IDEAS home Printed from https://ideas.repec.org/a/spr/comgts/v15y2018i3d10.1007_s10287-018-0330-0.html
   My bibliography  Save this article

Decision-dependent probabilities in stochastic programs with recourse

Author

Listed:
  • Lars Hellemo

    (SINTEF Technology and Society)

  • Paul I. Barton

    (Massachusetts Institute of Technology)

  • Asgeir Tomasgard

    (NTNU)

Abstract

Stochastic programming with recourse usually assumes uncertainty to be exogenous. Our work presents modelling and application of decision-dependent uncertainty in mathematical programming including a taxonomy of stochastic programming recourse models with decision-dependent uncertainty. The work includes several ways of incorporating direct or indirect manipulation of underlying probability distributions through decision variables in two-stage stochastic programming problems. Two-stage models are formulated where prior probabilities are distorted through an affine transformation or combined using a convex combination of several probability distributions. Additionally, we present models where the parameters of the probability distribution are first-stage decision variables. The probability distributions are either incorporated in the model using the exact expression or by using a rational approximation. Test instances for each formulation are solved with a commercial solver, BARON, using selective branching.

Suggested Citation

  • Lars Hellemo & Paul I. Barton & Asgeir Tomasgard, 2018. "Decision-dependent probabilities in stochastic programs with recourse," Computational Management Science, Springer, vol. 15(3), pages 369-395, October.
    • Handle: RePEc:spr:comgts:v:15:y:2018:i:3:d:10.1007_s10287-018-0330-0
    DOI: 10.1007/s10287-018-0330-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10287-018-0330-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10287-018-0330-0?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. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    2. George B. Dantzig, 1955. "Linear Programming under Uncertainty," Management Science, INFORMS, vol. 1(3-4), pages 197-206, 04-07.
    3. Georg Ch. Pflug & Alois Pichler, 2011. "Approximations for Probability Distributions and Stochastic Optimization Problems," International Series in Operations Research & Management Science, in: Marida Bertocchi & Giorgio Consigli & Michael A. H. Dempster (ed.), Stochastic Optimization Methods in Finance and Energy, edition 1, chapter 0, pages 343-387, Springer.
    4. Colvin, Matthew & Maravelias, Christos T., 2010. "Modeling methods and a branch and cut algorithm for pharmaceutical clinical trial planning using stochastic programming," European Journal of Operational Research, Elsevier, vol. 203(1), pages 205-215, May.
    5. Tore Jonsbråten & Roger Wets & David Woodruff, 1998. "A class of stochastic programs withdecision dependent random elements," Annals of Operations Research, Springer, vol. 82(0), pages 83-106, August.
    6. Viswanath, Kannan & Peeta, Srinivas & Salman, Sibel F., 2004. "Investing in the Links of a Stochastic Network to Minimize Expected Shortest Path. Length," Purdue University Economics Working Papers 1167, Purdue University, Department of Economics.
    7. Daniel Kuhn, 2009. "An Information-Based Approximation Scheme for Stochastic Optimization Problems in Continuous Time," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 428-444, May.
    8. Georg Pflug & David Wozabal, 2007. "Ambiguity in portfolio selection," Quantitative Finance, Taylor & Francis Journals, vol. 7(4), pages 435-442.
    9. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    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. Aigner, Kevin-Martin & Clarner, Jan-Patrick & Liers, Frauke & Martin, Alexander, 2022. "Robust approximation of chance constrained DC optimal power flow under decision-dependent uncertainty," European Journal of Operational Research, Elsevier, vol. 301(1), pages 318-333.
    2. Şafak, Özge & Çavuş, Özlem & Aktürk, M. Seli̇m, 2022. "A two-stage decision dependent stochastic approach for airline flight network expansion," Transportation Research Part B: Methodological, Elsevier, vol. 158(C), pages 78-101.
    3. Aldrighetti, Riccardo & Battini, Daria & Ivanov, Dmitry, 2023. "Efficient resilience portfolio design in the supply chain with consideration of preparedness and recovery investments," Omega, Elsevier, vol. 117(C).
    4. Lee, Enoch & Cen, Xuekai & Lo, Hong K., 2021. "Zonal-based flexible bus service under elastic stochastic demand," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).
    5. Lejeune, Miguel A. & Dehghanian, Payman & Ma, Wenbo, 2024. "Profit-based unit commitment models with price-responsive decision-dependent uncertainty," European Journal of Operational Research, Elsevier, vol. 314(3), pages 1052-1064.
    6. Feng, Wei & Feng, Yiping & Zhang, Qi, 2021. "Multistage robust mixed-integer optimization under endogenous uncertainty," European Journal of Operational Research, Elsevier, vol. 294(2), pages 460-475.
    7. Basciftci, Beste & Ahmed, Shabbir & Shen, Siqian, 2021. "Distributionally robust facility location problem under decision-dependent stochastic demand," European Journal of Operational Research, Elsevier, vol. 292(2), pages 548-561.
    8. Giovanni Pantuso, 2021. "A node formulation for multistage stochastic programs with endogenous uncertainty," Computational Management Science, Springer, vol. 18(3), pages 325-354, July.
    9. Zhang, Si & Sun, Huijun & Liu, Yang & Lv, Ying & Wu, Jianjun & Feng, Xiaoyan, 2024. "Carsharing equitable relocation problem: A two-stage stochastic programming approach with learning-embedded endogenous uncertainty in demand," Transportation Research Part B: Methodological, Elsevier, vol. 179(C).
    10. Escudero, Laureano F. & Garín, M. Araceli & Monge, Juan F. & Unzueta, Aitziber, 2020. "Some matheuristic algorithms for multistage stochastic optimization models with endogenous uncertainty and risk management," European Journal of Operational Research, Elsevier, vol. 285(3), pages 988-1001.
    11. Salo, Ahti & Andelmin, Juho & Oliveira, Fabricio, 2022. "Decision programming for mixed-integer multi-stage optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 299(2), pages 550-565.

