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Implementing bounds-based approximations in convex-concave two-stage stochastic programming

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Abstract

This paper is concerned with implementational issues and computational testing of bounds-based approximations for solving two-stage stochastic programs with fixed recourse. The implemented bounds are those derived by the authors previously, using first and cross moment information of the random parameters and a convex-concave saddle property of the recourse function. The paper first examines these bounds with regard to their tightness, monotonic behavior, convergence properties, and computationally exploitable decomposition structures. Subsequently, the bounds are implemented under various partitioning/refining strategies for the successive approximation. The detailed numerical experiments demonstrate the effectiveness in solving large scenario-based two-stage stochastic optimization problems throughsuccessive scenario clusters induced by refining the approximations.

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Authors and Affiliations

  1. Management Science Program, College of Business Administration, University of Tennessee, 37996, Knoxville, TN, USA

    N. C. P. Edirisinghe

  2. Management Science Division, Faculty of Commerce and Business Administration, University of British Columbia, V6T IY8, Vancouver, BC, Canada

    W. T. Ziemba

Authors
  1. N. C. P. Edirisinghe
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  2. W. T. Ziemba
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Correspondence to N. C. P. Edirisinghe.

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Edirisinghe, N.C.P., Ziemba, W.T. Implementing bounds-based approximations in convex-concave two-stage stochastic programming. Mathematical Programming 75, 295–325 (1996). https://doi.org/10.1007/BF02592157

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  • DOI: https://doi.org/10.1007/BF02592157

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