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Constraint qualifications in partial identification

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arXiv 2019年

作者： Kaido, Hiroaki Molinari, Francesca Stoye, Jörg Department of Economics Boston University United States Department of Economics Cornell University United States

The literature on stochastic programming typically restricts attention to problems that fulfill constraint qualifications. The literature on estimation and inference under partial identification frequently restricts the geometry of identified sets with diverse high-level assumptions. These superficially appear to be different approaches to closely related problems. We extensively analyze their relation. Among other things, we show that for partial identification through pure moment inequalities, numerous assumptions from the literature essentially coincide with the Mangasarian-Fromowitz constraint qualification. This clarifies the relation between well-known contributions, including within econometrics, and elucidates stringency, as well as ease of verification, of some high-level assumptions in seminal papers. Copyright © 2019, The Authors. All rights reserved.

关键词： stochastic programming

ATC-Based Scenario Decomposition Algorithm for Optimal Power Flow of Distribution Networks Considering High Photovoltaic Penetration

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arXiv 2022年

作者： Mo, Xiemin Liu, Tao Lyu, Xue Department of Electrical and Electronic Engineering The University of Hong Kong Hong Kong Shenzhen Institute of Research Innovation The University of Hong Kong Hong Kong Department of Electrical and Computer Engineering The University of Wisconsin-Madison Madison WI United States

This paper focuses on the analytical target cascading (ATC) based scenario decomposition method which applies to the stochastic OPF problem of distribution networks with high photovoltaic penetration. The original two-stage stochastic OPF model is decomposed into a master problem in the upper level and multiple subproblems in the lower level. This decomposition makes subproblems easier to be solved and can also effectively overcome the curse of dimensionality in the traditional scenario-based model. The global optimal solution can be obtained by only transferring some necessary coupling information between the upper and lower levels. Moreover, all the subproblems in the lower level can be solved in a parallel manner which improves the computational efficiency, in particular, for cases with a larger number of scenarios. Case studies on the IEEE 33-bus system and various larger systems verify the effectiveness and adaptability of the proposed algorithm. © 2022, CC BY-NC-ND.

关键词： stochastic programming

Combining uncertainty with electricity and gas sector coupling—is it worth the effort?

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arXiv 2020年

作者： Riepin, Iegor Möbius, Thomas Müsgens, Felix BTU Cottbus-Senftenberg Siemens-Halske-Ring 13 Cottbus03046 Germany

The interdependence of electricity and natural gas markets is becoming a major topic in energy research. Integrated energy models are used to assist decision-making for businesses and policymakers addressing challenges of energy transition and climate change. The analysis of complex energy systems requires large-scale models, which are based on extensive databases, intertemporal dynamics and a multitude of decision variables. Integrating such energy system models results in increased system complexity. This complexity poses a challenge for energy modellers to address multiple uncertainties that affect both markets. stochastic optimisation approaches enable an adequate consideration of uncertainties in investment and operation planning;however, stochastic modelling of integrated large-scale energy systems further scales the level of complexity. In this paper, we combine integrated and stochastic optimisation problems and parametrise our model for European electricity and gas markets. We analyse and compare the impact of uncertain input parameters, such as gas and electricity demand, renewable energy capacities and fuel and CO2prices, on the quality of the solution obtained in the integrated optimisation problem. Our results quantify the value of encoding uncertainty as a part of a model. While the methodological contribution should be of interest for energy modellers, our findings are relevant for industry experts and stakeholders with an empirical interest in the European energy system. Copyright © 2020, The Authors. All rights reserved.

