A Decomposition Method for Multiperiod Railway Network Expansion—With a Case Study for Germany
研究德国铁路网至2030年的最优扩建策略，提出多背包分解方法求解多期网络设计问题，帮助在年度预算约束下选择升级线路并安排实施时间表。
In this work, we report about the results of a joint research project between Friedrich–Alexander–Universität Erlangen–Nürnberg and Deutsche Bahn AG on the optimal expansion of the German railway network until 2030. The need to increase the throughput of the network is given by company-internal demand forecasts that indicate an increase in rail freight traffic of about 50% over the next two decades. Our focus is to compute an optimal investment strategy into line capacities given an available annual budget, i.e., we are to choose the most profitable lines to upgrade with respect to the demand scenario under consideration and to provide a schedule according to which the chosen measures are implemented. This leads to a multiperiod network design problem—a class of problems that has received increasing interest over the past decade. We develop a mixed-integer programming formulation to model the situation and solve it via a novel decomposition approach that we call multiple-knapsack decomposition. The method can both be used as a quick heuristic and allows for the extension to an exact algorithm for the problem. We demonstrate its potential by solving a real-world problem instance provided by Deutsche Bahn AG and use the results as the basis for a broad case study for the expansion of the German railway network until 2030.