Solving sum-of-ratios fractional programs using efficient points

Constrained maximization of a sum of p > 1 ratios is a difficult nonconvex optimization problem (even if all functions involved are linear) with many applications in management sciences. In this paper, we first give a brief introductory survey of this problem. Then we propose a general branch-and-bound algorithm which uses rectangular partitions in the Euclidean space of dimension p. Theoretically, this algorithm is applicable under very general assumptions. Practically, we give an efficient implementation for affine fractions. Here the bounding procedures use dual constructions and the calculation of efficient points of a corresponding multiple-objective optimization problem. Finally, we present some promising numerical results.