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A stochastic linear programming model for maximizing generation and firm output at a reliability in long-term hydropower reservoir operation

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JOURNAL OF HYDROLOGY 2023年第1期618卷

作者： Chen, Cheng Feng, Suzhen Liu, Shuangquan Zheng, Hao Zhang, Hong Wang, Jinwen Huazhong Univ Sci & Technol Sch Civil & Hydraul Engn Wuhan 430074 Peoples R China Huazhong Univ Sci & Technol Inst Water Resources & Hydropower Wuhan 430074 Peoples R China Yunnan Elect Power Dispatch & Control Ctr Kunming 650011 Yunnan Peoples R China Griffith Univ Sch Engn & Built Environm Gold Coast Campus Gold Coast Qld 4222 Australia

The firm output, usually determined in the design stage of a hydroplant to serve as a threshold to measure system reliability, can be regarded as an unknown parameter to be explored to its maximum in long-term hydropower reservoir operation (LHRO). An unknown firm output to be ensured at certain reliability, however, will make the problem much more nonlinear and then complicate the modeling. This work presents a stochastic linear pro-gramming (SLP-1) model that can explicitly incorporate reliability in ensuring an unknown firm output to be maximized by using a probability variable to represent a decision at a state and introducing binary variables to decide whether the decision will ensure the unknown firm output. The present SLP-1 is improved on 1) another previous SLP model (SLP-0) that must have a firm output prespecified at certain reliability, and compared with 2) the stochastic dynamic programming (SDP) model that can only manage to estimate the firm output at a reli-ability with trial and error. Case studies show the superiority of the present SLP to the SDP that can hardly make the reliability any closer to what the SLP can achieve, especially in ensuring a high firm output, with gaps to desired reliability ranging up to 42.33% for Xiaowan and 31.8% for Nuozhadu. Indeed, the SLP-1 will encounter the dimensional difficulty that needs further efforts to overcome when applied to cascaded reservoirs.

关键词： Long -term hydropower operation stochastic linear programming Firm output Reliability

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Estimating the Optimal Probability of a Candidate Basic Solution in stochastic linear programming 60

Estimating the Optimal Probability of a Candidate Basic Solu...

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60th Annual Conference of the Society-of-Instrument-and-Control-Engineers-of-Japan (SICE)

作者： Gao, Zhenzhong Inuiguchi, Masahiro Osaka Univ Grad Sch Engn Sci Toyonaka Osaka 5608531 Japan

ISBN: (纸本)9784907764739

In this paper, we study the linear programming problem with random objective coefficients that have specific probability distributions. Since a candidate basic solution is hard to maintain optimal in all conditions, it is essential to estimate its probability of being optimal. To accomplish the goal, we assume one can get the probability distribution of coefficients, which forms the corresponding stochastic problem. Aided by the optimality's characteristics of a feasible basic solution in linear programming, we propose the probability estimation approach by utilising the probability density functions of coefficients. Furthermore, we show that the approach can estimate multiple candidate basic solutions, enabling a decision-maker to choose the one with the most significant probability. For generality, we test the approach with coefficients in uniform distribution and normal distribution, where we also simulate the process and make a verification. Moreover, since one can regard the uniform distribution as equivalent to the interval one, we compare both results and show that our estimation is more convincible.

关键词： stochastic linear programming Optimality Candidate Basic Solution Random Coefficients Probability Density Function (p.d.f.)

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Application of stochastic linear programming in managerial accounting Scenario analysis approach

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INTERNATIONAL JOURNAL OF ACCOUNTING AND INFORMATION MANAGEMENT 2020年第1期28卷 184-204页

作者： Wu, Di Choi, Yong Li, Ji Calif State Univ Bakersfield Dept Accounting & Finance Bakersfield CA 93311 USA

Purpose This paper aims to focus on applications of stochastic linear programming (SLP) to managerial accounting issues by providing a theoretical foundation and practical examples. SLP models may have more implications - and broader ones - in industry practice than deterministic linear programming (DLP) models do. Design/methodology/approach This paper introduces both DLP and SLP methods. In addition, continuous and discrete SLP models are explained. Applications are demonstrated using practical examples and simulations. Findings This research work extends the current knowledge of SLP, especially concerning managerial accounting issues. Through numerical examples, SLP demonstrates its great ability of hedging against all scenarios. Originality/value This study serves as an addition to building a cumulative tradition of research on SLP in managerial accounting. Only a few SLP studies in managerial accounting have focused on the development of such an instrument. Thus, the measurement scales in this research can be used as the starting point for further refining the instrument of optimization in managerial accounting.

