Stochastic programming with integer variables

Schultz, Rüdiger

doi:10.1007/s10107-003-0445-z

Cited by 144 publications

(80 citation statements)

References 49 publications

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“…As Cath Labs are scarce and hence have limited capacities, the information of this study may be used to achieve schedules that are more efficient. Examples of these methods are scheduling the same cases consecutively in fasttrack pathways [22][23][24], scheduling cases in specific rooms [25], Stochastic Integer Programming [26]. In the Cath Lab under study, there is no holding were patients are prepared for the treatment.…”

Section: Discussionmentioning

confidence: 99%

Improving the efficiency of the cardiac catheterization laboratories through understanding the stochastic behavior of the scheduled procedures

et al. 2014

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Section: Discussionmentioning

confidence: 99%

Improving the efficiency of the cardiac catheterization laboratories through understanding the stochastic behavior of the scheduled procedures

et al. 2014

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“…These two approaches can be seen as dual to each other [32,33], as the former decomposes the problem by stage, while the latter decomposes by scenario. Naturally, both of them can be used as stand-alone procedures for solving a large-scale stochastic optimization problem.…”

Section: Algorithmic Frameworkmentioning

confidence: 99%

Decomposition methods for the two-stage stochastic Steiner tree problem

et al. 2017

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A new algorithmic approach for solving the stochastic Steiner tree problem based on three procedures for computing lower bounds (dual ascent, Lagrangian relaxation, Benders decomposition) is introduced. Our method is derived from a new integer linear programming formulation, which is shown to be strongest among all known formulations. The resulting method, which relies on an interplay of the dual information retrieved from the respective dual procedures, computes upper and lower bounds and combines them with several rules for fixing variables in order to decrease the size of problem instances. The effectiveness of our method is compared in an extensive computational study with the state-of-the-art exact approach, which employs a Benders decomposition based on two-stage branch-and-cut, and a genetic algorithm introduced during the DIMACS implementation challenge on Steiner trees. Our results indicate that the presented method significantly outperforms existing ones, both on benchmark instances from literature, as well as on large-scale telecommunication networks.

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“…In stochastic optimization, see [56] for a recent textbook, data uncertainty is captured by probability distributions. In finite dimension, there exists a rich theory and methodology of linear models [49,56] and, to lesser extent, linear mixed-integer or nonlinear models [13,46,50,63]. Stochastic optimization in continuous time has been analyzed in stochastic dynamic programming and stochastic control, see [30,19].…”

Section: Related Workmentioning

confidence: 99%

On Shape Optimization with Stochastic Loadings

Atwal

Conti

Geihe

et al. 2011

International Series of Numerical Mathematics

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Abstract. This article is concerned with different approaches to elastic shape optimization under stochastic loading. The underlying stochastic optimization strategy builds upon the methodology of two-stage stochastic programming. In fact, in the case of linear elasticity and quadratic objective functional our strategy leads to a computational cost which scales linearly in the number of linearly independent applied forces, even for a large set of realization of the random loading. We consider, besides minimization of the expectation value of suitable objective functionals, also two different risk-averse approaches, namely the expected excess and the excess probability. Numerical computations are performed using either a level-set approach representing implicit shapes of general topology in combination with composite finite elements to resolve elasticity in two and three dimensions, or a collocation boundary element approach, where polygonal shapes represent geometric details attached to a lattice and describing a perforated elastic domain. Topology optimization is performed using the concept of topological derivatives. We generalize this concept, and derive an analytical expression which takes into account the interaction between neighboring holes. This is expected to allow efficient and reliable optimization strategies of elastic objects with a large number of geometries details on a fine scale. Mathematics Subject Classification (2000). 90C15, 74B05, 65N30, 65N38, 34E08, 49K45.Keywords. shape optimization in elasticity, two-stage stochastic programming, risk averse optimization, level set method, boundary element method, topological derivative.

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Stochastic programming with integer variables

Cited by 144 publications

References 49 publications

Improving the efficiency of the cardiac catheterization laboratories through understanding the stochastic behavior of the scheduled procedures

Improving the efficiency of the cardiac catheterization laboratories through understanding the stochastic behavior of the scheduled procedures

Decomposition methods for the two-stage stochastic Steiner tree problem

On Shape Optimization with Stochastic Loadings

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