbers of constraints and variables) of the stochastic unit commitment problem by (i) fixing unchanged binary variables and by (ii) eliminating inactive inequality constraints. Our numerical results show that the reduced problem generally requires significantly less time to solve while obtaining high-quality solutions, which are very close to or indistinguishable from the one obtained by solving the original problem. We use an Illinois 200-bus system to illustrate and characterize the performance of the proposed problem-reduction method. © 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

关键词： stochastic programming

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Non-parametric generalised newsvendor model

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ANNALS OF OPERATIONS RESEARCH 2023年第1-2期321卷 241-266页

作者： Ghosh, Soham Mukhoti, Sujay Indian Inst Technol Indore Humanities & Social Sci Indore 453552 Madhya Pradesh India Indian Inst Management Indore Operat Management & Quantitat Tech Area Indore 453556 Madhya Pradesh India

In the present paper we generalise the classical newsvendor problem for critical perishable commodities having more severe costs than its linear alternative. Piece wise polynomial cost functions are introduced to accommodate the excess severity. stochastic demand is assumed to follow a completely unknown probability distribution. Non parametric estimator of the optimal order quantity has been developed from an estimating equation using a random sample. Strong consistency of the estimator is proved for unique optimal order quantity and the result is extended for multiple solutions. Simulation results indicate that non parametric estimator is efficient in terms of mean square error. Real life application of the proposed non-parametric estimator has been demonstrated with Avocado demand in the United States of America and Covid-19 test kit demand during second wave of SARS-COV2 pandemic across 86 countries.

关键词： stochastic programming Non-parametric estimation Strong consistency Monte-Carlo simulation Newsvendor problem Non-linear optimisation

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