A flexible bus static and dynamic cooperative scheduling method

Abstract

The present application relates to a kind of flexible public transport static and dynamic coordination scheduling method, including static scheduling and dynamic scheduling two stages, wherein static scheduling stage is gathered user demand by designing reservation time window, while considering the possibility of subsequent real-time request of each site, establishes and solves static scheduling model, determines the initial skip-stop route and timetable of flexible public transport, while the request matching result is fed back to user;Dynamic scheduling stage is based on real-time request on the basis of static scheduling, establishes and solves dynamic scheduling model, updates the skip-stop route and driving timetable of flexible public transport.The present application adds the probability of real-time request in static scheduling stage, prolongs the stop time of corresponding station, organically combines flexible public transport static scheduling and dynamic scheduling, is conducive to improving real-time request acceptance rate, and in low passenger flow area or non-peak period, through skip-stop and flexible timetable, avoid empty running and low load rate, reduce operating cost, improve service quality.

Description

Technical Field

[0001] The present invention relates to the fields of flexible public transportation and the Internet, and in particular to a method for dynamic and static coordinated scheduling of flexible public transportation. Background Art

[0002] According to different service modes, urban public transportation systems can be roughly divided into two categories: conventional public transportation and demand-responsive public transportation. Conventional buses run on fixed routes and fixed timetables, which can provide stable travel services for passengers and operate well in high passenger flow areas (such as residential areas, office areas, etc.). However, in low passenger flow areas (such as suburbs, industrial parks, etc.), if the departure frequency is high, the bus will have a serious empty running phenomenon, the full load rate will be low, and the operating cost will be high; if the departure frequency is low, the waiting time for passengers will be long. As a type of demand-responsive public transportation, flexible buses can not only run on fixed routes or stop at fixed stations, but also provide travel services on demand by changing routes or stops, reducing travel time and reducing operating costs.

[0003] Existing research on flexible public transportation scheduling can be categorized into three categories: static scheduling, dynamic scheduling, and two-stage dynamic and static scheduling. Two-stage scheduling research generally involves solving a static scheduling model in the first stage to address reservation needs and determine vehicle routes and schedules. Building on the first stage, the second stage involves solving a dynamic scheduling model to respond to real-time demands. The dynamic and static stages are relatively independent, and the static stage lacks consideration of the distribution of subsequent real-time requests, resulting in a low response rate for real-time requests. Furthermore, research on the coordinated dynamic and static scheduling of flexible public transportation is lacking. Summary of the Invention

[0004] The purpose of this invention is to provide a flexible bus dynamic and static coordinated scheduling method. According to historical demand and reservation demand, by designing skip-stop routes and flexible timetables, the flexible bus static scheduling plan is optimized, and on this basis, the skip-stop routes and timetables are dynamically adjusted to respond to real-time demand, reduce passenger travel time, and reduce bus operating costs.

[0005] The purpose of the present invention can be achieved by the following technical solutions:

[0006] A flexible public transportation dynamic and static coordinated scheduling method includes the following steps:

[0007] Obtain and count the historical request data of each bus station, and calculate the probability of real-time requests at each station in each time period;

[0008] Design a reservation time window and gather user reservation requests before the deadline through the online platform;

[0009] Based on the probability of real-time requests at each station and time period and user reservation requests, a flexible bus static scheduling model is established and solved to determine the flexible bus's skipping routes and the arrival, departure, and stopover times at each station, thus obtaining the initial flexible bus scheduling plan.

[0010] Feedback the user's reservation request matching results and instruct the bus to execute the initial scheduling plan;

[0011] After the deadline, users' dynamic requests are obtained in real time, and a dynamic dispatch model for flexible public transportation is established and solved. The flexible public transportation's skipping routes and the arrival, departure, and stop times of each station are updated to obtain an updated dispatch plan.

[0012] Feedback the user with the real-time request matching results and instruct the bus to execute the updated dispatch plan.

[0013] The probability of real-time requests occurring at each site in each time period is:

[0014]

[0015] Where B is the set of bus stops; T is the set of time periods divided in a day; For site v i The number of real-time requests in period t.

[0016] The reservation time window is a selectable pickup time period provided to the user, including the earliest pickup time and the latest pickup time.

[0017] The user reservation request includes the pick-up time window, pick-up station and delivery station information selected by each user.

