The pickup and delivery problem with transshipments (PDP-T) is generalized from the classical pickup and delivery problem (PDP) by allowing the transfer of requests between vehicles. After considering the time window constraints, the PDP-T is further generalized to the pickup and delivery problem with time windows and transshipments (PDPTW-T). In this paper, we review two state-of-the-art models for the PDP-T and PDPTW-T. We point out the possible issues existing in the models and provide our revisions. In addition, we develop a new mixed-integer linear programming formulation to solve the PDP-T and PDPTW-T. The performance of the proposed model is evaluated by solving 340 generated PDP-T instances and 360 open-access PDPTW-T instances. Computational results show that the proposed model outperforms the existing models in terms of solution quality and computing time. PTP-T instances with up to 25 requests and 2 transfer stations are solved to optimality by using the proposed model. As a comparison, the best-known benchmarks in the literature are instances with 5 requests and 1 transfer station. In addition, the computing time is significantly reduced. In our experiments, the average computational time for solving PDP-T is reduced by 96%. For PDPTW-T instances, the solvable scale is increased from 3 requests and 4 transfer stations to 5 requests and 4 transfer stations. The average computing time is reduced by 40%.

转运的取货和交付问题 (PDP-T) 是从经典的取货和交付问题 (PDP) 推广而来的，它允许在车辆之间传输请求。在考虑时间窗约束后，PDP-T 进一步推广到有时间窗和转运的提货和交付问题（PDPTW-T）。在本文中，我们回顾了 PDP-T 和 PDPTW-T 的两个最先进的模型。我们指出模型中可能存在的问题并提供我们的修订。此外，我们开发了一种新的混合整数线性规划公式来求解 PDP-T 和 PDPTW-T。通过求解 340 个生成的 PDP-T 实例和 360 个开放访问的 PDPTW-T 实例来评估所提出模型的性能。计算结果表明，所提出的模型在解决方案质量和计算时间方面优于现有模型。通过使用所提出的模型，可以优化具有多达 25 个请求和 2 个中转站的 PTP-T 实例。作为比较，文献中最著名的基准是具有 5 个请求和 1 个中转站的实例。此外，计算时间显着减少。在我们的实验中，求解 PDP-T 的平均计算时间减少了 96%。对于 PDPTW-T 实例，可解决规模从 3 个请求和 4 个中转站增加到 5 个请求和 4 个中转站。平均计算时间减少 40%。文献中最著名的基准是具有 5 个请求和 1 个中转站的实例。此外，计算时间显着减少。在我们的实验中，求解 PDP-T 的平均计算时间减少了 96%。对于 PDPTW-T 实例，可解决规模从 3 个请求和 4 个中转站增加到 5 个请求和 4 个中转站。平均计算时间减少 40%。文献中最著名的基准是具有 5 个请求和 1 个中转站的实例。此外，计算时间显着减少。在我们的实验中，求解 PDP-T 的平均计算时间减少了 96%。对于 PDPTW-T 实例，可解决规模从 3 个请求和 4 个中转站增加到 5 个请求和 4 个中转站。平均计算时间减少 40%。