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On a fractional minimal cost flow problem on networks

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Abstract

In a recent paper, (see Xu et al. in Optim. Lett. 5(2):307–317, 2011) presented an algorithm for solving linear fractional programming problems over networks, and proposed and analyzed a dual formulation for this problem. This note shows that the algorithm of Xu et al. is precisely that of Gilmore and Gomory (Oper. Res. 11(6):863–888, 1963), and the related duality results follow directly by adopting the transformation of Charnes and Cooper (Naval Logist. Q. 9(3–4):181–186, 1962) to equivalently rewrite the linear fractional program as a linear program and then applying linear programming duality.

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References

  1. Bazaraa M.S., Jarvis J.J., Sherali H.D.: Linear programming and network flows, 4th edn. John Wiley and Sons, New York (2010)

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  2. Bazaraa M.S., Sherali H.D., Shetty C.M.: Nonlinear programming: theory and algorithms, 3rd edn. John Wiley and Sons, New York (2006)

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  1. Grado Department of Industrial and Systems Engineering (0118), Virginia Tech, 250 Durham Hall, Blacksburg, VA, 24061, USA

    Hanif D. Sherali

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  1. Hanif D. Sherali
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Correspondence to Hanif D. Sherali.

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Sherali, H.D. On a fractional minimal cost flow problem on networks. Optim Lett 6, 1945–1949 (2012). https://doi.org/10.1007/s11590-011-0364-5

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  • DOI: https://doi.org/10.1007/s11590-011-0364-5

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