A complete algorithm for linear fractional programs

Abstract The linear fractional programming (LFP) algorithms attempt to optimize a quotient of two linear functions subject to a set of linear constraints. The existing LFP algorithms are problem dependent and none is superior to others in all cases. These algorithms explicitly require: (i) the denominator of the objective function does not vanish in the feasible region; (ii) the denominator of the objective function is positive; (iii) the feasible region is bounded. Moreover, some of these algorithms fail whenever: (iv) some constraints are redundant. We present a simplex type algorithm which is compact and efficiently detects conditions (i)-(iii) and relaxes assumption (iv). The proposed algorithm is evolutionary in the sense that it builds up in a systematic manner to solve any LFP type problems. Numerical examples illustrate the algorithm.