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Supply Shortage Hedging: Estimating the Electrical Power Margin for Optimizing Financial and Physical Assets With Chance-Constrained programming

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IEEE TRANSACTIONS ON POWER SYSTEMS 2009年第2期24卷 533-540页

作者： Zorgati, Riadh van Ackooij, Wim Apparigliato, Romain EDF R&D Dept Optimizat Simulat Risk & Stat F-92141 Clamart France Ecole Polytech Ctr Appl Math F-91128 Palaiseau France

This paper deals with estimating the maximal production capacity of a hydrothermal system. We will show why this is of interest and how such a problem arises in a context of hedging against supply shortage, using financial and physical assets. Therefore, we will formulate the supply shortage hedging as a stochastic optimization problem with chance constraints and show on an example why introducing physical assets in the hedging problem is of economical interest. We then highlight the inherent mathematical difficulties, introduced by optimizing physical assets. Using maximal production capacities of the hydrothermal system improves tractability of the hedging problem. However, focusing on the hydraulic production maximal capacity, we illustrate the combinatorial and nontrivial nature of this subproblem. Finally, we show how our problem formulation may lead to embedded chance constraints.

关键词： Chance-constrained programming (CCP) hedging hydraulic maximal capacity mixed-integer programming power margin supply shortage unit commitment

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Fast unit commitment based on optimal linear approximation to nonlinear fuel cost: Error analysis and applications

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ELECTRIC POWER SYSTEMS RESEARCH 2009年第11期79卷 1604-1613页

作者： Zhai, Qiaozhu Guan, Xiaohong Yang, Jiping Xi An Jiao Tong Univ SKLMS Lab Syst Engn Inst Xian 710049 Peoples R China

mixed-integer linear programming (MILP) based techniques are among the most widely applied methods for unit commitment (UC) problems. The fuel cost functions are often replaced by their piecewise linear approximations whereas it is more or less disturbing to use piecewise linear approximations without knowing the exact effect on solution deviation from the optima. Therefore, error analysis is important since the optimal solutions are different when different objective functions are adopted. Another important problem is balancing between solution quality and computation efficiency since better solution quality relies on finer discretization with exponentially increased computational efforts. A detailed error analysis is presented in this paper. It is found that the approximation error is inverse proportional to the square of the number of piecewise segments. Lower bounds on the minimum necessary number of discretization segments are also derived. A 2-Stage Procedure is then established to achieve a better balance between solution quality and computation efficiency. Numerical testing to 2 groups of UC problems is exciting. It is found that the operating cost increases no more than 0.6% in all cases while the CPU time is greatly reduced regarding other MILP approaches. The results are still valid in electric power market clearing computation. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Unit commitment Fuel cost function mixed-integer programming Optimal linear approximation Error analysis

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An extended fuzzy parametric programming-based approach for designing cellular manufacturing systems under uncertainty and dynamic conditions

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INTERNATIONAL JOURNAL OF COMPUTER INTEGRATED MANUFACTURING 2009年第6期22卷 538-548页

作者： Safaei, N. Tavakkoli-Moghaddam, R. Univ Toronto Dept Mech & Ind Engn Toronto ON M5S 3G8 Canada Univ Tehran Coll Engn Dept Ind Engn Tehran Iran

This paper proposes an extended fuzzy parametric programming (FPP) approach to solve a dynamic cell formation problem considering the uncertain part demand and machine capacity. The classical FPP approach gives the decision maker a number of alternative decisions for different grades of precision. Linear membership functions such as trapezoid, triangular and other piecewise forms have widely been used to express the uncertain parameters in the different engineering fields. Especially, to our best of knowledge, all researches related to the use of the fuzzy programming-based approaches for cellular manufacturing systems (CMSs) have been applied to the piecewise membership functions. In the case of lack of sufficient knowledge, there is a section in the piecewise forms called 'core', consisting of the fully included members (i.e. members with membership degree equal to one). This section, which represents the expert's ignorance, is not considered in the fuzzy programming-based approaches presented in the literature. In a highly cost-intensive production system, such as cellular manufacturing systems, the decision maker wants to know how big the changes of the cell configuration from one period to another are. These changes are caused by the fluctuations in some parameters of the system, such as part demand and machine capacity. However, when these parameters are uncertain as well as dynamic, the risk of decision making will increase significantly. On the other hand, in practice, a domain of uncertainty of data corresponds to a unique decision and hence the whole uncertainty in the system can be covered by only a few numbers of the alternative decisions, called 'applicable decisions'. This reduction in the decision space gives a better idea to the decision maker to make the final decision. The extended FPP proposed in this paper uses a simple strategy to extract all possible applicable solutions resulting from the core of the membership functions of the uncertain param

