A seat allocation method to reduce the risk of railway epidemic transmission

Abstract

The present invention discloses a seat allocation method for reducing the risk of railway epidemic transmission. The steps are as follows: obtaining train information and passenger information; establishing a railway train epidemic transmission and infection risk assessment method; obtaining an objective function in the train with the goal of minimizing the infection rate and maximizing the railway passenger ticket revenue according to the infection rate and passenger information; listing passenger group demand, infection rate, transportation capacity and social fairness constraints according to the objective function; solving the optimal solution of the model to obtain a seat allocation plan that takes into account the risk of epidemic transmission and the interests of the railway department. Based on the passenger group demand and infection rate constraints, the present invention establishes an optimization model with the seat allocation plan as the decision-making, and under the constraints of transportation capacity, group demand, infection rate, social fairness, etc., maximizes the railway department's revenue and minimizes the sum of infection rates as the goal, and obtains a seat allocation plan that takes into account the risk of epidemic transmission and the interests of the railway department, while ensuring the safety of passengers. Improve the economic benefits of the railway.

Description

Technical Field

[0001] The present invention relates to a method for optimizing railway passenger seat allocation for reducing the risk of epidemic spread and the probability of virus transmission in trains during the novel coronavirus infection epidemic. Background Art

[0002] The COVID-19 epidemic has become a major public health emergency in the world's history with the widest spread, fastest spread, and most difficult protection. As one of the main modes of long-distance transportation, railway passenger transport is not only the main artery of the national economy, but also an important link in controlling the spread of the COVID-19. Moreover, due to the long transportation time and the confined and narrow space of the train, the spread of the COVID-19 among railway passengers may be accelerated. Therefore, it is urgent to formulate an appropriate seat allocation strategy to reduce the risk of COVID-19 transmission on trains.

[0003] For railway operating departments, seat allocation is to optimize the allocation of seats (i.e. ticket quotas) based on passenger demand in the train operating section to increase train seat occupancy and improve railway operating efficiency. During the COVID-19 epidemic, when there are too many passengers on the train, the safe distance between passengers is reduced, which will increase the risk of COVID-19 transmission; when there are too few passengers on the train, the safe distance between passengers can be effectively guaranteed, but the railway's passenger ticket revenue will decrease. Therefore, how to formulate a train seat allocation strategy to balance the relationship between the risk of COVID-19 transmission and railway revenue has become an important research issue. Summary of the invention

[0004] The purpose of the present invention is to provide a seat allocation method that reduces the risk of railway epidemic transmission, so as to ensure that the railway department's revenue is increased under the premise of curbing the spread of the new coronavirus infection epidemic on trains.

[0005] The technical solution of the present invention is: a seat allocation method for reducing the risk of railway epidemic transmission, comprising the following steps:

[0006] Step S1, obtaining train information and passenger information;

[0007] Step S2, establishing a railway train epidemic transmission and infection risk assessment method;

[0008] Step S3, obtaining an objective function with the objectives of minimizing the infection rate and maximizing the railway ticket revenue within the train according to the infection rate and passenger information;

[0009] Step S4, based on the objective function, list passenger group demand, infection rate, transportation capacity and social fairness constraints;

[0010] Step S5, obtaining the optimal solution of the model according to the heuristic algorithm or solver, and obtaining a seat allocation plan that takes into account both the risk of epidemic transmission and the interests of the railway department.

[0011] Furthermore, the epidemic spread and infection risk assessment method in step S2 uses the infection rate parameter for assessment, and the infection rate SR is a standard normal function of z∈(x,y) in the x and y directions, and its size parameters a, b, c are used to determine the shape of the curve. The infection rate calculation formula and parameter settings are as follows:

[0012]

[0013] Among them, ax=0.6, bx=2.5, cx=0.25, ay=0.65, cy=2.7, cy=0.

[0014] The technical effect of the present invention is that: based on the passenger group demand and infection rate constraints, the present invention establishes an optimization model with seat allocation plan as the decision-making, and maximizes the railway department's revenue and minimizes the sum of infection rates under the constraints of transportation capacity, group demand, infection rate, social fairness, etc., and designs a solution algorithm to design a seat allocation plan that takes into account the risk of epidemic transmission and the interests of the railway department, thereby improving the economic benefits of the railway while ensuring the safety of passenger transportation. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a flow chart of the present invention.

[0016] Figure 2 It is the train operation route diagram of the present invention.

[0017] Figure 3 This is a distribution diagram of infected patients in the present invention.

[0018] Figure 4 This is a diagram of seat allocation results in the present invention.

