A stochastic branch and bound method for solving stochastic global optimization problems is proposed. As in the deterministic case, the feasible set is partitioned into compact subsets. To guide the partitioning proce...
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A stochastic branch and bound method for solving stochastic global optimization problems is proposed. As in the deterministic case, the feasible set is partitioned into compact subsets. To guide the partitioning process the method uses stochastic upper and lower estimates of the optimal value of the objective function in each subset. Convergence of the method is proved and random accuracy estimates derived. Methods for constructing stochastic upper and lower bounds are discussed. The theoretical considerations are illustrated with an example of a facility location problem. (C) 1998 The Mathematical programming Society, Inc. Published by Elsevier Science B.V.
We consider two-stage stochastic programming problems with integer recourse. The L-shaped method of stochastic linear programming is generalized to these problems by using generalized Benders decomposition. Nonlinear ...
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We consider two-stage stochastic programming problems with integer recourse. The L-shaped method of stochastic linear programming is generalized to these problems by using generalized Benders decomposition. Nonlinear feasibility and optimality cuts are determined via general duality theory and can be generated when the second stage problem is solved by standard techniques. Finite convergence of the method is established when Gomory's fractional cutting plane algorithm or a branch-and-bound algorithm is applied. (C) 1998 The Mathematical programming Society, Inc. Published by Elsevier Science B.V.
In this paper, an interior point algorithm for linear programs is adapted for solving multistage stochastic linear programs. The algorithm is based on Monteiro and Adler's path-following algorithm for deterministi...
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In this paper, an interior point algorithm for linear programs is adapted for solving multistage stochastic linear programs. The algorithm is based on Monteiro and Adler's path-following algorithm for deterministic linear programs. In practice, the complexity of the algorithm is linear with respect to the size of the sample space. The algorithm starts from a feasible solution of the problem and proceeds along a path of random vectors. The cubic polynomial complexity of the algorithm for deterministic linear programs is derived from the calculations of the Newton steps. In the algorithm developed in this paper, the probabilistic structure of the problem is taken into consideration while calculating a Newton step and the size of the sample space appears linearly in the complexity. The development of an algorithm that requires a relatively small number of arithmetic operations, in terms of the sample space size, allows the use of the algorithm for multistage stochastic linear programs with a very large number of scenarios.
In this paper, the authors consider interworking between statistical procedures for recovering the distribution of random parameters from observations and stochastic programming techniques, in particular stochastic gr...
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In this paper, the authors consider interworking between statistical procedures for recovering the distribution of random parameters from observations and stochastic programming techniques, in particular stochastic gradient (quasigradient) methods. The proposed problem formulation is based upon a class of statistical models known as Bayesian nets. The reason for the latter choice is that Bayesian nets are powerful and general statistical models emerged recently within the more general framework of Bayesian statistics, which is specifically designed for cases when the vector of random parameters can have considerable dimension and/or it is difficult to come up with traditional parametric models of the joint distribution of random parameters. We define the optimization problem on a Bayesian net. For the solution of this problem, we develop algorithms for sensitivity analysis of such a net and present combined optimization and sampling techniques.
Within the framework of some simple models, we explain how option theory can enhance the understanding and teaching of modeling under uncertainty. We discuss some common pitfalls in modeling and argue that these resul...
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Within the framework of some simple models, we explain how option theory can enhance the understanding and teaching of modeling under uncertainty. We discuss some common pitfalls in modeling and argue that these result from a failure tc, come to grips with options and flexibility. We examine a dynamic programming approach to evaluating options and a valuation by arbitrage approach and end by comparing the two approaches with respect to how they treat time and risk.
We develop multi-period dynamic models for fixed-income portfolio management under uncertainty, using multi-stage stochastic programming with recourse. The models integrate the prescriptive stochastic programs with de...
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We develop multi-period dynamic models for fixed-income portfolio management under uncertainty, using multi-stage stochastic programming with recourse. The models integrate the prescriptive stochastic programs with descriptive Monte Carlo simulation models of the term structure of interest rates. Extensive validation experiments are carried out to establish the effectiveness of the models in hedging against uncertainty, and to assess their performance vis-a-vis single-period models. An application to tracking the Salomon Brothers Mortgage Index is reported, with very encouraging results. Results that establish the efficacy of the models in hedging against out-of-sample scenarios are also reported for an application from money management. The multi-period models outperform classical models based on portfolio immunization and single-period models. (C) 1998 Elsevier Science B.V. All rights reserved.
Recently, a new technique called robust optimization has been proposed for addressing (dynamic) decision problems with uncertainty. This approach starts from a "nominal" optimization problem, say a linear pr...
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Weather has been one of the problems affecting sugarcane harvesting operation. This research aims at developing a scheduling method for mechanical sugarcane harvesting in order to minimize the effect of the weather. T...
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Weather has been one of the problems affecting sugarcane harvesting operation. This research aims at developing a scheduling method for mechanical sugarcane harvesting in order to minimize the effect of the weather. The amount of daily harvesting is decided by minimizing the expected cost due to cane loss during storage, the expected penalty cost due to lack of cane supply for the factory, and the operation cost.
stochastic integer programming is more complicated than stochastic linear programming, as will be explained for the case of the two‐stage stochastic programming model. A survey of the results accomplished in this rec...
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stochastic integer programming is more complicated than stochastic linear programming, as will be explained for the case of the two‐stage stochastic programming model. A survey of the results accomplished in this recent field of research is given.
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