The stability of stochastic programs with mixed-integer recourse and random right-hand sides under perturbations of the integrating probability measure is considered from a quantitative viewpoint. Objective-function v...
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The stability of stochastic programs with mixed-integer recourse and random right-hand sides under perturbations of the integrating probability measure is considered from a quantitative viewpoint. Objective-function values of perturbed stochastic programs are related to each other via a variational distance of probability measures based on a suitable Vapnik-Cervonenkis class of Borel sets in a Euclidean space. This leads to Holder continuity of local optimal values. In the context of estimation via empirical measures the general results imply qualitative and quantitative statements on the asymptotic convergence of local optimal values and optimal solutions.
Different classes of on-line algorithms are developed and analyzed for the solution of {0, 1} and relaxed stochastic knapsack problems, in which both profit and size coefficients are random variables. In particular, a...
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Different classes of on-line algorithms are developed and analyzed for the solution of {0, 1} and relaxed stochastic knapsack problems, in which both profit and size coefficients are random variables. In particular, a linear time on-line algorithm is proposed for which the expected difference between the optimum and the approximate solution value is O(log(3/2) n). An Omega(1) lower bound on the expected difference between the optimum and the solution found by any on-line algorithm is also shown to hold.
For two-stage stochastic programs with integrality constraints in the second stage, we study continuity properties of the expected recourse as a function both of the first-stage policy and the integrating probability ...
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For two-stage stochastic programs with integrality constraints in the second stage, we study continuity properties of the expected recourse as a function both of the first-stage policy and the integrating probability measure. Sufficient conditions for lower semicontinuity, continuity and Lipschitz continuity with respect to the first-stage policy are presented. Furthermore, joint continuity in the policy and the probability measure is established. This leads to conclusions on the stability of optimal values and optimal solutions to the two-stage stochastic program when subjecting the underlying probability measure to perturbations.
In this paper, a general branch-and-cut procedure for stochasticinteger programs with complete recourse and first stage binary variables is presented. It is shown to provide a finite exact algorithm for a number of s...
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In this paper, a general branch-and-cut procedure for stochasticinteger programs with complete recourse and first stage binary variables is presented. It is shown to provide a finite exact algorithm for a number of stochasticinteger programs, even in the presence of binary variables or continuous random variables in the second stage.
stochastic integer programming is a suitable tool for modeling hierarchical decision situations with combinatorial features. In continuation of our work on the design and analysis of heuristics for such problems, we n...
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