Empty vehicle dispatching method and system for demand-responsive public transportation

Abstract

The embodiment of the present invention discloses a method and system for dispatching empty vehicles of a demand-responsive bus. The method includes the following steps: S1: determining the station information and vehicle information of the demand-responsive bus; S2: constructing an empty vehicle dispatch matching model; S3: constructing an algorithm for solving the empty vehicle dispatch problem of the demand-responsive bus, and solving the empty vehicle dispatch problem of the demand-responsive bus; S4: obtaining the optimal dispatch decision for each vehicle, dispatching the empty vehicle according to the decision, and updating the new vehicle information, station information, and station status information. The present invention can significantly improve the operational efficiency of the demand-responsive bus system, so that the system can better respond to station demands. The present invention can help optimize the empty vehicle dispatch strategy so that empty vehicles are reasonably matched with station demands.

Description

Technical Field

[0001] The present invention relates to the field of intelligent transportation technology, and in particular to a method and system for dispatching empty vehicles of a demand-responsive public transportation. Background Art

[0002] Demand-responsive bus services, also known as on-demand bus services, are a type of public transportation service that flexibly adjusts based on passenger demand. This service can effectively improve the efficiency of bus resource utilization and alleviate traffic pressure during peak hours. In this model, buses dynamically adjust routes and schedules based on real-time passenger demand to achieve higher service coverage and greater passenger satisfaction. In recent years, with the development of data science and artificial intelligence technologies, demand-responsive bus services have been promoted in many cities. In the operation of demand-responsive bus services, vehicle scheduling algorithms are the core strategy guiding operations.

[0003] Existing scheduling algorithms primarily focus on matching people with vehicles, with less research on idle vehicle scheduling strategies. In actual operations, if idle vehicles can be properly dispatched and their coverage areas properly allocated, faster response times can be achieved, improving system operational efficiency. Summary of the Invention

[0004] The technical problem to be solved by the embodiments of the present invention is to provide a method and system for dispatching empty vehicles of a demand-responsive public transportation system, so as to improve the operational efficiency of the demand-responsive public transportation system.

[0005] In order to solve the above technical problems, an embodiment of the present invention proposes a method for dispatching empty buses of a demand-responsive public transportation system, comprising the following steps:

[0006] S1: Determine the station information and vehicle information of the demand-responsive bus, wherein the station information includes station information, stop station information, and required station information, and the vehicle information includes information of vehicles in different service states;

[0007] S2: Build an empty vehicle scheduling matching model to match demand stations with parking stations based on the demand volume of demand stations;

[0008] S3: Construct an algorithm to solve the empty vehicle scheduling problem of demand-responsive public transportation;

[0009] S4: Obtain the optimal dispatching decision for each vehicle, dispatch empty vehicles according to the decision, and update new vehicle information, station information, and parking station status information.

[0010] Accordingly, an embodiment of the present invention further provides a demand-responsive bus empty vehicle dispatching system, comprising:

[0011] Information determination module: determines the station information and vehicle information of the demand-responsive bus, wherein the station information includes station information, stop station information and required station information, and the vehicle information includes information of vehicles in different service states;

[0012] Model building module: Build an empty vehicle dispatch matching model to match demand stations with parking stations based on the demand volume of the demand stations;

[0013] Solution calculation module: Constructs a solution algorithm for the empty vehicle scheduling problem of demand-responsive public transportation and solves the empty vehicle scheduling problem of demand-responsive public transportation;

[0014] Vehicle dispatch module: obtains the optimal dispatch decision for each vehicle, dispatches empty vehicles according to the decision, and updates the new vehicle information, station information, and station status information.

[0015] The beneficial effects of the present invention are as follows: the present invention dispatches vehicles according to the expected demand at the station, so that the number of empty vehicles dispatched to the station matches the demand at the station, thereby optimizing the operational efficiency of demand-responsive public transportation. The present invention rationally optimizes the objective function so that the objective function can reflect the marginal diminishing effect of the number of vehicles matching demand and handle the situation where there is no vehicle coverage. The linear nature of the algorithm makes the solution more reasonable. The maximum dispatch distance and maximum response time parameters introduced in the present invention can be adjusted according to the actual situation of the system to achieve response to the dynamic demand environment and flexibly adapt to environmental changes in display operations.

