中文摘要：

仿照最小费用最大流问题的物理意义,将网络上的费用参数转换成为一种利润参数,提出一个与最小费用最大流问题类似、但意义完全相反的最大利润最小流问题,并建立了该问题的数学规划模型。此外,提出了一个求解该问题最优解的破除可增利润圈算法,该算法通过不断破除网络上的可增利润圈增流,使目标函数值不断增长,最终得到问题的最优解及目标函数值;同时给出了关于该算法正确性的证明过程,并对算法的复杂度进行了分析,最后用示例对算法的求解过程进行了演示。结果表明,该算法能快速有效地求得该问题的最优解及目标函数值,且比一般的线性规划方法更加方便且直观得多。

英文摘要：

This paper presented a maximum profit problem by means of the physical meaning of minimum cost flow theory, and by viewing cost as profit. This problem had a similar framework but different meaning with minimum cost flow theory. Then this paper constructed a mathematical programming mode/for this problem, and proposed a profit cycles-canceling algorithm for solving the model. The algorithm could figure out the optimum solution and the corresponding objective function value of problem by canceling the profit cycles on network. Meanwhile, it proved the accuracy of algorithm and made a complexity analysis for the algorithm. Finally, it demonstrated the solution process for the algorithm by using a study case, The results show that the algorithm can not only figure out the optimum solution and the corresponding objeetive function value of problem rapidly and effectively, but also be more convenient and intuitionistic than general linear programming algorithm.