Optimising railcar transfer chain via fuzzy programming and a simulated annealing algorithm

With the accelerated changes of trade and economic structure, the fluctuation of shipment size is increasing in railway transportation. Railway companies are facing continuous challenges about how to optimise railcar transfer chain to achieve the balance between the workload of railway network and daily changing transportation demands. In this paper, elastic capacity constraints are designed to solve the number fluctuation of railcars in shipments. We define available capacity belts to describe the elastic capacities of railway network, then fuzzy theory is introduced. A membership function is designed to designate the satisfaction degree for the number of railcars, and a non-linear integer programming model is developed. We test the model with two numerical examples from the 2019 Railway Applications Section Problem Solving Competition, and a simulated annealing algorithm is employed to solve the problem. In the experiment with 16 yards, the model generated 1304 variables. Furthermore, as the scale of the railway network increases, the number of variables exhibited exponential explosive growth. In the experiment with 32 yards, the model generated 76,037 variables and determined 365 direct train services, resulting in an operating cost of 245,014,388 car-hours. The results of the experiments effectively verify the effectiveness of the model.