关键词： Scenario analysis Data analytics Deterministic linear programming stochastic linear programming

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stochastic linear programming for Reservoir Operation with Constraints on Reliability and Vulnerability

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WATER 2018年第2期10卷 175-175页

作者： Chen, Cheng Kang, Chuanxiong Wang, Jinwen Huazhong Univ Sci & Technol Sch Hydropower & Informat Engn Wuhan 430074 Hubei Peoples R China

Reliability and vulnerability (RV) are two very important performance measures but, due to their stage-inseparable nature, they cannot be explicitly incorporated in stochastic dynamic programming (SDP), which is extensively used in reservoir operation. With inflows described as a Markov chain, a stochastic linear programming (SLP) model is formulated in this paper to explicitly incorporate the RV constraints in the reservoir operation, aimed at maximizing the expected power generation by determining the optimal scheduling decisions and their probabilities. Simulation results of the SLP and SDP models indicate the equivalence of the proposed SLP and SDP models without considering the RV constraints, as well as the strength of the SLP in explicitly incorporating the RV constraints. A simulated scheduling solution also reveals a reduction of power generation fluctuation, with the reservoir capacity emptied in advance to meet given reliability and vulnerability.

关键词： stochastic linear programming Markov chain reliability vulnerability reservoir operation stochastic dynamic programming

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Mitigating Uncertainty via Compromise Decisions in Two-Stage stochastic linear programming: Variance Reduction

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OPERATIONS RESEARCH 2016年第6期64卷 1422-1437页

作者： Sen, Suvrajeet Liu, Yifan Univ Southern Calif Daniel J Epstein Dept Ind & Syst Engn Los Angeles CA 90089 USA

stochastic programming (SP) has long been considered a well-justified yet computationally challenging paradigm for practical applications. Computational studies in the literature often involve approximating a large number of scenarios by using a small number of scenarios to be processed via deterministic solvers, or running Sample Average Approximation on some genre of high performance machines so that statistically acceptable bounds can be obtained. In this paper we show that for a class of stochastic linear programming problems, an alternative approach known as stochastic Decomposition (SD) can provide solutions of similar quality in far less computational time using ordinary desktop or laptop machines of today. In addition to these compelling computational results, we provide a stronger convergence result for SD, and introduce a new solution concept that we call the compromise decision. This new concept is attractive for algorithms that call for multiple replications in sampling-based convex optimization algorithms. For such replicated optimization, we show that the difference between an average solution and a compromise decision provides a natural stopping rule. We discuss three stopping criteria that enhance the reliability of the compromise decision, reducing bias and variance associated with the result. Finally our computational results cover a variety of instances from the literature, including a detailed study of SONET Switched Network (SSN), a network planning instance known to be more challenging than other test instances in the literature.

关键词： stochastic linear programming stochastic decomposition computational experiments

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Some Explicit Results for the Distribution Problem of stochastic linear programming

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Open Journal of Optimization 2016年第4期5卷 140-162页

作者： Afrooz Ansaripour Adriana Mata Sara Nourazari Hillel Kumin Penn State University State College PA USA CAF Development Bank Caracas Venezuela California State University at Long Beach Long Beach CA USA University of Oklahoma Norman OK USA

A technique is developed for finding a closed form expression for the cumulative distribution function of the maximum value of the objective function in a stochastic linear programming problem, where either the objective function coefficients or the right hand side coefficients are continuous random vectors with known probability distributions. This is the “wait and see” problem of stochastic linear programming. Explicit results for the distribution problem are extremely difficult to obtain;indeed, previous results are known only if the right hand side coefficients have an exponential distribution [1]. To date, no explicit results have been obtained for stochastic c, and no new results of any form have appeared since the 1970’s. In this paper, we obtain the first results for stochastic c, and new explicit results if b an c are stochastic vectors with an exponential, gamma, uniform, or triangle distribution. A transformation is utilized that greatly reduces computational time.

关键词： stochastic linear programming The Wait and See Problem Mathematics Subject Classification

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Risk Preferences of EV Fleet Aggregators in Day-Ahead Market Bidding: Mean-CVaR linear programming Model

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ENERGIES 2025年第1期18卷 93-93页

作者： Zoltowska, Izabela Warsaw Univ Technol Inst Control & Computat Engn PL-00665 Warsaw Poland

This paper introduces a mean profit- conditional value-at-risk (CVaR) model for purchasing electricity on the day-ahead market (DA) by electric vehicles fleet aggregator (EVA). EVA controls electric vehicles (EVs) during their workplace parking, enabling smart charging and cost savings by accessing market prices that are potentially lower than flat rates available during home charging. The proposed stochastic linear programming model leverages market price scenarios to optimize aggregated charging schedules, which serve as templates for constructing effective DA bidding curves. It integrates an aspiration/reservation-based formulation of the mean profit-risk criteria, specifically Conditional Value at Risk (CVaR) to address the EVA's risk aversion. By incorporating interactive analysis, the framework ensures adaptive and robust charging schedules and bids tailored to the aggregator's risk preferences. Its ability to balance profitability with risk is validated in case studies. This approach provides a practical and computationally efficient tool for EV aggregators of global companies that can benefit from the workplace charging their fleets thanks to buying energy in the DA market.

