The Model And Algorithm For The Railway Freight Empty Cars Allocation Problem Under Dynamic And Stochastic Environments

In recent years, with the deepening and development of the reform and opening-up, the railway freight transportation has been developing rapidly in our country. According to the Ministry of Railways’"twelfth five-year" development planning, the forecasting railway cargo volume will reach to5.5billion tons in2015, about2billion tons higher than that in2014. As an important component of the process of turnover of freight cars, how to reasonably allocate the freight empty cars to improve the use efficiency of freight cars gradually becomes a very important issue faced by the engineers and researchers.In this paper, we particularly study the freight empty car allocation with considering dynamics of networks and randomness of the transportation environments based on the related researches in literature. Specifically, by taking some uncertain factors in the real-world railway freight transportation network as random variables, we formulate a stochastic optimization model for freight empty car allocation. Then, based on the characteristics analysis of the proposed model, genetic algorithm and genetic-simulated annealing algorithm are respectively designed to solve the formulated model. Finally, numerical experiments are implemented to show the effectiveness and efficiency of the proposed model and algorithm. The content of this paper is summarized as follows:(1) Dynamic freight empty car allocation model with determine transportation environmentsTo describe the dynamics of freight empty car allocation, this paper applies the methods of discrete time-space network to dividing the continuous process of transportation into different time phases, which can analyze the dynamic changes of the transportation process clearly. Based on the corresponding assumptions, seven types of system constraints are considered:1) Supply capacity constraints;2) Site demand constraints;3) Network flow balance constraints;4) Road traffic capacity constraints;5) Site transfer capacity constraints;6) Phase dynamic demand constraints and7) Integer constraints of the decision variables. They are proposed to formulate the dynamic freight empty car allocation model. Finally, the freight empty car allocation problem is formulated as an integer programming model with the purpose of minimizing the travel cost and storage cost of empty cars. (2) Dynamic freight empty car allocation model within stochastic transportation environmentsFocus on uncertain factors in the transportation environment, this paper mainly uses the dynamic time-space network to analyze the paths of empty freight cars. Considering the random demands, which is based on the path selection method, we establish a stochastic expected value model to optimize two objectives—one is the minimum total cost, the other is the minimum total time. With the consideration of the randomness of transfer capability in networks and capacity parameters, stochastic chance-constrained model is formulated and the crisp equivalence of the stochastic chance constraints under special circumstances is further discussed.(3) Genetic algorithm and genetic-simulated annealing algorithmIn order to obtain a near-optimal solution, this paper designs an effective method to search for the potential paths based on the principle of branch and bound method, and then the genetic algorithm including selection, crossover and mutation operators are designed to solve the model. To further improve the searching efficiency of the algorithm, simulated annealing operator is added to the crossover and mutation operators of genetic algorithm, which can be called as genetic-simulated annealing algorithm.(4) Effectiveness of algorithm and numerical experiments analysisTo show the effectiveness of the designed algorithm, this paper uses the genetic algorithm and genetic-simulated annealing algorithm to solve the same experiment, respectively. By changing the values of parameters in the algorithm, the robustness of the algorithm are compared successfully. Moreover, through designing different experiments and analyzing the calculation results, the effectiveness of the genetic-simulated annealing algorithm is further demonstrated.