Programming with linear fractional functionals
Programming with linear fractional functionals
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DOI：
10.1002/nav.3800150308
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发表时间：
1968-09
期刊：
影响因子：
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通讯作者：
Stanley Zionts
中科院分区：
文献类型：
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作者：
Stanley Zionts
Charnes和库珀[1]证明了具有线性分式目标函数的线性规划问题可以通过最多求解两个普通线性规划问题来求解。此外，他们还证明了，在先验已知目标函数的分母在可行域中具有唯一符号的情况下，只需要解决一个问题。在本说明中，它表明，如果有限的解决方案的问题存在，只有一个线性规划问题必须解决。这是因为分母在可行域中不能有两个不同的符号，除非在不具有实际重要性的情况下。
Charnes and Cooper [1] showed that a linear programming problem with a linear fractional objective function could be solved by solving at most two ordinary linear programming problems. In addition, they showed that where it is known a priori that the denominator of the objective function has a unique sign in the feasible region, only one problem need be solved. In the present note it is shown that if a finite solution to the problem exists, only one linear programming problem must be solved. This is because the denominator cannot have two different signs in the feasible region, except in ways which are not of practical importance.