A solution approach to the multi-level linear fractional programming problems

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 30 تیر 1404

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.92296.1600

نویسندگان

Akram Baghalnezhad؛ Habibe Sadeghi^*

Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.

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.

کلیدواژه‌ها

Linear fractional programming؛ Multi-level programming؛ Vertex point؛ $K$th-best algorithm