    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. Steffen Rebennack, 2022. "Data-driven stochastic optimization for distributional ambiguity with integrated confidence region," Journal of Global Optimization, Springer, vol. 84(2), pages 255-293, October.
    2. Feng, Wei & Feng, Yiping & Zhang, Qi, 2021. "Multistage robust mixed-integer optimization under endogenous uncertainty," European Journal of Operational Research, Elsevier, vol. 294(2), pages 460-475.
    3. Zhi Chen & Melvyn Sim & Huan Xu, 2019. "Distributionally Robust Optimization with Infinitely Constrained Ambiguity Sets," Operations Research, INFORMS, vol. 67(5), pages 1328-1344, September.
    4. Hsien-Chung Wu, 2019. "Numerical Method for Solving the Robust Continuous-Time Linear Programming Problems," Mathematics, MDPI, vol. 7(5), pages 1-50, May.
    5. Guanglei Wang & Hassan Hijazi, 2018. "Mathematical programming methods for microgrid design and operations: a survey on deterministic and stochastic approaches," Computational Optimization and Applications, Springer, vol. 71(2), pages 553-608, November.
    6. Wolfram Wiesemann & Daniel Kuhn & Berç Rustem, 2012. "Multi-resource allocation in stochastic project scheduling," Annals of Operations Research, Springer, vol. 193(1), pages 193-220, March.
    7. Bora Tarhan & Ignacio Grossmann & Vikas Goel, 2013. "Computational strategies for non-convex multistage MINLP models with decision-dependent uncertainty and gradual uncertainty resolution," Annals of Operations Research, Springer, vol. 203(1), pages 141-166, March.
    8. Dimitris Bertsimas & Vineet Goyal, 2013. "On the approximability of adjustable robust convex optimization under uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(3), pages 323-343, June.
    9. Marla, Lavanya & Rikun, Alexander & Stauffer, Gautier & Pratsini, Eleni, 2020. "Robust modeling and planning: Insights from three industrial applications," Operations Research Perspectives, Elsevier, vol. 7(C).
    10. Shaghayegh Mokarami & S. Hashemi, 2015. "Constrained shortest path with uncertain transit times," Journal of Global Optimization, Springer, vol. 63(1), pages 149-163, September.
    11. Bakker, Hannah & Dunke, Fabian & Nickel, Stefan, 2020. "A structuring review on multi-stage optimization under uncertainty: Aligning concepts from theory and practice," Omega, Elsevier, vol. 96(C).
    12. Gregory, Christine & Darby-Dowman, Ken & Mitra, Gautam, 2011. "Robust optimization and portfolio selection: The cost of robustness," European Journal of Operational Research, Elsevier, vol. 212(2), pages 417-428, July.
    13. Jang Ho Kim & Woo Chang Kim & Frank J. Fabozzi, 2014. "Recent Developments in Robust Portfolios with a Worst-Case Approach," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 103-121, April.
    14. Dimitris Bertsimas & Vineet Goyal & Xu Andy Sun, 2011. "A Geometric Characterization of the Power of Finite Adaptability in Multistage Stochastic and Adaptive Optimization," Mathematics of Operations Research, INFORMS, vol. 36(1), pages 24-54, February.
    15. Hsien-Chung Wu, 2021. "Robust Solutions for Uncertain Continuous-Time Linear Programming Problems with Time-Dependent Matrices," Mathematics, MDPI, vol. 9(8), pages 1-52, April.
    16. Tahir Ekin & Nicholas G. Polson & Refik Soyer, 2017. "Augmented nested sampling for stochastic programs with recourse and endogenous uncertainty," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(8), pages 613-627, December.
    17. Algo Carè & Simone Garatti & Marco C. Campi, 2019. "The wait-and-judge scenario approach applied to antenna array design," Computational Management Science, Springer, vol. 16(3), pages 481-499, July.
    18. Nilay Noyan & Gábor Rudolf & Miguel Lejeune, 2022. "Distributionally Robust Optimization Under a Decision-Dependent Ambiguity Set with Applications to Machine Scheduling and Humanitarian Logistics," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 729-751, March.
    19. Pamela Alvarez & Jorge Vera, 2014. "Application of Robust Optimization to the Sawmill Planning Problem," Annals of Operations Research, Springer, vol. 219(1), pages 457-475, August.
    20. Hatami-Marbini, Adel & Arabmaldar, Aliasghar, 2021. "Robustness of Farrell cost efficiency measurement under data perturbations: Evidence from a US manufacturing application," European Journal of Operational Research, Elsevier, vol. 295(2), pages 604-620.

    More about this item

    Statistics

    Access and download statistics

    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:comgts:v:15:y:2018:i:3:d:10.1007_s10287-018-0330-0. 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.