考虑随机运能和送到时限的高铁快递运输计划优化方法

Optimization method for high-speed railway express transport plan considering stochastic capacity and delivery time windows

为充分利用高铁非高峰期的列车运能,高铁快运已成为铁路快捷货运发展新趋势.然而,受客运需求波动影响,载客动车组可用于高铁快递的运能呈现高度不确定性,给日常运营组织带来巨大挑战.为增强高铁快运系统应对随机运能的能力,提出一种考虑随机运能的高铁快递运输计划优化方法.首先,采用离散场景刻画列车运能的不确定性,以最大化高铁快运期望总收益为目标,综合考虑快递的送到时限和运营约束,针对场景概率分布精确已知情形,构建两阶段随机规划模型(SP);然后,进一步考虑场景概率分布信息部分已知情形,构建两阶段分布鲁棒优化模型(DRO),基于盒式模糊集,借助对偶理论将DRO模型转化为等价的整数线性规划模型并利用GUROBI求解;最后,基于宁杭高铁设计数值实验验证模型的有效性,结果表明,相较于SP模型,DRO模型体现出较强的鲁棒性,只需付出较小的代价即可有效抵抗运能波动对运输计划的影响,并且能够改善最坏情形下解的质量,切实改善高铁快递实际运营中的稳定性.

With the aim of fully utilizing the transport capacity of high-speed trains during non-peak periods,high-speed railway express delivery has become a new trend in the development of railway express delivery.However,the uncertain capacity of passenger trains for express delivery due to passenger flow demand poses a significant challenge to daily operations.To enhance the capability of high-speed railway express delivery in coping with uncertainty of train transport capacity,a stochastic optimization method for high-speed railway express delivery planning considering random capacity is proposed.Firstly,the uncertainty of capacity is modeled using discrete scenarios.With the precise probability distribution of the scenarios being known,the two-stage stochastic programming model(SP)is constructed to maximize the expected total revenue of high-speed railway express delivery,considering delivery time requirements and operational constraints of express delivery comprehensively.On this basis,a two-stage distributionally robust optimization model(DRO)is developed for scenarios where probability distribution information of uncertain capacity is partially known.By utilizing dual theory and box ambiguity set,the DRO model is transformed into an equivalent integer linear programming model,which is solved using the GUROBI solver.Finally,the effectiveness of the model is verified by numerical experiments based on the Nanjing-Hangzhou high-speed railway.Results show that,compared with the stochastic programming model,the DRO exhibits strong robustness and can effectively resist the impact of capacity fluctuations on the transport plan at a small cost.Moreover,it can improve the quality of solutions in the worst case and enhance the stability of high-speed railway express delivery operations in practice.