Assignment-Routing Optimization with Cutting-Plane Subtour Elimination: Solver and Benchmark Dataset

TL;DR

This paper introduces an exact MIP-based method with cutting-plane techniques for a joint assignment-routing problem, analyzes its computational limits, and provides a benchmark dataset for future research.

Contribution

It presents a novel MIP formulation with subtour elimination for joint assignment and routing, along with a benchmark dataset and analysis of computational challenges.

Findings

The method effectively solves small to medium instances.

Computational complexity increases rapidly with problem size.

Benchmark dataset facilitates future research in assignment-routing problems.

Abstract

We study a joint routing-assignment optimization problem in which a set of items must be paired one-to-one with a set of placeholders while simultaneously determining a Hamiltonian cycle that visits every node exactly once. Both the assignment and routing decisions are optimized jointly to minimize the total travel cost. In this work, we propose a method to solve this problem using an exact MIP formulation with Gurobi, including cutting-plane subtour elimination. With analysis of the computational complexity and through extensive experiments, we analyze the computational limitations of this approach as the problem size grows and reveal the challenges associated with the need for more efficient algorithms for larger instances. The dataset, formulations, and experimental results provided here can serve as benchmarks for future studies in this research area. GitHub repository: https://github.com/QL-YUAN/Joint-Assignment-Routing-Optimization