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Process-based risk measures and risk-averse control of discrete-time systems

MATHEMATICAL programming 2022年第1期191卷 113-140页

作者： Fan, Jingnan Ruszczynski, Andrzej Rutgers State Univ RUTCOR Piscataway NJ 08854 USA Rutgers State Univ Dept Management Sci & Informat Syst Piscataway NJ 08854 USA

For controlled discrete-time stochastic processes we introduce a new class of dynamic risk measures, which we call process-based. Their main feature is that they measure risk of processes that are functions of the history of a base process. We introduce a new concept of conditional stochastic time consistency and we derive the structure of process-based risk measures enjoying this property. We show that they can be equivalently represented by a collection of static law-invariant risk measures on the space of functions of the state of the base process. We apply this result to controlled Markov processes and we derive dynamic programming equations. We also derive dynamic programming equations for multistage stochastic programming with decision-dependent distributions.

关键词： Dynamic risk measures Time consistency Dynamic programming multistage stochastic programming

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multistage-multiresponse models for dynamic quality chain design problems

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QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL 2017年第6期33卷 1263-1279页

作者： Hejazi, Taha-Hossein Seyyed-Esfahani, Mirmehdi Amirkabir Univ Technol Dept Ind Engn Tehran Polytech Garmsar Campus Garmsar Iran Amirkabir Univ Technol Dept Ind Engn & Management Syst Tehran Polytech Tehran Iran

Quality of final products depends on several decision variables and design factors from several stages of operations. Multiresponse optimization is a well-grounded method for offline quality design that can consider several inputs and outputs. This study introduces a new methodology for quality optimization in multistage systems with multiple response variables. Several stochastic parameters, including response surfaces and covariates, are to be considered in this methodology. For this purpose, scenario-based multistage stochastic programming models are developed in three cases addressing (1) decision on control factors, (2) decision on control factors as well as targets of intermediate stages, and (3) scenario-based decision on control factors. An example is presented at the end to illustrate the mechanism of the methodology and applicability of the three cases.

关键词： covariate effects dynamic quality chain design multiresponse optimization multistage stochastic programming Nataf transformation

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The Value of Coordination in Multimarket Bidding of Grid Energy Storage

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OPERATIONS RESEARCH 2023年第1期71卷 1-22页

作者： Loehndorf, Nils Wozabalb, David Univ Luxembourg Luxembourg Ctr Logist & Supply Chain Management L-1511 Luxembourg Luxembourg Tech Univ Munich Sch Management D-80333 Munich Germany

We consider the problem of a storage owner who trades in a multisettlement electricity market comprising an auction-based day-ahead market and a continuous intraday market. We show in a stylized model that a coordinated policy that reserves capacity for the intraday market is optimal and that the gap to a sequential policy increases with intraday price volatility and market liquidity. To assess the value of coordination in a realistic setting, we develop amultistage stochastic programfor day-ahead bidding and hourly intraday trading along with a corresponding stochastic price model. We show how tight upper bounds can be obtained based on calculating optimal bilinear penalties for a novel information relaxation scheme. To calculate lower bounds, we propose a scenario tree generation method that lends itself to deriving an implementable policy based on reoptimization. We use these methods to quantify the value of coordination by comparing our policy with a sequential policy that does not coordinate day-ahead and intraday bids. In a case study, we find that coordinated bidding is most valuable for flexible storage assets with high price impact, like pumped-hydro storage. For small assets with low price impact, like battery storage, participation in the day-ahead auction is less important and intraday trading appears to be sufficient. For less flexible assets, like large hydro reservoirs without pumps, intraday trading is hardly profitable as most profit is made in the day-ahead market. A comparison of lower and upper bounds demonstrates that our policy is nearoptimal for all considered assets.

