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Optimizing financial and physical assets with chance-constrained programming in the electrical industry

OPTIMIZATION AND ENGINEERING 2011年第1-2期12卷 237-255页

作者： Zorgati, Riadh van Ackooij, Wim EDF R&D OSIRIS 1 F-92141 Clamart France

This paper deals with a chance-constrained programming formulation and approximate resolution of an offer-demand equilibrium problem in the context of electricity markets. First, we state the probabilistic model. Computing the coefficients of the problem matrix is easy for financial assets, but a challenging task for physical assets. By introducing maximal production capacities, the computation becomes tractable for thermal plants but still leads to a combinatorial problem for hydraulic production. The obtained problem matrix is sparse, large scale and with random coefficients describing underlying uncertainty factors affecting the available power of assets. Second, we suggest some ways for approximately solving the obtained combinatorial chance-constrained program, which is in fact a stochastic multi-knapsack problem. A formal link between joint and individual chance constraints is exhibited and may lead to a simplified processing of the problem. Finally we illustrate our approximate algorithm on a stylized example.

关键词： Unit commitment Hedging chance-constrained programming

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Multi-choice probabilistic linear programming problem

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OPSEARCH 2017年第1期54卷 122-142页

作者： Pradhan, Avik Biswal, M. P. Indian Inst Technol Kharagpur Dept Math Kharagpur 721302 W Bengal India

In this paper, we present a linear programming model where the parameter space contains some multi-choice parameters. Alternative choices of multi-choice parameter are considered as random variables. Using interpolating polynomial for each multi-choice parameter, the model has been transformed into a non-linear mixed integer probabilistic programming problem. Then chance constrained programming technique is used to obtain an equivalent deterministic model of the transformed problem. To find the deterministic form of the objective function four different models namely, E-model, V-model, probability maximization model and fractile criterion model are used. Assuming the values of the multi-choice parameters as independent normal random variables, the methodology is presented. A numerical example is also presented to illustrate the methodology.

关键词： chance-constrained programming Multi-choice programming Linear programming Probabilistic programming

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Distributionally robust appointment scheduling with moment-based ambiguity set

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OPERATIONS RESEARCH LETTERS 2017年第2期45卷 139-144页

作者： Zhang, Yiling Shen, Siqian Erdogan, S. Ayca Univ Michigan Dept Ind & Operat Engn Ann Arbor MI 48109 USA San Jose State Univ Dept Ind & Syst Engn San Jose CA 95192 USA

We study appointment scheduling under random service duration with unknown distributions. Given a sequence of appointments arriving at a single server, we assign their planned arrival time to minimize the expected total waiting time, while using a chance constraint to restrict the probability of server overtime. We consider a distributionally robust formulation based on an ambiguity set that uses the first two moments, and derive an approximate semidefinite programming model. We conduct computational studies by testing outpatient treatment scheduling instances. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Appointment scheduling Random service durations Distributionally robust optimization chance-constrained programming Semidefinite programming

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A solid transportation model with product blending and parameters as rough variables

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SOFT COMPUTING 2017年第9期21卷 2297-2306页

作者： Kundu, Pradip Kar, Mouhya B. Kar, Samarjit Pal, Tandra Maiti, Manoranjan IISER Kolkata Dept Math & Stat Mohanpur 741252 India Heritage Inst Technol Dept Comp Sci Kolkata 700107 India NIT Dept Math Durgapur 713209 India NIT Dept Comp Sci & Engn Durgapur 713209 India Vidyasagar Univ Dept Appl Math Midnapore 721102 India

In this paper, we formulate a practical solid transportation problem with product blending which is a common issue in many operational and planning models in the chemical, petroleum, gasoline and process industries. In the problem formulation, we consider that raw materials from different sources with different quality (or purity) levels are to be transported to some destinations so that the materials received at each destination can be blended together into the final product to meet minimum quality requirement of that destination. The parameters such as transportation costs, availabilities, demands are considered as rough variables in designing the model. We construct a rough chance-constrained programming (RCCP) model for the problem with rough parameters based on trust measure. This RCCP model is then transformed into deterministic form to solve the problem. Numerical example is presented to illustrate the problem model and solution strategy. The results are obtained using the standard optimization solver LINGO.

