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由于网络设计决策的长期性,许多参数会随时间而变化,因此在交通运输网络设计问题中考虑不确定性因素至关重要。研究了在交通运输网络中边的容量有随机损失时的鲁棒性网络设计问题。边的容量损失是指实际运行时的可用容量小于初始设立的容量。假设容量损失是1个随机变量,首先建立了带有机会约束的鲁棒性交通运输网络设计模型,然后利用Hoeffding’s不等式对机会约束进行了安全近似,将问题转化为一般的混合整数规划问题。鲁棒性模型使得当容量有波动时,网络仍以一定的概率正常运行。最后通过数值算例比较了单源和多源2种网络结构下网络设计的最优成本,并分析了成本与鲁棒性之间的关系,同时对容量的不确定性水平做了敏感性分析。
Due to the long-term nature of network design decisions, many of the parameters change over time, so it is important to consider the uncertainties in the transport network design issue. The problem of robust network design is studied when there is a random loss of capacity in the transport network. The capacity loss of the edge means that the available capacity of the actual operation is less than the initially set capacity. Assuming that capacity loss is a random variable, we first establish a robust transport network design model with chance constraints and then use Hoeffding’s inequality to make a safety approximation of chance constraints, which transforms the problem into a general mixed integer programming problem. The robust model allows the network to operate normally with a certain probability when the capacity fluctuates. Finally, a numerical example is given to compare the optimal cost of network design under single-source and multi-source network structures. The relationship between cost and robustness is also analyzed. At the same time, sensitivity analysis of the uncertainty of capacity is made .