Traditional valuation by comparable sales does not possess a formal methodology for the explicit incorporation of imperfect information. chance‐constrainedprogramming permits this and, at its simplest, facilitates v...
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This paper presents the results of a stochastic linear program for estimating the supply of corn residue for use as raw material in an ethanol plant. The model is based on the production capacity of an average Illinoi...
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This paper presents the results of a stochastic linear program for estimating the supply of corn residue for use as raw material in an ethanol plant. The model is based on the production capacity of an average Illinois farm, and considers the feasibility of three mutually exclusive residue harvesting alternatives-own baling, custom baling, and cob collection. Since the potential for residue use in animal feed may be even more promising, these results are directly useful for the feed industry. They also indicate the profitability of investing in residue harvesting equipment. From a methodological point of view, the paper contrasts the results of three OR approaches, a deterministic LP approach, a stochastic LP approach, and a chance-constrained approach. Because of the stochastic nature of the problem both Monte Carlo simulation and chance-constrained programming are found to be computationally viable, even though they differ in the way they incorporate risk information.
A deterministic linear programming model which optimizes the abatement of each SO2 emission source, is extended into a CCP form by introducing equations of probabilistic constrained through the incorporation of uncert...
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A deterministic linear programming model which optimizes the abatement of each SO2 emission source, is extended into a CCP form by introducing equations of probabilistic constrained through the incorporation of uncertainty in the source-receptor-specific transfer coefficients. Based on the calculation of SO2 and sulfate average residence time for Liuzhou City, a sulfur deposition model has been developed and the distribution of transfer coefficients have been found to be approximately log-normal. Sulfur removal minimization of the model shows that the abatement of emission sources in the city is more effective, while control cost optimization provides the lowest cost programmes for source abatement at each allowable deposition limit under varied environmental risk levels. Finally a practicable programme is recommended.
In formulating stochastic programming with recourse models, the parameters of the linear programs are usually assumed to be random variables with known distributions. In this paper, the requirement vector parameter is...
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This paper analyzes the problem of the operation of Aswan High Dam. A chance-constrained Model (CCM) is developed for the operation of the Dam. The model optimizes total benefits from the discharged water while incorp...
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A challenging problem in process control is the selection of input levels which will produce desirable output quality. This problem is complicated by the unsure relationships of cause and effect and by the trade-offs ...
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A challenging problem in process control is the selection of input levels which will produce desirable output quality. This problem is complicated by the unsure relationships of cause and effect and by the trade-offs between meeting conflicting output specifications. This paper proposes a new approach, which incorporates prediction-interval constraints into a goal-programming model. A process-control problem, originally solved by the desirability-function approach, is solved using this new model. Comparisons between the two approaches are discussed.
This paper introduces the CHAPS (chance-constrained programming system) algorithm, which uses linearization techniques but gives more accurate solutions than earlier, similar methods.
This paper introduces the CHAPS (chance-constrained programming system) algorithm, which uses linearization techniques but gives more accurate solutions than earlier, similar methods.
Decision environments involve the need to solve problems with varying degrees of uncertainty as well as multiple, potentially conflicting objectives. chance constraints consider the uncertainty encountered. Codes inco...
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Decision environments involve the need to solve problems with varying degrees of uncertainty as well as multiple, potentially conflicting objectives. chance constraints consider the uncertainty encountered. Codes incorporating chance constraints into a mathematical programming model are not available on a widespread basis owing to the non-linear form of the chance constraints. Therefore, accurate linear approximations would be useful to analyse this class of problems with efficient linear codes. This paper presents an approximation formula for chance constraints which can be used in either the single- or multiple-objective case. The approximation presented will place a bound on the chance constraint at least as tight as the true non-linear form, thus overachieving the chance constraint at the expense of other constraints or objectives.
The paper considers stochastically constrained nonlinear programming problems. A penalty function is constructed in terms of a “distance” between random variables, defined in terms of the ϕ-divergence functional (a ...
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The paper considers stochastically constrained nonlinear programming problems. A penalty function is constructed in terms of a “distance” between random variables, defined in terms of the ϕ-divergence functional (a generalization of the relative entropy). A duality theory is developed in which a general relation between ϕ-divergence and utility functions is revealed, via the conjugate transform, and a new type of certainty equivalent concept emerges.
The water distribution system is considered. It is assumed that the system comprises water reservoir network and agricultural users. The control problem consists in (i) optimal satisfying an agricultural user needs, (...
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The water distribution system is considered. It is assumed that the system comprises water reservoir network and agricultural users. The control problem consists in (i) optimal satisfying an agricultural user needs, (ii) avoiding floods and ecological losses. To solve the problem formulated, the following methods are applied: - the multilevel structure approach, - the chance-constrained approach and linear decision rules, - Frank-Wolfe algorithm for solution of upper level task and so called “radial” algorithm (proposed for multiplicative goal functions) for lower level tasks solution. Numerical results for different structures of a three-reservoir system are presented. Two types of decision rules are discussed and compared for all the structures considered.
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