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Investing in the Links of a Stochastic Network to Minimize Expected Shortest Path. Length

Author

Listed:
  • Viswanath, Kannan
  • Peeta, Srinivas
  • Salman, Sibel F.

Abstract

We consider a network whose links are subject to independent, random failures due to a disruptive event. The survival probability of a link is increased, if it is strengthened by investment. A given budget is to be allocated among the links with the objective of optimizing the post-event performances of the network. Specifically, we seek to minimize the expected shortest path Length between a specified origin node and destination node in the network. This criterion is defined through the use of a fixed penalty cost for those network realizations in the expectation, that do not have a path connecting the origin node to the destination node. This problem type arises in the pre-disasters, by upgrading its weakest elements. We model the problem as a two-stage stochastic program in which the underlying probability distribution of the random variables is dependent on the first stage decision variables. Using a path-based approach we construct its equivalent deterministic program and derive structural results for the objective function. We then propose an approximate solution procedure based on a first order approximation the objective function. The procedure is tested by numerical experiments on a small-size network. The test results show that it yields very good performance on the instances solved.

Suggested Citation

  • Viswanath, Kannan & Peeta, Srinivas & Salman, Sibel F., 2004. "Investing in the Links of a Stochastic Network to Minimize Expected Shortest Path. Length," Purdue University Economics Working Papers 1167, Purdue University, Department of Economics.
    • Handle: RePEc:pur:prukra:1167
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    Cited by:

    1. Miloš Kopa & Tomáš Rusý, 2021. "A decision-dependent randomness stochastic program for asset–liability management model with a pricing decision," Annals of Operations Research, Springer, vol. 299(1), pages 241-271, April.
    2. Bora Tarhan & Ignacio Grossmann & Vikas Goel, 2013. "Computational strategies for non-convex multistage MINLP models with decision-dependent uncertainty and gradual uncertainty resolution," Annals of Operations Research, Springer, vol. 203(1), pages 141-166, March.
    3. Stefano Starita & M. Paola Scaparra & Jesse R. O’Hanley, 2017. "A dynamic model for road protection against flooding," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(1), pages 74-88, January.
    4. Lars Hellemo & Paul I. Barton & Asgeir Tomasgard, 2018. "Decision-dependent probabilities in stochastic programs with recourse," Computational Management Science, Springer, vol. 15(3), pages 369-395, October.
    5. Qingxia Kong & Shan Li & Nan Liu & Chung-Piaw Teo & Zhenzhen Yan, 2020. "Appointment Scheduling Under Time-Dependent Patient No-Show Behavior," Management Science, INFORMS, vol. 66(8), pages 3480-3500, August.
    6. Yueyue Fan & Changzheng Liu, 2010. "Solving Stochastic Transportation Network Protection Problems Using the Progressive Hedging-based Method," Networks and Spatial Economics, Springer, vol. 10(2), pages 193-208, June.
    7. Kopa, Miloš & Rusý, Tomáš, 2023. "Robustness of stochastic programs with endogenous randomness via contamination," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1259-1272.
    8. Solak, Senay & Clarke, John-Paul B. & Johnson, Ellis L. & Barnes, Earl R., 2010. "Optimization of R&D project portfolios under endogenous uncertainty," European Journal of Operational Research, Elsevier, vol. 207(1), pages 420-433, November.

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