This paper addresses a multistage stochastic model for the optimal operation of wind farm, pumped storage and thermal power plants. The output of the wind farm and the electrical demand are considered as two independe...
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This paper addresses a multistage stochastic model for the optimal operation of wind farm, pumped storage and thermal power plants. The output of the wind farm and the electrical demand are considered as two independent stochastic processes. The evolution of these processes over time is modeled as a scenario tree. Considering all possible realizations of stochastic process, leads to a huge set of scenarios. These scenarios are reduced by a particle swarm optimization based scenario reduction algorithm. The scenario tree modeling transforms the cost model to a stochastic model. The stochastic model can be used to estimate the operation costs of the hybrid system under the influence of the uncertainties. The stochastic model is solved using adaptive particle swarm optimization.
In this paper, we examine the rationale for financial reinsurance in the casualty insurance business. As opposed to regular reinsurance, financial reinsurance refers to an investment strategy that uses the financial m...
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In this paper, we examine the rationale for financial reinsurance in the casualty insurance business. As opposed to regular reinsurance, financial reinsurance refers to an investment strategy that uses the financial markets to hedge insurance risk. The casualty insurer takes positions in derivatives on underlying assets whose prices are highly positively or negatively correlated with specific insurance risks. We formulate the asset liability management problem for a mutually owned casualty insurer, in the context of a dynamic stochastic portfolio selection model. Using numerical studies of the resulting large-scale non-linear program, we compare properties of optimal portfolios with and without the possibility of financial reinsurance. We let an alleged representative policyholder, endowed with a linear plus negative exponential utility function, evaluate the various optimal portfolios. When policyholders' utility functions exhibit reasonable levels of risk aversion, we find that portfolios reflecting financial reinsurance dominate portfolios that are not financially reinsured. (C) 2003 Elsevier B.V. All rights reserved.
Danish mortgage loans have several features that make them interesting: Short-term revolving adjustable-rate mortgages are available, as well as fixed-rate, 10-, 20- or 30-year annuities that contain embedded options ...
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Danish mortgage loans have several features that make them interesting: Short-term revolving adjustable-rate mortgages are available, as well as fixed-rate, 10-, 20- or 30-year annuities that contain embedded options (call and delivery options). The decisions faced by a mortgagor are therefore non-trivial, both in terms of deciding on an initial mortgage, and in terms of managing (rebalancing) it optimally. We propose a two-factor, arbitrage-free interest-rate model, calibrated to observable security prices, and implement on top of it a multi-stage, stochastic optimization program with the purpose of optimally composing and managing a typical mortgage loan. We model accurately both fixed and proportional transaction costs as well as tax effects. Risk attitudes are addressed through utility functions and through worst-case (min-max) optimization. The model is solved in up to 9 stages, having 19,683 scenarios. Numerical results, which were obtained using standard soft- and hardware, indicate that the primary determinant in choosing between adjustable-rate and fixed-rate loans is the short-long interest rate differential (i.e., term structure steepness), but volatility also matters. Refinancing activity is influenced by volatility and, of course, transaction costs. (C) 2003 Elsevier B.V. All rights reserved.
Linear programs with joint probabilistic constraints (PCLP) are known to be highly intractable due to the non-convexity of the feasible region. We consider a special case of PCLP in which only the right-hand side is r...
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ISBN:
(纸本)9783540727910
Linear programs with joint probabilistic constraints (PCLP) are known to be highly intractable due to the non-convexity of the feasible region. We consider a special case of PCLP in which only the right-hand side is random and this random vector has a finite distribution. We present a mixed integer programming formulation and study the relaxation corresponding to a single row of the probabilistic constraint, yielding two strengthened formulations. As a byproduct of this analysis, we obtain new results for the previously studied mixing set, subject to an additional knapsack inequality. We present computational results that indicate that by using our strengthened formulations, large scale instances can be solved to optimality.
Operational uncertainties create disincentives for use of recycled materials in metal alloy production. One that greatly influences remelter batch optimization is variation in the raw material composition, particularl...
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Operational uncertainties create disincentives for use of recycled materials in metal alloy production. One that greatly influences remelter batch optimization is variation in the raw material composition, particularly for secondary materials. Currently, to accommodate compositional variation, firms commonly set production targets well inside the window of compositional specification required for performance reasons. Window narrowing, while effective, does not make use of statistical sampling data, leading to sub-optimal usage of recycled materials. This paper explores the use of a chance-constrained optimization method, which allows explicit consideration of statistical information on composition. The framework and a case study of cast and wrought production with available scrap materials are presented. Results show that it is possible to increase the use of recycled material without compromising the likelihood of batch errors, when using this method compared to conventional window narrowing. This benefit of the chance-constrained method grows with increase in compositional uncertainty and is driven by scrap portfolio diversification. (C) 2007 Elsevier B.V. All rights reserved.
stochastic programming is a technique for optimization in the presence of uncertainty. The objective of a stochastic program is to find an optimal strategy that is feasible for all data outcomes and minimizes (or maxi...
