The main difficulty of a logistic management problem is in the face of uncertainty about the future. Since many logistic models encounter uncertainty and noisy data in which variables or parameters have the probabilit...
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The main difficulty of a logistic management problem is in the face of uncertainty about the future. Since many logistic models encounter uncertainty and noisy data in which variables or parameters have the probability of occurrence, a highly promising technique of solving stochastic optimization problems is the robust programming proposed by Mulvey et al. (Operations Research 43(2) (1995a) 264-281) and Mulvey and Ruszczynski (Operations Research 43 (3) (1995b) 477-490). However, heavy computational burden has prevented wider applications in practice. In this study, we reformulate a stochastic management problem as a highly efficient robust optimization model capable of generating solutions that are progressively less sensitive to the data in the scenario set. The method proposed herein to transform a robust model into a linear program only requires adding n + m variables (where n and m are the number of scenarios and total control constraints, respectively). Whereas, the current robust programming methods proposed by Mulvey Pt al., Mulvey and Ruszczynski and Bai et al, (Management Science 43 (7)(1997) 895-907) require adding 2n + 2m. Two logistic examples, logistic management problems involving a wine company and an airline company, demonstrate the computational efficiency of the proposed model. (C) 2000 Elsevier Science B.V. All rights reserved.
In this contribution we present an online scheduling algorithm for a real world multiproduct batch plant, which includes an explicit representation of uncertainties. An ideal online scheduler is approximated by a hier...
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In this contribution we present an online scheduling algorithm for a real world multiproduct batch plant, which includes an explicit representation of uncertainties. An ideal online scheduler is approximated by a hierarchical approach with two-levels, on which optimisation problems are formulated as mathematical programs and solved by non-standard algorithms. The focus is on the hierarchical framework and the upper level planning problem where uncertainties are modelled explicitly. The key features of the planning model and of the solution algorithm are explained and numerical results are presented. (C) 2000 Elsevier Science Ltd. All rights reserved.
In this contribution we present an online scheduling algorithm for a real world multiproduct batch plant, which includes an explicit representation of uncertainties. An ideal online scheduler is approximated by a hier...
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In this contribution we present an online scheduling algorithm for a real world multiproduct batch plant, which includes an explicit representation of uncertainties. An ideal online scheduler is approximated by a hierarchical approach with two-levels, on which optimisation problems are formulated as mathematical programs and solved by non-standard algorithms. The focus is on the hierarchical framework and the upper level planning problem where uncertainties are modelled explicitly. The key features of the planning model and of the solution algorithm are explained and numerical results are presented. (C) 2000 Elsevier Science Ltd. All rights reserved.
Uncertainty is an inherent characteristic in most industrial processes, and a variety of approaches including sensitivity analysis, stochastic programming and robust optimisation have been proposed to deal with such u...
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Uncertainty is an inherent characteristic in most industrial processes, and a variety of approaches including sensitivity analysis, stochastic programming and robust optimisation have been proposed to deal with such uncertainty. Uncertainty in Real-Time Optimisation (RTO), particularly making robust decisions under uncertainty in real-time has received little attention. This paper discusses various sources of uncertainty within the closed RTO loop. A method, based on stochastic programming, that explicitly incorporates uncertainty into the RTO problem is presented and allows solution using conventional optimisation algorithms. A gasoline blending example is used to demonstrate the proposed robust RTO approach.
The linear stochastic optimization problem with incomplete information on a random purpose vector is considered. It arises in one-period portfolio selection problem in case of unknown statistical parameters of assert ...
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The linear stochastic optimization problem with incomplete information on a random purpose vector is considered. It arises in one-period portfolio selection problem in case of unknown statistical parameters of assert returns distributions. The optimal solutions are chosen on a base of minimax and mean-variance approaches. A notion of an adjoint stochastic optimization problem with incomplete information is introduced. The properties of the adjoint problems are used for a correction of efficient controls after obtaining new information on the random purpose vector. This paper is devoted to the dual relations in the statistically uncertain stochastic optimization problem with observation and their application to the portfolio selection problem.
In the literature on stochastic programming models for practical portfolio investment problems, relatively little attention has been devoted to the question how the necessarily approximate description of the asset-pri...
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In the literature on stochastic programming models for practical portfolio investment problems, relatively little attention has been devoted to the question how the necessarily approximate description of the asset-price uncertainty in these models influences the optimal solution. In this paper we will show that it: is important that asset prices in such a description are arbitrage-free. Descriptions which have been suggested in the literature are often inconsistent with observed market prices and/or use sampling to obtain a set of scenarios about the future. We will show that this effectively introduces arbitrage opportunities in the optimization model. For an investor who cannot exploit arbitrage opportunities directly because of market imperfections and trading restrictions, we will illustrate that the presence of such arbitrage opportunities may cause substantial biases in the optimal investment strategy. (C) 1997 Elsevier Science B.V.
Papers deals with multicriterion reliability-oriented optimization of truss structures by stochastic programming. Deterministic approach to structural optimization appears to be insufficient when loads acting upon a s...
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Papers deals with multicriterion reliability-oriented optimization of truss structures by stochastic programming. Deterministic approach to structural optimization appears to be insufficient when loads acting upon a structure and material properties of the structure elements have a random nature. The aim of this paper is to show importance of random modelling of the structure and influence of random parameters on an optimal solution. Usually, quality of engineering structure design is considered in terms of displacements, total cost and reliability. Therefore, optimization problem has been formulated and then solved in order to show interaction between displacement and a total cost objective function. The examples of 4-bar and 25-bar truss structures illustrate our considerations. The results of optimization are presented in the form of diagrams.
stochastic programming problems have very large dimension and characteristic structures which are tractable by decomposition. We review basic ideas of cutting plane methods, augmented Lagrangian and splitting methods,...
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stochastic programming problems have very large dimension and characteristic structures which are tractable by decomposition. We review basic ideas of cutting plane methods, augmented Lagrangian and splitting methods, and stochastic decomposition methods for convex polyhedral multi-stage stochastic programming problems. (C) 1997 The Mathematical programming Society, Inc. Published by Elsevier Science B.V.
Classical stochastic programming has already been used with large-scale LP models for long-term analysis of energy-environment systems. We propose a Minimax Regret formulation suitable for large-scale linear programmi...
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Classical stochastic programming has already been used with large-scale LP models for long-term analysis of energy-environment systems. We propose a Minimax Regret formulation suitable for large-scale linear programming models. It has been experimentally verified that the minimax regret strategy depends only on the extremal scenarios and not on the intermediate ones, thus making the approach computationally efficient. Key results of minimax regret and minimum expected value strategies for Greenhouse Gas abatement in the Province of Quebec, are compared. (C) 1999 Elsevier Science B.V. All rights reserved.
This paper deals with an important engineering problem, namely the elastoplastic analysis of structures under uncertainty. The analysis model incorporates a class of piecewise linear hardening laws that are sufficient...
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This paper deals with an important engineering problem, namely the elastoplastic analysis of structures under uncertainty. The analysis model incorporates a class of piecewise linear hardening laws that are sufficiently general to encompass a wide range of practically observed material behavior. The uncertainty we deal with is due to both loads and material parameters. We first formulate the problem as a stochastic nonlinear programming problem and then propose anew simple method for solving it via some approximation techniques.
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