关键词： cellular manufacturing system dynamic and uncertain environment mixed-integer programming fuzzy parametric programming

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Network Formulations of mixed-integer Programs

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MATHEMATICS OF OPERATIONS RESEARCH 2009年第1期34卷 194-209页

作者： Conforti, Michele Di Summa, Marco Eisenbrand, Friedrich Wolsey, Laurence A. Univ Padua Dipartimento Matemat Pura & Applicata I-35121 Padua Italy Catholic Univ Louvain Ctr Operat Res & Econometr B-1348 Louvain Belgium Ecole Polytech Fed Lausanne Inst Math CH-1015 Lausanne Switzerland

We consider mixed-integer sets described by system of linear inequalities in which the constraint matrix A is totally unimodular;the right-hand side is arbitrary vector;and a subset of the variables is required to be integer. We show that the problem of checking nonemptiness of a set of this type is NP-complete, even in the case in which the linear system describes mixed-integer network flows with half-integral requirement on the nodes. This is in contrast to the case in which A is totally unimodular and contains at most two nonzeros per row. In this case, we provide an extended formulation for the convex hull of solutions whose constraint matrix is a dual-network matrix with an integral right-hand-side vector. The size of this formulation depends on the number of distinct fractional parts taken by the continuous variables in the extreme points of the convex hull of the given set. When this number is polynomial in the dimension of A, the extended formulation is of polynomial size. If, in addition, the corresponding list of fractional parts can be computed efficiently, then our result provides a polynomial algorithm for the optimization problem over these sets. We show that there are instances for which this list is of exponential size, and we also give conditions under which it is short and can be efficiently computed. Finally, we show that these results provide a unified framework leading to polynomial-size extended formulations for several generalizations of mixing sets and lot-sizing sets studied in the last few years.

关键词： mixed-integer programming compact extended formulations

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Event-driven optimization-based control of hybrid systems with integral continuous-time dynamics

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AUTOMATICA 2009年第5期45卷 1243-1251页

作者： Di Cairano, S. Bemporad, A. Julvez, J. Tech Univ Catalonia Dept Software Barcelona Spain Univ Siena Dept Informat Engn I-53100 Siena Italy Ford Motor Co Res & Adv Engn Powertrain Control Dept Dearborn MI USA

In this paper we introduce a class of continuous-time hybrid dynamical systems called integral continuous-time hybrid automata (icHA) for which we propose an event-driven optimization-based control strategy. Events include both external actions applied to the system and changes of continuous dynamics (mode switches). The icHA formalism subsumes a number of hybrid dynamical systems with practical interest, e.g., linear hybrid automata. Different cost functions, including minimum-time and minimum-effort criteria, and constraints are examined in the event-driven optimal control formulation. This is translated into a finite-dimensional mixed-integer optimization problem, in which the event instants and the corresponding values of the control input are the optimization variables. As a consequence, the proposed approach has the advantage of automatically adjusting the attention of the controller to the frequency of event occurrence in the hybrid process. A receding horizon control scheme exploiting the event-based optimal control formulation is proposed as a feedback control strategy and proved to ensure either finite-time or asymptotic convergence of the closed-loop. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Hybrid systems Discrete-event systems Optimal control Model predictive control mixed-integer programming

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Manufacturing System Design Considering Stochastic Product Evolution and Task Recurrence

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JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING-TRANSACTIONS OF THE ASME 2009年第5期131卷 0510121-05101212页

作者： Ko, Jeonghan Hu, S. Jack Univ Nebraska Lincoln NE 68588 USA Univ Michigan Dept Mech Engn Ann Arbor MI 48109 USA

The conventional approaches to manufacturing system design and line balancing have often focused on a single generation of products, thus leading to new design or rebalancing when new products are introduced or different models are produced in the same line. As the life cycles of product models become shorter and shorter, this new product then new system-design approach is becoming increasingly ineffective due to too frequent production interruption. Therefore, effective solutions to system-design problems should consider the evolution of products over multiple generations and models, and this paper presents such new methods. mixed-integer programming models are developed for (1) designing manufacturing system configurations that are cost effective for product evolution involving uncertainty and (2) maximizing the recurrences of manufacturing tasks on the same machines throughout product evolution. A decomposition-based solution procedure is also developed to reduce computational complexity. These new methods can provide a stable system-design solution enabling quick product launches with less line change-over for new or different products. [DOI: 10.1115/1.4000095]

