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The Transportation Problem (Simplex Method)

  • Loo-Keng Hua
  • Yuan Wang
  • J. G. C. Heijmans
Part of the Mathematical Modeling book series (MMO, volume 2)

Abstract

As far as we know, the graphical method is inefficient if the number of sources, destinations or cycles in a map is comparatively large, and so, in 1958, the simplex method (Dantzig’s method) was also introduced and popularized to the workers in the transportation departments of China. In this chapter, we will illustrate the method following the lecture notes written by Yu Ming-I, Wan Zhe Xian and Wang Yuan in 1958. The notations of the preceding chapter are also used here. Now let us start with the following example.

Keywords

Feasible Solution Lattice Point Transportation Cost Simplex Method Transportation Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Dantzig G. B. Linear Programming and Extensions, Princeton Univ. Press, N.J., 1963.MATHGoogle Scholar
  2. Hitchcock, F.L. Distribution of a Product from several Sources to numerous Localities, J. of Math. Phy, 1941, 224–230.Google Scholar
  3. Kantorowitch L. V. Mathematical Methods in the Organization and Planning of Production, Pub. House of the Leningrad State University, 1939.Google Scholar
  4. Wan Zhe Xian and Wang Yuan. Mathematical Methods in Transportation Problem, Science Press, Beijing, 1959.Google Scholar
  5. Yu Ming-I, Wan Zhe Xian and Wang Yuan etc. (edited). The Theory arud Application of Linear Programming, People’s Education Press, Beijing, 1959.Google Scholar
  6. Bazaraa, M.S. and J.J. Jarvis. Linear Programming and Network Flows. John Wiley & Sons, Inc., 1977.MATHGoogle Scholar
  7. Hillier F.S., and G.J. Lieberman. Introduction to Operations Research. 4-th ed., Holden-Day Inc., 1986.Google Scholar

Copyright information

© Birkhäuser Boston 1989

Authors and Affiliations

  • Loo-Keng Hua
  • Yuan Wang
    • 1
  • J. G. C. Heijmans
    • 2
  1. 1.Academia SinicaInstitute of MathematicsBeijingPeople’s Republic of China
  2. 2.Department of MathematicsUniversity of Texas at ArlingtonArlingtonUSA

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