[0018] The flexible public transportation static scheduling model comprehensively considers factors including user travel time, vehicle travel time, and vehicle passenger capacity to establish constraints, and the flexible public transportation dynamic scheduling model comprehensively considers factors including the time between users in the vehicle and users planning to ride, and vehicle passenger capacity to establish constraints.

[0019] The request matching result includes whether the request will be served, the bus number assigned to the request, and the estimated pick-up time of the bus.

[0020] In order to maximize the benefits, the objective function of the flexible bus static scheduling model is:

[0021] max(C1+C2-C3-C4)

[0022] Where C1 is the revenue from serving expected real-time requests, C2 is the revenue from serving reservation requests, C3 is the vehicle operating cost, and C4 is the passenger travel time cost;

[0023]

[0024]

[0025]

[0026]

[0027] Where V is the set of bus stops; K is the set of buses; R WA A collection of pending reservation requests; is a decision variable, which represents the stopping time of vehicle k at station i; is a decision variable, indicating whether vehicle k serves order r, 1 for service and 0 for non-service; is a decision variable, indicating whether vehicle k passes through the road section (v i ,v j ); α is the unit service revenue, β is the unit vehicle travel time cost; γ is the unit passenger travel time cost; t p The length of the period for statistical site request probability; P i is the probability of a real-time request occurring at site i in period t; is the number of real-time requests to site i; d ij is the travel time of the bus from station i to station j; s r is the expected travel time of passenger r, e r is the direct bus travel time between the pick-up stop and the drop-off stop for passenger r.

[0028] The flexible bus static scheduling model meets the following constraints:

[0029] A1) Each order can only be served by one bus at most:

[0030]

[0031] A2) Time Constraints:

[0032] A21) The bus arrives at the pick-up point within the passenger's scheduled time window:

[0033]

[0034]

[0035] A22) The duration of a bus stop is the difference between the time the bus leaves and arrives at the stop:

[0036]

[0037] A23) The length of bus stops should be limited to the time it takes to serve passengers getting on and off the bus:

[0038]

[0039] A24) If the bus skips stop i, the stop time is 0, and the stop time is less than the maximum value:

[0040]

[0041] A25) If a vehicle passes through the road section (v i ,v j ), the vehicle arrives at v j The time at the station should be greater than the time at the departure i The sum of the time at the stop and the travel time on the segment:

[0042]

[0043] A3) Capacity constraint: The number of passengers in the vehicle cannot exceed the vehicle capacity limit, ensuring one person per seat:

[0044]

[0045]

[0046] A4) Flow balance means that except for the origin and destination stations, vehicle k arrives at station v i You need to leave after:

[0047]

[0048]

[0049] A5) Restricting buses to arrive at stops where passengers are getting on and off:

[0050]

[0051] A6) Constraints on one-way bus travel:

[0052]

[0053] A7) Variable constraints:

[0054]

[0055]

[0056] Where R is the request set; V rP is the set of pick-up stations for request r∈R, V rD is the set of destination sites for request r∈R; is a decision variable, indicating that vehicle k arrives at station v i time; is a decision variable, indicating that vehicle k leaves station v i time; is the number of passengers in vehicle k when it arrives at station i; is the number of passengers boarding at station i; is the number of passengers getting off at station i; cap k is the maximum passenger capacity of vehicle k; The earliest pick-up time in the reserved time window for the passenger, The latest pick-up time in the reserved time window for passengers; ser Unit service time; s max is the maximum stop time; M is a preconfigured large constant.

[0057] In order to maximize the benefits, the objective function of the flexible bus dynamic scheduling model is:

[0058] max(C5-C6)

[0059] Where C5 is the revenue from serving real-time requests, and C6 is the additional vehicle travel time cost from serving real-time requests.

[0060]

[0061]

[0062] Where R WE A collection of real-time requests to be processed; d U The travel time between stations that have not yet passed when the trigger is triggered.

