Abstract: In the situation that Fourth Party Logistics (4PL) takes the logistics task of many supply-demand pairs, for the uncertainty of duration time, the problem of 4PL many-to-many network design with duration time distributed normally is studied. A chance constrained programming model of 4PL many-to-many network design is formulated, which minimizes the total logistics costs under the constraint of stochastic delivery time. According to the characteristic of the problem, a differential evolution is developed to solve it, and an improved differential evolution is proposed. Finally, several experiments for the problems of different sizes are presented to test the significance of the model as well as the effectiveness of the proposed algorithm.

Key words: Fourth Party Logistics (4PL), many-to-many network design, duration time of normal distribution, chance constrained programming, differential evolution

摘要： 在第四方物流(4PL)承担多个供需点对之间物流任务的情况下，针对处理时间的不确定性，研究考虑正态分布处理时间的4PL多到多网络设计问题。建立了以最小化总物流成本为目标，带有随机配送时间约束的4PL多到多网络设计机会约束规划模型。根据问题特点，设计差分进化算法进行求解，并对其进行改进。最后，通过对不同规模的问题进行仿真实验来证明模型的合理性及算法的有效性。

关键词: 第四方物流, 多到多网络设计, 正态分布处理时间机会约束规划, 差分进化