An alternative method for solving quadratic fractional programming problems with homogenous constraints

In this paper, we use extended simplex method and all solution method for solving quadratic fractional programming (QFP) problems when some of its constraints are homogenous. Swarup's extended simplex method fails to solve QFP problems when some of its constraints are homogenous. So, solving such problems, we first convert this problem into a QFP problem with non-homogeneous constraints and use matrix transformation for this convert. We then choose a new optimizing value with optimality condition and replace new entering value by outgoing value in some sequential tables. This is the way of choosing new basic solutions. We continue this process until we reach the optimality condition. After that we again use matrix transformation to get the final result of the original problem. In addition, we also develop an algorithm with a computer technique (using MATHEMATICA) for solving QFP problems with homogeneous constraints directly. A numerical example is illustrated to demonstrate our methods.