Parametric Approaches to Integer Linear Fractional Programming: Computational Study

Abstract

In this paper, we focus on the integer linear fractional optimization problem, a special case of fractional programming where all functions in the objective function and constraints are linear and all variables are bounded and discrete. To derive the optimal solution, the parametric algorithms are considered, and the efficiency of the algorithms is investigated computationally. Unlike traditional parametric algorithms such as Newton's method, which create a unidirectional sequence approaching the optimal function value, our proposed algorithm generates both upper and lower bounds converging to this value. To demonstrate its effectiveness across various production and operations management problems, the suggested algorithms are used to solve the fractional knapsack problem by comparison to other algorithms (e.g., Newton’s method) under the randomized experimental conditions. The relative practical performance measured by the number of function calls demonstrates that the proposed algorithms are fast and robust for solving the linear fractional programs with discrete variables. Leveraging this algorithm holds the potential to overcome situations in traditional production and operations problems where non-fractional objective functions were previously unconsidered, thereby expecting to derive new outcomes and significance.