Maximum probabilistic all-or-nothing paths

Noam Goldberg, Michael Poss

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish
Pages (from-to)279-289
Number of pages11
JournalEuropean Journal of Operational Research
Issue number1
StatePublished - 16 May 2020

Bibliographical note

Publisher Copyright:
© 2019 Elsevier B.V.


  • Dynamic programming
  • Integer non-linear programming
  • Networks


Dive into the research topics of 'Maximum probabilistic all-or-nothing paths'. Together they form a unique fingerprint.

Cite this