Skip to main content
SpringerLink
Log in

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

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

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 R1 is one example. It is found that the average distance traveled by an item in the TLP increases with N1/2; 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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Daganzo, C.F. (1984a). “The Length of Tours in Zones of Different Shapes.” Trans. Res. B 18B, 135–146.

    Article  Google Scholar 

  • Daganzo, C.F. (1984b). “The Distance Traveled to Visit N Points With a Maximum of C Stops Per Vehicle: An Analytic Model and an Application.” Transportation Science 18(4), 331–350.

    Google Scholar 

  • Daganzo, C.F. and K. Smilowitz. (2000). “Asymptotic Approximations for the Transportation LP and Other Scalable Network Problems.” ITS Working Paper, University of California, Berkeley; www.ce.berkeley.edu/Programs/Transportation/Daganzo/tlp.pdf;revised as

  • Daganzo, C.F. and K. Smilowitz. (2004). “Bounds and Approximations for the Transportation LP.” Transportation Science, 38(3), 343–356.

    Article  Google Scholar 

  • Eilon, S., C.D.T. Watson-Gandy, and N. Christofides. (1971). Distribution Management: Mathematical Modelling and Practical Analysis, Hafner, NY, NY.

  • Feller, W. (1971). An Introduction to Probability Theory and Applications, Vol.2. Wiley, NY,NY.

  • Haimovich, M.A., A.H.G. Rinnooy-Kan, and L. Stougie. (1985). “Bounds and Heuristics for Capacitated Routing Problems.” Math. Opns. Res, 10, 527–542.

    Google Scholar 

  • Karp, R.M. (1977). “Probabilistic Analysis of Partitioning Algorithms for the Traveling Salesman Problem.” Math. Opns. Res. 2, 209–224.

    Article  Google Scholar 

  • Newell, G.F. and C.F. Daganzo. (1986). “Design of Multiple Vehicle Delivery Tours-1: A Ring-Radial Network.” Trans. Res. B, 20B(5), 345–364.

    Article  Google Scholar 

  • Newell, G.F. and C.F. Daganzo. (1986a). “Design of Multiple Vehicle Delivery Tours-II: Other Metrics.” Trans. Res. B. 20B(5), 365–376.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Transportation Studies and Department of Civil and Environmental Engineering, Evanston, IL, USA, 60208-3119

    Carlos F. Daganzo

  2. Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL, USA, 60208-3119

    Karen R. Smilowitz

  3. Technological Institute M233, 2145 Sheridan Road, Evanston, IL, USA, 60208-3119

    Karen R. Smilowitz

Authors
  1. Carlos F. Daganzo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Karen R. Smilowitz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Karen R. Smilowitz.

Additional information

Research supported in part by the University of California Transportation Center.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Daganzo, C.F., Smilowitz, K.R. A note on asymptotic formulae for one-dimensional network flow problems. Ann Oper Res 144, 153–160 (2006). https://doi.org/10.1007/s10479-006-0010-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-006-0010-2

Keywords

Search

Navigation