This paper addresses a new multi-commodity unpaired pickup and delivery vehicle routing problem in which each vehicle is allowed to visit each customer more than once for both pickup and delivery of each commodity. It is a complex variant of the classical capacitated vehicle routing problem and comes from resource transfer among different plants in a distributed manufacturing environment. Notably, the pairing decisions of pickup and delivery for each commodity and the routing decisions among customers are interdependent, and they need to be made simultaneously and collaboratively. Firstly, a mixed integer programming model is developed, and then new valid inequalities are derived to improve the linear programming relaxation. Afterwards, a branch-and-cut algorithm is proposed by exploring different branching strategies and tailored separation algorithms. Computational results based on real-case instances from an automobile manufacturing company demonstrate that the costs are considerably reduced by considering the multiple visits compared to the single visit of each customer. In addition, our proposed branch-and-cut algorithm outperforms a manual solution method adopted by the company in practice and two solution methods in the literature. Furthermore, two adaptations of our branch-and-cut algorithm also perform better than two state-of-the-art algorithms in solving two closely-related problems in terms of solution quality and computation time. Sensitivity analyses with respect to vehicle capacity, vehicle duration, and vehicle speed are conducted to derive several valuable managerial insights.

中文翻译：

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多商品、多次访问的不配对取货和配送车辆路径问题的精确算法

本文解决了一种新的多商品不配对取货和送货车辆路由问题，其中允许每辆车多次拜访每个客户以取货和送货每种商品。它是经典容量车辆路径问题的复杂变体，来自分布式制造环境中不同工厂之间的资源转移。值得注意的是，每种商品的取货和配送的配对决策以及客户之间的路线决策是相互依赖的，并且需要同时协作地做出。首先，开发了混合整数规划模型，然后导出新的有效不等式以改进线性规划松弛。随后，通过探索不同的分支策略和定制的分离算法，提出了分支剪切算法。基于汽车制造公司真实案例的计算结果表明，与每个客户的单次访问相比，考虑多次访问可以大大降低成本。此外，我们提出的分支剪切算法优于公司在实践中采用的手动求解方法和文献中的两种求解方法。此外，在解决两个密切相关的问题时，我们的分支剪切算法的两种改进在解决方案质量和计算时间方面也比两种最先进的算法表现得更好。对车辆容量、车辆持续时间和车辆速度进行敏感性分析，以获得一些有价值的管理见解。