A solution approach to the multi-level linear fractional programming problems
چکیده
In this paper, we consider multi-level linear fractional programming problems over a bounded polytope set. We present a characterization of the optimum solution to the $n$-level linear fractional programming problem for case $n > 2$. Then, we propose an extension of the $K$th-best algorithm, for solving the $n$-level linear fractional programming problem with $n > 2$, and prove its convergence. Furthermore, we consider a previously published paper on such problems. It is shown that some results and proofs presented in that paper are incorrect by providing a counterexample. Finally, some numerical examples are presented, and the results are compared to those obtained from existing methods to show the accuracy and efficiency of the proposed algorithm.
