# Revisiting transportation problems under Monge costs with applications to location problems

arXiv: https://arxiv.org/abs/2602.15151 · HTML: https://mlsanity.com/paper/2602.15151/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Feb 2026.

## Built on by (most cited first, 1 of 1)

- [From Cone Geometry to Monge Structure: Local Defects and Global Regret in High-Dimensional Optimal Transport](https://mlsanity.com/paper/2606.04695/) (2026)

## Abstract (arXiv)

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.