[0016] This invention addresses aspects previously overlooked by algorithms, further improving system operational efficiency. It prioritizes site demand and schedules empty vehicles to cover sites. Its objective function accounts for diminishing marginal utility. When dealing with vehicle coverage, the contribution of the first vehicle is 1, and that of subsequent vehicles is 0.5. It also accounts for the case of no vehicle coverage. Furthermore, the model's linear nature ensures reasonable computational complexity.

[0017] This invention helps better match stops with high-demand stops, optimizes vehicle scheduling strategies, and improves the overall operational efficiency of the public transportation system. By analyzing stop demand and applying advanced algorithms to rationally dispatch empty vehicles, the invention dynamically adjusts stop vehicle configuration based on demand, maximizing the coverage of the public transportation system's service area. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is a flow chart of an empty vehicle scheduling method for demand-responsive public transportation according to an embodiment of the present invention. DETAILED DESCRIPTION

[0019] It should be noted that, unless there is a conflict, the embodiments in this application and the features in the embodiments can be combined with each other. The present invention is further described in detail below with reference to the drawings and specific embodiments.

[0020] In the embodiments of the present invention, if there are directional indications (such as up, down, left, right, front, back, etc.), they are only used to explain the relative position relationship and movement status of the various components under a specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly.

[0021] In addition, the terms "first," "second," and so on, used in this disclosure are for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features being referred to. Therefore, features specified as "first" or "second" may explicitly or implicitly include at least one of these features.

[0022] The method for dispatching empty buses of a demand-responsive bus according to the embodiment of the present invention includes the following steps S1 to S4. Figure 1 .

[0023] S1: Determine the station information and vehicle information of the demand-responsive bus (a bus mode that is different from the traditional bus operating on a fixed line network. In this mode, the bus responds to the needs of passengers and runs between certain stations. The route changes dynamically with the changes in passenger demand. In this mode, relevant algorithms are required to optimize the vehicle's route, and the algorithm plays an important role in operational decisions). The station information includes station information, stop station information and demand station information, and the vehicle information includes information on vehicles in different service states. The present invention inputs the demand quantity of each station, derives the demand priority of each station, and then reasonably allocates empty vehicles to each stop station. Empty vehicle scheduling: In a demand-responsive bus operation system, the process of scheduling empty vehicles to stop stations. The present invention meets the maximum passenger demand by optimizing the empty vehicle scheduling behavior.

[0024] Specific process:

[0025] Form a station collection : Determine the number of vehicle stops (i.e., vehicle stops, service stops for demand-responsive public transportation, which carry passenger demand. The stops are connected to form a service line network for demand-responsive public transportation, and each stop corresponds to its nearest vehicle stop) and determine their location information.

[0026] Form a set of parking sites (i.e., sites where empty vehicles are parked. When vehicles are not in service, they are parked here. The sites have capacity constraints). : Determine the number of parking sites and collect information about each site, including location, number of existing vehicles, and maximum capacity.

[0027] Forming a demand site collection : Determine the number of demand stations, collect the demand for each station, and reflect the number of passengers that the demand station needs to satisfy.

[0028] Forming a vehicle collection , according to the different states of the vehicles, the vehicles are grouped into corresponding sets.

[0029] in, Represents the collection of vehicles in service. Represents the set of vehicles in the process of dispatching empty vehicles to parking stations, A collection of vehicles waiting for service at a stop. A collection of vehicles that have completed their service and are waiting to be dispatched.

[0030] For vehicles in different service states, determine the number of vehicles in each state and collect basic information of each vehicle, such as vehicle ID, current location, etc.

[0031] S2: Construct an empty vehicle scheduling matching model to match demand stations with parking stations based on the demand at those stations. This method identifies station demand and dispatches empty vehicles from parking stations to corresponding demand stations. With the goal of maximizing vehicle coverage of station demand, an objective function is established that considers diminishing marginal returns and the absence of vehicle coverage. The feasibility constraints are analyzed, ultimately leading to the development of an empty vehicle scheduling optimization model.

