A Bi-level Planning Model For Urban Rail Transit Fare Based On Cumulative Prospect Theory

With the rapid development of the economy and urbanization,urban transportation problems have become increasingly serious,while urban rail transit has become the major modes of transportation of America,Japan,Europe countries,and some metropolis due to its advantages of mass transit,high speed,safety,on time,environmental protection and energy conservation.Urban rail transit industry in China is currently in a golden period of development.Except for megacities and large cities,rail transit in many medium-sized cities is also under construction or planning.But there is still not a complete set of urban rail transit fare system.So,it is of great practical significance to discuss the issue.However,as a kind of quasi-public goods,the fare setting of rail transit must not only consider its economic benefits,but also its social benefits,which means it needs to consider the profit of the operating companies and the affordability of the travelers.And different travelers have different travel preferences and perceptions,so the traditional expectation utility theory is difficult to accurately describe the travel decision-making behavior of the travelers.Therefore,from the perspective of the enterprise operators and the limited rationality of the travelers,this paper establishes a bi-level planning model of urban rail transit fare based on the cumulative prospect theory to maximize the profit of the corporate operators and minimize the total generalized prospect of the travelers.Firstly,it gives an introduction of the cumulative prospect theory.Secondly,it analyzes the factors affecting the pricing of rail transit.Due to the cooperative relationship between public transport modes during the travel of residents,the model considers two types of travel modes: rail transit and regular public transport.The operating costs are analyzed,which includes vehicle-related costs,line-related costs,station-related costs and so on,to build an upper-level planning model that more closely matches the actuality.Thirdly,it analyzes the impacting factors of residents' travel mode choices,and establishes a generalized travel cost function that considers time costs,economic costs,and comfort costs for different travel modes.Because of the limited rationality of travelers,based on the framework of the cumulative prospect theory,the endogenous reference point,the corresponding value function and weight function are determined.And then,it establishes the lower-level model-travel mode selection model based on the cumulative prospect theory with the goal of minimal total generalized travel prospect.Finally,a bi-level urban rail transit planning model is established.Besides,an example is used to illustrate the applicability of the model using genetic algorithm.According to the calculation results,the paper gives a segmented fare strategy of the rail transit of the A city.