The stochastic Eulerian tour problem

Srimathy Mohan, Michel Gendreau, Jean Marc Rousseau

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


This paper defines the stochastic Eulerian tour problem (SETP) and investigates several characteristics of this problem. Given an undirected Eulerian graph G = (V, E), a subset R (\R\ = n) of the edges in E that require service, and a probability distribution for the number of edges in R that have to be visited in any given instance of the graph, the SETP seeks an a priori Eulerian tour of minimum expected length. We derive a closed-form expression for the expected length of a given Eulerian tour when the number of required edges that have to be visited follows a binomial distribution. We also show that the SETP is NP-hard, even though the deterministic counterpart is solvable in polynomial time. We derive further properties and a worst-case ratio of the deviation of the expected length of a random Eulerian tour from the expected length of the optimal tour. Finally, we present some of the desirable properties in a good a priori tour using illustrative examples.

Original languageEnglish (US)
Pages (from-to)166-174
Number of pages9
JournalTransportation Science
Issue number2
StatePublished - May 2008


  • Arc routing
  • Eulerian tour problem
  • Stochastic demand

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Transportation


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