A complete algorithm for linear fractional programs

• Published in: Computers & mathematics with applications (1987) Vol. 20; no. 7; pp. 11 - 23
• Main Authors: Arsham, H., Kahn, A.B.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 1990; Elsevier
• Subjects: Applied sciences; Exact sciences and technology; Mathematical programming; Operational research and scientific management; Operational research. Management science; Redundancy; Economic function; Simplex method; Linear programming; Feasibility; Fractional programming; Algorithm; Mathematical programming; Numerical example
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/0898-1221(90)90344-J

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.