IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v80y2014i2p161-191.html
   My bibliography  Save this article

Generalized light robustness and the trade-off between robustness and nominal quality

Author

Listed:
  • Anita Schöbel

Abstract

Robust optimization considers optimization problems with uncertainty in the data. The common data model assumes that the uncertainty can be represented by an uncertainty set. Classic robust optimization considers the solution under the worst case scenario. The resulting solutions are often too conservative, e.g. they have high costs compared to non-robust solutions. This is a reason for the development of less conservative robust models. In this paper we extract the basic idea of the concept of light robustness originally developed in Fischetti and Monaci (Robust and online large-scale optimization, volume 5868 of lecture note on computer science. Springer, Berlin, pp 61–84, 2009 ) for interval-based uncertainty sets and linear programs: fix a quality standard for the nominal solution and among all solutions satisfying this standard choose the most reliable one. We then use this idea in order to formulate the concept of light robustness for arbitrary optimization problems and arbitrary uncertainty sets. We call the resulting concept generalized light robustness. We analyze the concept and discuss its relation to other well-known robustness concepts such as strict robustness (Ben-Tal et al. in Robust optimization. Princeton University Press, Princeton, 2009 ), reliability (Ben-Tal and Nemirovski in Math Program A 88:411–424, 2000 ) or the approach of Bertsimas and Sim (Oper Res 52(1):35–53, 2004 ). We show that the light robust counterpart is computationally tractable for many different types of uncertainty sets, among them polyhedral or ellipsoidal uncertainty sets. We furthermore discuss the trade-off between robustness and nominal quality and show that non-dominated solutions with respect to nominal quality and robustness can be computed by the generalized light robustness approach. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Anita Schöbel, 2014. "Generalized light robustness and the trade-off between robustness and nominal quality," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(2), pages 161-191, October.
  • Handle: RePEc:spr:mathme:v:80:y:2014:i:2:p:161-191
    DOI: 10.1007/s00186-014-0474-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-014-0474-9
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s00186-014-0474-9?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. Aharon Ben-Tal & Dimitris Bertsimas & David B. Brown, 2010. "A Soft Robust Model for Optimization Under Ambiguity," Operations Research, INFORMS, vol. 58(4-part-2), pages 1220-1234, August.
    2. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    3. James E. Ward & Richard E. Wendell, 1985. "Using Block Norms for Location Modeling," Operations Research, INFORMS, vol. 33(5), pages 1074-1090, October.
    4. Alan L. Erera & Juan C. Morales & Martin Savelsbergh, 2009. "Robust Optimization for Empty Repositioning Problems," Operations Research, INFORMS, vol. 57(2), pages 468-483, April.
    5. Marc Goerigk & Marie Schmidt & Anita Schöbel & Martin Knoth & Matthias Müller-Hannemann, 2014. "The Price of Strict and Light Robustness in Timetable Information," Transportation Science, INFORMS, vol. 48(2), pages 225-242, May.
    6. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    7. Matteo Fischetti & Domenico Salvagnin & Arrigo Zanette, 2009. "Fast Approaches to Improve the Robustness of a Railway Timetable," Transportation Science, INFORMS, vol. 43(3), pages 321-335, August.
    8. 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)

