This paper proposes an outer space branching search method, which is used to globally solve the generalized affine fractional optimization problem (GAFOP). First, we will convert the GAFOP into an equivalent problem (EP). Next, we structure the linear relaxation problem (LRP) of the EP by using the linearization technique. By subsequently partitioning the initial outer space rectangle and successively solving a series of LRPs, the proposed algorithm globally converges to the optimum solution of the GAFOP. Finally, comparisons of numerical results are reported to show the superiority and the effectiveness of the presented algorithm.

This paper presented an efficient algorithm for addressing large-scale linear fractional program problems, which are widely used in hospital management. First of all, we converted the initial problem into an equivalent problem by applying the Charnes-Cooper transformation technique. Next, by directly relaxing the nonlinear constraints, a mixed-integer linear relaxation problem was then constructed. Subsequently, by successively partitioning the initial output space rectangle and solving a series of mixed-integer linear relaxation problems, we proposed an efficient branch-relaxation-bound algorithm for globally addressing large-scale linear fractional program problems for the first time. Moreover, the computation complexity of the algorithm was analyzed, and the maximum number of iterations of the algorithm in the worst-case scenario was estimated. Furthermore, the experimental results demonstrated the high efficiency of the proposed algorithm in solving the investigated large-scale linear fractional program problem.