IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v142y2006i1p215-24110.1007-s10479-006-6169-8.html
   My bibliography  Save this article

The empirical behavior of sampling methods for stochastic programming

Author

Listed:
  • Jeff Linderoth
  • Alexander Shapiro
  • Stephen Wright

Abstract

We investigate the quality of solutions obtained from sample-average approximations to two-stage stochastic linear programs with recourse. We use a recently developed software tool executing on a computational grid to solve many large instances of these problems, allowing us to obtain high-quality solutions and to verify optimality and near-optimality of the computed solutions in various ways. Copyright Springer Science + Business Media, Inc. 2006

Suggested Citation

  • Jeff Linderoth & Alexander Shapiro & Stephen Wright, 2006. "The empirical behavior of sampling methods for stochastic programming," Annals of Operations Research, Springer, vol. 142(1), pages 215-241, February.
  • Handle: RePEc:spr:annopr:v:142:y:2006:i:1:p:215-241:10.1007/s10479-006-6169-8
    DOI: 10.1007/s10479-006-6169-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-006-6169-8
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s10479-006-6169-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. T. Glenn Bailey & Paul A. Jensen & David P. Morton, 1999. "Response surface analysis of two‐stage stochastic linear programming with recourse," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(7), pages 753-776, October.
    2. Athanassios N. Avramidis & James R. Wilson, 1996. "Integrated Variance Reduction Strategies for Simulation," Operations Research, INFORMS, vol. 44(2), pages 327-346, April.
    3. Julia L. Higle & Suvrajeet Sen, 1991. "Stochastic Decomposition: An Algorithm for Two-Stage Linear Programs with Recourse," Mathematics of Operations Research, INFORMS, vol. 16(3), pages 650-669, August.
    4. Julia L. Higle, 1998. "Variance Reduction and Objective Function Evaluation in Stochastic Linear Programs," INFORMS Journal on Computing, INFORMS, vol. 10(2), pages 236-247, May.
    5. Rubinstein, Reuven Y. & Shapiro, Alexander, 1990. "Optimization of static simulation models by the score function method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(4), pages 373-392.
    6. John M. Mulvey & Andrzej Ruszczyński, 1995. "A New Scenario Decomposition Method for Large-Scale Stochastic Optimization," Operations Research, INFORMS, vol. 43(3), pages 477-490, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. T. Glenn Bailey & Paul A. Jensen & David P. Morton, 1999. "Response surface analysis of two‐stage stochastic linear programming with recourse," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(7), pages 753-776, October.
    2. Jangho Park & Rebecca Stockbridge & Güzin Bayraksan, 2021. "Variance reduction for sequential sampling in stochastic programming," Annals of Operations Research, Springer, vol. 300(1), pages 171-204, May.
    3. Trukhanov, Svyatoslav & Ntaimo, Lewis & Schaefer, Andrew, 2010. "Adaptive multicut aggregation for two-stage stochastic linear programs with recourse," European Journal of Operational Research, Elsevier, vol. 206(2), pages 395-406, October.
    4. Suvrajeet Sen & Yifan Liu, 2016. "Mitigating Uncertainty via Compromise Decisions in Two-Stage Stochastic Linear Programming: Variance Reduction," Operations Research, INFORMS, vol. 64(6), pages 1422-1437, December.
    5. Rebecca Stockbridge & Güzin Bayraksan, 2016. "Variance reduction in Monte Carlo sampling-based optimality gap estimators for two-stage stochastic linear programming," Computational Optimization and Applications, Springer, vol. 64(2), pages 407-431, June.
    6. Michael Freimer & Jeffrey Linderoth & Douglas Thomas, 2012. "The impact of sampling methods on bias and variance in stochastic linear programs," Computational Optimization and Applications, Springer, vol. 51(1), pages 51-75, January.
    7. Diana Barro & Elio Canestrelli, 2005. "Time and nodal decomposition with implicit non-anticipativity constraints in dynamic portfolio optimization," GE, Growth, Math methods 0510011, University Library of Munich, Germany.
    8. Blanchot, Xavier & Clautiaux, François & Detienne, Boris & Froger, Aurélien & Ruiz, Manuel, 2023. "The Benders by batch algorithm: Design and stabilization of an enhanced algorithm to solve multicut Benders reformulation of two-stage stochastic programs," European Journal of Operational Research, Elsevier, vol. 309(1), pages 202-216.
    9. Panos Parpas & Berk Ustun & Mort Webster & Quang Kha Tran, 2015. "Importance Sampling in Stochastic Programming: A Markov Chain Monte Carlo Approach," INFORMS Journal on Computing, INFORMS, vol. 27(2), pages 358-377, May.
    10. Chia-Hung Chen & Shangyao Yan & Miawjane Chen, 2010. "Short-term manpower planning for MRT carriage maintenance under mixed deterministic and stochastic demands," Annals of Operations Research, Springer, vol. 181(1), pages 67-88, December.
    11. Fengqi You & Ignacio Grossmann, 2013. "Multicut Benders decomposition algorithm for process supply chain planning under uncertainty," Annals of Operations Research, Springer, vol. 210(1), pages 191-211, November.
    12. Helga Meier & Nicos Christofides & Gerry Salkin, 2001. "Capital Budgeting Under Uncertainty---An Integrated Approach Using Contingent Claims Analysis and Integer Programming," Operations Research, INFORMS, vol. 49(2), pages 196-206, April.
    13. D. Kuhn, 2009. "Convergent Bounds for Stochastic Programs with Expected Value Constraints," Journal of Optimization Theory and Applications, Springer, vol. 141(3), pages 597-618, June.
    14. István Deák, 2011. "Testing successive regression approximations by large-scale two-stage problems," Annals of Operations Research, Springer, vol. 186(1), pages 83-99, June.
    15. Ketabchi, Saeed & Behboodi-Kahoo, Malihe, 2015. "Augmented Lagrangian method within L-shaped method for stochastic linear programs," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 12-20.
    16. V.I. Norkin & G.C. Pflug & A. Ruszczynski, 1996. "A Branch and Bound Method for Stochastic Global Optimization," Working Papers wp96065, International Institute for Applied Systems Analysis.
    17. Riis, Morten & Andersen, Kim Allan, 2005. "Applying the minimax criterion in stochastic recourse programs," European Journal of Operational Research, Elsevier, vol. 165(3), pages 569-584, September.
    18. Emelogu, Adindu & Chowdhury, Sudipta & Marufuzzaman, Mohammad & Bian, Linkan & Eksioglu, Burak, 2016. "An enhanced sample average approximation method for stochastic optimization," International Journal of Production Economics, Elsevier, vol. 182(C), pages 230-252.
    19. Maher, Stephen J., 2021. "Implementing the branch-and-cut approach for a general purpose Benders’ decomposition framework," European Journal of Operational Research, Elsevier, vol. 290(2), pages 479-498.
    20. E Saliby & R J Paul, 2009. "A farewell to the use of antithetic variates in Monte Carlo simulation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(7), pages 1026-1035, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:142:y:2006:i:1:p:215-241:10.1007/s10479-006-6169-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.