# Assignment-Routing Optimization: Solvers for Problems Under Constraints

arXiv: https://arxiv.org/abs/2512.18618 · HTML: https://mlsanity.com/paper/2512.18618/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 9 references that are in the map.
- First posted on arXiv 21 Dec 2025.

## Builds on (most cited first, 2 of 2)

- [Assignment-Routing Optimization with Cutting-Plane Subtour Elimination: Solver and Benchmark Dataset](https://mlsanity.com/paper/2510.17888/) (2025)
- [An Efficient and Almost Optimal Solver for the Joint Routing-Assignment Problem via Partial JRA and Large-α Optimization](https://mlsanity.com/paper/2511.09563/) (2025)

## Abstract (arXiv)

We study the Joint Routing-Assignment (JRA) problem in which items must be assigned one-to-one to placeholders while simultaneously determining a Hamiltonian cycle visiting all nodes exactly once. Extending previous exact MIP solvers with Gurobi and cutting-plane subtour elimination, we develop a solver tailored for practical packaging-planning scenarios with richer constraints.These include multiple placeholder options, time-frame restrictions, and multi-class item packaging. Experiments on 46 mobile manipulation datasets demonstrate that the proposed MIP approach achieves global optima with stable and low computation times, significantly outperforming the shaking-based exact solver by up to an orders of magnitude. Compared to greedy baselines, the MIP solutions achieve consistent optimal distances with an average deviation of 14% for simple heuristics, confirming both efficiency and solution quality. The results highlight the practical applicability of MIP-based JRA optimization for robotic packaging, motion planning, and complex logistics .