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

翻译：本文研究一个联合路径-分配优化问题：在将一组物品与一组占位符进行一一配对的同时，需确定一条访问每个节点恰好一次的哈密顿回路。分配决策与路径决策被联合优化，以最小化总旅行成本。本研究提出采用精确混合整数规划（MIP）配合Gurobi求解器的方法来解决该问题，其中包含割平面子回路消除策略。通过对计算复杂度的分析以及大量实验，我们剖析了该方法随问题规模扩大而显现的计算局限性，并揭示了针对更大规模实例需要更高效算法所面临的挑战。本文提供的数据集、数学模型及实验结果，可作为该研究领域未来工作的基准参考。GitHub仓库：https://github.com/QL-YUAN/Joint-Assignment-Routing-Optimization