关键词： Solid transportation problem Blending Rough variable Trust measure chance-constrained programming

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Risk assessment and bi-level optimization dispatch of virtual power plants considering renewable energy uncertainty

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IEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERING 2017年第4期12卷 510-518页

作者： Zhang, Gao Jiang, Chuanwen Wang, Xu Li, Bosong Shanghai Jiao Tong Univ Sch Elect Informat & Elect Engn Shanghai 200240 Peoples R China

Aiming at the effective management of distributed energy resources (DERs), we propose a bi-level optimization dispatch model which consists of a virtual power plant (VPP) and an independent system operator (ISO) in order to achieve a coordinated dispatch between the upper level objective function of minimizing system's operation cost and the lower level objective function of maximizing the VPP's net profit. However, the VPP's dispatch strategy is variable due to the threat from unavoidable uncertainties including unit outage, load forecast deviation, and renewable energy forecasting error. In order to evaluate the influences of these risks on VPP's dispatch strategy, a proper definition of expected energy not supplied (EENS) and its relationship with VPP's reserve capacity are provided. Also, chance-constrained programming (CCP) is adopted during the analysis. By including VPP's risk cost into the dispatch model, VPP's dispatch strategy is able to keep a balance between the potential risk and economic profit. In addition, a further discussion regarding the risk cost is conducted in view of renewable energy capacity proportion and the VPP capacity proportion. Based on the analysis results of the case study provided, the proposed model serves as a foundation for VPP's economic and risk-balanced dispatch. (C) 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

关键词： bi-level optimization dispatch virtual power plant distributed energy resources risk assessment chance-constrained programming

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Uncapacitated -hub location problem with fixed costs and uncertain flows

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JOURNAL OF INTELLIGENT MANUFACTURING 2017年第3期28卷 705-716页

作者： Qin, Zhongfeng Gao, Yuan Beihang Univ Sch Econ & Management Beijing 100191 Peoples R China Beijing Jiaotong Univ State Key Lab Rail Traff Control & Safety Beijing 100044 Peoples R China

Hub location problem is an important problem and has many applications in various areas, such as transportation and telecommunication. Since the problem involves long-term strategic decision, the future flows will change with time. However, it is difficult or costly to obtain the data of flows, which implies that it is necessary to consider hub location problems in the absence of data. A commonly used way is to estimate future flows by experts' subjective information. As a result, this paper presents a new uncapacitated -hub location problem, in which the flows are described by uncertain variables. Two uncertain programming models are formulated to respectively minimize the expected cost and the -cost with the corresponding constraints. Equivalent forms are given when the information about uncertainty distributions of flows is further provided. A genetic algorithm is designed to solve the proposed models and its effectiveness is illustrated by numerical examples.

关键词： P-hub location problem Uncertain variable Uncertain measure Expected value model chance-constrained programming

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Simulation-based mine extraction sequencing with chance constrained risk tolerance

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SIMULATION-TRANSACTIONS OF THE SOCIETY FOR MODELING AND SIMULATION INTERNATIONAL 2017年第6期93卷 527-539页

作者： Kumral, Mustafa Sari, Yuksel Asli McGill Univ Dept Min & Mat Engn 3450 Univ St Montreal PQ H3A 2A7 Canada

Technical and financial uncertainties present significant risks to the profitability and efficiency of mining operations. Unexpected realizations (e.g., price or grade) may result in catastrophic consequences. This phenomenon forces mining industries to use probabilistic decision-making tools to assess, mitigate, and manage the risks associated with these uncertainties. In this context, mining operations need robust schedules, which are insensitive to market changes and/or unexpected grade realizations. The mine production scheduling problem consists of three sub-problems: extraction sequencing (timing), ore-waste discrimination (classification) and production rates (utilization). The solutions to these problems are generated under significant parameter uncertainties. This paper proposes an extraction sequencing approach in which the net present value of a mining project is, for a given risk tolerance, maximized and the actual risk tolerance is then verified through Monte-Carlo simulations. The risk tolerance is a measure of uncertainty and that secures the project net present value with a given probability. Risk tolerance is derived through the use of standard deviations of block economic values in the medium of multiple grade and economic images of orebody. The proposed approach is demonstrated on a case study using gold mine data. The results of the case study show that the proposed approach, combining chance-constrained programming and Monte-Carlo simulation, can be used to solve the mine extraction sequencing problem in an uncertain financial and technical environment.

