IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v292y2020i2d10.1007_s10479-019-03244-9.html
   My bibliography  Save this article

Bounds in multi-horizon stochastic programs

Author

Listed:
  • Francesca Maggioni

    (University of Bergamo)

  • Elisabetta Allevi

    (Brescia University)

  • Asgeir Tomasgard

    (Norwegian University of Science and Technology)

Abstract

In this paper, we present bounds for multi-horizon stochastic optimization problems, a class of problems introduced in Kaut et al. (Comput Manag Sci 11:179–193, 2014) relevant in many industry-life applications typically involving strategic and operational decisions on two different time scales. After providing three general mathematical formulations of a multi-horizon stochastic program, we extend the definition of the traditional Expected Value problem and Wait-and-See problem from stochastic programming in a multi-horizon framework. New measures are introduced allowing to quantify the importance of the uncertainty at both strategic and operational levels. Relations among the solution approaches are then determined and chain of inequalities provided. Numerical experiments based on an energy planning application are finally presented.

Suggested Citation

  • Francesca Maggioni & Elisabetta Allevi & Asgeir Tomasgard, 2020. "Bounds in multi-horizon stochastic programs," Annals of Operations Research, Springer, vol. 292(2), pages 605-625, September.
    • Handle: RePEc:spr:annopr:v:292:y:2020:i:2:d:10.1007_s10479-019-03244-9
    DOI: 10.1007/s10479-019-03244-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-019-03244-9
    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/s10479-019-03244-9?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. C. C. Huang & I. Vertinsky & W. T. Ziemba, 1977. "Sharp Bounds on the Value of Perfect Information," Operations Research, INFORMS, vol. 25(1), pages 128-139, February.
    2. C. C. Huang & W. T. Ziemba & A. Ben-Tal, 1977. "Bounds on the Expectation of a Convex Function of a Random Variable: With Applications to Stochastic Programming," Operations Research, INFORMS, vol. 25(2), pages 315-325, April.
    3. Albert Madansky, 1960. "Inequalities for Stochastic Linear Programming Problems," Management Science, INFORMS, vol. 6(2), pages 197-204, January.
    4. Francesca Maggioni & Stein Wallace, 2012. "Analyzing the quality of the expected value solution in stochastic programming," Annals of Operations Research, Springer, vol. 200(1), pages 37-54, November.
    5. Francesca Maggioni & Elisabetta Allevi & Marida Bertocchi, 2014. "Bounds in Multistage Linear Stochastic Programming," Journal of Optimization Theory and Applications, Springer, vol. 163(1), pages 200-229, October.
    6. Schütz, Peter & Tomasgard, Asgeir & Ahmed, Shabbir, 2009. "Supply chain design under uncertainty using sample average approximation and dual decomposition," European Journal of Operational Research, Elsevier, vol. 199(2), pages 409-419, December.
    7. Seljom, Pernille & Tomasgard, Asgeir, 2015. "Short-term uncertainty in long-term energy system models — A case study of wind power in Denmark," Energy Economics, Elsevier, vol. 49(C), pages 157-167.
    8. Francesca Maggioni & Elisabetta Allevi & Marida Bertocchi, 2016. "Monotonic bounds in multistage mixed-integer stochastic programming," Computational Management Science, Springer, vol. 13(3), pages 423-457, July.
    9. Seljom, Pernille & Tomasgard, Asgeir, 2017. "The impact of policy actions and future energy prices on the cost-optimal development of the energy system in Norway and Sweden," Energy Policy, Elsevier, vol. 106(C), pages 85-102.
    10. Adrian S. Werner & Alois Pichler & Kjetil T. Midthun & Lars Hellemo & Asgeir Tomasgard, 2013. "Risk Measures in Multi-Horizon Scenario Trees," International Series in Operations Research & Management Science, in: Raimund M. Kovacevic & Georg Ch. Pflug & Maria Teresa Vespucci (ed.), Handbook of Risk Management in Energy Production and Trading, edition 127, chapter 0, pages 177-201, Springer.
    11. Sönmez, Erkut & Kekre, Sunder & Scheller-Wolf, Alan & Secomandi, Nicola, 2013. "Strategic analysis of technology and capacity investments in the liquefied natural gas industry," European Journal of Operational Research, Elsevier, vol. 226(1), pages 100-114.
    12. Karl Frauendorfer, 1988. "Solving SLP Recourse Problems with Arbitrary Multivariate Distributions---The Dependent Case," Mathematics of Operations Research, INFORMS, vol. 13(3), pages 377-394, August.
    13. Michal Kaut & Kjetil Midthun & Adrian Werner & Asgeir Tomasgard & Lars Hellemo & Marte Fodstad, 2014. "Multi-horizon stochastic programming," Computational Management Science, Springer, vol. 11(1), pages 179-193, January.
    14. Raimund M. Kovacevic & Georg Ch. Pflug & Maria Teresa Vespucci (ed.), 2013. "Handbook of Risk Management in Energy Production and Trading," International Series in Operations Research and Management Science, Springer, edition 127, number 978-1-4614-9035-7, March.
    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. Castro, Jordi & Escudero, Laureano F. & Monge, Juan F., 2023. "On solving large-scale multistage stochastic optimization problems with a new specialized interior-point approach," European Journal of Operational Research, Elsevier, vol. 310(1), pages 268-285.
    2. Guo, Peijun, 2022. "Dynamic focus programming: A new approach to sequential decision problems under uncertainty," European Journal of Operational Research, Elsevier, vol. 303(1), pages 328-336.

