@article{Ge2025, 
author = {Zhiguo Ge and Hongwei Jiao},
title = {Efficient algorithm for addressing large-scale linear fractional program problems},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {9},
pages = {21004-21024},
keywords = {large-scale linear fractional program, global optimization, branch-and-bound algorithm, computation complexity},
url = {https://www.sciopen.com/article/10.3934/math.2025938},
doi = {10.3934/math.2025938},
abstract = {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.}
}