A simplex algorithm for a class of Leontief flow problems

P. H. Ng, D. K. Wagner

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


A matrix N is Leontief if it has exactly one positive entry per column and there exists a nonnegative x such that Nx > 0. A Leontief flow problem is a linear-programming problem of the form min{c(T)x | Nx = b;x ≤ 0}, where N is a certain type of Leontief matrix. It is shown that for b > 0 this problem can be solved in O(n2Ulog npU) pivots by the simplex method using Dantzig's rule for choosing the entering variable, where n is the number of variables, p is the largest entry of N in absolute value, and U is a valid upper bound on any extreme-point solution. Classes of problems where this is a strongly polynomial bound axe identified.

Original languageEnglish (US)
Pages (from-to)69-75
Number of pages7
JournalMathematical and Computer Modelling
Issue number7
StatePublished - Oct 1996
Externally publishedYes


  • Computational complexity
  • Leontief matrices
  • Linear programming
  • Network flows
  • Simplex algorithm


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