[0032] (1) The set definition is shown in Table 1:

[0033]

[0034] (2) The definitions of time-space related parameters are shown in Table 2:

[0035]

[0036] (3) System parameter definitions are shown in Table 3:

[0037]

[0038] (4) Decision variables are shown in Table 4:

[0039]

[0040] (5) Intermediate calculation variables are shown in Table 5:

[0041]

[0042] (6) Objective function:

[0043] Maximize the weighted service effect of the entire system, while taking into account demand distribution and diminishing marginal utility:

[0044] (1)

[0045] The objective function is for all time periods and all stations Perform a double summation.

[0046] in Indicates the station In the time period The expected demand is used as the weight coefficient.

[0047] The term reflects the marginal contribution of the number of vehicles, The term reflects the basic contribution of whether there is car coverage, and the two are added together to calculate the coverage effect.

[0048] (7) Constraints:

[0049] (2)

[0050] Formula (2) controls and Whether the dispatchable vehicles in the set are allowed to be dispatched, where Is an external input 0-1 parameter, when When the vehicle Can be dispatched, otherwise cannot be dispatched; this constraint allows the system to interface with external systems and control the vehicle's dispatch authority.

[0051] (3)

[0052] Formula (3) indicates that each dispatchable vehicle can be assigned to at most one parking station;

[0053] (4)

[0054] Formula (4) represents the , in each period The number of vehicles in a parking station does not exceed its maximum capacity;

[0055] (5)

[0056] Formula (5) indicates that the vehicle driving distance generated by the vehicle scheduling decision cannot exceed the maximum parking distance threshold set by the system to ensure scheduling efficiency;

[0057] (6)

[0058] Formula (6) is the coverage determination constraint of the parking site;

[0059] (7)

[0060] Formula (7) calculates the total number of available vehicles. The first term reflects the vehicles that are about to arrive, the second term reflects the vehicles currently at the stop, and the third term reflects the vehicles brought by the new scheduling decision.

[0061] (8)

[0062] Formula (8) controls the coverage representation variable , the contribution value is 0 when achieving car-free coverage;

[0063] (9)

[0064] Formula (9) controls the variable domain, Indicates scheduling decision, coverage relationship and coverage status, which is a 0-1 variable. Represents the number of vehicles, which is a non-negative integer.

[0065] S3: Construct an algorithm to solve the empty vehicle scheduling problem of demand-responsive public transportation. The specific process is as follows:

[0066] 1. Input: .

[0067] 2. Output: Return a list of vehicle dispatch information and a list of the status of each stop.

[0068] 3. Main loop: S31 initializes the network structure; calculates and assigns the nearest stop for each station; traverses each empty car that needs to be dispatched ; Build a coverage matrix from site to stop .

[0069] 4. S32 defines the decision variable: constructs a 0-1 variable that determines whether vehicle v goes to stop i ; Construct a 0-1 variable to indicate whether a vehicle covers the parking site i at time t ; Construct a 0-1 variable to determine whether stop i can cover station j within the maximum response time ; Construct the variable of the total number of available vehicles at stop i in time period t ; Construct the total number of covered vehicles variable for station j in time period t .

[0070] 5. S33 builds optimization objectives: establishes an objective function to maximize site demand coverage.

[0071] 6. S34 adds constraints:

[0072] Constraint 1: Scheduling feasibility constraint;

[0073] Constraint 2: Vehicle single assignment constraint;

[0074] Constraint 3: Stop capacity constraint;

[0075] Constraint 4: Maximum parking distance constraint.

[0076] 7. S35 solves the optimization problem: calls the solver to solve the mixed integer programming problem;

[0077] Case 1: Find the optimal solution; extract the values ​​of the decision variables and construct a plan for assigning vehicles to parking stations;

[0078] Case 2: There is no optimal solution, and an empty allocation plan is returned.

[0079] 8. End: Return a list of vehicle dispatch information and a list of the status of each stop.

[0080] The present invention establishes a network structure, defines decision variables, constructs optimization objectives, adds constraints, reasonably sets model parameters, and uses a mixed integer programming solver to solve the model to obtain the optimal scheduling plan and stop information, thereby optimizing the operational decisions of demand-responsive public transportation.

[0081] S4: Obtain the optimal scheduling decision for each vehicle, dispatch empty vehicles based on the decision, and update the new vehicle information, station information, and parking station status information. The present invention calls a solver to solve this problem, obtain the optimal scheduling decision for each vehicle, and update the new vehicle, station information, and parking station status.