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stochastic programming is a technique for optimization in the presence of uncertainty. The objective of a stochastic program is to find an optimal strategy that is feasible for all data outcomes and minimizes (or maximizes) a first-stage objective plus the expected second-stage objective. Benders' decomposition is perhaps the most widely used algorithm for solving two-stage stochastic linear programs. In this algorithm, a restricted master problem (RMP) containing only the first-stage variables is formed. Feasibility and optimality subproblems contain only the second stage variables and take the values of the first-stage variables as an input from the master problem. After solving the RMP, the values of first-stage variables are passed on to the subproblems and the subproblems are solved. By using the dual values of the subproblem variables, feasibility or optimality cuts are generated and inserted into the RMP. After this, the RMP is resolved with a new set of constraints and the algorithm proceeds iteratively until optimality is reached. Column generation methodology is commonly used to solve mathematical problems that involve a large number of variables. Instead of considering all the columns of such a problem explicitly, column generation techniques employ a master problem that contains a subset of all possible columns and a pricing subproblem that generates promising new columns. The algorithm follows a loop in which the master problem is solved, and the dual solution is passed on to the pricing problem, which tries to find the most favorable reduced cost among excluded columns. If such a column exists, it is inserted into the master problem and if not, the algorithm stops. We developed a method for incorporating column generation within a stochastic programming framework. This method generates columns for the RMP, while simultaneously adding feasibility and optimality cuts generated from the second-stage subproblem. We discuss convergence issues and preliminar
This paper presents a model for optimally designing a collateralized mortgage obligation (CMO) with a planned amortization class (PAC)-companion structure using dynamic cash reserve. In this structure, the mortgage po...
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This paper presents a model for optimally designing a collateralized mortgage obligation (CMO) with a planned amortization class (PAC)-companion structure using dynamic cash reserve. In this structure, the mortgage pool's cash flow is allocated by rule to the two bond classes such that PAC bondholders receive substantial prepayment protection, that protection being provided by the companion bondholders. The structure we propose provides greater protection to the PAC bondholders than current structures during periods of rising interest rates when this class of bondholders faces greater extension risk. We do so by allowing a portion of the cash flow from the collateral to be reserved to meet the PAC's scheduled cash flow in subsequent periods. The greater protection is provided by the companion bondholders exposure to interest loss. To tackle this problem, we transform the problem of designing the optimal PAC-companion structure into a standard stochastic linear programming problem which can be solved efficiently. Moreover, we present an extended model by considering the quality of the companion bond and by relaxing the PAC bondholder shortfall constraint. Based on numerical experiments through Monte Carlo simulation, we show the utility of the proposed model. (c) 2006 Elsevier B.V. All rights reserved.
In this article a stochastic location-routing problem is defined and cast as a two-stage model. In a first stage the set of plants and a family of routes are determined;in a second stage a recourse action is applied t...
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In this article a stochastic location-routing problem is defined and cast as a two-stage model. In a first stage the set of plants and a family of routes are determined;in a second stage a recourse action is applied to adapt these routes to the actual set of customers to visit, once they are known. A two-phase heuristic is developed. An initial feasible solution is built by solving a sequence of subproblems, and an improvement phase is then applied. A lower bound based on bounding separately different parts of the cost of any feasible solution is also developed. Computational results are reported. (c) 2006 Elsevier B.V. All rights reserved.
This article addresses the problem of a traffic network design problem (NDP) under demand uncertainty. The origin-destination trip matrices are taken as random variables with known probability distributions. Instead o...
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This article addresses the problem of a traffic network design problem (NDP) under demand uncertainty. The origin-destination trip matrices are taken as random variables with known probability distributions. Instead of finding optimal network design solutions for a given future scenario, we are concerned with solutions that are in some sense "good" for a variety of demand realizations. We introduce a definition of robustness accounting for the planner's required degree of robustness. We propose a formulation of the robust network design problem (RNDP) and develop a methodology based on genetic algorithm (GA) to solve the RNDP. The proposed model generates globally near-optimal network design solutions, f, based on the planner's input for robustness. The study makes two important contributions to the network design literature. First, robust network design solutions are significantly different from the deterministic NDPs and not accounting for them could potentially underestimate the network-wide impacts. Second, systematic evaluation of the performance of the model and solution algorithm is conducted on different test networks and budget levels to explore the efficacy of this approach. The results highlight the importance of accounting for robustness in transportation planning and the proposed approach is capable of producing high-quality solutions.
The paper proposes a method to optimize the cost and time of a project. The method considers principles from risk management and applying model predictive control (MPC). The control variables (continuous or discrete) ...
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The paper proposes a method to optimize the cost and time of a project. The method considers principles from risk management and applying model predictive control (MPC). The control variables (continuous or discrete) are the mitigation actions that must be executed in order to reduce risk exposure. Risk impacts are considered to be stochastic variables to model uncertainties that could potentially appear. As a consequence, a stochastic mixed integer quadratic optimization problem is obtained. Furthermore, Monte Carlo simulation is executed by considering random variables on different variables. A real-life risk management problem related to the construction of semiconductor manufacturing facilities is presented. The given solution illustrates the effectiveness of the method. (c) 2007 Elsevier Ltd. All rights reserved.
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