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Operations Research Proceedings 2014 pp 369–375Cite as

Multistage Optimization with the Help of Quantified Linear Programming

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Part of the book series: Operations Research Proceedings ((ORP))

Abstract

Quantified linear integer programs (QIPs) are linear integer programs (IPs) with variables being either existentially or universally quantified. They can be interpreted as two-person zero-sum games between an existential and a universal player on the one side, or multistage optimization problems under uncertainty on the other side. Solutions of feasible QIPs are so called winning strategies for the existential player that specify how to react on moves—certain fixations of universally quantified variables—of the universal player to certainly win the game. In order to solve the QIP optimization problem, where the task is to find an especially attractive winning strategy, we examine the problem’s hybrid nature and combine linear programming techniques with solution techniques from game-tree search.

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Acknowledgments

Research partially supported by German Research Foundation (DFG), Lo 1396/2-1 and SFB 805.

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Authors and Affiliations

  1. Fluid Systems, Technische Universität Darmstadt, Darmstadt, Germany

    T. Ederer, U. Lorenz & T. Opfer

  2. Chair of Technology Management, University Siegen, Siegen, Germany

    T. Ederer, U. Lorenz, T. Opfer & J. Wolf

Authors
  1. T. Ederer
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  2. U. Lorenz
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  3. T. Opfer
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  4. J. Wolf
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Corresponding author

Correspondence to U. Lorenz .

Editor information

Editors and Affiliations

  1. Operations Research, RWTH Aachen University, Aachen, Germany

    Marco Lübbecke

  2. Lehrstuhl II für Mathematik, RWTH Aachen University, Aachen, Germany

    Arie Koster

  3. RWTH Aachen University, Aachen, Nordrhein-Westfalen, Germany

    Peter Letmathe

  4. E.ON Energy Research Center, RWTH Aachen University, Aachen, Nordrhein-Westfalen, Germany

    Reinhard Madlener

  5. Management Science, RWTH Aachen University, Aachen, Nordrhein-Westfalen, Germany

    Britta Peis

  6. Chair of Operations Management, RWTH Aachen University, Aachen, Germany

    Grit Walther

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© 2016 Springer International Publishing Switzerland

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Ederer, T., Lorenz, U., Opfer, T., Wolf, J. (2016). Multistage Optimization with the Help of Quantified Linear Programming. In: Lübbecke, M., Koster, A., Letmathe, P., Madlener, R., Peis, B., Walther, G. (eds) Operations Research Proceedings 2014. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-28697-6_52

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