[0063] The flexible bus dynamic scheduling model meets the following constraints:

[0064] B1) Each order can only be served by one bus at most:

[0065]

[0066] B2) Time constraints:

[0067] B21) For pending real-time requests, limit the bus arrival time at the pick-up point to within the user's expected boarding time range:

[0068]

[0069] B22) For real-time requests for scheduled services, the bus's arrival time at the pick-up stop cannot exceed the passenger's maximum waiting time at the stop:

[0070]

[0071] B23) For reservation requests for scheduled services, the bus's arrival time at the pick-up stop must not exceed the passenger's maximum waiting time at the stop, and its departure time must not be earlier than the vehicle's scheduled arrival time:

[0072]

[0073]

[0074] B24) The time it takes for a bus to arrive at the destination cannot exceed the maximum passenger delay time:

[0075]

[0076] B25) Calculate the bus stop time:

[0077]

[0078] B26) The vehicle's stop time should be sufficient to accommodate each passenger's boarding and alighting time:

[0079]

[0080] B27) Limit the maximum and minimum bus stop time:

[0081]

[0082] B28) If a vehicle passes through the road section (v i ,v j ), the vehicle arrives at v j The time at the station should be greater than the time at the departure i The sum of the time at the stop and the travel time on the segment:

[0083]

[0084] B3) Capacity constraint: The number of passengers in the vehicle cannot exceed the vehicle capacity limit, ensuring one seat per person:

[0085]

[0086]

[0087] B4) Flow balance means that except for the origin and destination stations, vehicle k arrives at station v i You need to leave after:

[0088]

[0089]

[0090] B5) Restrict buses to only pass through stops where passengers are getting on or off:

[0091]

[0092] B6) The first station in the station set has not yet been passed, and the arrival time and capacity are consistent with the last updated plan:

[0093]

[0094]

[0095] B7) Variable constraints:

[0096]

[0097]

[0098]

[0099] Where R SA The set of reservation requests for the planned service; R SE A collection of real-time requests for planning services; V P is the set of sites that have been passed; V U A collection of sites that have not yet been visited; is a decision variable, indicating that vehicle k arrives at station v i time; is a decision variable, indicating that vehicle k leaves station v i time; is a decision variable, indicating that vehicle k is at station v i Stop time; To request the user's expected ride time in real time; The time when the bus arrives at the pick-up point is fed back to the user in real time; The vehicle k arrives at station v, which is the feedback given to the user in the static stage. i time; The vehicle k that is fed back to the user in the static phase leaves the station v i time; The vehicle k at station v is fed back to the user in the static phase. i Stop time; s amax The maximum waiting time for passengers requesting a reservation; s delay is the longest stop time of the bus; s emax To request the maximum waiting time of passengers in real time; The number of times vehicle k arrives at station v in the last update plan i time; The number of times vehicle k arrives at station v in the last update plani The number of passengers in the car at that time.

[0100] Compared with the prior art, the present invention has the following beneficial effects:

[0101] (1) Compared with conventional public transportation, the present invention designs reservation time windows according to the density of travel demand, designs flexible skip-stop routes and timetables based on the user's personalized travel needs, and updates them dynamically. It can reduce unnecessary mileage in low passenger flow areas and non-peak hours, avoid empty trips and low load rates, improve service quality, and reduce operating costs.

[0102] (2) Compared with the existing technology, the present invention organically combines flexible bus static scheduling with dynamic scheduling. By adding the probability of real-time requests in static scheduling, the stations with a high possibility of real-time requests in the dynamic stage are taken into consideration, and the stop time at the corresponding stations is increased, which is conducive to improving the acceptance rate of real-time requests. BRIEF DESCRIPTION OF THE DRAWINGS

[0103] Figure 1 is a flow chart of the method of the present invention;

[0104] Figure 2 This is a bus skip-stop route map in one embodiment of the present invention. DETAILED DESCRIPTION

[0105] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0106] This embodiment provides a flexible bus dynamic and static coordinated scheduling method, such as Figure 1 As shown, the following steps are included:

[0107] Step 1) Obtain and count the historical request data of each bus station, and calculate the probability of real-time requests at each station in each time period:

[0108]

[0109] Where V is the set of bus stops; T is the set of time periods divided in a day; For site v i The number of real-time requests in period t.

[0110] like Figure 2 As shown in Figure 1, a bus route is 12 km long and has 13 stops numbered 1, 2, ..., and 13, with the distances between stops shown in Table 1. The nonlinearity coefficient is 2.82, and the bus trip time is 33 minutes. Two buses are in operation.

[0111] Table 1 Example Bus Stop Distance (m)

[0112]

[0113] Step 2) Design a reservation time window and aggregate user reservation requests before the deadline through the online platform, including the pick-up time window, pick-up station, and drop-off station information selected by each user.

