基于时空网络的铁路空车调配动态优化模型

为合理配置空车资源，研究了路局（公司）管内空车调配的动态优化问题。构建区分时段长度的时空网络，以准确描述车站作业能力的变化。借鉴运输问题（TP）的基本思想，通过引入空车供需约束，将动态空车调配问题转化为基于时空网络的多商品网络流问题。结合空车调配的特点，设置2组整数决策变量，将分界站排空与局（公司）管内配空分开考虑。设置0-1辅助变量构建车种代用约束。在此基础上，以总费用最小为目标，构建了空车调配动态优化的混合整数规划模型。以中国铁路昆明局集团有限公司管内空车调配为例，验证了模型的可行性与有效性。算例结果表明，与静态空车调配方法相比，构建的动态空车调配模型不仅降低了空车调配总成本，而且调配方案更加贴合实际。与现有动态空车调配方法相比，通过改变时空网络中时段的划分方式，降低了模型求解的复杂度，构建的模型在获取空车调配方案的同时能够更加直观的看出空车在不同时间的作业状态。 

An Optimization Model of Dynamic Allocation of Empty Railway Cars Based on Time-space Network

The paper studies the dynamic optimization of the empty car distribution within the railway administration (or company)to reasonably allocate empty cars. The time-space network with different periods is constructed to describe the changes in work capacities of railway stations. By referring to transportation problems, dynamic empty-car distribution is transformed into the multi-commodity network flow based on the time-space network by increasing the supply and demand constraints. Combining the characteristics of empty car distribution, the paper develops two sets of integer decision variables and considers discharging and assigning empty cars separately. 0-1 auxiliary variables are set to construct substitution constraints of car types. On this basis, a mixed-integer programming model for the dynamic optimization of empty-car distribution is constructed to minimize the total cost. The feasibility and effectiveness of the model are verified by taking empty-car distribution in Kunming railway administration as a case study. The results show that dynamic empty-car distribution is superior to static empty-car distribution in reducing the total cost and fitting the actual process. The complexity of solving the model is reduced by improving the time-space network compared with the existing methods of dynamic empty-car distribution. The model can obtain the scheme of empty-car distribution and check the operation status of empty cars at different times intuitively.