Railroad Blocking: A Network Design Application
将铁路编组问题建模为带节点度数和流量约束的网络设计问题，提出启发式拉格朗日松弛方法求解，测试表明可大幅降低铁路运营成本。
In this study, we formulate the railroad blocking problems as a network design problem with maximum degree and flow constraints on the nodes and propose a heuristic Lagrangian relaxation approach to solve the problem. The newapproach decomposes the complicated mixed integer programming problem into two simple subproblems so that the storage requirement and computational effort are greatly reduced. A set of inequalities are added to one subproblem to tighten the lower bounds and facilitate generating feasible solutions. Subgradient optimization is used to solve the Lagrangian dual. An advanced dual feasible solution is generated to speed up the convergence of the subgradient method. The model is tested on blocking problems from a major railroad, and the results show that the blocking plans generated have the potential to reduce the railroad's operating costs by millions of dollars annually.