在大规模自然灾害发生时，救援人员经常面临不确定的需求和信息网络中断。而在科学研究层面，大多数关于人道主义救援的模型大都继承了商业模型中的一些特点，并未充分考虑在救援过程中的实际问题。基于救援过程中的有限历史数据和极大不确定性，本文假设在救援过程中所面临的需求和提前期为均匀分布，研究救援物资的最优订货量问题。首先，提出了单周期、多周期和无限周期的随机报童模型，随后给出了三种模型的理论解析解。通过解析证明、数值计算和蒙特卡洛模拟三种方法，发现最优救援订货量可能随着提前期波动的增大而减小，并非常规认为的单调增大。利用随机占优理论，本文就最优救援订货量与提前期波动之间的关系进行了进一步探讨，证明了在提前期内需求的分布情况满足一定条件时，最优订货量与提前期波动之间可能存在上述不确定关系。

Nowadays, humanitarian disasters such as large-scale earthquakes face irregular demand and communication network disruption. On the other hand, existing models in humanitarian logistics inherit commercial logistics which are not practical in real world phenomenon. In the paper we develop a series of newsboy models with uniformly distributed lead time and demand which is appropriate when there are limited historical data about relief operations, including a single period model, a multi-period model and an infinite period model. The closed-formed and approximation solution of the optimal relief order quantity are derived. The effect of lead time uncertainty on the optimal solution is tested analytically. This paper also simulates the model based on the Monte Carlo methods. Both of the analytical and simulation results suggest that lead time uncertainty may lead to an increase or decrease in relief order quantity, which depends on the coefficient of variation of lead time. In the end, proofs based on stochastic dominance give a reasonable explanation for the relationship between order quantity and lead time uncertainty. Finally, the conclusions are drawn and future research directions are outlined.