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Restricted Recourse Strategies for Dynamic Networks with Random Arc Capacities

Author

Listed:
  • Warren B. Powell

    (Princeton University, Princeton, New Jersey 08544)

  • Linos F. Frantzeskakis

    (AT&T Bell Laboratories, Holmdel, New Jersey 07733-1988)

Abstract

We consider a class of multistage stochastic programming problems that can be formulated as networks with random arc capacities. Large problems have proved intractable using exact methods and hence various approximations have been proposed, ranging from approximating the recourse function to sampling a small number of scenarios to capture future uncertainties. We explore the use of specialized recourse strategies that are not as general as network recourse but nonetheless capture some of the important tradeoffs. These new recourse strategies allow us to develop approximations to the recourse function that can be used to solve problems with thousands of random variables. Given these approximations, classical optimization methods can be used. The concept of hierarchical recourse is introduced and used to synthesize and generalize earlier notions of nodal recourse and cyclic recourse.

Suggested Citation

  • Warren B. Powell & Linos F. Frantzeskakis, 1994. "Restricted Recourse Strategies for Dynamic Networks with Random Arc Capacities," Transportation Science, INFORMS, vol. 28(1), pages 3-23, February.
    • Handle: RePEc:inm:ortrsc:v:28:y:1994:i:1:p:3-23
    DOI: 10.1287/trsc.28.1.3
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    Cited by:

    1. Yan, Shangyao & Tang, Ching-Hui, 2009. "Inter-city bus scheduling under variable market share and uncertain market demands," Omega, Elsevier, vol. 37(1), pages 178-192, February.
    2. 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.
    3. Shangyao Yan & Fei-Yen Hsiao & Yi-Chun Chen, 2015. "Inter-School Bus Scheduling Under Stochastic Travel Times," Networks and Spatial Economics, Springer, vol. 15(4), pages 1049-1074, December.
    4. Crainic, Teodor Gabriel & Laporte, Gilbert, 1997. "Planning models for freight transportation," European Journal of Operational Research, Elsevier, vol. 97(3), pages 409-438, March.
    5. Song, Haiqing & Cheung, Raymond K. & Wang, Haiyan, 2014. "An arc-exchange decomposition method for multistage dynamic networks with random arc capacities," European Journal of Operational Research, Elsevier, vol. 233(3), pages 474-487.
    6. Shangyao Yan & Ching-Hui Tang, 2008. "An Integrated Framework for Intercity Bus Scheduling Under Stochastic Bus Travel Times," Transportation Science, INFORMS, vol. 42(3), pages 318-335, August.
    7. G Barbarosoǧlu & Y Arda, 2004. "A two-stage stochastic programming framework for transportation planning in disaster response," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(1), pages 43-53, January.
    8. Alexander S. Estes & Michael O. Ball, 2020. "Equity and Strength in Stochastic Integer Programming Models for the Dynamic Single Airport Ground-Holding Problem," Transportation Science, INFORMS, vol. 54(4), pages 944-955, July.
    9. David P. Morton & R. Kevin Wood, 1999. "Restricted-Recourse Bounds for Stochastic Linear Programming," Operations Research, INFORMS, vol. 47(6), pages 943-956, December.
    10. Alexander S. Estes & Michael O. Ball, 2021. "Monge Properties, Optimal Greedy Policies, and Policy Improvement for the Dynamic Stochastic Transportation Problem," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 785-807, May.

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