A note on asymptotic formulae for one-dimensional network flow problems

Carlos Daganzo and Karen Smilowitz ()

Annals of Operations Research, 2006, vol. 144, issue 1, 153-160

Abstract: This note develops asymptotic formulae for single-commodity network flow problems with random inputs. The transportation linear programming problem (TLP) where N points lie in a region of R 1 is one example. It is found that the average distance traveled by an item in the TLP increases with N 1/2 ; i.e., the unit cost is unbounded when N and the length of the region are increased in a fixed ratio. Further, the optimum distance does not converge in probability to the average value. These one-dimensional results are a useful stepping stone toward a network theory for two and higher dimensions. Copyright Springer Science+Business Media, LLC 2006

Keywords: Transportation problem; Distance approximations (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/s10479-006-0010-2

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