[0019] Figure 5 This is a diagram of the "sitting with alternate numbers" strategy in the present invention. DETAILED DESCRIPTION

[0020] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0021] See also Figure 1 , Figure 1The flowchart of the present invention. A seat allocation method for reducing the risk of railway epidemic transmission of the present invention has the following steps: 1. Obtain train information and passenger information, and give the definition of each variable in the model; 2. Establish a railway train epidemic transmission and infection risk assessment method; 3. According to the infection rate and passenger information, obtain the objective function in the train with the goal of minimizing the infection rate and maximizing the railway passenger ticket revenue; 4. According to the objective function, list the constraints such as passenger group demand, infection rate, transportation capacity, social fairness, etc.; 5. Design a solution algorithm to obtain a seat allocation plan that takes into account the risk of epidemic transmission and the interests of the railway department.

[0022] 1. Get information

[0023] like Figure 2 As shown, a train has a starting station A, stop stations B and C, and a terminal station C on its route.

[0024] 1.1 Get train information: the number of OD pairs of the train is J=6, the number of sections passed is I=4, the train transportation capacity on the i-th section is Ci=20, the number of rows of seats in the carriage is M=4, and the number of columns is N=5.

[0025] 1.2 Obtaining passenger information: There are K = 16 passenger groups in total. The corresponding relationship between groups and OD pairs is shown in Table 2.

[0026] 1.3 Symbol Definition: j represents the jth OD pair, j∈{1,2,…,J}; k represents the kth group, k∈{1,2,…,K}; i represents the ith segment, i∈{1,2,…,I}; m represents the mth row, m∈{1,2,…,M}; n represents the nth column, n∈{1,2,…,N}; W j represents the set of communities on the jth OD pair; U i represents the set of groups that pass through segment i; V k represents the set of segments that group k passes through; P j represents the fare of the jth OD pair; G k represents the number of members of the kth group; C i represents the train transport capacity on the i-th section. In this paper, without considering train overcrowding, the section transport capacity is the train capacity C; μ represents the available seat ratio coefficient; SR r represents the infection rate (shedding rate) of contact type r; the three decision variables are: Z k Z indicates that the request of the kth group is accepted k =1; otherwise, Z k =0; It means that the member from group k is sitting in row m and column n. otherwise, represents the cumulative sum of the infection rates of members of other groups to members from group k sitting in row m and column n.

[0027] Table 2 Correspondence between groups and OD pairs

[0028]

[0029] 2. Infection risk assessment methods

[0030] The infection rate SR calculation formula and parameter settings are as follows:

[0031]

[0032] Among them, a x =0.6,b x =2.5,c x =0.25,a y =0.65,b y =2.7,c y =0.

[0033] Distribution of infected patients Figure 3 As shown. Letters represent infected patients, and numbers represent the type of contact with infected patients. "1" represents sitting next to the patient, "2" represents sitting in front of the patient, "3" represents sitting diagonally in front of the patient, "4" represents sitting apart from the patient, and "5" and "6" represent sitting across the aisle from the patient.

[0034] The article assumes that the seat width and aisle width are 0.4m, and the distance between the front and back seats is 0.8m. Based on the above infection rate calculation formula, the infection rates obtained by different contact types are: SR1 = 0.99987, SR2 = 0.9226, SR3 = 0.9126, SR4 = SR5 = 0.6833, SR6 = 0.6315.

[0035] 3. Objective Function

[0036] 3.1 Calculate railway ticket revenue:

[0037]

[0038] Where Pj refers to the ticket price.

[0039] 3.2 Calculate the risk of epidemic transmission on trains:

[0040]

[0041] In the formula It refers to the cumulative infection rate of members from other groups on members from group k sitting in row m and column n in the i-th interval.

[0042] 3.3 Objective function:

[0043] maxαO1-(1-α)O2

[0044] The formula allocates seats with the goal of maximizing the railway sector's revenue and minimizing the risk of epidemic transmission on trains. α refers to the weighting coefficient.

[0045] 4. Constraints

[0046] 4.1 Section seat capacity constraint: When a train runs in any section, the sum of the cumulative ticket quotas of all OD pairs in each section shall not exceed the capacity limit of that section.

[0047]

[0048] Where μ refers to the capacity control ratio.

[0049] 4.2 Restrictions on the number of group members:

[0050]

[0051] In the formula is a 0-1 variable, when a member from group k sits in row m and column n otherwise,

[0052] 4.3 Seat quantity constraint: In any section, each seat can be allocated to at most one member of a group.

[0053]

[0054] 4.4 Order priority constraints:

[0055] Z k(1) ≥Z k(2) ≥Z k(3) ≥…≥Z k(16) ,k∈W j

[0056] Here k(T) represents the arrival order, k(1) refers to the first arriving group, and k(16) refers to the last arriving group.

