IDEAS home Printed from https://ideas.repec.org/a/spr/aqjoor/v19y2021i1d10.1007_s10288-020-00434-1.html
   My bibliography  Save this article

Min-max controllable risk problems

Author

Listed:
  • Evgeny Gurevsky

    (Université de Nantes)

  • Sergey Kovalev

    (INSEEC Business School)

  • Mikhail Y. Kovalyov

    (National Academy of Sciences of Belarus)

Abstract

A min-max controllable risk problem, defined on combinatorial structures which are either simple paths of a directed multigraph or spanning trees of an undirected multigraph, with resource dependent risk functions of the arcs or the edges, is studied. The resource amount is limited, and the objective is to distribute it between the arcs or the edges so that the maximum risk over the arcs of a simple path or the edges of a spanning tree is minimized. Two new solution approaches are presented, which are asymptotically faster than the solution approaches suggested in the literature.

Suggested Citation

  • Evgeny Gurevsky & Sergey Kovalev & Mikhail Y. Kovalyov, 2021. "Min-max controllable risk problems," 4OR, Springer, vol. 19(1), pages 93-101, March.
    • Handle: RePEc:spr:aqjoor:v:19:y:2021:i:1:d:10.1007_s10288-020-00434-1
    DOI: 10.1007/s10288-020-00434-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10288-020-00434-1
    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/s10288-020-00434-1?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. Cheng, T.C. Edwin & Kovalyov, Mikhail Y. & Shakhlevich, Natalia V., 2006. "Scheduling with controllable release dates and processing times: Total completion time minimization," European Journal of Operational Research, Elsevier, vol. 175(2), pages 769-781, December.
    2. Cheng, T.C. Edwin & Kovalyov, Mikhail Y. & Shakhlevich, Natalia V., 2006. "Scheduling with controllable release dates and processing times: Makespan minimization," European Journal of Operational Research, Elsevier, vol. 175(2), pages 751-768, December.
    3. Janiak, Adam & Kovalyov, Mikhail Y. & Kubiak, Wieslaw & Werner, Frank, 2005. "Positive half-products and scheduling with controllable processing times," European Journal of Operational Research, Elsevier, vol. 165(2), pages 416-422, September.
    4. C T Daniel Ng & T C E Cheng & M Y Kovalyov, 2003. "Batch scheduling with controllable setup and processing times to minimize total completion time," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(5), pages 499-506, May.
    5. Nimrod Megiddo, 1979. "Combinatorial Optimization with Rational Objective Functions," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 414-424, November.
    6. Janiak, Adam & Kovalyov, Mikhail Y., 1996. "Single machine scheduling subject to deadlines and resource dependent processing times," European Journal of Operational Research, Elsevier, vol. 94(2), pages 284-291, October.
    7. Coffman, E.G. Jr & Matsypura, D. & Timkovsky, V.G., 2010. "Portfolio Margining: Strategy vs Risk," Working Papers 03/2010, University of Sydney Business School, Discipline of Business Analytics.
    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. Leyvand, Yaron & Shabtay, Dvir & Steiner, George, 2010. "A unified approach for scheduling with convex resource consumption functions using positional penalties," European Journal of Operational Research, Elsevier, vol. 206(2), pages 301-312, October.
    2. Wan, Guohua & Vakati, Sudheer R. & Leung, Joseph Y.-T. & Pinedo, Michael, 2010. "Scheduling two agents with controllable processing times," European Journal of Operational Research, Elsevier, vol. 205(3), pages 528-539, September.
    3. Gurel, Sinan & Akturk, M. Selim, 2007. "Considering manufacturing cost and scheduling performance on a CNC turning machine," European Journal of Operational Research, Elsevier, vol. 177(1), pages 325-343, February.