关键词： stochastic programming

stochastic Optimization Approaches for an Operating Room and Anesthesiologist Scheduling Problem

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arXiv 2022年

作者： Tsang, Man Yiu Shehadeh, Karmel S. Curtis, Frank E. Hochman, Beth Brentjens, Tricia E. Department of Industrial and Systems Engineering Lehigh University BethlehemPA United States Divisions of General Surgery & Critical Care Medicine Columbia University Medical Center New YorkNY United States Department of Anesthesiology Columbia University Medical Center New YorkNY United States

We propose combined allocation, assignment, sequencing, and scheduling problems under uncertainty involving multiple operation rooms (ORs), anesthesiologists, and surgeries, as well as methodologies for solving such problems. Specifically, given sets of ORs, regular anesthesiologists, on-call anesthesiologists, and surgeries, our methodologies solve the following decision-making problems simultaneously: (1) an allocation problem that decides which ORs to open and which on-call anesthesiologists to call in, (2) an assignment problem that assigns an OR and an anesthesiologist to each surgery, and (3) a sequencing and scheduling problem that determines the order of surgeries and their scheduled start times in each OR. To address uncertainty of each surgery’s duration, we propose and analyze stochastic programming (SP) and distributionally robust optimization (DRO) models with both risk-neutral and risk-averse objectives. We obtain near-optimal solutions of our SP models using sample average approximation and propose a computationally efficient column-and-constraint generation method to solve our DRO models. In addition, we derive symmetry-breaking constraints that improve the models’ solvability. Using real-world, publicly available surgery data and a case study from a health system in New York, we conduct extensive computational experiments comparing the proposed methodologies empirically and theoretically, demonstrating where significant performance improvements can be gained. Additionally, we derive several managerial insights relevant to practice. Copyright © 2022, The Authors. All rights reserved.

关键词： stochastic programming

A primal decomposition algorithm for the two-dimensional bin packing problem

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arXiv 2019年

作者： Côté, Jean-Fraņcois Haouari, Mohamed Iori, Manuel 2325 rue de la Terrasse QúebecQuébecG1V 0A6 Canada Dmie College of Engineering Qatar University Doha Qatar Dismi University of Modena and Reggio Emilia Via Amendola 2 Reggio Emilia42122 Italy

The Two-dimensional Bin Packing Problem calls for packing a set of rectangular items into a minimal set of larger rectangular bins. Items must be packed with their edges parallel to the borders of the bins, cannot be rotated and cannot overlap among them. The problem is of interest because it models many real-world applications, including production, warehouse management and transportation. It is, unfortunately, very difficult, and instances with just 40 items are unsolved to proven optimality, despite many attempts, since the 1990s. In this paper, we solve the problem with a combinatorial Benders decomposition that is based on a simple model in which the two-dimensional items and bins are just represented by their areas, and infeasible packings are imposed by means of exponentially-many no-good cuts. The basic decomposition scheme is quite naive, but we enrich it with a number of preprocessing techniques, valid inequalities, lower bounding methods, and enhanced algorithms to produce the strongest possible cuts. The resulting algorithm behaved very well on the benchmark sets of instances, improving on average upon previous algorithms from the literature and solving for the first time a number of open instances. Copyright © 2019, The Authors. All rights reserved.

关键词： stochastic programming

The Impact of Pumped Hydro Energy Storage Configurations on Investment Planning of Hybrid Systems with Renewables

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SSRN

SSRN 2023年

作者： Yurter, Gulin Nadar, Emre Kocaman, Ayse Selin Department of Industrial Engineering Bilkent University Ankara Turkey Energy Initiative Massachusetts Institute of Technology CambridgeMA United States

The pumped hydro energy storage (PHES) systems can be installed in various configurations depending on the specific geographical and hydrological conditions. The closed-loop PHES systems are off-stream and have no natural inflow to the system. However, the open-loop systems are on-stream and have natural inflows to the upper and/or lower reservoirs. In this study, we develop two-stage stochastic programming models for various PHES configurations to investigate how the choice of PHES configuration impacts the sizing decisions and costs of a hybrid system that includes a renewable power generator co-operated with PHES. Our numerical results show that using a PHES facility instead of a conventional hydropower system reduces the expected system cost and mismatched demand significantly. Open-loop PHES facilities perform better than closed-loop PHES and seawater PHES facilities, dramatically lowering the need for fossil fuels in demand fulfillment. The most cost-efficient PHES configuration is when there is natural inflow to the upper reservoir. Using solar energy instead of wind as the renewable source significantly increases the requirement for larger upper reservoirs in on-stream open-loop PHES facilities, while simultaneously reducing the expected system cost for all configurations. © 2023, The Authors. All rights reserved.