[0114] The appointment time window is the optional pick-up time period provided to users, including the earliest pick-up time and the latest pick-up time

[0115] In one embodiment, the passenger reservation and real-time travel information within 30 minutes (7:00-7:30) is obtained as shown in Table 2. k For 20 people, the length of the reservation window Set to 30 minutes, the deadline for appointments is set to 30 minutes in advance.

[0116] Table 2 Example Passenger scheduled travel and real-time travel information

[0117]

[0118] Before the deadline, passengers submit reservation requests through mobile APP or online network platforms such as platforms, that is, submit travel requests for [7:00-7:30] before 6:30 and submit travel requests for [7:30-8:00] before 7:00.

[0119] Step 3) Based on the probability of real-time requests at each station and time period and user reservation requests, and taking into account constraints such as user travel time, vehicle travel time, and vehicle passenger capacity, a static scheduling model for flexible public transportation is established and solved. This model determines the skipping routes of flexible public transportation and the arrival, departure, and stop times of each station, thereby obtaining the initial scheduling plan for the flexible public transportation.

[0120] In order to maximize revenue, the objective function of the flexible bus static scheduling model is:

[0121] max(C1+C2-C3-C4) (2)

[0122] Where C1 is the revenue from serving expected real-time requests, C2 is the revenue from serving reservation requests, C3 is the vehicle operating cost, and C4 is the passenger travel time cost;

[0123]

[0124]

[0125]

[0126]

[0127] Where V is the set of bus stops; K is the set of buses; R WA A collection of pending reservation requests; is a decision variable, which represents the stopping time of vehicle k at station i; is a decision variable, indicating whether vehicle k serves order r, 1 for service and 0 for non-service; is a decision variable, indicating whether vehicle k passes through the road section (v i ,v j ); α is the unit service revenue, β is the unit vehicle travel time cost; γ is the unit passenger travel time cost; t p The length of the period for statistical site request probability; P i is the probability of a real-time request occurring at site i in period t; is the number of real-time requests to site i; d ij is the travel time of the bus from station i to station j; s r is the expected travel time of passenger r, e r is the direct bus travel time between the pick-up stop and the drop-off stop for passenger r.

[0128] The flexible bus static scheduling model satisfies the following constraints:

[0129] Constraint (7) indicates that each order can be served by at most one bus;

[0130]

[0131] Constraints (8)-(13) are time constraints;

[0132] Constraints (8) and (9) indicate that the bus's arrival time at the pick-up station is within the passenger's reservation time window;

[0133]

[0134]

[0135] Constraint (10) indicates that the bus stop duration is the difference between the bus departure time and arrival time;

[0136]

[0137] Constraint (11) limits the bus stop time to the time it takes to serve passengers getting on and off the bus;

[0138]

[0139] Constraint (12) means that if the bus skips station i, the stop time is 0, and the stop time is less than the maximum value;

[0140]

[0141] Constraint (13) means that if the vehicle passes through the road segment (v i ,v j ), the vehicle arrives at v j The time at the station should be greater than the time at the departure i The sum of the time at the stop and the journey time on the road segment;

[0142]

[0143] Constraints (14) and (15) are capacity constraints, which means that the number of passengers in the vehicle cannot exceed the vehicle capacity limit, ensuring that one person has one seat;

[0144]

[0145]

[0146] Constraints (16) and (17) are flow balance, which means that except for the origin and destination, vehicle k arrives at station v i You need to leave later;

[0147]

[0148]

[0149] Constraint (18) restricts the bus to arrive at the station where passengers get on and off;

[0150]

[0151] Constraint (19) indicates that the bus travels in one direction;

[0152]

[0153] Constraints (20)-(21) are variable constraints;

[0154]

[0155]

[0156] Where R is the request set; V rP is the set of pick-up stations for request r∈R, V rD is the set of destination sites for request r∈R; is a decision variable, indicating that vehicle k arrives at station v i time; is a decision variable, indicating that vehicle k leaves station v i time; is the number of passengers in vehicle k when it arrives at station i; is the number of passengers boarding at station i; is the number of passengers getting off at station i; cap k is the maximum passenger capacity of vehicle k; The earliest pick-up time in the reserved time window for the passenger, The latest pick-up time in the reserved time window for passengers; ser Unit service time; s max is the longest stop time; M is a large constant.

