A Comparative Study on Bilevel Fractional Programming Problem in Pricing-Production System Solution
N. A. Ebeid *
Department of Information Systems, Faculty of Computers and Artificial Intelligence, Capital University, Helwan, Egypt.
O. E. Emam
Department of Information Systems, Faculty of Computers and Artificial Intelligence, Capital University, Helwan, Egypt.
H. A. Suleiman
Department of Information Systems, Faculty of Computers and Artificial Intelligence, Capital University, Helwan, Egypt.
*Author to whom correspondence should be addressed.
Abstract
Bilevel fractional programming (BLFP) models combine hierarchical decision-making with efficiency-based objective functions. Such models naturally arise in pricing–production systems where strategic decisions influence operational responses, and performance is evaluated using ratio-based measures. Despite their modeling power, BLFP problems are computationally challenging due to the interaction between the bilevel structure and fractional objectives.
This paper presents a structured comparative study of three solution approaches for BLFP problems: direct enumeration of upper-level decisions, duality-based single-level reformulation, and Charnes–Cooper transformation with mixed-integer linear programming (MILP) reformulation. A pricing–production framework is developed to illustrate the methodology. Numerical experiments demonstrate that although all approaches yield identical optimal solutions for small instances, their computational scalability differs significantly. The MILP reformulation emerges as the most robust and scalable method. The study offers practical insights into the solvability of BLFP models and provides guidance for selecting appropriate solution strategies.
This study contributes by systematically analyzing structural reformulation mechanisms and identifying scalability boundaries for each approach.
Keywords: Bilevel fractional programming, leader–follower optimization, Charnes–cooper transformation, mixed-integer linear programming, pricing strategy, comparative algorithm study