Research On Optimization Of China Railway Express Operation Plan Considering Customers’ Choice Behavior And Trunk-Branch Combination Mode

With the support of the Belt and Road Initiative,CHINA RAILWAY Express(CR express)connects the international markets of China and Europe,accelerates international circulation,supports the construction of new development pattern,and plays an important role in promoting economic development,enhancing national cooperation and improving people’s livelihood.However,between the international markets of China and Europe,customers can also choose maritime services,and the CR express faces a strong competitive relationship with maritime transport.At the same time,with the increase in the number of cities,paths,and routes operated by the CR express,the CR express has also exposed the problems of deviation between train paths and actual demand,and insufficient use of train paths.Based on this,the trunk-branch combination mode that can optimize the train paths of the CR express is proposed,but at present,the mode only relies on manual experience in the application and has not yet launched accurate mathematical research.Therefore,the purpose of this paper is to research the operation plan of the CR express by using the mathematical model,considering the customers’ choice behavior and the trunk-branch combination mode,so as to optimize the plotting of the train paths in the basic train timetable of the CR express.First,on the basis of mastering the current situation of the CR express research,sorting out and summarizing the existing research of the CR express trunk-branch combination mode.Based on the core idea of the trunk-branch combination mode,the definition of "trunk" and "branch" and the basis of judgment is reinforced,and the core idea of the mode is shown by means of diagrams,and the necessity of the CR express trunk-branch combination mode is demonstrated.Secondly,a bi-level mixed-integer programming model considering customers’ choice behavior and the trunk-branch combination mode is built to optimize the CR express operation plan.The upper-level model aims at maximizing the revenue of the railway operator and considers constraints such as section carrying capacity and the conditions for the trunk-branch combination mode;the lower-level model aims at minimizing the customer’s expenditure and considers constraints such as restrictions on the number of logistics service options,supply and demand balance,cargo flow restrictions and service carrying capacity.Then,the bi-level mixed-integer programming model is transformed into a single-level mixed-integer linear programming model by linearization and using a method based on Karush-Kuhn-Tucker(KKT)conditions,and an example is designed to verify the validity of the model.The nonlinearized part of the upper model is first linearized,and then the lower model is transformed into a constraint of the upper model using a method based on KKT conditions.The lower model transformation process is divided into three steps;the first step directly transforms the lower model into the upper model constraints using the KKT conditions,the second step reformulates the complementary relaxation constraints by linearization,and the third step strengthens the relevant constraints in the second step.Finally,taking the CR express Western Corridor as a case,using Gurobi to solve the model,and collating the output results to obtain the CR express operation plan and the CR express trunk-branch combination plan considering the customers’ choice behavior and the trunk-branch combination mode.The results show that,firstly,at this stage,customers prefer to choose the CR express;secondly,the CR express operation plan considering the trunk-branch combination mode can effectively reduce the number of the occupied CR express train paths and optimize the plotting of the CR express train paths.