考虑到普通带时间窗约束的车辆路径问题 (vehicle routing problem with time windows, VRPTW) 模型不能真正反映顾客对时间的偏好, 故在车辆路径优化模型的基础上, 结合顾客时间满意度函数, 同时放松需求点经过即被服务的约束限制, 允许多次经过同一需求点的情况发生, 而需求点只能被同一辆车服务一次, 建立了基于顾客时间满意度的车辆配送 (vehicle routing problem with satisfaction, VRPWS) 模型, 并利用模拟退火算法编程求解. 为验证 VRPWS 模型的有效性 进行了数值实验. 实验结果表明: 与传统的带软时间窗约束的车辆路径优化 (vehicle routing problems with soft time window, VRPSTW) 模型和 VRPTW 相比, VRPWS 模型配送效益提升了 170.0% 和 3.2%. 分析结果表明该工作在一定程度上有助于物流企业在配送过程中提高顾客满意度和降低运输成本.

Considering the fact that the common vehicle routing problem model with time window (VRPTW) constraint cannot truly reflect customers' preferences of time, a modified vehicle routing optimization model based on customer time satisfaction function (vehicle routing problem with satisfaction (VRPWS) model) has been proposed. This new model is designed by relaxing the restriction that each demand point should be served if passed so as to allow vehicles to pass all demand points many times. And the simulate anneal algorithm is used to solve this problem. In order to illustrate the validity of VRPWS, a numerical example has been introduced. Through the numerical simulation and calculation, it is found that the VRPWS model is superior to the traditional vehicle routing optimization model with soft time window (VRPSTW) constraints and the vehicle routing optimization model with time window constraints in that it increases the delivery revenue by 170.0% and 3.2% respectively. This study helps logistics enterprises to improve their customer satisfaction and reduce their transportation costs in the delivery process.