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On the Existence of a Feasible Flow in a Stochastic Transportation Network

Author

Listed:
  • András Prékopa

    (Rutgers University, New Brunswick, New Jersey)

  • Endre Boros

    (Rutgers University, New Brunswick, New Jersey)

Abstract

Many transportation networks, e.g., networks of cooperating power systems, and hydrological networks involve a real-valued demand function, defined on the set of nodes, and it is said to be feasible if there exists a flow such that at each node the sum of the incoming flow values is greater than or equal to the demand assigned to this node. By the theorem of D. Gale and A. Hoffman, a system of linear inequalities involving the demand and the arc capacity functions, gives necessary and sufficient condition for the feasibility of the demand. If the demands and/or the arc capacities are random, then an important problem is to find the probability that all these inequalities are satisfied. This paper proposes a new method to eliminate all redundant inequalities for given lower and upper bounds of the demand function, and finds sharp lower and upper bounds for the probability that a feasible flow exists. The results can be used to support transportation network analysis and design.

Suggested Citation

  • András Prékopa & Endre Boros, 1991. "On the Existence of a Feasible Flow in a Stochastic Transportation Network," Operations Research, INFORMS, vol. 39(1), pages 119-129, February.
    • Handle: RePEc:inm:oropre:v:39:y:1991:i:1:p:119-129
    DOI: 10.1287/opre.39.1.119
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    Citations

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    Cited by:

    1. Jia Shu & Haiqing Heng, 2016. "The probability of the existence of a feasible flow in a stochastic transportation network," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(6), pages 479-491, September.
    2. Alper Atamtürk & Muhong Zhang, 2007. "Two-Stage Robust Network Flow and Design Under Demand Uncertainty," Operations Research, INFORMS, vol. 55(4), pages 662-673, August.
    3. András Prékopa & Merve Unuvar, 2015. "Single Commodity Stochastic Network Design Under Probabilistic Constraint with Discrete Random Variables," Operations Research, INFORMS, vol. 63(6), pages 1512-1527, December.
    4. Anna Timonina‐Farkas & René Y. Glogg & Ralf W. Seifert, 2022. "Limiting the impact of supply chain disruptions in the face of distributional uncertainty in demand," Production and Operations Management, Production and Operations Management Society, vol. 31(10), pages 3788-3805, October.
    5. Gergely Mádi-Nagy & András Prékopa, 2004. "On Multivariate Discrete Moment Problems and Their Applications to Bounding Expectations and Probabilities," Mathematics of Operations Research, INFORMS, vol. 29(2), pages 229-258, May.
    6. Talal Alharbi & Anh Ninh & Ersoy Subasi & Munevver Mine Subasi, 2022. "The value of shape constraints in discrete moment problems: a review and extension," Annals of Operations Research, Springer, vol. 318(1), pages 1-31, November.
    7. András Prékopa & Anh Ninh & Gabriela Alexe, 2016. "On the relationship between the discrete and continuous bounding moment problems and their numerical solutions," Annals of Operations Research, Springer, vol. 238(1), pages 521-575, March.
    8. András Prékopa & Anh Ninh & Gabriela Alexe, 2016. "On the relationship between the discrete and continuous bounding moment problems and their numerical solutions," Annals of Operations Research, Springer, vol. 238(1), pages 521-575, March.

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