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

Xianfeng Ding () and Meiling Hu
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Xianfeng Ding: Southwest Petroleum University
Meiling Hu: Southwest Petroleum University

Journal of Combinatorial Optimization, 2025, vol. 50, issue 1, No 8, 21 pages

Abstract: Abstract 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.

Keywords: Linear fractional multiple products; Global optimization; Branch and bound; Linear relaxation (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10878-025-01333-z

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