A two-stage stochastic programming with recourse model for the problem of determining optimal planting plans for a vegetable crop is presented in this paper. Uncertainty caused by factors such as weather on yields is ...
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A two-stage stochastic programming with recourse model for the problem of determining optimal planting plans for a vegetable crop is presented in this paper. Uncertainty caused by factors such as weather on yields is a major influence on many systems arising in horticulture. Traditional linear programming models are generally unsatisfactory in dealing with the uncertainty and produce solutions that are considered to involve an unacceptable level of risk. The first stage of the model relates to finding a planting plan which is common to all scenarios and the second stage is concerned with deriving a harvesting schedule for each scenario. Solutions are obtained for a range of risk aversion factors that not only result in greater expected profit compared to the corresponding deterministic model, but also are more robust.
This paper investigates some common interest rate models for scenario generation in financial applications of stochastic optimization. We discuss conditions for the underlying distributions of state variables which pr...
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This paper investigates some common interest rate models for scenario generation in financial applications of stochastic optimization. We discuss conditions for the underlying distributions of state variables which preserve convexity of value functions in a multistage stochastic program. One- and multi-factor term structure models are estimated based on historical data Fur the Swiss Franc. An analysis of the dynamic behavior of interest rates generated with these models reveals several deficiencies which have an impact on the performance of investment policies derived from the stochastic program. While barycentric approximation is used here for the generation of scenario trees, these insights may be generalized to other discretization techniques as well.
We consider linear two-stage stochastic programs with mixed-integer recourse. Instead of basing the selection of an optimal first-stage solution on expected costs alone, we include into the objective a risk term refle...
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We consider linear two-stage stochastic programs with mixed-integer recourse. Instead of basing the selection of an optimal first-stage solution on expected costs alone, we include into the objective a risk term reflecting the probability that a preselected cost threshold is exceeded. After we have put the resulting mean-risk model into perspective with stochastic dominance, we study further structural properties of the model and derive some basic stability results. In the algorithmic part of the paper, we propose a scenario decomposition method and report initial computational experience.
stochastic programming is concerned with practical procedures for decision making under uncertainty, by modelling uncertainties and risks associated with decision in a form suitable for optimization. The field is deve...
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stochastic programming is concerned with practical procedures for decision making under uncertainty, by modelling uncertainties and risks associated with decision in a form suitable for optimization. The field is developing rapidly with contributions from many disciplines such as operations research, probability and statistics, and economics. A stochastic linear program with recourse can equivalently be formulated as a convex programming problem. The problem is often large-scale as the objective function involves an expectation, either over a discrete set of scenarios or as a multi-dimensional integral. Moreover, the objective function is possibly nondifferentiable. This paper provides a brief overview of recent developments on smooth approximation techniques and Newton-type methods for solving two-stage stochastic linear programs with recourse, and parallel implementation of these methods. A simple numerical example is used to signal the potential of smoothing approaches. (C) 2000 Elsevier Science Ltd. All rights reserved.
Some developments in structure and stability of stochastic programs during the last decade together with interrelations to optimization theory and stochastics are reviewed. With weak convergence of probability measure...
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Some developments in structure and stability of stochastic programs during the last decade together with interrelations to optimization theory and stochastics are reviewed. With weak convergence of probability measures as a backbone we discuss qualitative and quantitative stability of recourse models that possibly involve integer variables. We sketch stability in chance constrained stochastic programming and provide some applications in statistical estimation. Finally, an outlook is devoted to issues that were not discussed in detail and to some open problems.
In this paper we use a stochastic programming approach to develop currency option hedging models which can address problems with multiple random factors in an imperfect market. The portfolios considered in our model a...
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In this paper we use a stochastic programming approach to develop currency option hedging models which can address problems with multiple random factors in an imperfect market. The portfolios considered in our model are rebalanced at the end of each time period, and reinvestments are allowed during the hedging process. These sequential decisions (reinvestments) are based on the evolution of random parameters such as exchange rates, interest rates, etc. We also allow the inclusion of a variety of instruments in the hedging portfolio, including short term derivative securities, short term options, and futures. These instruments help generate strategies that provide good liquidity and low trade intensity. One of the important features of the model is that it incorporates constraints on sensitivity measures such as Delta and Gamma. By ensuring that these hedge parameters track a desired trajectory (e.g., the parameters of a target option), the new model provides investment strategies that are robust with respect to the perturbations measured by Delta and Gamma. In order to manage the explosion of scenarios due to multiple random factors. we incorporate sampling within a scenario aggregation algorithm. We illustrate that when compared with other myopic hedging methods in imperfect markets, the new stochastic programming model can provide better performance. Our tramples also illustrate stochastic programming as a practical computational tool for realistic hedging problems.
In this paper, a new stochastic programming approach is presented to address chemical process optimization problems under uncertainty. The novel algorithm, named as delayed sampling approach, solves an equivalent dete...
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In this paper, a new stochastic programming approach is presented to address chemical process optimization problems under uncertainty. The novel algorithm, named as delayed sampling approach, solves an equivalent deterministic optimization model transformed from the stochastic optimization problem between two stochastic simulations. The sampling numbers are reduced considerably and the computational burden is then alleviated remarkably. A complex crude distillation unit is modeled and optimized using the new stochastic approach. Savings of up to 80% in CPU time has been achieved without significant loss of solution precision compared to the conventional stochastic optimization method. (C) 2000 Elsevier Science Ltd. All rights reserved.
This paper proposes and tests an approximation of the solution of a class of piecewise deterministic control problems, typically used in the modeling of manufacturing flow processes. This approximation uses a stochast...
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This paper proposes and tests an approximation of the solution of a class of piecewise deterministic control problems, typically used in the modeling of manufacturing flow processes. This approximation uses a stochastic programming approach on a suitably discretized and sampled system. The method proceeds through two stages: (i) the Hamilton-Jacobi-Bellman (HJB) dynamic programming equations for the finite horizon continuous time stochastic control problem are discretized over a set of sampled times;this defines an associated discrete time stochastic control problem which, due to the finiteness of the sample path set for the Markov disturbance process, can be written as a stochastic programming problem;and (ii) the very large event tree representing the sample path set is replaced with a reduced tree obtained by randomly sampling over the set of all possible paths. It is shown that the solution of the stochastic program defined on the randomly sampled tree converges toward the solution of the discrete time control problem when the sample size increases to infinity. The discrete time control problem solution converges to the solution of the flow control problem when the discretization mesh tends to zero. A comparison with a direct numerical solution of the dynamic programming equations is made for a single part manufacturing flow control model in order to illustrate the convergence properties. Applications to larger models affected by the curse of dimensionality in a standard dynamic programming techniques show the possible advantages of the method.
In this paper, a new stochastic programming approach is presented to address chemical process optimization problems under uncertainty. The novel algorithm, named as delayed sampling approach, solves an equivalent dete...
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In this paper, a new stochastic programming approach is presented to address chemical process optimization problems under uncertainty. The novel algorithm, named as delayed sampling approach, solves an equivalent deterministic optimization model transformed from the stochastic optimization problem between two stochastic simulations. The sampling numbers are reduced considerably and the computational burden is then alleviated remarkably. A complex crude distillation unit is modeled and optimized using the new stochastic approach. Savings of up to 80% in CPU time has been achieved without significant loss of solution precision compared to the conventional stochastic optimization method. (C) 2000 Elsevier Science Ltd. All rights reserved.
A scenario-based, multistage stochastic programming model is developed for the management of the Highland Lakes by the Lower Colorado River Authority (LCRA) in Central Texas. The model explicitly considers two objecti...
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