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A new decomposition approach for the thermal unit commitment problem

APPLIED ENERGY 2009年第9期86卷 1667-1674页

作者： Niknam, Taher Khodaei, Amin Fallahi, Farhad Shiraz Univ Technol Elect & Elect Dept Shiraz 71555313 Iran Niroo Res Inst Tehran Iran

In this paper, we propose a new formulation based on benders decomposition approach to solve the thermal unit commitment (UC) problem. In the proposed approach, the UC problem is decomposed into a master problem, which is an integer optimization problem, and a subproblem, which is a nonlinear optimization problem. The proper on/off states of the generating units are found by solving the master problem using the mixed-integer programming method. The subproblem utilizes the solution of the master problem to form appropriate cuts and returns the cuts to the master problem for running the next iteration of the UC problem. In both optimization problems, corresponding constraints are exactly modeled. To demonstrate the effectiveness of the proposed approach, simulation results are compared with the results obtained by other methods. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Benders decomposition mixed-integer programming Unit commitment

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The Value of Compressed-Air Energy Storage for Enhancing Variable-Renewable-Energy Integration: The Case of Ireland

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ENERGY TECHNOLOGY 2017年第11期5卷 2026-2038页

作者： Nikolakakis, Thomas Fthenakis, Vasilis Columbia Univ Ctr Life Cycle Anal Earth & Environm Engn New York NY 10027 USA

mixed integer programming (MIP) was used to formulate a unit commitment and economic dispatch (UCED) algorithm that included two models for simulating the dynamic performance of compressed-air energy storage (CAES) units. The first model assumes CAES operating with fixed efficiencies (FEs) on both the compression and expansion side, similar to models commonly used in industry and academia. The second model is a detailed thermoeconomic (TE) model, which uses power curves obtained by CAES manufacturers to model the effect of cavern pressure on operation limits of both the compressor and expander. The UCED and CAES models were combined to identify the contribution of CAES on minimizing the impacts of wind integration into the Irish power sector in 2020. The results of the UCED-TE model show that the addition of a CAES unit in the North Ireland grid can reduce wind curtailment, CO2 emissions, and system costs. The cost reductions result mainly from reductions in wind curtailment and coal-fired generation. The FE model shows much higher reductions of wind curtailment, CO2 emissions, and total system costs. However, both models show that the benefit of CAES on the system increases with variable renewable energy and CAES installed capacity. The difference in the results of the two models is reduced in scenarios of high CAES capacity. The main conclusions of the study are that existing fixed-efficiencies CAES models overestimate reductions on wind curtailment whereas both models show the system-wide economic benefits of CAES grow considerably as wind production grows.

关键词： compressed air energy storage mixed-integer programming renewable resources wind power

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Exploiting complete linear descriptions for decentralized power market problems with integralities

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MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2022年第3期95卷 451-474页

作者： Huembs, Lukas Martin, Alexander Schewe, Lars Friedrich Alexander Univ Erlangen Nurnberg Dept Data Sci Cauerstr 11 Erlangen Germany Univ Edinburgh Sch Math James Clerk Maxwell Bldg Edinburgh EH9 3FD Midlothian Scotland

It is well known that linear prices supporting a competitive equilibrium exist in the case of convex markets, however, in the presence of integralities this is open and hard to decide in general. We present necessary and sufficient conditions for the existence of such prices for decentralized market problems where market participants have integral decision variables and their feasible sets are given in complete linear description. We utilize total unimodularity and the aforementioned conditions to show that such linear prices exist and present some applications. Furthermore, we compute competitive equilibria for two classes of decentralized market problems arising in energy markets and show that competitive equilibria may exist regardless of integralities.

关键词： mixed-integer programming Competitive equilibrium Linear prices Total unimodularity

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A bi-objective analysis of the r-all-neighbor p-center problem

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COMPUTERS & INDUSTRIAL ENGINEERING 2014年第1期72卷 114-128页

作者： Medal, Hugh R. Rainwater, Chase E. Pohl, Edward A. Rossetti, Manuel D. Mississippi State Univ Dept Ind & Syst Engn Starkville MS 39762 USA Univ Arkansas Dept Ind Engn Fayetteville AR 72701 USA

