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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
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    References listed on IDEAS

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    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. 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.
    3. 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.
    4. 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.
    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.
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