An iterative method for integrated hump sequencing, train makeup, and classification track assignment in railway shunting yard

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.