[0157] The flexible bus stop time obtained in this embodiment is shown in Table 3. The planned travel time is 25 minutes, and the bus route is:

[0158] Vehicle 1: 1→2→3→4→5→7→8→9→11→13

[0159] Vehicle 2:—

[0160] Table 3 Flexible bus stop schedule according to the embodiment

[0161]

[0162] Step 4) Feedback the user with the reservation request matching result, including whether the request will be served, the bus number assigned to take, and the estimated pick-up time of the bus, and instruct the bus to execute the initial scheduling plan.

[0163] In this embodiment, the online platform provides users with feedback on the matching results and the scheduled pick-up time. Passengers then go to the bus stop at the corresponding time. The bus executes the initial dispatch plan to respond to passenger needs.

[0164] Step 5) After the deadline, real-time user dynamic requests are obtained (passengers can submit real-time requests through mobile apps or online platforms such as bus platforms). Taking into account constraints such as the time constraints of users on board and those planning to board, as well as vehicle passenger capacity, a dynamic scheduling model for flexible public transportation is established and solved. The skip-stop routes and arrival, departure, and stop times of the flexible public transportation are updated to obtain an updated scheduling plan.

[0165] In order to maximize revenue, the objective function of the flexible bus dynamic scheduling model is:

[0166] maxC5-C6)(22)

[0167] Where C5 is the revenue from serving real-time requests, and C6 is the additional vehicle travel time cost from serving real-time requests.

[0168]

[0169]

[0170] Where R WE A collection of real-time requests to be processed; d U The travel time between stations that have not yet passed when the trigger is triggered.

[0171] The flexible bus dynamic scheduling model satisfies the following constraints:

[0172] Constraint (25) indicates that each order can be served by at most one bus;

[0173]

[0174] Constraints (26)-(34) are time constraints;

[0175] Constraint (26) limits the time when the bus arrives at the pick-up station to the user's expected boarding time for the real-time request to be processed;

[0176]

[0177] Constraint (27) For real-time requests for scheduled services, the time it takes for a bus to arrive at the pick-up station cannot exceed the maximum waiting time of passengers at the station;

[0178]

[0179] Constraints (28)-(30) for reservation requests for scheduled services;

[0180] Constraints (28) and (29) respectively indicate that the time for a bus to arrive at the pick-up station cannot exceed the maximum waiting time of passengers at the station, and the time for the bus to leave the pick-up station cannot be earlier than the time the vehicle is scheduled to arrive at the station;

[0181]

[0182]

[0183] Constraint (30) indicates that the time it takes for the bus to arrive at the delivery station cannot exceed the maximum delay time of the passenger;

[0184]

[0185] Constraint (31) calculates the bus stop time;

[0186]

[0187] Constraint (32) indicates that the vehicle's stop time should satisfy the time it takes for each passenger to get on and off the bus;

[0188]

[0189] (33) Limit the maximum and minimum bus stop times;

[0190]

[0191] Constraint (34) means that if the vehicle passes through the road segment (v i ,v j ), the vehicle arrives at v j The time at the station should be greater than the time at the departure i The sum of the time at the stop and the journey time on the road segment;

[0192]

[0193] Constraints (35) and (36) are capacity constraints, which means that the number of passengers in the vehicle cannot exceed the vehicle capacity limit, ensuring that one person has one seat;

[0194]

[0195]

[0196] Constraints (37) and (38) are flow balance, which means that except for the origin and destination, vehicle k arrives at station v i You need to leave later;

[0197]

[0198]

[0199] Constraint (39) restricts the bus to passing through stops where passengers are getting on or off;

[0200]

[0201] Constraints (40)-(41) indicate that the first station in the station set has not yet been passed, and the arrival time and capacity are consistent with the last updated plan;

[0202]

[0203]

[0204] Constraints (42)-(44) are variable constraints;

[0205]

[0206]

[0207]

[0208] Where R SA The set of reservation requests for the planned service; R SE A collection of real-time requests for planning services; V P is the set of sites that have been passed; V U A collection of sites that have not yet been visited; is a decision variable, indicating that vehicle k arrives at station v i time; is a decision variable, indicating that vehicle k leaves station v i time; is a decision variable, indicating that vehicle k is at station v i Stop time; To request the user's expected ride time in real time; The time when the bus arrives at the pick-up point is fed back to the user in real time; The vehicle k arrives at station v, which is the feedback given to the user in the static stage. i time; The vehicle k that is fed back to the user in the static phase leaves the station v i time; The vehicle k at station v is fed back to the user in the static phase. i Stop time; s amax The maximum waiting time for passengers requesting a reservation; s delay is the longest stop time of the bus; s emax To request the maximum waiting time of passengers in real time; The number of times vehicle k arrives at station v in the last update plan i time; The number of times vehicle k arrives at station v in the last update plan i The number of passengers in the car at that time.

