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Abstract The optimization of integer linear plus linear fractional programs (ILLFPs) presents significant challenges in the research field. This study introduces two innovative methods designed to efficiently address the non-convex and non-linear characteristics of ILLFPs. The first method proposed is an implicit exploration or branch and cut approach, which systematically explores the problem domain until the optimal solution is attained. The second method is a parametric approach that employs a linear integer program, adjusting parameter values until the solution matches the optimal solution of the ILLFP. Computational experiments were conducted using randomly generated instances to evaluate the effectiveness of these methods. The results indicate that the parametric approach outperforms the branch and cut method.
Cherfaoui et al. (Mon,) studied this question.