The Minimum-Cost and Maximum-Flow Algorithm for Railway Empty Cars Distribution

Railway empty cars distribution is a complicated problem of flow distribution in railway network. Because empty cars are insufficient in China, the directions of empty cars flow have been arranged under a very strict daily plan. Combined with the conditions of empty cars supply-demand equilibrium, the linear programming model for distribution of empty cars is established in order to realize empty cars running distance minimum. To solve the model, the problem of railway empty cars distribution is converted into single source and sink network through dummy source node and dummy sink node. The optimal scheme of railway empty cars distribution can be reached by finding a maximum-flow of minimum-cost from the source node to the sink node of the network. In this paper, we firstly find the maximum of the network and constantly adjust increment cycle so as to decrease the cost of the network, eventually obtain the optimal solution. Experimental results show that the feasibility and validity of railway network of empty cars distribution model.