[0057] 4.5 Decision variable constraints:

[0058]

[0059] 4.6 Infection rate constraint: To calculate the infection rate of k groups of passengers sitting in row m and column n in interval i We calculate based on the positions of other group passengers sitting in the same row m and the previous row m-1.

[0060] 4.6.1 Infection rate constraints in the first row:

[0061]

[0062] 4.6.2 Infection rate constraints in the second row and beyond:

[0063]

[0064] 5. Solving Algorithm

[0065] 5.1 Use the solver CPLEX to solve the above optimization model.

[0066] 5.2 Solving the problem The seat allocation scheme is to arrange the passengers of group k to the seats of m rows and n columns. Matlab software and yalmip toolbox are used to call CPLEX for solution. The solution time is 32 seconds. The seat allocation result is as follows: Figure 4 As shown, the optimal solution of the objective function is 57.2, where the railway revenue is 268 and the infection rate is 0.

[0067] In order to illustrate the superiority of the proposed method, three different seat allocation methods were designed for comparison, with the same settings for each parameter.

[0068] The "first come, first served" ticketing strategy refers to accepting the needs of passenger groups in the order in which passengers purchase reservations. As long as the necessary condition of not exceeding the interval capacity constraint is met, the railway department will not refuse the needs of passenger groups until it can no longer accept them. In other words, the passenger group will know immediately whether their request is accepted, but the specific seat position will not be allocated until all the demands are accepted. The ticketing strategy of maximizing revenue here refers to maximizing the railway passenger ticket revenue through the objective function according to the needs of the passenger group, so as to decide which passenger group's requests to accept. In other words, the passenger group submits the request first, and then knows whether their request is accepted and the specific seat position arrangement after acceptance.

[0069] The "separate number sitting" method is as follows Figure 5 The group allocation principle is a method adopted by the present invention, which makes the positions of each passenger group member as close as possible, while the distances between different groups are as far as possible.

[0070] The four strategies are as follows:

[0071] Strategy 1: Not considering two optimization goals: the "first come, first served" ticketing strategy and the "seating in alternate numbers" method for groups.

[0072] Strategy 2: Only consider minimizing the risk of epidemic transmission: "first come, first served" ticket sales strategy and the principle of group allocation.

[0073] Strategy three: Only consider profit maximization: the ticket selling strategy of maximizing profit and the method of "sitting in alternate numbers".

[0074] Strategy 4: The seat optimization method adopted in this article takes into account both maximizing passenger ticket revenue and minimizing the risk of epidemic transmission: the ticket sales strategy of maximizing revenue and the principle of group allocation.

[0075] Table 3 Comparison of 4 strategies

[0076] Strategy 1 Strategy 2 Strategy Three Strategy 4 Railway revenue 268 268 286 286 Infection rate 10.6033 0.6315 12.1485 0 Objective function value 17.53 26.23 17.70 28.60

[0077] The comparison of the four strategies is shown in Table 3. By comparing the objective function values, it can be concluded that the objective function value of strategy 4 is the largest, which is 28.6. Among them, the railway revenue is also the largest, 286, and the infection rate is the smallest, 0. By comparing with other methods, it is shown that the seat optimization method proposed in this paper is the best.

Claims

1. A seat allocation method for reducing the risk of epidemic spread on railways, characterized in that: The following steps are involved: Step S1, obtaining train information and passenger information; Step S2, establish a railway train epidemic transmission and infection risk assessment method; specifically: use infection rate parameters for assessment, infection rate For and Directional The standard normal function of is: in, ; Step S3, based on the infection rate and passenger information, obtain the objective function with the goal of minimizing the infection rate and maximizing the railway ticket revenue in the train; the objective function is: , is the weighting coefficient, , They are railway ticket revenue and the risk of epidemic transmission on trains; Step S4, based on the objective function, list the passenger group demand, infection rate, transportation capacity and social fairness constraints; Step S5, obtaining the optimal solution of the model according to the heuristic algorithm or solver, and obtaining a seat allocation plan that takes into account both the risk of epidemic transmission and the interests of the railway department.

2. The seat allocation method for reducing the risk of railway epidemic transmission according to claim 1 is characterized in that: The railway ticket revenue is: In the formula Refers to the fare, Indicates OD pairs, , Indicates groups, ; Indicates The number of members in a group; Indicates When the request of a group is accepted ;otherwise, .

3. The seat allocation method for reducing the risk of railway epidemic transmission according to claim 1, characterized in that: The risk of epidemic transmission on the train is: In the formula Point to the interval, members of other groups sit Row Column from The cumulative infection rate of group members, Indicates Row, ; Indicates List, .

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