关键词： manufacturing system design stochastic product change task recurrence mixed-integer programming line balancing

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A Projection-Based Method for Production Planning of Multiproduct Facilities

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AICHE JOURNAL 2009年第10期55卷 2614-2630页

作者： Sung, Charles Maravelias, Christos T. Univ Wisconsin Dept Chem & Biol Engn Madison WI 53706 USA

An algorithm is presented for identifying the projection of a scheduling model's feasible region onto the space of production tat-gets. The projected feasible region is expressed using one of two mixed-integer programming formulations, which can be readily used to address integrated production planning and scheduling problems that were previously intractable. Production planning is solved in combination with a surrogate model representing the region of feasible production amounts to provide optimum production targets, while a detailed scheduling is solved in a rolling-horizon manner to define feasible schedules for meeting these targets. The proposed framework provides solutions of higher quality and yields tighter bounds than previously proposed approaches. (C) 2009 American Institute of Chemical Engineers AIChE J, 55: 2614-2630, 2009

关键词： production planning scheduling mixed-integer programming projection

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A mixed-integer programming model for gas purchase and transportation

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ANNALS OF OPERATIONS RESEARCH 2005年第1期139卷 39-63页

作者： Contesse, L Ferrer, JC Maturana, S Pontificia Univ Catolica Chile Sch Engn Santiago 22 Chile

The natural gas supply chain involves three main agents: producers, transportation companies, and local distribution companies (LDCs). We present a MIP model that is the basis for a decision support system developed for a Chilean LDC. This model takes into account many of the complexities of the purchasing and transportation contracts to help optimize daily purchase and transportation decisions in the absence of local storage facilities. The model was solved to optimality within a reasonable time. We show how the model handles several contractual issues and give some insights for the case when demand scenarios are used to deal with uncertainty.

关键词： mixed-integer programming natural gas logistics

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Integration of production planning and scheduling: Overview, challenges and opportunities

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COMPUTERS & CHEMICAL ENGINEERING 2009年第12期33卷 1919-1930页

作者： Maravelias, Christos T. Sung, Charles Univ Wisconsin Dept Chem & Biol Engn Madison WI 53706 USA

We review the integration of medium-term production planning and short-term scheduling. We begin with an overview of supply chain management and the associated planning problems. Next, we formally define the production planning problem and explain why integration with scheduling leads to better solutions. We present the major modeling approaches for the integration of scheduling and planning decisions, and discuss the major solution strategies. We close with an account of the challenges and opportunities in this area. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Supply chain management Production planning Scheduling mixed-integer programming

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Component and Mode Models for the Short-Term Scheduling of Combined-Cycle Units

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IEEE TRANSACTIONS ON POWER SYSTEMS 2009年第2期24卷 976-990页

作者： Liu, Cong Shahidehpour, Mohammad Li, Zuyi Fotuhi-Firuzabad, Mahmoud IIT Dept Elect & Comp Engn Chicago IL 60616 USA Sharif Univ Technol Dept Elect Engn Tehran Iran

We propose a component model for the scheduling of combined-cycle gas turbine (CCGT) units by mixed-integer programming (MIP) in which combustion turbines (CTs) and steam turbines (STs) are modeled as individual units. The hourly schedule of CCGT based on the component model is compared with that of the mode model. The modeling of modes, which includes a combination of CTs and STs, would require certain approximations for representing fuel input-power output curves, ramping rate limits, minimum operating time limits, etc. The approximations can result in sub-optimal schedules. Furthermore, the commitment and dispatch of CCGTs based on the mode model will require a real-time dispatch to individual CT and ST components of CCGT. In comparison, the mode modeling approximations will no longer be required in the component model as individual CTs and STs are modeled and dispatched. The enhancement tools such as duct burners, loggers, and peak firing for increasing the CCGT output can be easily modeled in the component model. Case studies show that the proposed component model is effective for representing CCGTs, and verify that the proposed component model can potentially save CCGT operating costs. Numerical simulations in this paper also demonstrate the application of the component model of CCGT to schedule a cogeneration unit.

关键词： Combined-cycle gas turbine component model mixed-integer programming mode model short-term unit commitment state transition diagram

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