关键词： Geostatistical simulation mine production sequencing risk-based decision making chance-constrained programming Monte-Carlo simulation

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A two-stage fuzzy chance-constrained water management model

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ENVIRONMENTAL SCIENCE AND POLLUTION RESEARCH 2017年第13期24卷 12437-12454页

作者： Xu, Jiaxuan Huang, Guohe Li, Zoe Chen, Jiapei Univ Regina Fac Engn & Appl Sci Regina SK S4S 0A2 Canada McMaster Univ Dept Civil Engn Hamilton ON L8S 4L8 Canada

In this study, an inexact two-stage fuzzy gradient chance-constrained programming (ITSFGP) method is developed and applied to the water resources management in the Heshui River Basin, Jiangxi Province, China. The optimization model is established by incorporating interval programming, two-stage stochastic programming, and fuzzy gradient chance-constrained programming within an optimization framework. The hybrid model can address uncertainties represented as fuzzy sets, probability distributions, and interval numbers. It can effectively tackle the interactions between pre-regulated economic targets and the associated environmental penalties attributed to water allocation schemes and reflect the tradeoffs between economic revenues and systemfailure risk. Furthermore, uncertainties associated with the decision makers' preferences are considered in decision-making processes. The obtained results can provide decision support for the local sustainable economic development and water resources allocation strategies under multiple uncertainties.

关键词： Fuzzy gradient chance-constrained programming Stochastic programming Optimization modeling Water resources management Uncertainty

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Noisy Immune Optimization for chance-constrained programming Problems

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3rd International Conference on Measuring Technology and Mechatronics Automation (ICMTMA 2011)

作者： Zhang Zhu-hong Guizhou Univ Coll Sci Inst Syst Sci & Informat Technol Guiyang 550025 Guizhou Peoples R China

ISBN: (纸本)9783037850190

This work puts forward a parameter-less and practical immune optimization mechanism in noisy environments to deal with single-objective chance-constrained programming problems without prior noisy information. In this practical mechanism, an adaptive sampling scheme and a new concept of reliability-dominance are established to evaluate individuals, while three immune operators borrowed from several simplified immune metaphors in the immune system and the idea of fitness inheritance are utilized to evolve the current population, in order to weaken noisy influence to the optimized quality. Under the mechanism, three kinds of algorithms are obtained through changing its mutation rule. Experimental results show that the mechanism can achieve satisfactory performances including the quality of optimization, noise compensation and performance efficiency.

关键词： stochastic programming chance-constrained programming immune optimization noisy attenuation

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Uncertain supply chain network design considering carbon footprint and social factors using two-stage approach

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CLEAN TECHNOLOGIES AND ENVIRONMENTAL POLICY 2017年第10期19卷 2491-2519页

作者： Das, Rakhi Shaw, Krishnendu Indian Inst Technol ISM Dhanbad Dept Management Studies Dhanbad 826004 Bihar India

Sustainable development has become one of the leading global issues over the period of time. Currently, implementation of sustainability in supply chain has been continuously in center of attention due to introducing stringent legislations regarding environmental pollution by various governments and increasing stakeholders' concerns toward social injustice. Unfortunately, literature is still scarce on studies considering all three dimensions (economical, environmental and social) of sustainability for the supply chain. An effective supply chain network design (SCND) is very important to implement sustainability in supply chain. This study proposes an uncertain SCND model that minimizes the total supply chain-oriented cost and determines the opening of plants, warehouses and flow of materials across the supply chain network by considering various carbon emissions and social factors. In this study, a new AHP and fuzzy TOPSIS-based methodology is proposed to transform qualitative social factors into quantitative social index, which is subsequently used in chance-constrained SCND model with an aim at reducing negative social impact. Further, the carbon emission of supply chain is estimated by considering a composite emission that consists of raw material, production, transportation and handling emissions. In the model, a carbon emission cap is imposed on total supply chain to reduce the carbon footprint of supply chain. To solve the proposed model, a code is developed in AMPL software using a nonlinear solver SNOPT. The applicability of the proposed model is illustrated with a numerical example. The sensitivity analysis examines the effects of reducing carbon footprint cap, negative social impacts and varying probability on the total cost of the supply chain. It is observed that a stricter carbon cap over supply chain network leads to opening of more plants across the supply chain. In addition, carbon footprint of supply chain is found to be decreased in certain extent

关键词： chance-constrained programming Supply chain network design Carbon footprint Sustainability Stochastic programming Social sustainability

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