[0082] 1. Output scheduling results:

[0083] Output the dispatch information of each vehicle and display the vehicle Which stop to go to .

[0084] 2. Output the status of the parking station:

[0085] Count and output the current number of vehicles at each stop, whether there are any vehicles parked there, and the required stops it covers.

[0086] 3. Evaluate optimization results:

[0087] Calculate and output the final optimization target value to check the optimization effect and system performance.

[0088] The demand-responsive bus empty vehicle dispatching system according to an embodiment of the present invention includes:

[0089] Information determination module: determines the station information and vehicle information of the demand-responsive bus, wherein the station information includes station information, stop station information and required station information, and the vehicle information includes information of vehicles in different service states;

[0090] Model building module: Build an empty vehicle dispatch matching model to match demand stations with parking stations based on the demand volume of the demand stations;

[0091] Solution calculation module: Constructs a solution algorithm for the empty vehicle scheduling problem of demand-responsive public transportation and solves the empty vehicle scheduling problem of demand-responsive public transportation;

[0092] Vehicle dispatch module: obtains the optimal dispatch decision for each vehicle, dispatches empty vehicles according to the decision, and updates the new vehicle information, station information, and station status information.

[0093] As an embodiment, the model uses the following objective function for all time periods and all stations Perform a double summation:

[0094] ;

[0095] in, is the set of stations (i.e. vehicle stops), T is the set of time intervals, Indicates the station In the time period The expected demand, For the station In the time period Total number of covered vehicles; A 0-1 variable representing a station In the time period Is there vehicle coverage? If so, ,otherwise .

[0096] As an embodiment, the constraints of the model include:

[0097] (1) Scheduling feasibility constraints:

[0098] ;

[0099] in, Is an external input 0-1 parameter, when When the vehicle Can be scheduled, otherwise cannot be scheduled; I is the set of parking sites; A 0-1 variable representing a vehicle Whether to dispatch to the parking site If the vehicle is heading to the station ,but ,otherwise in ; Gather vehicles waiting for service at the stop; A collection of vehicles that have completed their service and are waiting to be dispatched;

[0100] (2) Vehicle single allocation constraint:

[0101] ;

[0102] (3) Capacity constraints of parking sites:

[0103] ;

[0104] in, For parking sites In the time period Total number of available vehicles; For parking sites Total berth capacity;

[0105] (4) Maximum parking distance constraint:

[0106] ;

[0107] in, For vehicles To the parking site driving time, is the preset maximum parking distance threshold;

[0108] (5) Constraints for determining the coverage of parking sites:

[0109] ;

[0110] in, Indicates a parking site Can the station be covered within the maximum response time? , is the maximum response time threshold, From the parking site To the station driving time;

[0111] (6) Calculate the total number of available vehicles:

[0112] ;

[0113] in, The collection of vehicles in the process of dispatching empty vehicles to the parking station, Indicates empty vehicle on the way Arrival at the stop time period, Indicates vehicle Is it at a parking site? , Indicates vehicle Arrival at the stop the time period;

[0114] (7) Control coverage representation variables , the contribution value is 0 when no car coverage is achieved:

[0115] ;

[0116] Where M is a sufficiently large number (in the Big M method, M is a constant much larger than other variables to ensure that the constraint remains valid when a condition is not met);

[0117] (8) Control variable domain:

[0118] ;

[0119] in, Indicates scheduling decision, coverage relationship, and coverage status, which is a 0-1 variable; Represents the number of vehicles, which is a non-negative integer.

[0120] As an embodiment, the solution calculation module solves the demand-responsive bus empty vehicle scheduling problem according to the following steps:

[0121] Initialize the network structure: calculate and assign the nearest stop for each station, and traverse each empty car that needs to be dispatched , build a coverage matrix from site to stop site ;

[0122] Define decision variables: Construct a 0-1 variable that determines whether vehicle v goes to stop i , construct a 0-1 variable to indicate whether the stop i is covered by a vehicle at time t , construct a 0-1 variable to determine whether stop i can cover station j within the maximum response time , construct the total number of available vehicles at stop i in time period t , construct the total number of covered vehicles variable of station j in time period t ;

[0123] Establish optimization objectives: Establish an objective function to maximize site coverage requirements;

[0124] Add constraints: scheduling feasibility constraints, vehicle single allocation constraints, parking site capacity constraints, and maximum parking distance constraints;

[0125] Solve the demand-responsive bus empty vehicle dispatch problem. If an optimal solution is found, extract the values ​​of the decision variables and construct a plan for assigning vehicles to stops. If no optimal solution is found, return an empty plan. Upon completion, return a list of vehicle dispatch information and a list of the status of each stop.

