Solving linear fractional multi-level programs

In this paper, we study the linear fractional multi-level programming problem and prove that an optimal solution to this problem occurs at a boundary feasible extreme point. Hence the Kth-best algorithm can be proposed to solve the problem. We also show that this property can be applied to quasiconcave multi-level problems provided that the first (n-1) level objective functions are explicitly quasimonotonic, otherwise it cannot be proved that there exists a boundary feasible extreme point that solves the LFMP problem.