IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v193y2012i1p3-1910.1007-s10479-010-0811-1.html
   My bibliography  Save this article

Approximation and contamination bounds for probabilistic programs

Author

Listed:
  • Martin Branda
  • Jitka Dupačová

Abstract

Development of applicable robustness results for stochastic programs with probabilistic constraints is a demanding task. In this paper we follow the relatively simple ideas of output analysis based on the contamination technique and focus on construction of computable global bounds for the optimal value function. Dependence of the set of feasible solutions on the probability distribution rules out the straightforward construction of these concavity-based global bounds for the perturbed optimal value function whereas local results can still be obtained. Therefore we explore approximations and reformulations of stochastic programs with probabilistic constraints by stochastic programs with suitably chosen recourse or penalty-type objectives and fixed constraints. Contamination bounds constructed for these substitute problems may be then implemented within the output analysis for the original probabilistic program. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Martin Branda & Jitka Dupačová, 2012. "Approximation and contamination bounds for probabilistic programs," Annals of Operations Research, Springer, vol. 193(1), pages 3-19, March.
    • Handle: RePEc:spr:annopr:v:193:y:2012:i:1:p:3-19:10.1007/s10479-010-0811-1
    DOI: 10.1007/s10479-010-0811-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-010-0811-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-010-0811-1?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. Y.M. Ermoliev & T.Y. Ermolieva & G.J. MacDonald & V.I. Norkin, 2000. "Stochastic Optimization of Insurance Portfolios for Managing Exposure to Catastrophic Risks," Annals of Operations Research, Springer, vol. 99(1), pages 207-225, December.
    2. Dupacova, Jitka & Gaivoronski, Alexei & Kos, Zdenek & Szantai, Tamas, 1991. "Stochastic programming in water management: A case study and a comparison of solution techniques," European Journal of Operational Research, Elsevier, vol. 52(1), pages 28-44, May.
    3. B. K. Pagnoncelli & S. Ahmed & A. Shapiro, 2009. "Sample Average Approximation Method for Chance Constrained Programming: Theory and Applications," Journal of Optimization Theory and Applications, Springer, vol. 142(2), pages 399-416, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Feng Shan & Liwei Zhang & Xiantao Xiao, 2014. "A Smoothing Function Approach to Joint Chance-Constrained Programs," Journal of Optimization Theory and Applications, Springer, vol. 163(1), pages 181-199, October.
    2. Martin Branda, 2013. "On relations between chance constrained and penalty function problems under discrete distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(2), pages 265-277, April.
    3. Takashi Hasuike, 2014. "Risk-control approach for bottleneck transportation problem with randomness and fuzziness," Journal of Global Optimization, Springer, vol. 60(4), pages 663-678, December.
    4. Lukáš Adam & Martin Branda & Holger Heitsch & René Henrion, 2020. "Solving joint chance constrained problems using regularization and Benders’ decomposition," Annals of Operations Research, Springer, vol. 292(2), pages 683-709, September.
    5. Martin Branda & Miloš Kopa, 2014. "On relations between DEA-risk models and stochastic dominance efficiency tests," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 22(1), pages 13-35, March.