[0209] This embodiment obtains the following results through the flexible public dynamic scheduling model: no update is performed when real-time request 9 is triggered, and when real-time request 10 is triggered, the flexible public transportation planned travel time is updated to 28 minutes, and the updated bus route is:

[0210] Vehicle 1: 1 → 2 → 3 → 4 → 5 → 7 → 8 → 9 → 11 → 12 → 13

[0211] Vehicle 2:—

[0212] Step 6) The online platform provides real-time feedback to the user on the request matching results, including whether the request will be served, the assigned bus number, and the estimated pick-up time. The passenger then proceeds to the stop at the corresponding time. The bus then executes the updated dispatch plan to respond to the passenger's needs.

[0213] The present method was compared with a flexible bus dynamic and static scheduling method and a conventional bus scheduling method. Flexible bus dynamic and static scheduling is static scheduling without incorporating the probability of real-time requests. Otherwise, the present method is identical. Conventional buses operate on fixed routes and schedules with a 10-minute departure interval. The comparison results of the three methods are shown in Table 4.

[0214] Compared with flexible public transportation dynamic and static scheduling, the flexible public transportation dynamic and static coordinated scheduling method of the present invention effectively improves the service rate of real-time requests. Compared with conventional public transportation, the flexible public transportation scheduling method of the present invention has a significant optimization effect, effectively reducing vehicle travel time and passenger travel time. This helps to reduce public transportation operating costs and improve public transportation service quality.

[0215] Table 4 Optimization effect of the present invention

[0216]

[0217] The above describes in detail the preferred embodiments of the present invention. It should be understood that those skilled in the art can make numerous modifications and variations based on the concepts of the present invention without inventive effort. Therefore, any technical solutions that can be derived by those skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined by the claims.