    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. Bomze, Immanuel M. & Gabl, Markus & Maggioni, Francesca & Pflug, Georg Ch., 2022. "Two-stage stochastic standard quadratic optimization," European Journal of Operational Research, Elsevier, vol. 299(1), pages 21-34.
    2. Francesca Maggioni & Elisabetta Allevi & Marida Bertocchi, 2016. "Monotonic bounds in multistage mixed-integer stochastic programming," Computational Management Science, Springer, vol. 13(3), pages 423-457, July.
    3. Giovanni Pantuso & Trine K. Boomsma, 2020. "On the number of stages in multistage stochastic programs," Annals of Operations Research, Springer, vol. 292(2), pages 581-603, September.
    4. Francesca Maggioni & Matteo Cagnolari & Luca Bertazzi, 2019. "The value of the right distribution in stochastic programming with application to a Newsvendor problem," Computational Management Science, Springer, vol. 16(4), pages 739-758, October.
    5. Ringkjøb, Hans-Kristian & Haugan, Peter M. & Nybø, Astrid, 2020. "Transitioning remote Arctic settlements to renewable energy systems – A modelling study of Longyearbyen, Svalbard," Applied Energy, Elsevier, vol. 258(C).
    6. Martin Glanzer & Georg Ch. Pflug, 2020. "Multiscale stochastic optimization: modeling aspects and scenario generation," Computational Optimization and Applications, Springer, vol. 75(1), pages 1-34, January.
    7. Backe, Stian & Ahang, Mohammadreza & Tomasgard, Asgeir, 2021. "Stable stochastic capacity expansion with variable renewables: Comparing moment matching and stratified scenario generation sampling," Applied Energy, Elsevier, vol. 302(C).
    8. Audrius Kabašinskas & Francesca Maggioni & Kristina Šutienė & Eimutis Valakevičius, 2019. "A multistage risk-averse stochastic programming model for personal savings accrual: the evidence from Lithuania," Annals of Operations Research, Springer, vol. 279(1), pages 43-70, August.
    9. Amiri-Aref, Mehdi & Klibi, Walid & Babai, M. Zied, 2018. "The multi-sourcing location inventory problem with stochastic demand," European Journal of Operational Research, Elsevier, vol. 266(1), pages 72-87.
    10. Gambella, Claudio & Maggioni, Francesca & Vigo, Daniele, 2019. "A stochastic programming model for a tactical solid waste management problem," European Journal of Operational Research, Elsevier, vol. 273(2), pages 684-694.
    11. Ching-Hui Tang, 2018. "Two-stage stochastic modeling of transportation outsourcing plans for transshipment centers," 4OR, Springer, vol. 16(1), pages 67-94, March.
    12. İ. Esra Büyüktahtakın, 2022. "Stage-t scenario dominance for risk-averse multi-stage stochastic mixed-integer programs," Annals of Operations Research, Springer, vol. 309(1), pages 1-35, February.
    13. Wim Ackooij & Debora Daniela Escobar & Martin Glanzer & Georg Ch. Pflug, 2020. "Distributionally robust optimization with multiple time scales: valuation of a thermal power plant," Computational Management Science, Springer, vol. 17(3), pages 357-385, October.
    14. Steftcho P. Dokov & David P. Morton, 2005. "Second-Order Lower Bounds on the Expectation of a Convex Function," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 662-677, August.
    15. 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.
    16. Backe, Stian & Zwickl-Bernhard, Sebastian & Schwabeneder, Daniel & Auer, Hans & Korpås, Magnus & Tomasgard, Asgeir, 2022. "Impact of energy communities on the European electricity and heating system decarbonization pathway: Comparing local and global flexibility responses," Applied Energy, Elsevier, vol. 323(C).
    17. Fodstad, Marte & Crespo del Granado, Pedro & Hellemo, Lars & Knudsen, Brage Rugstad & Pisciella, Paolo & Silvast, Antti & Bordin, Chiara & Schmidt, Sarah & Straus, Julian, 2022. "Next frontiers in energy system modelling: A review on challenges and the state of the art," Renewable and Sustainable Energy Reviews, Elsevier, vol. 160(C).
    18. Tan, Caixia & Yu, Min & Wang, Jing & Geng, Shiping & Niu, Dongxiao & Tan, Zhongfu, 2022. "Feasibility study on the construction of multi-energy complementary systems in rural areas—Eastern, central, and western parts of China are taken as examples," Energy, Elsevier, vol. 249(C).
    19. Cavagnini, Rossana & Bertazzi, Luca & Maggioni, Francesca, 2022. "A rolling horizon approach for a multi-stage stochastic fixed-charge transportation problem with transshipment," European Journal of Operational Research, Elsevier, vol. 301(3), pages 912-922.
    20. Klibi, Walid & Martel, Alain & Guitouni, Adel, 2016. "The impact of operations anticipations on the quality of stochastic location-allocation models," Omega, Elsevier, vol. 62(C), pages 19-33.

    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:292:y:2020:i:2:d:10.1007_s10479-019-03244-9. 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.