In a railway shunting yard, the transformation of inbound trains into properly composed outbound trains is a complex task because it involves decisions of multiple operations processes. This study addresses the integrated optimization of hump sequencing, train makeup, and classification track assignment problem in a railway shunting yard. Several key practical yard operation constraints are considered, including train formulation constraints, hump sequencing constraints, and limitations of the maximum number and capacity of classification tracks. By introducing a new representation of block flow, the integrated problem, which adopts the extended single-stage strategy and the train-to-track policy, is formulated as a unified 0-1 integer linear programming model. The objective of the proposed model is to minimize the weighted-sum of the total dwell time of all railcars and the formulation deviation penalties of all outbound trains. Then, an iterative two-phase decomposition approach is developed to reduce the complexity of solving the integrated problem. The first phase aims to explore all feasible humping sequences using a Branch-and-Bound (B&B) algorithm. Each time a new humping sequence is generated in the first phase, the second phase containing a Branch-and-Price (B&P) algorithm is applied to solve the integrated train makeup and classification track assignment problem with the known humping sequence found in the first phase. In addition, greedy heuristics and lower bounding techniques are designed in both phases to improve computational efficiency. Comprehensive experiments are investigated based on a set of real-life instances. The results show that exact approaches provide optimal solutions, whereas heuristic approaches yield satisfactory solutions within a shorter computation time. Moreover, sensitivity analyses on the number of classification tracks and the effects of different deviation penalties are also performed to gain more managerial insights.

中文翻译：

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一种用于铁路调车场集成驼峰排序、列车组成和分类轨道分配的迭代方法


在铁路调车场中，将进站列车转换为正确组合的出站列车是一项复杂的任务，因为它涉及多个运营流程的决策。本研究解决了铁路调车场中驼峰排序、列车组成和分类轨道分配问题的综合优化。考虑了几个关键的实用堆场操作约束，包括列车公式约束、驼峰排序约束以及分类轨道的最大数量和容量的限制。通过引入新的区块流表示，将采用扩展单阶段策略和列车到轨道策略的集成问题表述为统一的 0-1 整数线性规划模型。所提出的模型的目标是最小化所有轨道车的总停留时间和所有出站列车的公式偏差惩罚的加权和。然后，开发了一种迭代两阶段分解方法，以降低求解集成问题的复杂性。第一阶段旨在使用 Branch-and-Bound （B&B） 算法探索所有可行的驼峰序列。每次在第一阶段生成新的驼峰序列时，都会应用包含 Branch-and-Price （B&P） 算法的第二阶段，以使用第一阶段中发现的已知驼峰序列来解决集成的列车构成和分类轨道分配问题。此外，在这两个阶段都设计了贪婪启发式和下界技术，以提高计算效率。根据一组真实实例调查了全面的实验。 结果表明，精确方法提供最佳解决方案，而启发式方法在较短的计算时间内产生令人满意的解决方案。此外，还对分类轨道的数量和不同偏差惩罚的影响进行了敏感性分析，以获得更多的管理洞察力。