关键词： aggregator smart charging bid curve CVaR stochastic linear programming

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New Approach of Blind Adaptive Equalizer Based on Genetic Algorithms

TELECOM

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TELECOM 2025年第1期6卷 6-6页

作者： Silva, Caroline A. D. Fernandes, Marcelo A. C. Fed Univ Rio Grande do Norte UFRN InovAI Lab nPITI IMD BR-59078970 Natal Brazil Fed Univ Rio Grande do Norte UFRN Leading Adv Technol Ctr Excellence LANCE nPITI IMD BR-59078970 Natal RN Brazil Fed Univ Rio Grande do Norte UFRN Dept Comp Engn & Automat BR-59078970 Natal Brazil

This paper introduces a novel approach to blind adaptive equalization for digital communication systems using genetic algorithms (GAs). Unlike traditional methods that rely on linear programming and suffer from local minima issues, this technique utilizes a stochastic linear programming cost function with GAs for robust optimization. The proposed method termed Blind linear Equalizer based on genetic algorithm (BLE-GA) enhances performance by leveraging a GA's ability to handle stochastic variables, offering rapid convergence and resilience against signal noise and inter-symbol interference. Extensive simulations demonstrate the effectiveness of BLE-GA across different QAM systems, outperforming conventional techniques like the Constant Modulus Algorithm in scenarios with high modulation levels. This study validates the potential of using GAs in adaptive blind equalization to achieve reliable and efficient communication, even in complex and noisy channel conditions.

关键词： blind equalization genetic algorithms linear programming stochastic linear programming

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Service-oriented container slot allocation policy under stochastic demand

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TRANSPORTATION RESEARCH PART B-METHODOLOGICAL 2023年第1期176卷

作者： Liang, Jinpeng Li, Liming Zheng, Jianfeng Tan, Zhijia Dalian Maritime Univ Sch Transportat Engn Dalian Peoples R China Huazhong Univ Sci & Technol Sch Management Wuhan Peoples R China

The liner shipping industry plays a pivotal role in global cargo transportation, catering to both contract and spot shippers. Proper capacity allocation between these shippers is vital for maintaining service quality and improving revenue. This research investigates the service oriented container slot allocation problem under stochastic demand, aiming to maximize total freight revenue while providing adequate service levels to contract shippers for sustaining their market loyalty. We use the fill rate (i.e., the proportion of satisfied demand) as a metric for service level and formulate the research problem as a stochastic linear programming model. To solve this model, we convert it into a multi-objective attainability problem by setting a target for total revenue, and apply Blackwell's Approachability Theorem to theoretically determine the feasibility of any given revenue and service level requirements. Leveraging these insights, we devise near-optimal policies to guide the slot allocation decision under each demand scenario. Numerical experiments demonstrate that our approach outperforms the benchmark policies in the literature. Furthermore, it can also achieve near-optimal performance closely resembling the sampling average approximation (SAA) solution while significantly reducing the computational time.

关键词： Liner shipping Container slot allocation stochastic demand stochastic linear programming Service level

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Generalized adaptive partition-based method for two-stage stochastic linear programs : Geometric oracle and analysis

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OPERATIONS RESEARCH LETTERS 2022年第4期50卷 452-457页

作者： Forcier, Mail Leclere, Vincent Ecole Ponts CERMICS Marne France

Adaptive Partition-based Methods (APM) are numerical methods that solve, in particular, two-stage stochastic linear problems (2SLP). We say that a partition of the uncertainty space is adapted to the current first stage control x over titlde if we can aggregate scenarios while conserving the true value of the expected recourse cost at x over titlde. The core idea of APM is to iteratively construct an adapted partition to all past tentative first stage controls. Relying on the normal fan of the dual admissible set, we give a necessary and sufficient condition for a partition to be adapted even for non-finite distribution, and provide a geometric method to obtain an adapted partition. Further, by showing the connection between APM and the L-shaped algorithm, we prove convergence and complexity bounds of the APM methods. The paper presents the fixed recourse case and ends with elements to forgo this assumption. (C) 2022 Elsevier B.V. All rights reserved.

关键词： stochastic linear programming Exact method Adaptive partition methods

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