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<p>In this paper, we propose a Branch–Reduction–Bound (BRB) algorithm to solve fractional multiplicative product programming problems, with the aim of finding globally optimal solutions. The method introduces two innovative linear transformation techniques that simplify the solution process by converting the original problem into two equivalent linear relaxation problems. Building on this, a novel branch-and-delete rule is developed to efficiently manage sub-problem selection using a dynamic priority queue approach, and the computational process is further optimized through a region deletion rule. The synergy of these techniques significantly accelerates the algorithm's convergence rate, providing an efficient global optimization strategy. We compare the BRB algorithm with four other algorithms through numerical experiments, and the results confirm its feasibility, effectiveness, and superior computational efficiency, highlighting its advantages in solving complex optimization problems.</p>

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A Branch–Reduction–Bound algorithm for linear fractional multi-product planning problems

  • 期刊论文

  • 发表日期：

    2025年7月28日

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  • Xianfeng Ding,
  • Meiling Hu

摘要

In this paper, we propose a Branch–Reduction–Bound (BRB) algorithm to solve fractional multiplicative product programming problems, with the aim of finding globally optimal solutions. The method introduces two innovative linear transformation techniques that simplify the solution process by converting the original problem into two equivalent linear relaxation problems. Building on this, a novel branch-and-delete rule is developed to efficiently manage sub-problem selection using a dynamic priority queue approach, and the computational process is further optimized through a region deletion rule. The synergy of these techniques significantly accelerates the algorithm's convergence rate, providing an efficient global optimization strategy. We compare the BRB algorithm with four other algorithms through numerical experiments, and the results confirm its feasibility, effectiveness, and superior computational efficiency, highlighting its advantages in solving complex optimization problems.