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Multistage Stochastic Integer Programs: An Introduction

In: Online Optimization of Large Scale Systems

Author

Listed:
  • Werner Römisch

    (Humboldt-Universität zu Berlin, Institut für Mathematik)

  • Rüdiger Schultz

    (Gerhard-Mercator-Universität Duisburg, Fachbereich Mathematik)

Abstract

We consider linear multistage stochastic integer programs and study their functional and dynamic programming formulations as well as conditions for optimality and stability of solutions. Furthermore, we study the application of the Rockafellar-Wets dualization approach as well as the structure and algorithmic potential of corresponding dual problems. For discrete underlying probability distributions we discuss possible large scale mixed-integer linear programming formulations and three dual decomposition approaches, namely, scenario, component and nodal decomposition.

Suggested Citation

  • Werner Römisch & Rüdiger Schultz, 2001. "Multistage Stochastic Integer Programs: An Introduction," Springer Books, in: Martin Grötschel & Sven O. Krumke & Jörg Rambau (ed.), Online Optimization of Large Scale Systems, pages 581-600, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-04331-8_29
    DOI: 10.1007/978-3-662-04331-8_29
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