[0126] The present invention can significantly improve the operational efficiency of demand-responsive public transportation systems, enabling them to better respond to station demands. It can also help optimize empty vehicle scheduling strategies, ensuring a reasonable match between empty vehicles and station demands.

[0127] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A method for dispatching empty buses of a demand-responsive public transport system, characterized in that: The following steps are involved: S1: Determine the station information and vehicle information of the demand-responsive bus, wherein the station information includes station information, stop station information, and required station information, and the vehicle information includes information of vehicles in different service states; S2: Build an empty vehicle scheduling matching model to match demand stations with parking stations based on the demand volume of demand stations; S3: Construct an algorithm to solve the empty vehicle scheduling problem of demand-responsive public transportation; S4: Obtain the optimal dispatch decision for each vehicle, dispatch empty vehicles according to the decision, and update new vehicle information, station information, and parking station status information; The model uses the following objective function for all time periods and all stations Perform a double summation: ； in, is the set of stations, T is the set of time intervals, Indicates the station In the time period The expected demand, For the station In the time period Total number of covered vehicles; A 0-1 variable representing a station In the time period Is there vehicle coverage? If so, ,otherwise .

2. The method for dispatching empty buses of a demand-responsive public transportation system according to claim 1, wherein: The constraints of the model include: (1) Scheduling feasibility constraints: ； in, Is an external input 0-1 parameter, when When the vehicle Can be scheduled, otherwise cannot be scheduled; I is the set of parking sites; A 0-1 variable representing a vehicle Whether to dispatch to the parking station If the vehicle is heading to the station ,but ,otherwise in ; Gather vehicles waiting for service at the stop; A collection of vehicles that have completed their service and are waiting to be dispatched; (2) Vehicle single allocation constraint: ； Where I is the set of stop sites; A 0-1 variable representing a vehicle Whether to dispatch to the parking station , ; Gather vehicles waiting for service at the stop; A collection of vehicles that have completed their service and are waiting to be dispatched; (3) Capacity constraints of parking sites: ； in, For parking sites In the time period Total number of available vehicles; For parking sites Total berth capacity; (4) Maximum parking distance constraint: ； in, For vehicles To the parking site driving time, is the preset maximum parking distance threshold; (5) Constraints for determining the coverage of parking sites: ； in, Indicates a parking site Can the station be covered within the maximum response time? , is the maximum response time threshold, From the parking site To the station driving time; (6) Calculate the total number of available vehicles: ； in, The collection of vehicles in the process of dispatching empty vehicles to the parking station, Indicates empty vehicle on the way Arrival at the stop time period, Indicates vehicle Is it at a parking site? , Indicates vehicle Arrival at the stop the time period; (7) Control coverage representation variables , the contribution value is 0 when no car coverage is achieved: ； Where M is a sufficiently large number; (8) Control variable domain: ； in, 、 、 Indicates scheduling decision, coverage relationship, and coverage status, which is a 0-1 variable; Represents the number of vehicles, which is a non-negative integer.

3. The method for dispatching empty buses of a demand-responsive public transportation system as claimed in claim 2, wherein: Step S3 includes the following sub-steps: S31, initialize the network structure: calculate and assign the nearest stop for each station, and traverse each empty car that needs to be dispatched , build a coverage matrix from site to stop site ; S32, define decision variables: construct a 0-1 variable to determine whether vehicle v goes to stop i , construct a 0-1 variable to indicate whether the stop i is covered by a vehicle at time t , construct a 0-1 variable to determine whether stop i can cover station j within the maximum response time , construct the total number of available vehicles at stop i in time period t , construct the total number of covered vehicles variable of station j in time period t ; S33, construct optimization objectives: establish an objective function to maximize site demand coverage; S34, add constraints: scheduling feasibility constraint, vehicle single allocation constraint, parking site capacity constraint, and maximum parking distance constraint; S35, solves the empty vehicle scheduling problem of demand-responsive public transportation. If an optimal solution is found, the values ​​of the decision variables are extracted and a distribution plan for vehicles to the stop sites is constructed; if there is no optimal solution, an empty distribution plan is returned.

