Assignment-Routing Optimization: Solvers for Problems Under Constraints

TL;DR

This paper introduces a specialized MIP solver for the Joint Routing-Assignment problem, effectively handling complex constraints and outperforming existing methods in robotic packaging and logistics scenarios.

Contribution

Develops a tailored MIP solver for JRA problems with richer constraints, demonstrating superior performance over existing solvers in practical applications.

Findings

Achieves global optima with low computation times.

Outperforms shaking-based solvers by up to an order of magnitude.

Maintains solution quality close to optimal with 14% deviation.

Abstract

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 .