On a fractional minimal cost flow problem on networks

摘要

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.