Integrated optimisation of production scheduling and distribution decision is necessary for reducing the whole cost of the supply chain in the make-to-order business environment. This paper studies a new integrated production scheduling and vehicle routing problem (IPSVRP) with inventory holding, delivery, and tardiness costs. The considered IPSVRP is modelled as a triple-objective optimisation problem, where the first objective aims to obtain the minimal total holding cost in the inventory, the second one attempts to achieve the minimal total travelling cost, and the third one tries to acquire the minimal total tardiness cost. To obtain a set of diverse non-dominated solutions in the Pareto-optimal front of the problem, we first derive several key structural properties used to provide necessary conditions for any solution to be Pareto-optimal through theoretical investigation. Based on the derived structural properties, a level-based multi-objective particle swarm optimizer (LMPSO) is subsequently designed. The performance of LMPSO is analysed by conducting a set of experiments, and its superiority is verified through comparing with other optimisation algorithms. Moreover, the convergence behaviour of LMPSO is also investigated, and the experimental results prove that it has the ability to achieve a set of non-dominated solutions proximity to the true Pareto front.

生产调度和配送决策的综合优化对于降低按订单生产的商业环境中供应链的整体成本是必要的。本文研究了一个新的集成生产调度和车辆路线问题 (IPSVRP)，其中包含库存持有、交付和迟到成本。考虑的IPSVRP被建模为三目标优化问题，其中第一个目标旨在获得库存中的最小总持有成本，第二个目标试图实现最小的总旅行成本，第三个目标试图获得最小的总迟到成本。为了在问题的帕累托最优前沿获得一组不同的非支配解，我们首先通过理论研究推导出几个关键的结构特性，这些特性用于为任何解决方案成为帕累托最优提供必要条件。基于导出的结构特性，随后设计了基于水平的多目标粒子群优化器（LMPSO）。通过一组实验分析了LMPSO的性能，并通过与其他优化算法的比较验证了其优越性。此外，还研究了 LMPSO 的收敛行为，实验结果证明它有能力实现一组接近真实 Pareto 前沿的非支配解。通过一组实验分析了LMPSO的性能，并通过与其他优化算法的比较验证了其优越性。此外，还研究了 LMPSO 的收敛行为，实验结果证明它有能力实现一组接近真实 Pareto 前沿的非支配解。通过一组实验分析了LMPSO的性能，并通过与其他优化算法的比较验证了其优越性。此外，还研究了 LMPSO 的收敛行为，实验结果证明它有能力实现一组接近真实 Pareto 前沿的非支配解。