Study On Passenger Transport Scheduling Problem Considering The Influence Of Ticket Pricing

Ticket price and operating schedule are the key elements of passenger transport service.As the service demander,passengers have preferences for ticket price and departure time.As the service supplier,passenger transport firms can significantly affect passengers’ travel choices through ticket pricing and scheduling decisions,further change the passenger flow and affect the benefits of firms.In reality,these two factors not only have respective impacts on the benefits of firms,but also have an interactive relationship.However,the interaction between pricing and scheduling is rarely considered in traditional studies.Calculating the optimal schedule of passenger transport firms under the premise of considering the influence of ticket pricing,can make firm decisions closer to reality,which has important theoretical and practical significance.This study combines the facility location model with the customer behavior theory and proposes the two-stage pricing and scheduling base model of passenger transport firms.The model is universal for the scheduling decisions of various passenger transport modes.Different variables are introduced to build scheduling models suitable for complex situations.The base model is empirically simulated in the application scenario of subway pricing and scheduling optimization.(1)Based on the facility location model,the base model of passenger transport scheduling under the influence of ticket pricing is proposed.In the classical facility location model,the probabilistic customer behavior hypothesis is introduced to derive the game process of two firms,and the facility location is transformed into scheduling in a linear period and applied to the scheduling problem of passenger transportation firms.A two-stage pricing and scheduling method is established after the introduction of price factors,which includes a pricing stage and a scheduling stage,clarifying the calculation process and the basic nature of the objective function.It is found that the Nash equilibrium solution of the single scheduling game between two firms in the passenger transport market is the central moment of the target period;the objective function of the scheduling optimization model is a convex function on the firm’s price and a submodular function on the transport frequency.(2)The transport frequency is introduced to construct a frequency decision model for passenger transport pricing and scheduling optimization.To achieve the goal of maximizing firm profit,different firm behaviors are simulated by sequential scheduling mode and simultaneous scheduling mode.An approximate branch and bound method based on a cover range variable is proposed to accelerate the optimum speed in simultaneous mode.The two scheduling modes are applied for simulating calculation and comparison,the optimal transport frequency and schedule are solved by marginal analysis and get the corresponding maximum profit.The results show that the marginal profit of new shifts decreases with the increase of transport frequency.Sequential scheduling mode can produce higher profits than simultaneous scheduling mode,which is an advantageous strategy for the entrant firm.(3)Introduce a variety of pricing regimes to build a short-term and long-term game model between firms.The differential pricing regime based on different departure times is introduced into the passenger transport pricing and scheduling model,the BFGS method along with the Hessian matrix is used to solve the optimal solution.When the scheduling optimization problem is extended to the long-term game,the transport pricing and scheduling equilibrium model is constructed,a generalized greedy algorithm with tolerance parameter is proposed to prevent the problem of non-convergence in repeated games.The results of scheduling optimization and equilibrium model of three pricing regimes are calculated,study the impact of pricing regimes and firms’ gaming behavior on profits and social welfare.The results show that in the optimization model,differential pricing regime will lead to more convenient schedule allocation for passengers,but simultaneously reduce firm profit.The repeated scheduling game between firms is conducive to the improvement of firm profit,but its impact on social welfare is complex.(4)The Beijing subway is selected for the empirical study of passenger transport pricing and scheduling optimization.Calculate the optimal price and the change in passenger demand of every period according to the Ramsey differential pricing model.Based on passenger travel data,the multi-objective path identification is completed to obtain the passenger demand of each station at each time.The subway scheduling optimization model is constructed to minimize the average passenger waiting time.The tabu search algorithm is used to obtain the optimal solution of the uneven interval schedules through several local neighborhood search iterations.The results show that after implementing the price discount,the average waiting time of passengers will increase under the limitation of certain load factors.The implementation of an uneven departure mode is conducive to reducing the average waiting time of passengers on the premise of constant transport frequency.By adjusting the service price and making scientific decisions on the transport schedule,the subway firm can improve the service quality while ensuring the operation economy.The main contribution of this study is combining the passenger behavior changes caused by transport pricing adjustment with the transport scheduling problem,introducing the idea of facility location theory,constructing a comprehensive decision-making model to solve the problems of pricing regimes,scheduling optimization,and transport frequency,expands the ideas and methods of traditional researches.In this thesis,the actual effects of different scheduling decision modes are compared,the differential pricing regime based on different departure times is proposed,and the pricing and scheduling equilibrium model framework is constructed in the long-term game,which has made research contributions in the theoretical application,model construction,and algorithm optimization aspects.This thesis provides a decision-making basis for passenger transport firms in different market environments and can serve the passenger transport market supervision department in the aspects of price supervision and market access permission.