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Maximum probabilistic all-or-nothing paths

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  • Goldberg, Noam
  • Poss, Michael

Abstract

We consider the problem of a maximum probabilistic all-or-nothing network path. Each arc is associated with a profit and a probability and the objective is to select a path with maximum value for the product of probabilities multiplied by the sum of arc profits. The problem can be motivated by applications including serial-system design or subcontracting of key project activities that may fail. When subcontracting such critical success activities, each must be completed on time, according to the specs, and in a satisfactory manner in order for the entire project to be deemed successful. We develop a dynamic programming (DP) method for this problem in the acyclic graph setting, under an independence assumption. Two different fully-polynomial approximation schemes are developed based on the DP formulations, one of which applies repeated rounding and scaling to the input data, while the other uses only rounding. In experiments we compare the DP approach with mixed-integer nonlinear programming (MINLP) using a branch-and-cut method, on synthetic randomly generated instances as well as realistic ones.

Suggested Citation

  • Goldberg, Noam & Poss, Michael, 2020. "Maximum probabilistic all-or-nothing paths," European Journal of Operational Research, Elsevier, vol. 283(1), pages 279-289.
    • Handle: RePEc:eee:ejores:v:283:y:2020:i:1:p:279-289
    DOI: 10.1016/j.ejor.2019.11.011
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    References listed on IDEAS

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    1. Soroush, H. M., 1994. "The most critical path in a PERT network: A heuristic approach," European Journal of Operational Research, Elsevier, vol. 78(1), pages 93-105, October.
    2. Icmeli-Tukel, Oya & Rom, Walter O., 1997. "Ensuring quality in resource constrained project scheduling," European Journal of Operational Research, Elsevier, vol. 103(3), pages 483-496, December.
    3. Rebi Daldal & Iftah Gamzu & Danny Segev & Tonguç Ünlüyurt, 2016. "Approximation algorithms for sequential batch‐testing of series systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(4), pages 275-286, June.
    4. Noam Goldberg, 2017. "Non‐zero‐sum nonlinear network path interdiction with an application to inspection in terror networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(2), pages 139-153, March.
    5. Mordechai I. Henig, 1994. "Efficient Interactive Methods for a Class of Multiattribute Shortest Path Problems," Management Science, INFORMS, vol. 40(7), pages 891-897, July.
    6. Arthur Warburton, 1987. "Approximation of Pareto Optima in Multiple-Objective, Shortest-Path Problems," Operations Research, INFORMS, vol. 35(1), pages 70-79, February.
    7. Yosi Ben-Dov, 1981. "Optimal Testing Procedures for Special Structures of Coherent Systems," Management Science, INFORMS, vol. 27(12), pages 1410-1420, December.
    8. David Pisinger, 1997. "A Minimal Algorithm for the 0-1 Knapsack Problem," Operations Research, INFORMS, vol. 45(5), pages 758-767, October.
    9. John P. Dickerson & Ariel D. Procaccia & Tuomas Sandholm, 2019. "Failure-Aware Kidney Exchange," Management Science, INFORMS, vol. 65(4), pages 1768-1791, April.
    10. Refael Hassin, 1992. "Approximation Schemes for the Restricted Shortest Path Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 36-42, February.
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    Cited by:

    1. Lee, Jisun & Joung, Seulgi & Lee, Kyungsik, 2022. "A fully polynomial time approximation scheme for the probability maximizing shortest path problem," European Journal of Operational Research, Elsevier, vol. 300(1), pages 35-45.

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