A major portion of the delay in the Air Traffic Management Systems (ATMS) in US arises from the stochastic disturbances such as convective weather. However, in the current practice, the predicted storm zones are compl...
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ISBN:
(纸本)0780383354
A major portion of the delay in the Air Traffic Management Systems (ATMS) in US arises from the stochastic disturbances such as convective weather. However, in the current practice, the predicted storm zones are completely avoided as if they are deterministic obstacles. As a result, the current strategy is too conservative and incurs a high delay. In this paper, we seek to reduce the system delay through explicitly modelling the dynamic and stochastic nature of the storms and adding recourse in the routing and the flow management problem. We address the multi-aircraft flow management problem using a stochastic dynamic programming algorithm, where the evolution of the weather is modelled as a stationary Markov chain. Our solution provides a dynamic routing strategy for "N-aircraft" that minimizes the expected delay of the overall system while taking into consideration the constraints obtained by the sector capacities, as well as avoidance of conflicts among the aircraft. Our simulation suggests that a significant improvement in delay can be obtained by using our methods over the existing methods.
A large number of problems in production planning and scheduling, location, transportation, finance, and engineering design require that decisions be made in the presence of uncertainty. Uncertainty, for instance, gov...
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A large number of problems in production planning and scheduling, location, transportation, finance, and engineering design require that decisions be made in the presence of uncertainty. Uncertainty, for instance, governs the prices of fuels, the availability of electricity, and the demand for chemicals. A key difficulty in optimization under uncertainty is in dealing with an uncertainty space that is huge and frequently leads to very large-scale optimization models. Decision-making under uncertainty is often further complicated by the presence of integer decision variables to model logical and other discrete decisions in a multi-period or multi-stage setting. This paper reviews theory and methodology that have been developed to cope with the complexity of optimization problems under uncertainty. We discuss and contrast the classical recourse-based stochastic programming, robust stochastic programming, probabilistic (chance-constraint) programming, fuzzy programming, and stochastic dynamic programming. The advantages and shortcomings of these models are reviewed and illustrated through examples. Applications and the state-of-the-art in computations are also reviewed. Finally, we discuss several main areas for future development in this field. These include development of polynomial-time approximation schemes for multi-stage stochastic programs and the application of global optimization algorithms to two-stage and chance-constraint formulations. (C) 2003 Elsevier Ltd. All rights reserved.
In the recent optimization world, mathematical programs with equilibrium constraints (MPECs) have been receiving much attention and there have been proposed a number of methods for solving MPECs. In this paper, we pro...
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ISBN:
(纸本)0769521509
In the recent optimization world, mathematical programs with equilibrium constraints (MPECs) have been receiving much attention and there have been proposed a number of methods for solving MPECs. In this paper, we provide a brief review of the recent achievements in the MPEC field and, as further applications of MPECs, we also mention the developments of the stochastic mathematical programs with equilibrium constraints (SMPECs).
In this paper, three approaches are presented for generating scenario trees for financial portfolio problems. These are based on simulation, optimization and hybrid simulation/optimization. In the simulation approach,...
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In this paper, three approaches are presented for generating scenario trees for financial portfolio problems. These are based on simulation, optimization and hybrid simulation/optimization. In the simulation approach, the price scenarios at each time period are generated as the centroids of random scenario simulations generated sequentially or in parallel. The optimization method generates a number of discrete outcomes which satisfy specified statistical properties by solving either a sequence of non-linear optimization models (one at each node of the scenario tree) or one large optimization problem. In the hybrid approach, the optimization problem is reduced in size by fixing price variables to values obtained by simulation. These procedures are backtested using historical data and computational results are presented. (C) 2003 Elsevier B.V. All rights reserved.
This paper develops a model that can be used as a decision support aid, helping manufacturers make profitable decisions in upgrading the features of a family of high-technology products over its life cycle. The model ...
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This paper develops a model that can be used as a decision support aid, helping manufacturers make profitable decisions in upgrading the features of a family of high-technology products over its life cycle. The model integrates various organizations in the enterprise: product design, marketing, manufacturing, production planning, and supply chain management. Customer demand is assumed random and this uncertainty is addressed using scenario analysis. A branch-and-price (B&P) solution approach is devised to optimize the stochastic problem effectively. Sets of random instances are generated to evaluate the effectiveness of our solution approach in comparison with that of commercial software on the basis of run time. Computational results indicate that our approach outperforms commercial software on all of our test problems and is capable of solving practical problems in reasonable run time. We present several examples to demonstrate how managers can use our models to answer "what if" questions.