Claims

1. A flexible public transportation dynamic and static coordinated scheduling method, characterized in that: The following steps are involved: Obtain and count the historical request data of each bus station, and calculate the probability of real-time requests at each station in each time period; Design a reservation time window and gather user reservation requests before the deadline through the online platform; Based on the probability of real-time requests at each station and time period and user reservation requests, a flexible bus static scheduling model is established and solved to determine the flexible bus's skipping routes and the arrival, departure, and stopover times at each station, thus obtaining the initial flexible bus scheduling plan. Feedback the user's reservation request matching results and instruct the bus to execute the initial scheduling plan; After the deadline, users' dynamic requests are obtained in real time, and a dynamic dispatch model for flexible public transportation is established and solved. The flexible public transportation's skipping routes and the arrival, departure, and stop times of each station are updated to obtain an updated dispatch plan. Feedback the user with the real-time request matching results and instruct the bus to execute the updated dispatch plan; The probability of real-time requests occurring at each site in each time period is: Where V is the set of bus stops; T is the set of time periods divided in a day; For site v i The number of real-time requests in period t; In order to maximize the benefits, the objective function of the flexible bus static scheduling model is: max(C1+C2-C3-C4) Where C1 is the revenue from serving expected real-time requests, C2 is the revenue from serving reservation requests, C3 is the vehicle operating cost, and C4 is the passenger travel time cost; Where V is the set of bus stops; K is the set of buses; R wA A collection of pending reservation requests; is a decision variable, which represents the stopping time of vehicle k at station i; is a decision variable, indicating whether vehicle k serves order r, 1 for service and 0 for non-service; is a decision variable, indicating whether vehicle k passes through the road section (v i ,v j ); α is the unit service revenue, β is the unit vehicle travel time cost; γ is the unit passenger travel time cost; t p The length of the period for statistical site request probability; P i is the probability of a real-time request occurring at site i in period t; is the number of real-time requests to site i; d ij is the travel time of the bus from station i to station j; s r is the expected travel time of passenger r, e r is the direct bus travel time between the pick-up stop and the drop-off stop for passenger r; The flexible bus static scheduling model meets the following constraints: A1) Each order can only be served by one bus at most: A2) Time constraints include: the time for the bus to arrive at the pick-up station is within the passenger's reservation time window; the bus stop time is the difference between the bus's departure time and arrival time; the bus stop time must be sufficient to serve the passengers getting on and off; if the bus skips station i, the stop time is 0, and the stop time is less than the maximum value; if the vehicle passes through the road section (v i ,v j ), the vehicle arrives at v j The time at the station should be greater than the time at the departure i The sum of the time at the stop and the journey time on the road segment; A3) Capacity constraint, which means the number of passengers in the vehicle cannot exceed the vehicle capacity limit, ensuring one person per seat; A4) Flow balance means that except for the origin and destination stations, vehicle k arrives at station v i You need to leave later; A5) Restrict buses to arrive at stops where passengers are getting on or off; A6) One-way travel restrictions for buses; A7) Variable constraints, including for decision variables and constraints; In order to maximize the benefits, the objective function of the flexible bus dynamic scheduling model is: max(C5-C6) Where C5 is the revenue from serving real-time requests, and C6 is the additional vehicle travel time cost from serving real-time requests. Where R WE is the set of real-time requests to be processed; V is the set of bus stops; K is the set of buses; is a decision variable, indicating whether vehicle k serves order r, with 1 for service and 0 for non-service; α is the unit service revenue, and β is the unit vehicle travel time cost; is a decision variable, indicating whether vehicle k passes through the road section (v i ,v j );d ij is the travel time of the bus from station i to station j; d U The travel time between stations that have not been passed at the time of triggering; The flexible bus dynamic scheduling model meets the following constraints: B1) Each order can only be served by one bus at most; B2) Time constraints, including: for real-time requests to be processed, the time for the bus to arrive at the pick-up station must be within the user's expected boarding time range; for real-time requests for planned services, the time for the bus to arrive at the pick-up station must not exceed the maximum waiting time of the passengers at the station; for reservation requests for planned services, the time for the bus to arrive at the pick-up station must not exceed the maximum waiting time of the passengers at the station, and the time for the bus to leave the pick-up station must not be earlier than the time the vehicle is scheduled to arrive at the station; the time the bus arrives at the delivery station must not exceed the maximum delay time of the passengers; the bus stop time is calculated, and the stop time of the bus should meet the time taken for each passenger to get on and off the bus; the maximum and minimum values ​​of the bus stop time are limited; if the vehicle passes through the road section (v i ,v j ), the vehicle arrives at v j The time at the station should be greater than the time at the departure i The sum of the time at the stop and the journey time on the road segment; B3) Capacity constraint, which means the number of passengers in the vehicle cannot exceed the vehicle capacity limit, ensuring one person per seat; B4) Flow balance means that except for the origin and destination stations, vehicle k arrives at station v i You need to leave later; B5) Restricting buses to pass through stops where passengers are getting on or off; B6) The first station in the station set has not been passed yet, and the arrival time and capacity are consistent with the last updated plan; B7) Variable constraints, including for decision variables and constraints.

2. A flexible public transportation dynamic and static coordinated scheduling method according to claim 1, characterized in that: The reservation time window is a selectable pickup time period provided to the user, including the earliest pickup time and the latest pickup time.

3. A flexible public transportation dynamic and static coordinated scheduling method according to claim 1, characterized in that: The user reservation request includes the pick-up time window, pick-up station and delivery station information selected by each user.

4. A flexible public transportation dynamic and static coordinated scheduling method according to claim 1, characterized in that: The flexible public transportation static scheduling model comprehensively considers factors including user travel time, vehicle travel time, and vehicle passenger capacity to establish constraints, and the flexible public transportation dynamic scheduling model comprehensively considers factors including the time between users in the vehicle and users planning to ride, and vehicle passenger capacity to establish constraints.

5. The method for flexible public transportation dynamic and static coordinated scheduling according to claim 1 is characterized in that: The request matching result includes whether the request will be served, the bus number assigned to the request, and the estimated pick-up time of the bus.

