This study investigates a joint optimisation of routing and truck deployment for a small-package shipping company. Bus tour-based services are provided to collect express packages at customer bases. The objective of the optimisation problem is to minimise the average waiting time for packages stored at the customer bases. We first propose a mixed-integer nonlinear programming model. The proposed formulation is linearised and made solvable by an off-the-shelf mixed-integer linear programming solver. For solving larger instances of the problem, we propose two optimisation approaches that can obtain near-optimal solutions – a local branching-based method and a particle swarm optimisation-based method. We conduct numerical experiments to validate the effectiveness and efficiency of the proposed solution methods. The results indicate that both methods can obtain optimal solutions quickly for most of the small-scale instances. For medium-size instances, the local branching-based method performs best, and the PSO-based method outperforms the others for large-size instances.

本研究调查了一家小型运输公司的路线和卡车部署联合优化。提供基于巴士旅行的服务，以在客户群中收集快递包裹。优化问题的目的是最小化存储在客户群中的包裹的平均等待时间。我们首先提出一个混合整数非线性规划模型。所提出的公式是线性的，并且可以通过现成的混合整数线性规划求解器求解。为了解决更大的问题，我们提出了两种可以获得最佳解决方案的优化方法-基于局部分支的方法和基于粒子群优化的方法。我们进行数值实验，以验证所提出的解决方法的有效性和效率。结果表明，这两种方法都可以针对大多数小规模实例快速获得最佳解决方案。对于中型实例，基于本地分支的方法效果最佳，而对于大型实例，基于PSO的方法要优于其他方法。