关键词： multistage stochastic programming energy storage electricity price model limit order book scenario tree generation information relaxation

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A Distributed Interior-Point KKT Solver for multistage stochastic Optimization

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INFORMS JOURNAL ON COMPUTING 2017年第4期29卷 612-630页

作者： Huebner, Jens Schmidt, Martin Steinbach, Marc C. HaCon Ingenieurgesellschaft mbH D-30163 Hannover Germany Friedrich Alexander Univ Erlangen Nurnberg Dept Math D-91058 Erlangen Germany Energie Campus Nurnberg D-90429 Nurnberg Germany Leibniz Univ Hannover Inst Appl Math D-30167 Hannover Germany

multistage stochastic optimization leads to NLPs over scenario trees that become extremely large when many time stages or fine discretizations of the probability space are required. Interior-point methods are well suited for these problems if the arising huge, structured KKT systems can be solved efficiently, for instance, with a large scenario tree but a moderate number of variables per node. For this setting we develop a distributed implementation based on data parallelism in a depth-first distribution of the scenario tree over the processes. Our theoretical analysis predicts very low memory and communication overheads. Detailed computational experiments confirm this prediction and demonstrate the overall performance of the algorithm. We solve multistage stochastic quadratic programs with up to 400 x 10(6) variables and 8.59 x 10(9) KKT matrix entries or 136 x 10(6) variables and 12.6 x 10(9) entries on a compute cluster with 384 GB RAM.

关键词： interior-point methods KKT systems multistage stochastic programming parallel computing distributed computing portfolio optimization

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Risk-Averse Regret Minimization in multistage stochastic Programs

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OPERATIONS RESEARCH 2024年第4期72卷 1727-1738页

作者： Poursoltani, Mehran Delage, Erick Georghiou, Angelos HEC Montreal GERAD Montreal PQ H3T 2A7 Canada HEC Montreal Dept Decis Sci Montreal PQ H3T 2A7 Canada Univ Cyprus Dept Business & Publ Adm CY-1678 Nicosia Cyprus

Within the context of optimization under uncertainty, a well-known alternative to minimizing expected value or the worst-case scenario consists in minimizing regret. In a multistage stochastic programming setting with a discrete probability distribution, we explore the idea of risk-averse regret minimization, where the benchmark policy can only benefit from foreseeing increment steps into the future. The increment -regret model naturally interpolates between the popular ex ante and ex post regret models. We provide theoretical and numerical insights about this family of models under popular coherent risk measures and shed new light on the conservatism of the increment -regret minimizing solutions.

关键词： regret minimization risk measures multistage stochastic programming robust optimization

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EXACT QUANTIZATION OF multistage stochastic LINEAR PROBLEMS

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SIAM JOURNAL ON OPTIMIZATION 2024年第1期34卷 533-562页

作者： Forcier, Mael Gaubert, Stephane Leclere, Vincent CERMICS Ecole Ponts F-77420 Champs Sur Marne Marne France CNRS Ecole Polytech INRIA IP ParisCMAP F-91128 Palaiseau France

We show that the multistage stochastic linear problem (MSLP) with an arbitrary cost distribution is equivalent to an MSLP on a finite scenario tree. We establish this exact quantization result by analyzing the polyhedral structure of MSLPs. In particular, we show that the expected costto-go functions are polyhedral and affine on the cells of a chamber complex, which is independent of the cost distribution. This leads to new complexity results, showing that MSLP becomes polynomial when certain parameters are fixed.

关键词： stochastic optimization multistage stochastic programming polyhedron complexity

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Optimal operation of a CHP plant participating in the German electricity balancing and day-ahead spot market

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2017年第1期261卷 390-404页

作者： Kumbartzky, Nadine Schacht, Matthias Schulz, Katrin Werners, Brigitte Ruhr Univ Bochum Fac Management & Econ Univ Str 150 D-44801 Bochum Germany

During the last years, operators of combined heat and power (CHP) plants are challenged by changing circumstances in the electricity markets. While ensuring a stable heat and power supply for customers, CHP plant operators seek to maximise the profitability of the CHP plant operation. We propose a comprehensive concept and illustrate its potential for increasing the profitability when operating a CHP plant with heat storage by participating in multiple electricity markets. For this purpose, the structure of the decision-making process consisting of bid submission, market clearing and CHP plant operation planning is represented. A multistage stochastic mixed-integer linear programming (MILP) model is developed that simultaneously optimises the operation of the CHP plant with heat storage and bidding in sequential electricity markets. Price uncertainty is captured by means of stochastic processes. The proposed concept is applied to the real case of a municipal energy supply company that participates in the German day ahead spot and balancing market. Results of the case study illustrate how trading in sequential electricity markets can result in an increased profitability of the CHP plant operation, where additional revenues from trading offset higher generation costs. Furthermore, we exemplify how the optimal operation of the CHP plant and heat storage device are adjusted according to revenue potential in multiple electricity markets. (C) 2017 Elsevier B.V. All rights reserved.

