Question B: Urban rail transit train timetable optimization problem
The problem of train schedule optimization is one of the classic problems of train organization in the field of rail transit. The train timetable stipulates the arrival and departure (or passing) time of trains at each station, which is usually represented by a train diagram in actual operation. Figure 1 is an example of a running diagram. Each line in the figure represents a train, the horizontal axis represents a station, and the vertical axis represents time. Each line reflects the relative position of a train at different times, also known as run line. For example, the red running line in the picture indicates that the train departs from Station D at 9:02, arrives at Station C at 9:05, leaves after staying for 1 minute, arrives at Station B at 9:09, and departs after staying for 1 minute. Arrived at 10:03
Station A.
Figure 1: Schematic diagram of train operation diagram
In actual operation, before drawing the train operation diagram, the train operation plan must first be determined. The train operation plan includes three parts: the train marshalling plan, the train stop plan and the train crossing plan.
The train formation plan stipulates the type of train and the number of formations (that is, the number of sections of the train). In this problem, a unified type of type and number of formations is used.
The train stop plan is a plan that stipulates which stations the train stops at. In this problem, the station stop plan is adopted (that is, the train will stop at each passing station).
The train routing plan refers to the way trains run back and forth on the specified operating lines, that is, it specifies which stations the trains run between and the number of trains. The large and small traffic mode is a commonly used traffic mode in urban rail operations, and refers to the length and length of urban rail transit lines. In layman's terms, a large crossing means that the train runs the entire distance, and a small crossing means that a certain two stations in the whole journey are used as temporary starting points or ending points. station) can be used as the starting point or ending point of the intersection. Figure 2 is a schematic diagram of a large and small intersection scheme, which shows that 10 pairs of trains run on the large intersection starting from station A and ending at station D, and 5 pairs of trains run on the small intersection starting from station A and ending at station C.
In the large and small crossing scheme, the number of rows and trains of large and small crossing trains is usually 1:n or n:1, that is, after every n large (small) crossing trains, one small (large) crossing train runs , and the number of stations that the small crossing roads pass through must be limited: too short a small crossing road section will lead to frequent turn-backs of trains, which will increase operating costs; too long a small crossing road section will not reflect the operation mode of the large and small crossing roads.
effect.
Figure 2: Schematic diagram of large and small intersections
In the operation mode of large and small crossroads, passengers are usually divided into 6 types, as shown in Figure 3,
Among them, 
!− 
n is the interval of large intersection, and 
a− 
b is the interval of small intersection.
Passengers of categories I, II, and III all start at [ 
! , 
a], and no matter which section the end point is in, passengers can only take large-scale cross-road trains.
Class IV and V passengers start at [ 
a, 
b]. Among them, the terminal of category IV passengers is located at [ 
a, 
b], and passengers can take either large-interchange trains or small-interchange trains; the terminal of category V passengers is located at [ 
b, 
n], passengers can take small-interchange trains Go to 
b to transfer, or directly take the Dajiao train.
Class VI passengers start at [ 
b, 
n] and end at [ 
b, 
n]. Passengers can only take Dajiao Road
train.
Figure 3: Schematic diagram of passenger type classification
In the formulation of the train operation plan, it is necessary to meet the needs of the passenger flow with the minimum operating cost and the maximum service level (passenger on-board time and passenger waiting time). The operating cost of the enterprise includes fixed costs (the number of vehicles required) and the variable cost (total kilometers traveled by the train) are composed of two parts. Due to the constraints of station capacity and service level requirements, the number of trains departing within a certain period of time is also limited.
After formulating the train operation plan, the train operation diagram can be drawn according to the plan with the same goal of minimizing the operating cost of the enterprise and maximizing the service level, that is, to determine the departure and arrival of each train
specific moment. Existing train timetables are usually parallel running graphs with equal intervals, that is, the departure interval (such as a train every 5 minutes) and the stop time at the same station are equal. There will be certain restrictions on the length of the departure interval: if the departure interval is too short, it will affect the safety of train operation; if the departure interval is too long, it will increase the average waiting time of passengers, thereby affecting the service level. Similarly, the stop time also needs to be limited. Generally speaking, the stop time of a train at a station is proportional to the number of passengers getting on and off at that station. In addition, it should be noted that when two trains are tracking and running in the same section, a certain safety interval (tracking interval) needs to be kept.
In the train operation diagram of the operation mode of large and small intersections, trains on large and small intersections will generally run alternately. For example, when the ratio of trains on large and small intersections is 2:1, trains on every three lines It is a combination (the first 2 trains are large crossing trains, and the third train is a small crossing train).
In the following problems, it is only necessary to develop a one-way train schedule.
Question 1: Under the condition of satisfying the demand of passenger flow, and aiming at minimizing the operating cost of the enterprise and maximizing the service level, formulate a train operation plan. That is to determine the running number of trains in the section of large crossing roads, the running interval and running number of small crossing roads. (The output format is detailed in Appendix 6)
Question 2: Under the train operation plan formulated in Question 1, we also aim to minimize the operating cost of the enterprise, maximize the service level and meet the passenger flow demand as much as possible, and formulate a parallel operation diagram with equal intervals. (For details on the output format, please refer to Attachment 7, and upload Attachment 7 to the competition system separately)
Question 3: What good methods or suggestions does your team have for reducing operating costs and improving service levels? Based on passenger flow and station data, provide corresponding quantitative analysis support.
Glossary:
Passenger on-board time: the time elapsed by passengers from getting on the train to getting off the train, including the running time of the train section and the stop time.
Passenger waiting time: It is the waiting time of passengers waiting at the platform.
Cross-section passenger flow: the number of passengers passing through a certain section of the line along the same direction within a unit time.
How to calculate the number of trains required for each section according to the passenger flow of the section: number of trains = ⌈passenger flow of the section/train capacity ⌉ (rounded up).
OD passenger flow: the number of passengers from the starting station to the ending station within a unit time.
Supplementary explanation on equal intervals: When using the operation mode of large and small intersections, equal intervals mean that the departure intervals in the overlapping sections of large and small intersections are equal.
Input and output data:
The given data is the real data of an actual rail transit line. There are 30 stations along the route, and the period of passenger flow data is 7:00 - 8:00. See the appendix for details.
Attachment 1: Station Data.xlsx
Attachment 2: Interval running time.xlsx
Attachment 3: OD Passenger Flow Data.xlsx
Attachment 4: Cross-sectional passenger flow data.xlsx
Attachment 5: Other data.xlsx
Attachment 6: Output Example of Question 1.xlsx
Attachment 7: Example output of question 2.xlsx