    4. Yim, Seho & Hong, Sung-Pil & Park, Myoung-Ju & Chung, Yerim, 2022. "Inverse interval scheduling via reduction on a single machine," European Journal of Operational Research, Elsevier, vol. 303(2), pages 541-549.
    5. Yuri N. Sotskov & Natalja M. Matsveichuk & Vadzim D. Hatsura, 2020. "Schedule Execution for Two-Machine Job-Shop to Minimize Makespan with Uncertain Processing Times," Mathematics, MDPI, vol. 8(8), pages 1-51, August.
    6. Shabtay, Dvir, 2022. "Single-machine scheduling with machine unavailability periods and resource dependent processing times," European Journal of Operational Research, Elsevier, vol. 296(2), pages 423-439.
    7. Yaron Leyvand & Dvir Shabtay & George Steiner & Liron Yedidsion, 2010. "Just-in-time scheduling with controllable processing times on parallel machines," Journal of Combinatorial Optimization, Springer, vol. 19(3), pages 347-368, April.
    8. Faramroze G. Engineer & George L. Nemhauser & Martin W. P. Savelsbergh & Jin-Hwa Song, 2012. "The Fixed-Charge Shortest-Path Problem," INFORMS Journal on Computing, INFORMS, vol. 24(4), pages 578-596, November.
    9. Choi, Byung-Cheon & Yoon, Suk-Hun & Chung, Sung-Jin, 2007. "Single machine scheduling problem with controllable processing times and resource dependent release times," European Journal of Operational Research, Elsevier, vol. 181(2), pages 645-653, September.
    10. Liu Guiqing & Li Kai & Cheng Bayi, 2015. "Preemptive Scheduling with Controllable Processing Times on Parallel Machines," Journal of Systems Science and Information, De Gruyter, vol. 3(1), pages 68-76, February.
    11. Steffen Rebennack & Ashwin Arulselvan & Lily Elefteriadou & Panos M. Pardalos, 2010. "Complexity analysis for maximum flow problems with arc reversals," Journal of Combinatorial Optimization, Springer, vol. 19(2), pages 200-216, February.
    12. Cheng, T. C. Edwin & Janiak, Adam & Kovalyov, Mikhail Y., 2001. "Single machine batch scheduling with resource dependent setup and processing times," European Journal of Operational Research, Elsevier, vol. 135(1), pages 177-183, November.
    13. Hassin, Refael & Sarid, Anna, 2018. "Operations research applications of dichotomous search," European Journal of Operational Research, Elsevier, vol. 265(3), pages 795-812.
    14. Pursals, Salvador Casadesús & Garzón, Federico Garriga, 2009. "Optimal building evacuation time considering evacuation routes," European Journal of Operational Research, Elsevier, vol. 192(2), pages 692-699, January.
    15. Michael Holzhauser & Sven O. Krumke & Clemens Thielen, 2016. "Budget-constrained minimum cost flows," Journal of Combinatorial Optimization, Springer, vol. 31(4), pages 1720-1745, May.
    16. Xu, Zhou, 2012. "A strongly polynomial FPTAS for the symmetric quadratic knapsack problem," European Journal of Operational Research, Elsevier, vol. 218(2), pages 377-381.
    17. Jianzhong Zhang & Zhenhong Liu, 2002. "A General Model of Some Inverse Combinatorial Optimization Problems and Its Solution Method Under l ∞ Norm," Journal of Combinatorial Optimization, Springer, vol. 6(2), pages 207-227, June.
    18. Sergio Cabello, 2023. "Faster distance-based representative skyline and k-center along pareto front in the plane," Journal of Global Optimization, Springer, vol. 86(2), pages 441-466, June.
    19. Andrés Gómez & Oleg A. Prokopyev, 2021. "A Mixed-Integer Fractional Optimization Approach to Best Subset Selection," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 551-565, May.
    20. Akiyoshi Shioura, 2015. "Polynomial-Time Approximation Schemes for Maximizing Gross Substitutes Utility Under Budget Constraints," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 192-225, February.

    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:aqjoor:v:19:y:2021:i:1:d:10.1007_s10288-020-00434-1. 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.