    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. Jonas Ide & Anita Schöbel, 2016. "Robustness for uncertain multi-objective optimization: a survey and analysis of different concepts," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(1), pages 235-271, January.
    2. Xie, Chen & Wang, Liangquan & Yang, Chaolin, 2021. "Robust inventory management with multiple supply sources," European Journal of Operational Research, Elsevier, vol. 295(2), pages 463-474.
    3. Marcus Ang & Yun Fong Lim & Melvyn Sim, 2012. "Robust Storage Assignment in Unit-Load Warehouses," Management Science, INFORMS, vol. 58(11), pages 2114-2130, November.
    4. Roos, Ernst & den Hertog, Dick, 2019. "Reducing conservatism in robust optimization," Other publications TiSEM ad0238cd-de7a-4366-b487-b, Tilburg University, School of Economics and Management.
    5. 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).
    6. Gabrel, Virginie & Murat, Cécile & Thiele, Aurélie, 2014. "Recent advances in robust optimization: An overview," European Journal of Operational Research, Elsevier, vol. 235(3), pages 471-483.
    7. Huan Xu & Constantine Caramanis & Shie Mannor, 2012. "Optimization Under Probabilistic Envelope Constraints," Operations Research, INFORMS, vol. 60(3), pages 682-699, June.
    8. Yongzhen Li & Jia Shu & Miao Song & Jiawei Zhang & Huan Zheng, 2017. "Multisourcing Supply Network Design: Two-Stage Chance-Constrained Model, Tractable Approximations, and Computational Results," INFORMS Journal on Computing, INFORMS, vol. 29(2), pages 287-300, May.
    9. Ben-Tal, Aharon & Chung, Byung Do & Mandala, Supreet Reddy & Yao, Tao, 2011. "Robust optimization for emergency logistics planning: Risk mitigation in humanitarian relief supply chains," Transportation Research Part B: Methodological, Elsevier, vol. 45(8), pages 1177-1189, September.
    10. Varas, Mauricio & Maturana, Sergio & Pascual, Rodrigo & Vargas, Ignacio & Vera, Jorge, 2014. "Scheduling production for a sawmill: A robust optimization approach," International Journal of Production Economics, Elsevier, vol. 150(C), pages 37-51.
    11. Valentina Cacchiani & Alberto Caprara & Laura Galli & Leo Kroon & Gábor Maróti & Paolo Toth, 2012. "Railway Rolling Stock Planning: Robustness Against Large Disruptions," Transportation Science, INFORMS, vol. 46(2), pages 217-232, May.
    12. Jia Shu & Miao Song, 2014. "Dynamic Container Deployment: Two-Stage Robust Model, Complexity, and Computational Results," INFORMS Journal on Computing, INFORMS, vol. 26(1), pages 135-149, February.
    13. Carrizosa, Emilio & Goerigk, Marc & Schöbel, Anita, 2017. "A biobjective approach to recoverable robustness based on location planning," European Journal of Operational Research, Elsevier, vol. 261(2), pages 421-435.
    14. Ernst Roos & Dick den Hertog, 2020. "Reducing Conservatism in Robust Optimization," INFORMS Journal on Computing, INFORMS, vol. 32(4), pages 1109-1127, October.
    15. Wenqing Chen & Melvyn Sim & Jie Sun & Chung-Piaw Teo, 2010. "From CVaR to Uncertainty Set: Implications in Joint Chance-Constrained Optimization," Operations Research, INFORMS, vol. 58(2), pages 470-485, April.
    16. Stefan Mišković, 2017. "A VNS-LP algorithm for the robust dynamic maximal covering location problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(4), pages 1011-1033, October.
    17. M. J. Naderi & M. S. Pishvaee, 2017. "Robust bi-objective macroscopic municipal water supply network redesign and rehabilitation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(9), pages 2689-2711, July.
    18. Mínguez, R. & García-Bertrand, R., 2016. "Robust transmission network expansion planning in energy systems: Improving computational performance," European Journal of Operational Research, Elsevier, vol. 248(1), pages 21-32.
    19. Antonio G. Martín & Manuel Díaz-Madroñero & Josefa Mula, 2020. "Master production schedule using robust optimization approaches in an automobile second-tier supplier," 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. 28(1), pages 143-166, March.
    20. Hamed Mamani & Shima Nassiri & Michael R. Wagner, 2017. "Closed-Form Solutions for Robust Inventory Management," Management Science, INFORMS, vol. 63(5), pages 1625-1643, May.

    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:80:y:2014:i:2:p:161-191. 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.