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On the use of the simplex method for a type of allocation problems

Author

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  • Tanaka, Yoshihiro

Abstract

In this study we discuss the use of the simplex method to solve allocation problems whose flow matrices are doubly stochastic. Although these problems can be solved via a 0-1 integer programming method, H.W. Kuhn [4] suggested the use of linear programming in addition to the Hungarian method. Specifically, we use the Birkhoff's theorem to prove that the simplex method enables solving these problems. We also provide insights how to obtain a partition that includes a particular unit.

Suggested Citation

  • Tanaka, Yoshihiro, 2018. "On the use of the simplex method for a type of allocation problems," Discussion paper series. A 331, Graduate School of Economics and Business Administration, Hokkaido University.
    • Handle: RePEc:hok:dpaper:331
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    File URL: http://hdl.handle.net/2115/71733
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    File URL: https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/71733/1/DPA331.pdf
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