IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v74y2011i3p445-465.html
   My bibliography  Save this article

Postoptimality for mean-risk stochastic mixed-integer programs and its application

Author

Listed:
  • Zhiping Chen
  • Feng Zhang
  • Li Yang

Abstract

The mean-risk stochastic mixed-integer programs can better model complex decision problems under uncertainty than usual stochastic (integer) programming models. In order to derive theoretical results in a numerically tractable way, the contamination technique is adopted in this paper for the postoptimality analysis of the mean-risk models with respect to changes in the scenario set, here the risk is measured by the lower partial moment. We first study the continuity of the objective function and the differentiability, with respect to the parameter contained in the contaminated distribution, of the optimal value function of the mean-risk model when the recourse cost vector, the technology matrix and the right-hand side vector in the second stage problem are all random. The postoptimality conclusions of the model are then established. The obtained results are applied to two-stage stochastic mixed-integer programs with risk objectives where the objective function is nonlinear with respect to the probability distribution. The current postoptimality results for stochastic programs are improved. Copyright Springer-Verlag 2011

Suggested Citation

  • Zhiping Chen & Feng Zhang & Li Yang, 2011. "Postoptimality for mean-risk stochastic mixed-integer programs and its application," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(3), pages 445-465, December.
    • Handle: RePEc:spr:mathme:v:74:y:2011:i:3:p:445-465
    DOI: 10.1007/s00186-011-0373-2
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-011-0373-2
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00186-011-0373-2?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. PAVLO A. Krokhmal, 2007. "Higher moment coherent risk measures," Quantitative Finance, Taylor & Francis Journals, vol. 7(4), pages 373-387.
    2. Trine Kristoffersen, 2005. "Deviation Measures in Linear Two-Stage Stochastic Programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(2), pages 255-274, November.
    3. Hiroshi Konno & Hiroaki Yamazaki, 1991. "Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market," Management Science, INFORMS, vol. 37(5), pages 519-531, May.
    4. Guglielmo Lulli & Suvrajeet Sen, 2004. "A Branch-and-Price Algorithm for Multistage Stochastic Integer Programming with Application to Stochastic Batch-Sizing Problems," Management Science, INFORMS, vol. 50(6), pages 786-796, 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. Jun-ya Gotoh & Akiko Takeda & Rei Yamamoto, 2014. "Interaction between financial risk measures and machine learning methods," Computational Management Science, Springer, vol. 11(4), pages 365-402, October.
    2. Wei Liu & Li Yang & Bo Yu, 2021. "KDE distributionally robust portfolio optimization with higher moment coherent risk," Annals of Operations Research, Springer, vol. 307(1), pages 363-397, December.
    3. Gupta, Pankaj & Mittal, Garima & Mehlawat, Mukesh Kumar, 2013. "Expected value multiobjective portfolio rebalancing model with fuzzy parameters," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 190-203.
    4. Giovanni Bonaccolto & Massimiliano Caporin & Sandra Paterlini, 2018. "Asset allocation strategies based on penalized quantile regression," Computational Management Science, Springer, vol. 15(1), pages 1-32, January.
    5. Minjiao Zhang & Simge Küçükyavuz & Saumya Goel, 2014. "A Branch-and-Cut Method for Dynamic Decision Making Under Joint Chance Constraints," Management Science, INFORMS, vol. 60(5), pages 1317-1333, May.
    6. Wojtek Michalowski & Włodzimierz Ogryczak, 2001. "Extending the MAD portfolio optimization model to incorporate downside risk aversion," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(3), pages 185-200, April.
    7. Ahumada, Omar & Rene Villalobos, J. & Nicholas Mason, A., 2012. "Tactical planning of the production and distribution of fresh agricultural products under uncertainty," Agricultural Systems, Elsevier, vol. 112(C), pages 17-26.
    8. Ogryczak, Wlodzimierz & Ruszczynski, Andrzej, 1999. "From stochastic dominance to mean-risk models: Semideviations as risk measures," European Journal of Operational Research, Elsevier, vol. 116(1), pages 33-50, July.
    9. Najafi, Alireza & Taleghani, Rahman, 2022. "Fractional Liu uncertain differential equation and its application to finance," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    10. Liu, Yong-Jun & Zhang, Wei-Guo, 2015. "A multi-period fuzzy portfolio optimization model with minimum transaction lots," European Journal of Operational Research, Elsevier, vol. 242(3), pages 933-941.
    11. Leitner Johannes, 2005. "Optimal portfolios with expected loss constraints and shortfall risk optimal martingale measures," Statistics & Risk Modeling, De Gruyter, vol. 23(1/2005), pages 49-66, January.
    12. Massimiliano Caporin & Grégory M. Jannin & Francesco Lisi & Bertrand B. Maillet, 2014. "A Survey On The Four Families Of Performance Measures," Journal of Economic Surveys, Wiley Blackwell, vol. 28(5), pages 917-942, December.
    13. Michelle Alvarado & Lewis Ntaimo, 2018. "Chemotherapy appointment scheduling under uncertainty using mean-risk stochastic integer programming," Health Care Management Science, Springer, vol. 21(1), pages 87-104, March.
    14. Murat Köksalan & Ceren Tuncer Şakar, 2016. "An interactive approach to stochastic programming-based portfolio optimization," Annals of Operations Research, Springer, vol. 245(1), pages 47-66, October.
    15. Branda, Martin, 2013. "Diversification-consistent data envelopment analysis with general deviation measures," European Journal of Operational Research, Elsevier, vol. 226(3), pages 626-635.
    16. Viet Anh Nguyen & Fan Zhang & Shanshan Wang & Jose Blanchet & Erick Delage & Yinyu Ye, 2021. "Robustifying Conditional Portfolio Decisions via Optimal Transport," Papers 2103.16451, arXiv.org, revised Apr 2024.
    17. Eduardo Correia & Rodrigo Calili & José Francisco Pessanha & Maria Fatima Almeida, 2023. "Definition of Regulatory Targets for Electricity Non-Technical Losses: Proposition of an Automatic Model-Selection Technique for Panel Data Regressions," Energies, MDPI, vol. 16(6), pages 1-22, March.
    18. Milan Vaclavik & Josef Jablonsky, 2012. "Revisions of modern portfolio theory optimization model," 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. 20(3), pages 473-483, September.
    19. Justo Puerto & Moises Rodr'iguez-Madrena & Andrea Scozzari, 2019. "Location and portfolio selection problems: A unified framework," Papers 1907.07101, arXiv.org.
    20. Jinping Zhang & Keming Zhang, 2022. "Portfolio selection models based on interval-valued conditional value at risk (ICVaR) and empirical analysis," Papers 2201.02987, arXiv.org, revised Jul 2022.

    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:mathme:v:74:y:2011:i:3:p:445-465. 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.