4. A demand-responsive bus empty vehicle dispatching system, characterized in that: include: Information determination module: determines the station information and vehicle information of the demand-responsive bus, wherein the station information includes station information, stop station information and required station information, and the vehicle information includes information of vehicles in different service states; Model building module: Build an empty vehicle dispatch matching model to match demand stations with parking stations based on the demand volume of the demand stations; Solution calculation module: Constructs a solution algorithm for the empty vehicle scheduling problem of demand-responsive public transportation and solves the empty vehicle scheduling problem of demand-responsive public transportation; Vehicle dispatch module: obtains the optimal dispatch decision for each vehicle, dispatches empty vehicles based on the decision, and updates the new vehicle information, station information, and station status information; The model uses the following objective function for all time periods and all stations Perform a double summation: ； in, is the set of stations, T is the set of time intervals, Indicates the station In the time period The expected demand, For the station In the time period Total number of covered vehicles; A 0-1 variable representing a station In the time period Is there vehicle coverage? If so, ,otherwise .

5. The demand-responsive bus empty vehicle dispatching system according to claim 4, characterized in that: The constraints of the model include: (1) Scheduling feasibility constraints: ； in, Is an external input 0-1 parameter, when When the vehicle Can be scheduled, otherwise cannot be scheduled; I is the set of parking sites; A 0-1 variable representing a vehicle Whether to dispatch to the parking station If the vehicle is heading to the station ,but ,otherwise in ; Gather vehicles waiting for service at the stop; A collection of vehicles that have completed their service and are waiting to be dispatched; (2) Vehicle single allocation constraint: ； Where I is the set of stop sites; A 0-1 variable representing a vehicle Whether to dispatch to the parking station , ; Gather vehicles waiting for service at the stop; A collection of vehicles that have completed their service and are waiting to be dispatched; (3) Capacity constraints of parking sites: ； in, For parking sites In the time period Total number of available vehicles; For parking sites Total berth capacity; (4) Maximum parking distance constraint: ； in, For vehicles To the parking site driving time, is the preset maximum parking distance threshold; (5) Constraints for determining the coverage of parking sites: ； in, Indicates a parking site Can the station be covered within the maximum response time? , is the maximum response time threshold, From the parking site To the station driving time; (6) Calculate the total number of available vehicles: ； in, The collection of vehicles in the process of dispatching empty vehicles to the parking station, Indicates empty vehicle on the way Arrival at the stop time period, Indicates vehicle Is it at a parking site? , Indicates vehicle Arrival at the stop the time period; (7) Control coverage representation variables , the contribution value is 0 when no car coverage is achieved: ； Where M is a sufficiently large number; (8) Control variable domain: ； in, 、 、 Indicates scheduling decision, coverage relationship, and coverage status, which is a 0-1 variable; Represents the number of vehicles, which is a non-negative integer.

6. The demand-responsive bus empty vehicle dispatching system according to claim 5, characterized in that: The solution calculation module solves the demand-responsive bus empty vehicle scheduling problem according to the following steps: Initialize the network structure: calculate and assign the nearest stop for each station, and traverse each empty car that needs to be dispatched , build a coverage matrix from site to stop site ; Define decision variables: Construct a 0-1 variable that determines whether vehicle v goes to stop i , construct a 0-1 variable to indicate whether the stop i is covered by a vehicle at time t , construct a 0-1 variable to determine whether stop i can cover station j within the maximum response time , construct the total number of available vehicles at stop i in time period t , construct the total number of covered vehicles variable of station j in time period t ; Establish optimization objectives: Establish an objective function to maximize site coverage requirements; Add constraints: scheduling feasibility constraints, vehicle single allocation constraints, parking site capacity constraints, and maximum parking distance constraints; Solve the empty vehicle dispatch problem of demand-responsive public transportation. If an optimal solution is found, extract the values ​​of the decision variables and construct an allocation plan for vehicles to parking stops. If no optimal solution is found, return an empty allocation plan.

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