6. A flexible public transportation dynamic and static coordinated scheduling method according to claim 1, characterized in that: The flexible bus static scheduling model meets the following constraints: A1) Each order can only be served by one bus at most: A2) Time Constraints: A21) The bus arrives at the pick-up point within the passenger's scheduled time window: A22) The duration of a bus stop is the difference between the time the bus leaves and arrives at the stop: A23) The length of bus stops should be limited to the time it takes to serve passengers getting on and off the bus: A24) If the bus skips stop i, the stop time is 0, and the stop time is less than the maximum value: A25) If a vehicle passes through the road section (v i ,v j ), the vehicle arrives at v j The time at the station should be greater than the time at the departure i The sum of the time at the stop and the travel time on the segment: A3) Capacity constraint: The number of passengers in the vehicle cannot exceed the vehicle capacity limit, ensuring one person per seat: A4) Flow balance means that except for the origin and destination stations, vehicle k arrives at station v i You need to leave after: A5) Restricting buses to arrive at stops where passengers are getting on and off: A6) Constraints on one-way bus travel: A7) Variable constraints: Where R is the request set; V rP is the set of pick-up stations for request r∈R, V rD is the set of destination sites for request r∈R; is a decision variable, indicating that vehicle k arrives at station v i time; is a decision variable, indicating that vehicle k leaves station v i time; is the number of passengers in vehicle k when it arrives at station i; is the number of passengers boarding at station i; is the number of passengers getting off at station i; cap k is the maximum passenger capacity of vehicle k; The earliest pick-up time in the reserved time window for the passenger, The latest pick-up time in the reserved time window for passengers; ser Unit service time; s max is the maximum stop time; M is a preconfigured large constant.

7. The method for flexible public transportation dynamic and static coordinated scheduling according to claim 1 is characterized in that: The flexible bus dynamic scheduling model meets the following constraints: B1) Each order can only be served by one bus at most: B2) Time constraints: B21) For pending real-time requests, limit the bus arrival time at the pick-up point to within the user's expected boarding time range: B22) For real-time requests for scheduled services, the bus's arrival time at the pick-up stop cannot exceed the passenger's maximum waiting time at the stop: B23) For reservation requests for scheduled services, the bus's arrival time at the pick-up stop must not exceed the passenger's maximum waiting time at the stop, and its departure time must not be earlier than the vehicle's scheduled arrival time: B24) The time it takes for a bus to arrive at the destination cannot exceed the maximum passenger delay time: B25) Calculate the bus stop time: B26) The vehicle's stop time should be sufficient to accommodate each passenger's boarding and alighting time: B27) Limit the maximum and minimum bus stop time: B28) If a vehicle passes through the road section (v i ,v j ), the vehicle arrives at v j The time at the station should be greater than the time at the departure i The sum of the time at the stop and the travel time on the segment: B3) Capacity constraint: The number of passengers in the vehicle cannot exceed the vehicle capacity limit, ensuring one seat per person: B4) Flow balance means that except for the origin and destination stations, vehicle k arrives at station v i You need to leave after: B5) Restrict buses to only pass through stops where passengers are getting on or off: B6) The first station in the station set has not yet been passed, and the arrival time and capacity are consistent with the last updated plan: B7) Variable constraints: Where R SA The set of reservation requests for the planned service; R SE A collection of real-time requests for planning services; V P is the set of sites that have been passed; V U A collection of sites that have not yet been visited; is a decision variable, indicating that vehicle k arrives at station v i time; is a decision variable, indicating that vehicle k leaves station v i time; is a decision variable, indicating that vehicle k is at station v i Stop time; To request the user's expected ride time in real time; The time when the bus arrives at the pick-up point is fed back to the user in real time; The vehicle k arrives at station v, which is the feedback given to the user in the static stage. i time; The vehicle k that is fed back to the user in the static phase leaves the station v i time; The vehicle k at station v is fed back to the user in the static phase. i Stop time; s amax Requesting the maximum waiting time for passengers for a reservation; s delay The maximum stop time for buses; s emax To request the maximum waiting time of passengers in real time; The number of times vehicle k arrives at station v in the last update plan i time; The number of times vehicle k arrives at station v in the last update plan i The number of passengers in the car at the time; V rP is the set of pick-up stations for request r∈R, V rD is the set of destination sites for request r∈R; is the number of passengers in vehicle k when it arrives at station i; is the number of passengers boarding at station i; is the number of passengers getting off at station i; cap k is the maximum passenger capacity of vehicle k; a ser Unit service time; s max is the maximum stop time; M is a preconfigured large constant.

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