In this paper we consider a generalization of the p-center problem called the r-all-neighbor p-center problem (RANPCP). The objective of the RANPCP is to minimize the maximum distance from a demand point to its rth-closest located facility. The RANPCP is applicable to facility location with disruptions because it considers the maximum transportation distance after (r - 1) facilities are disrupted. While this problem has been studied from a single-objective perspective, this paper studies two bi-objective versions. The main contributions of this paper are (1) algorithms for computing the Pareto-efficient sets for two pairs of objectives (closest distance vs rth-closest distance and cost vs. rth-closest distance) and (2) an empirical analysis that gives several useful insights into the RANPCP. Based on the empirical results, the RANPCP produces solutions that not only minimize vulnerability but also perform reasonably well when disruptions do not occur. In contrast, if disruptions are not considered when locating facilities, the consequence due to facility disruptions is much higher, on average, than if disruptions had been considered. Thus, our results show the importance of optimizing for vulnerability. Therefore, we recommend a bi-objective analysis. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Facility location Interdiction mixed-integer programming Bi-objective programming Disruptions Risk assessment

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A robust optimization approach to diet problem with overall glycemic load as objective function

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APPLIED MATHEMATICAL MODELLING 2014年第19-20期38卷 4926-4940页

作者： Bas, Esra Istanbul Tech Univ Dept Ind Engn TR-34367 Istanbul Turkey

The main purpose of the paper is to introduce a mixed-integer programming model for the diet problem with glycemic load (GL) values of foods as objective function parameters. It is assumed that the glycemic load values are subject to uncertainty. The diet problem with minimum cost function is well-known in the literature. However, the diet problem with minimum total daily GL values of foods that satisfies the daily nutritional and serving size requirements has not been proposed. Robust optimization approach is used to account for uncertainty in the GL values of foods. The decision maker is flexible to tune the degree of uncertainty rather than assuming a worst-case scenario. An experimental analysis with a total of 177 foods is performed based on the nutritional and serving size requirements and the basic food groups recommended by the U.S. Department of Health and Human Services & U.S. Department of Agriculture (USDA). The results of the experimental analysis with different scenarios give different solutions for different degrees of uncertainty. However, some foods are frequently found to be in the optimum solutions. These foods are in good agreement with the literature advising them as a part of a daily diet for attaining low level of blood glucose levels. Although we believe that the proposed diet problem with minimum total GL has contributions for satisfying the daily nutritional and serving size requirements with a minimum level of effect on blood glucose levels, it has several limitations. It is a basic diet problem, and assumes that the overall GL is a linear combination of number of serving sizes with the GL values of foods. It also does not consider any other factors such as several combinations of foods and their varying effects on blood glucose levels. These factors should be considered for the next research. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Diet problem Glycemic index Glycemic load Robustness mixed-integer programming

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Activity-Based Costing and Management applied in a hybrid Decision Support System for order management

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DECISION SUPPORT SYSTEMS 2011年第1期52卷 142-156页

作者： Khataie, Amir H. Bulgak, Akif A. Segovia, Juan J. Concordia Univ Dept Mech & Ind Engn Off EV 13 105 Montreal PQ H3G 1M8 Canada Concordia Univ John Molson Sch Business Off MB 14 229 Montreal PQ H3G 1M8 Canada

This article introduces a new Cost Management and Decision Support System (DSS) applicable to Order Management. This model is better fit and compatible with today's competitive, and constantly changing, business environment. The presented Profitable-To-Promise (PTP) approach is a novel modeling approach which integrates System Dynamics (SD) simulation with mixed-integer programming (MIP). This Order Management model incorporates Activity-Based Costing and Management (ABC/M) as a link to merge the two models. MIP and SD. This combination is introduced as a hybrid Decision Support System. Such a system can evaluate the profitability of each Order Fulfillment policy and generate valuable cost information. Unlike existing optimization-based DSS models, the presented hybrid modeling approach can perform on-time cost analysis. This will lead to better business decisions based on the updated information. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Activity-Based Costing and Management Decision Support System mixed-integer programming System Dynamics Supply chain management Cost control

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Environmental integrated introduction and recycling management

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1997年第2期97卷 308-326页

作者： Spengler, T Puchert, H Penkuhn, T Rentz, O UNIV KARLSRUHE INST IND PRODHERTZSTR 16D-76187 KARLSRUHEGERMANY

Environmental integrated production and recycling planning is of great importance for the competitive position of production enterprises. Due to increasing disposal costs for industrial byproducts and waste as well as stronger emission standards. companies will be required to setup and control advanced, environmental friendly production technologies, so that emissions and byproducts will be reduced drastically. Nonavoidable byproducts and used products at the end of their lifetime have to be recycled by the producers. The complexity of the resulting decision problems requires adequate. operations research methods. The following paper deals with the development of sophisticated operations research models for two selected planning problems: recycling of industrial byproducts and dismantling and recycling of products at the end of their lifetime. The models have been applied successfully to large industrial problems in practice in the fields of recycling of demolition waste in a German-French region and byproduct management in the steel industry. The presentations of these two applications follow a case study point of view.