关键词： OR in energy Combined heat and power multistage stochastic programming Bidding Electricity markets

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A flexible planning approach for integrated lot sizing and rework planning with random proportion of defective products

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2024年第19期62卷 6961-6978页

作者： Kohlmann, Pierre Sahling, Florian Univ Kaiserslautern Landau RPTU Chair Prod Management RPTU Sch Business & Econ Gottlieb Daimler Str D-67663 Kaiserslautern Germany

We consider a stochastic capacitated lot sizing problem with in-line rework. Both defective and defect-free products can be the result of an imperfect production process in real-world production systems. However, the proportion of defective items in a production lot is subject to uncertainty. For economic and environmental reasons, the possibility to rework defective products appears reasonable since these products usually have considerable value. In this paper, a nonlinear model formulation for integrated lot sizing and rework planning is proposed. We use a sample average approach to approximate the generic nonlinear model formulation. To cope with the randomness of the proportion of defective products, we apply a flexible planning approach that allows the adjustment of production and rework quantities. We conduct extensive numerical investigations to evaluate the performance of the proposed planning approach.

关键词： Lot sizing rework stochastic proportion of defective products imperfect production process multistage stochastic programming

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Development of a Sequential Decision-Making Model for Controlling Multiple Air Pollutants Under stochastic Uncertainty

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WATER AIR AND SOIL POLLUTION 2012年第1期223卷 443-465页

作者： Lv, Ying Huang, Guohe Li, Yongping Yang, Zhifeng Sun, Wei N China Elect Power Univ MOE Key Lab Reg Energy Syst Optimizat SC Energy & Environm Res Acad Beijing 102206 Peoples R China Beijing Normal Univ Sch Environm Beijing 100875 Peoples R China Univ Regina Fac Engn Regina SK S4S 0A2 Canada

Most of previous programming methods for air-quality management merely considered single pollutant from point sources. However, air pollution control is characterized by multiple pollutants from various sources. Meanwhile, uncertain information in the decision-making process cannot be neglected in the real-world cases. Thus, an inexact multistage stochastic programming model with joint chance constraints based on the air quality index (air-quality management model with joint chance constraints (AQM-JCC)) is developed for controlling multiple pollutants deriving from point and mobile sources and applied to a regional air-quality management system. In the model, integrated air quality associated with the joint probability existing in terms of environmental constraints is evaluated;uncertainties expressed as probability distributions and interval values are addressed;risks of violating the overall air-quality target under joint chance constraints are examined;and dynamics of system uncertainties and decision processes under a complete set of scenarios within a multistage context are reflected. The results indicate that useful solutions for air quality management practices in sequential stochastic decision environments have been generated, which can help decision makers to identify cost-effective control strategies for overall air quality improvement under uncertainties.

关键词： Air quality Decision making Uncertainty multistage stochastic programming Joint chance constraint

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Electric power infrastructure planning under uncertainty: stochastic dual dynamic integer programming (SDDiP) and parallelization scheme

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OPTIMIZATION AND ENGINEERING 2020年第4期21卷 1243-1281页

作者： Lara, Cristiana L. Siirola, John D. Grossmann, Ignacio E. Carnegie Mellon Univ 5000 Forbes Ave Pittsburgh PA 15213 USA Sandia Natl Labs Ctr Comp Res POB 5800 Albuquerque NM 87185 USA

We address the long-term planning of electric power infrastructure under uncertainty. We propose a multistage stochastic Mixed-integer programming formulation that optimizes the generation expansion to meet the projected electricity demand over multiple years while considering detailed operational constraints, intermittency of renewable generation, power flow between regions, storage options, and multiscale representation of uncertainty (strategic and operational). To be able to solve this large-scale model, which grows exponentially with the number of stages in the scenario tree, we decompose the problem using stochastic Dual Dynamic Integer programming (SDDiP). The SDDiP algorithm is computationally expensive but we take advantage of parallel processing to solve it more efficiently. The proposed formulation and algorithm are applied to a case study in the region managed by the Electric Reliability Council of Texas for scenario trees considering natural gas price and carbon tax uncertainty for the reference case, and a hypothetical case without nuclear power. We show that the parallelized SDDiP algorithm allows in reasonable amounts of time the solution of multistage stochastic programming models of which the extensive form has quadrillions of variables and constraints.

关键词： Generation expansion planning multistage stochastic programming stochastic dual dynamic integer programming

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