Accelerated Benders decomposition for bi-objective mixed integer programming
Abstract
We investigate bi-objective mixed integer programming to which Benders decomposition can be applied, a widely used technique for exploiting problem structures in real-world applications. Our study focuses on a sustainable supply chain network design problem that aims to minimise both economic and environmental objectives. To address the bi-objective nature, we employ the weighted sum method, which requires solving similar problems repeatedly with different weight values. To tackle this, we propose a straightforward acceleration technique that reuses Benders cuts generated in previous iterations of the weighted sum method. This approach enables the Benders decomposition master problem to be initialised with pre-generated cuts. Our computational experiments demonstrate that reusing these cuts significantly reduces computing time.
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BibTeX
@misc{an2026accelerated,
title = {{Accelerated Benders decomposition for bi-objective mixed integer programming}},
author = {Duleabom An and Chungmok Lee and Sophie N. Parragh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04070},
eprint = {2610.04070},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04070},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Accelerated Benders decomposition for bi-objective mixed integer programming
AU - Duleabom An
AU - Chungmok Lee
AU - Sophie N. Parragh
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.04070
UR - https://arxiv.org/abs/2610.04070
AB - We investigate bi-objective mixed integer programming to which Benders decomposition can be applied, a widely used technique for exploiting problem structures in real-world applications. Our study focuses on a sustainable supply chain network design problem that aims to minimise both economic and environmental objectives. To address the bi-objective nature, we employ the weighted sum method, which requires solving similar problems repeatedly with different weight values. To tackle this, we propose a straightforward acceleration technique that reuses Benders cuts generated in previous iterations of the weighted sum method. This approach enables the Benders decomposition master problem to be initialised with pre-generated cuts. Our computational experiments demonstrate that reusing these cuts significantly reduces computing time.
ER -