    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. I. Bremer & R. Henrion & A. Möller, 2015. "Probabilistic constraints via SQP solver: application to a renewable energy management problem," Computational Management Science, Springer, vol. 12(3), pages 435-459, July.
    2. Rezapour, Shabnam & Srinivasan, Ramakrishnan & Tew, Jeffrey & Allen, Janet K. & Mistree, Farrokh, 2018. "Correlation between strategic and operational risk mitigation strategies in supply networks," International Journal of Production Economics, Elsevier, vol. 201(C), pages 225-248.
    3. Martin Branda, 2013. "On relations between chance constrained and penalty function problems under discrete distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(2), pages 265-277, April.
    4. X. Qin & G. Huang, 2009. "An Inexact Chance-constrained Quadratic Programming Model for Stream Water Quality Management," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 23(4), pages 661-695, March.
    5. Erfan Mohagheghi & Mansour Alramlawi & Aouss Gabash & Pu Li, 2018. "A Survey of Real-Time Optimal Power Flow," Energies, MDPI, vol. 11(11), pages 1-20, November.
    6. Zhuqi Miao & Balabhaskar Balasundaram & Eduardo L. Pasiliao, 2014. "An exact algorithm for the maximum probabilistic clique problem," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 105-120, July.
    7. 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.
    8. G. Pantuso & L. M. Hvattum, 2021. "Maximizing performance with an eye on the finances: a chance-constrained model for football transfer market decisions," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 583-611, July.
    9. Jianqiang Cheng & Richard Li-Yang Chen & Habib N. Najm & Ali Pinar & Cosmin Safta & Jean-Paul Watson, 2018. "Chance-constrained economic dispatch with renewable energy and storage," Computational Optimization and Applications, Springer, vol. 70(2), pages 479-502, June.
    10. Zhang, Lele & Ding, Pengyuan & Thompson, Russell G., 2023. "A stochastic formulation of the two-echelon vehicle routing and loading bay reservation problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 177(C).
    11. Hadi Karimi & Sandra D. Ekşioğlu & Michael Carbajales-Dale, 2021. "A biobjective chance constrained optimization model to evaluate the economic and environmental impacts of biopower supply chains," Annals of Operations Research, Springer, vol. 296(1), pages 95-130, January.
    12. repec:dgr:rugsom:02a06 is not listed on IDEAS
    13. Li, Y.P. & Huang, G.H. & Zhang, N. & Nie, S.L., 2011. "An inexact-stochastic with recourse model for developing regional economic-ecological sustainability under uncertainty," Ecological Modelling, Elsevier, vol. 222(2), pages 370-379.
    14. Gaivoronski, Alexei & Sechi, Giovanni M. & Zuddas, Paola, 2012. "Cost/risk balanced management of scarce resources using stochastic programming," European Journal of Operational Research, Elsevier, vol. 216(1), pages 214-224.
    15. Meskarian, Rudabeh & Xu, Huifu & Fliege, Jörg, 2012. "Numerical methods for stochastic programs with second order dominance constraints with applications to portfolio optimization," European Journal of Operational Research, Elsevier, vol. 216(2), pages 376-385.
    16. Li, Y.P. & Huang, G.H. & Nie, S.L. & Chen, X., 2011. "A robust modeling approach for regional water management under multiple uncertainties," Agricultural Water Management, Elsevier, vol. 98(10), pages 1577-1588, August.
    17. Ran Ji & Miguel A. Lejeune, 2018. "Risk-budgeting multi-portfolio optimization with portfolio and marginal risk constraints," Annals of Operations Research, Springer, vol. 262(2), pages 547-578, March.
    18. Reus, Lorenzo & Pagnoncelli, Bernardo & Armstrong, Margaret, 2019. "Better management of production incidents in mining using multistage stochastic optimization," Resources Policy, Elsevier, vol. 63(C), pages 1-1.
    19. T. Ermolieva & T. Filatova & Y. Ermoliev & M. Obersteiner & K. M. de Bruijn & A. Jeuken, 2017. "Flood Catastrophe Model for Designing Optimal Flood Insurance Program: Estimating Location‐Specific Premiums in the Netherlands," Risk Analysis, John Wiley & Sons, vol. 37(1), pages 82-98, January.
    20. Ming Liu & Yueyu Ding & Lihua Sun & Runchun Zhang & Yue Dong & Zihan Zhao & Yiting Wang & Chaoran Liu, 2023. "Green Airline-Fleet Assignment with Uncertain Passenger Demand and Fuel Price," Sustainability, MDPI, vol. 15(2), pages 1-22, January.
    21. Yi Zhao & Qingwan Xue & Xi Zhang, 2018. "Stochastic Empty Container Repositioning Problem with CO 2 Emission Considerations for an Intermodal Transportation System," Sustainability, MDPI, vol. 10(11), pages 1-24, November.

    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:193:y:2012:i:1:p:3-19:10.1007/s10479-010-0811-1. 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.