An extended mathematical programming framework

Ferris, Michael C.; Dirkse, Steven P.; Jagla, Jan-Hendrick; Meeraus, Alexander

doi:10.1016/j.compchemeng.2009.06.013

Cited by 56 publications

(34 citation statements)

References 46 publications

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“…All of the computational results in this paper are solved using the Extended Mathematical Programming (EMP) [9,7,3] features of the GAMS modeling system [4]. The EMP framework exists to enable formulations of problems that fall outside the standard framework within the modeling system.…”

Section: A Extended Mathematical Programmingmentioning

confidence: 99%

Equilibrium, uncertainty and risk in hydro-thermal electricity systems

2016

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The correspondence of competitive partial equilibrium with a social optimum is well documented in the welfare theorems of economics. These theorems can be applied to single-period electricity pool auctions in which price-taking agents maximize profits at competitive prices, and extend naturally to standard models with locational marginal prices. In hydro-thermal markets where the auctions are repeated over many periods, agents seek to optimize their current and future profit accounting for future prices that depend on uncertain inflows. This makes the agent problems multistage stochastic optimization models, but perfectly competitive partial equilibrium still corresponds to a social optimum when all agents are risk neutral and share common knowledge of the probability distribution governing future inflows. The situation is complicated when agents are risk averse. In this setting we show under mild conditions that a social optimum corresponds to a competitive market equilibrium if agents have time-consistent dynamic coherent risk measures and there are enough traded market instruments to hedge inflow uncertainty. We illustrate some of the consequences of risk aversion on market outcomes using a simple two-stage competitive equilibrium model with three agents.

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Section: A Extended Mathematical Programmingmentioning

confidence: 99%

Equilibrium, uncertainty and risk in hydro-thermal electricity systems

2016

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“…Model CEN is solved via the CONOPT solver due to the nonlinearity introduced by the net-head dependency (see Section 5.1). Models RN and RA have been coded using the extended mathematical programing (EMP) feature of GAMS [24], and the resulting mixed-complementary problems have been solved with PATH.…”

Section: Methodsmentioning

confidence: 99%

“…. , s M )⊥π represents the spot market clearing where quantities are traded at price π (see [24]). In an electricity market it is common to assume that the utility function of generation companies is the obtained profit, i.e., the difference between market incomes and the generation costs.…”

Section: Market Equilibrium Concept With Risk Aversion Agentsmentioning

confidence: 99%

Impact of Risk Aversion on the Operation of Hydroelectric Reservoirs in the Presence of Renewable Energy Sources

et al. 2018

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Abstract:The increasing share of renewable energy sources, such as wind and solar generation, has a direct impact on the planning and operation of power systems. In addition, the consideration of risk criteria within the decision support tools used by market participants (generation companies, energy services companies, and arbitrageurs) is becoming a common activity given the increasing level of uncertainties faced by them. As a consequence, the behavior of market participants is affected by their level of risk aversion, and the application of equilibrium-based models is a common technique used in order to simulate their behavior. This paper presents a multi-stage market equilibrium model of risk-averse agents in order to analyze up to what extent the operation of hydro reservoirs can be affected by the risk-averse profile of market participants in a context of renewable energy source penetration and fuel price volatility.

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“…The advantage of starting with a GDP mode, is that it can be used as basis to derive mixedinteger programs that exhibit good relaxation properties, which is especially useful in many large-scale scheduling models. Software for GDP problems is available in the GAMS based codes LOGMIP (Vecchietti and Grosmann, 1999) and EMP (Ferris et al, 2009). …”

Section: Logic-based Optimization Methodologiesmentioning

confidence: 99%

Advances in mathematical programming models for enterprise-wide optimization

Grossmann

2012

Computers & Chemical Engineering

187

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Enterprise-wide optimization (EWO) is an area that lies at the interface of chemical engineering and operations research, and has become a major goal in the process industries due to the increasing pressures for remaining competitive in the global marketplace. EWO involves optimizing the operations of supply, manufacturing and distribution activities of a company to reduce costs, inventories and environmental impact, and to maximize profits and responsiveness. A major focus in EWO is the optimal operation of manufacturing facilities that often require the use of nonlinear process models. Major operational items include planning, scheduling, real-time optimization and control. We provide an overview of EWO in terms of a mathematical programming framework. We first provide a brief overview of mathematical programming techniques (mixed-integer linear and nonlinear optimization methods), as well as decomposition methods, stochastic programming and modeling systems. We then address some of the major issues involved in the modeling and solution of these problems. Finally, based on the EWO program at the Center of Advanced Process Decision-making at Carnegie Mellon, we describe several applications to show the potential of this area. Keywords

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An extended mathematical programming framework

Cited by 56 publications

References 46 publications

Equilibrium, uncertainty and risk in hydro-thermal electricity systems

Equilibrium, uncertainty and risk in hydro-thermal electricity systems

Impact of Risk Aversion on the Operation of Hydroelectric Reservoirs in the Presence of Renewable Energy Sources

Advances in mathematical programming models for enterprise-wide optimization

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