Any comments on any of the topics of this page are welcome.
Any comments on any of the topics of this page are welcome. Please do not hesitate to contact me. You can find the data for the models disscussed in the articele here.
Model data for the jeep problems discussed in the article. Decision Making with Dominance Constraints in Two-Stage Stochastic Integer Programming Two-stage stochastic programming models are considered as attractive tools for making optimal decisions under uncertainty.
Traditionally, optimality is formalized by applying statistical parameters such as the expectation or the conditional value at risk to the distributions of objective values. Uwe Gotzes analyzes an approach to account for risk aversion in two-stage models based upon partial orders on the set of real random variables.
These stochastic orders enable the incorporation of the characteristics of whole distributions into the decision process. The profit or cost distributions must pass a benchmark test with a given acceptable distribution. Thus, additional objectives can be optimized. For this new class of stochastic optimization problems, results on structure and stability are proven and a tailored algorithm to tackle large problem instances is developed.
The implications of the modelling background and numerical results from the application of the proposed algorithm are demonstrated with case studies from energy trading. A note on second-order stochastic dominance constraints induced by mixed-integer linear recourseMathematical Programming, pp.
We introduce stochastic integer programs with dominance constraints induced by mixed-integer linear recourse. Closedness of the constraint set mapping with respect to perturbations of the underlying probability measure is derived.
For discrete probability measures, large-scale, block-structured, mixed-integer linear programming equivalents to the dominance constrained stochastic programs are identified.
For these models, a decomposition algorithm is proposed. Computational tests with instances from power optimization and Sudoku puzzling conclude the paper. Stochastic integer programming, stochastic dominance, mixed-integer optimization M.
In this paper we present the problem faced by an electricity retailer which searches to determine the forward contracting portfolio and the selling price for its clients. This problem is formulated as a two-stage stochastic program including second-order stochastic dominance constraints.
The stochastic dominance theory is used in order to reduce the risk suffering from low profits. The resulting deterministic equivalent problem is a mixed-integer linear program which is solved using commercial branch-and-cut software.
Numerical results are reported and a realistic case study is solved. Finally, relevant conclusions are drawn.Pattern recognition is based on a sample-to-sample approach.
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