Revisiting transportation problems under Monge costs with applications to location problems
Abstract
We investigate the transportation problem under a Monge cost structure and derive compact formulas for optimal dual solutions based on the northwest-corner rule. As an application illustrating how these formulas yield structural insight while enhancing computational performance, we consider a broad class of facility location problems. In particular, the expressions are used within a Benders decomposition framework to derive novel formulations for the Discrete Ordered Median Problem with non-increasing weights. Numerical experiments validate that the resulting formulations achieve state-of-the-art performance and exhibit strong robustness across a wide range of instances.
Cite
@article{arxiv.2602.15151,
title = {Revisiting transportation problems under Monge costs with applications to location problems},
author = {Stefan Nickel and Justo Puerto and Simon Ramoser and Alberto Torrejon},
journal= {arXiv preprint arXiv:2602.15151},
year = {2026}
}
Comments
59 pages, 3 figures, 3 tables. Includes supplementary material with detailed numerical results. Minor revisions: corrected typos, updated keywords, and small revisions to Section 4. Results and conclusions remain unchanged