This work focuses on the basic stochastic decomposition (SD) algorithm of Higle and Sen [J.L. Higle, S. Sen, stochastic Decomposition, Kluwer Academic Publishers, 1996] for two-stage stochastic linear programming prob...
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This work focuses on the basic stochastic decomposition (SD) algorithm of Higle and Sen [J.L. Higle, S. Sen, stochastic Decomposition, Kluwer Academic Publishers, 1996] for two-stage stochastic linear programming problems with complete recourse. The algorithm uses sampling when the random variables are represented by continuous distribution functions. Traditionally, this method has been applied by using Monte Carlo (MC) sampling to generate the samples of the stochastic variables. However, Monte Carlo methods can result in large error bounds and variance. Hence, some other approaches use importance sampling to reduce variance and achieving convergence faster that the method based on the Monte Carlo sampling technique. This work proposes an improvement on this respect. Hence, we propose to replace the use of the Monte Carlo sampling technique or the importance sampling in the SD algorithm by the use of the novel Hammersley sequence sampling (HSS) technique. Recently, such a technique has proved to provide better uniformity properties than other sampling techniques and, as a consequence, the variance and the number of samples required for convergence are reduced. Also, we use a fractal dimension approach to characterize the error of the estimation of the recourse function based on sampling. The computational implementation of the algorithm involves a framework that integrates the GAMS modeling environment, the HSS sampling code (FORTRAN) and a C++ program which generates appropriate LP problems for each SD iteration. The algorithm has been tested with several case studies representing chemical engineering applications and the results are discussed. (C) 2004 Elsevier Ltd. All rights reserved.
The increasing number of applications of supply chain network optimization models to strategic planning has created new challenges for model practitioners and their clients. These challenges are discussed in the conte...
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The increasing number of applications of supply chain network optimization models to strategic planning has created new challenges for model practitioners and their clients. These challenges are discussed in the context of four categories of modeling and organizational imperatives. (C) 2003 Elsevier Ltd. All rights reserved.
The first phase of this research demonstrates improvements in the performance of branch-and-price algorithms (B&P) for solving integer programs by (i) stabilizing dual variables during column generation, (ii) perf...
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The first phase of this research demonstrates improvements in the performance of branch-and-price algorithms (B&P) for solving integer programs by (i) stabilizing dual variables during column generation, (ii) performing strong branching, (iii) inserting multiple near-optimal columns from each subproblem, (iv) heuristically improving feasible integer solutions, and by applying several other techniques. Computational testing on generalized-assignment problems shows that solution times decrease over "naive" B&P by as much as 96%; and, some problems that could not be solved by standard branch and bound on the standard model formulation have become easy. In the second phase, this research shows how to solve a class of difficult, stochastic mixed-integer programs using B&P. A new, column-oriented formulation of a stochastic facility-location problem (SFLP), using a scenario representation of uncertainty, provides a vehicle for demonstrating this method's viability. Computational results show that B&P can be orders of magnitude faster than solving the original problem by branch and bound, and this can be true even for single-scenario problems; i. e., for deterministic problems. B&P also solves SFLP exactly when random parameters are modeled through certain continuous probability distributions. In practice, these problems solve more quickly than comparable scenario-based problems, with say, 50 scenarios.
This paper presents the results of surveys of the use of simple controls - opening of windows, the closing of window blinds, and the use of lighting, heaters, and fans - by building occupants. Information is also pres...
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This paper introduces branching processes as a stochastic tool for understanding the characteristics of the abuse of leaked information, and the associated risks. To understand the risk associated with information lea...
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ISBN:
(纸本)0889864284
This paper introduces branching processes as a stochastic tool for understanding the characteristics of the abuse of leaked information, and the associated risks. To understand the risk associated with information leakage, it is important to produce models capturing important aspects of the abuse of leaked information. This understanding is necessary to limit such risks effectively and efficiently. Filling part of an apparent gap in this area, a stochastic model based on a discrete-time branching process is introduced. Some general challenges associated with modelling information leak risks are identified, as well as some challenges associated with using branching processes to analyze operational risk.
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