关键词： stochastic programming

Random Field Optimization

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arXiv 2022年

作者： Pulsipher, Joshua L. Davidson, Benjamin R. Zavala, Victor M. Department of Chemical and Biological Engineering University of Wisconsin-Madison 1415 Engineering Dr MadisonWI53706 United States

We present a new modeling paradigm for optimization that we call random field optimization. Random fields are a powerful modeling abstraction that aims to capture the behavior of random variables that live on infinite-dimensional spaces (e.g., space and time) such as stochastic processes (e.g., time series, Gaussian processes, and Markov processes), random matrices, and random spatial fields. This paradigm involves sophisticated mathematical objects (e.g., stochastic differential equations and space-time kernel functions) and has been widely used in neuroscience, geoscience, physics, civil engineering, and computer graphics. Despite of this, however, random fields have seen limited use in optimization;specifically, existing optimization paradigms that involve uncertainty (e.g., stochastic programming and robust optimization) mostly focus on the use of finite random variables. This trend is rapidly changing with the advent of statistical optimization (e.g., Bayesian optimization) and multi-scale optimization (e.g., integration of molecular sciences and process engineering). Our work extends a recently-proposed abstraction for infinite-dimensional optimization problems by capturing more general uncertainty representations. Moreover, we discuss solution paradigms for this new class of problems based on finite transformations and sampling, and identify open questions and challenges. © 2022, CC BY.

关键词： stochastic programming

Fitting random cash management models to data

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arXiv 2024年

作者： Salas-Molina, Francisco Universitat Politènica de València Ferrandiz y Carbonell s/n Alcoy03801 Spain

Organizations use cash management models to control balances to both avoid overdrafts and obtain a profit from short-term investments. Most management models are based on control bounds which are derived from the assumption of a particular cash flow probability distribution. In this paper, we relax this strong assumption to fit cash management models to data by means of stochastic and linear programming. We also introduce ensembles of random cash management models which are built by randomly selecting a subsequence of the original cash flow data set. We illustrate our approach by means of a real case study showing that a small random sample of data is enough to fit sufficiently good bound-based *** Codes 68T01, 91B28 © 2024, CC BY-NC-ND.

关键词： stochastic programming

Where to Market Flexibility? Optimal Participation of Industrial Energy Systems in Balancing-Power, Day-Ahead, and Continuous Intraday Electricity Markets

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arXiv 2022年

作者： Nolzen, Niklas Ganter, Alissa Baumgärtner, Nils Leenders, Ludger Bardow, André Energy & Process Systems Engineering Department of Mechanical and Process Engineering ETH Zürich Tannenstrasse 3 Zürich8092 Switzerland Institute of Technical Thermodynamics RWTH Aachen University Schinkelstraße 8 Aachen52062 Germany Energy Trading and Dispatching Currenta GmbH & Co. OHG Kaiser-Wilhelm-Allee 80 Leverkusen51373 Germany Forschungszentrum Jülich GmbH Wilhelm-Johnen-Straße Jülich52425 Germany

The rising share of volatile renewable generation increases the demand for flexibility in the electricity grid. Flexible capacity can be offered by industrial energy systems through participation on either the continuous intraday, day-ahead, or balancing-power markets. Thus, industrial energy systems face the problem of where to market their flexible capacity. Here, we propose a method to integrate trading on the continuous intraday market into a multi-market optimization for flexible industrial energy systems. To estimate the intraday market revenues, we employ option-price theory. Subsequently, a multi-stage stochastic optimization determines an optimized bidding strategy and allocates the flexible capacity. The method is applied to a case study of a multi-energy system showing that coordinated bidding in all three considered markets reduces cost most. A sensitivity analysis for the intraday market volatility reveals changing market preferences, thus emphasizing the need for multi-market optimization. The proposed method provides a practical decision-support tool in short-term electricity and balancing-power markets. Copyright © 2022, The Authors. All rights reserved.

关键词： stochastic programming