关键词： environment mixed-integer programming production recycling

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The Weighted Fair Sequences Problem

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COMPUTERS & OPERATIONS RESEARCH 2018年 91卷 121-131页

作者： Pessoa, Bruno Jefferson de S. Aloise, Daniel Cabral, Lucidio A. F. Univ Fed Paraiba UFPB Ctr Informat Joao Pessoa Paraiba Brazil Ecole Polytech Comp Engn Dept Montreal PQ Canada

Scheduling problems on which constraints are imposed with regard to the temporal distances between successive executions of the same task have numerous applications, ranging from task scheduling in real-time systems to automobile production on a mixed-model assembly line. This paper introduces a new NP-hard optimization problem belonging to this class of problems, namely the Weighted Fair Sequences Problem (WFSP). We present a mathematical formulation for the WFSP based on mixed-integer linear programming (MILP) as well as a series of cuts to improve its resolution via exact methods. Finally, we propose a heuristic solution method that works with much less variables of the WFSP formulation. The reported computational experiments show that, for a given time horizon, the proposed MILP-based heuristic increases the size of WFSP instances that can be tackled in practice. Moreover, its results should be considered as optimal whether a presented conjecture on the WFSP problem is proved true in the future. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Scheduling Fair sequences mixed-integer programming

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THE FLEET ASSIGNMENT PROBLEM - SOLVING A LARGE-SCALE integer-PROGRAM

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MATHEMATICAL programming 1995年第2期70卷 211-232页

作者： HANE, CA BARNHART, C JOHNSON, EL MARSTEN, RE NEMHAUSER, GL SIGISMONDI, G GEORGIA INST TECHNOL SCH IND & SYST ENGNATLANTAGA 30332

Given a flight schedule and set of aircraft, the fleet assignment problem is to determine which type of aircraft should fly each flight segment. This paper describes a basic daily, domestic fleet assignment problem and then presents chronologically the steps taken to solve it efficiently. Our model of the fleet assignment problem is a large multi-commodity flow problem with side constraints defined on a time-expanded network. These problems are often severely degenerate, which leads to poor performance of standard linear programming techniques. Also, the large number of integer variables can make finding optimal integer solutions difficult and time-consuming. The methods used to attack this problem include an interior-point algorithm, dual steepest edge simplex, cost perturbation, model aggregation, branching on set-partitioning constraints and prioritizing the order of branching. The computational results show that the algorithm finds solutions with a maximum optimality gap of 0.02% and is more than two orders of magnitude faster than using default options of a standard LP-based branch-and-bound code.

关键词： LINEAR programming mixed-integer programming LARGE-SCALE OPTIMIZATION AIRLINE FLEET ASSIGNMENT

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Exploiting Sparsity in SDP Relaxation for Harmonic Balance Method

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IEEE ACCESS 2020年 8卷 115957-115965页

作者： Yang, Cheng-Hsiung Deng, Ben Shen Natl Taiwan Univ Sci & Technol Grad Inst Automat & Control Taipei 10607 Taiwan Natl Taiwan Univ Sci & Technol Ctr Cyber Phys Syst Innovat Taipei 10607 Taiwan

In general, harmonic balance problems are extremely nonconvex and difficult to solve. A convex relaxation in the form of semidefinite programming has attracted a lot of attention recently, as it finds a global solution with high accuracy without the need for initial values. However, the computational cost of solving large-scale optimization poses a major challenge for the application in many real-world practical cases. This work proposes a heuristic optimization approach to find the Fourier coefficients of harmonic balance problems. The structural sparsity in the Harmonic Balance problem is exploited to improve numerical tractability and efficiency at the cost of adding smaller-sized semidefinite constraints in the problem formulation. After exploiting sparsity, the simulation results show that the size of the largest semidefinite constraint and the number of decision variables are greatly reduced. In addition, the computation speed shows an improvement rate of 3 or 7.5 times for larger instance problems and a reduction in memory occupation. Moreover, the proposed formulation can also solve nonlinear circuits with nonpolynomial nonlinearities with high accuracy.

关键词： Harmonic analysis Optimization Frequency-domain analysis programming Time-domain analysis Nonlinear systems Fourier series Harmonic balance method mixed-integer programming nonlinear circuits periodic solutions steady-state problems

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