A Security Personnel Scheduling Method for Terminal Considering the Randomness of Personnel Requirements

Abstract

The present invention discloses a method for scheduling security inspection personnel in a terminal considering the randomness of personnel requirements, belonging to the field of personnel scheduling. The method includes the following steps: grouping security inspection employees to obtain the grouped security inspection employees; obtaining the passenger arrival rate information for each time period of each day on a weekly basis; determining the security inspection queue length based on the passenger arrival rate information; constructing a personnel allocation model based on the security inspection queue length and the grouped security inspection employees; converting the personnel allocation model into a mixed integer programming model to obtain the personnel requirement quantity for each time period; constructing a security inspection personnel scheduling model considering the randomness of personnel requirements based on the personnel requirement quantity; and converting the security inspection personnel scheduling model considering the randomness of personnel requirements into a deterministic model to obtain a personnel scheduling plan.

Description

Technical Field

[0001] The present invention belongs to the technical field of personnel scheduling, and particularly relates to a scheduling method for security inspection personnel in the terminal considering the randomness of personnel requirements. Background Art

[0002] In modern air transportation, terminal security inspection is one of the key links to ensure civil aviation safety. With the continuous increase in air passenger flow, how to efficiently and accurately arrange the scheduling of security inspection personnel to cope with the changing passenger flow has become a major challenge. Traditional scheduling methods usually rely on historical data and fixed patterns for personnel allocation. This method often lacks flexibility and response speed when dealing with peak periods or emergencies, and cannot effectively respond to changes in the demand for security inspection personnel in situations such as flight delays, fluctuations in passenger flow, and special holidays. When the allocation of security inspection personnel cannot meet the needs of passenger security inspection, terminal managers need to temporarily dispatch personnel, which will interfere with the normal life of employees.

[0003] Considering the uncertainty and randomness of passenger arrivals, reasonably scheduling the security inspection personnel in the terminal can not only reduce the operating costs of the airport terminal, improve operational efficiency, but also reduce the waiting time of passengers, bring a more comfortable travel experience for passengers, and improve the service level of the airport. Therefore, there is an urgent need to propose a scheduling method for security inspection personnel in the terminal considering the randomness of personnel requirements. Summary of the Invention

[0004] To solve the above technical problems, the present invention proposes a scheduling method for security inspection personnel in the terminal considering the randomness of personnel requirements to solve the problems existing in the above prior art.

[0005] To achieve the above object, the present invention provides a scheduling method for security inspection personnel in the terminal considering the randomness of personnel requirements, including:

[0006] Grouping security inspection employees to obtain the grouped security inspection employees;

[0007] Obtaining the passenger arrival rate information for each time period of each day on a weekly basis;

[0008] Determining the security inspection queue length based on the passenger arrival rate information;

[0009] Constructing a personnel allocation model based on the security inspection queue length and the grouped security inspection employees;

[0010] Converting the personnel allocation model into a mixed integer programming model to obtain the number of personnel required for each time period;

[0011] Constructing a security inspection personnel scheduling model considering the randomness of personnel requirements based on the number of personnel required;

[0012] Convert the security personnel scheduling model considering the randomness of personnel requirements into a deterministic model to obtain a personnel scheduling plan.

[0013] Optionally, the calculation formula for the security queue length is:

[0014] L t-1 +λ t ·Δ=l(ρ t ,s t )+ρ t ·s t ·μ·Δ

[0015] In the formula, L t-1 is the system queue length at the end of the (t - 1) period, λ t ·Δ is the number of passengers entering the system in the t period, ρ t ·s t ·μ·Δ is the number of passengers leaving the system in the t period, l(ρ t ,s t ) is the steady - state queue length of the system, and Δ is the length of the time period.

[0016] Optionally, construct the personnel allocation model with the goal of minimizing the total working hours of all teams within a week; the expression of the personnel allocation model is:

[0017]

[0018] In the formula, Ld,t represents the system queue length at the end of the t period on the d - th day, L d,0 = 0 sets the queue length of the first period of each day to zero, ρ d,t represents the service intensity within the t period on the d - th day, the parameter L max represents the maximum security queue length, L max is the maximum security queue length, L d,t-1 is the system queue length at the end of the (t - 1) period on the d - th day, Δ is the length of the time period, l is the calculation formula for the steady - state queue length, q d,t is the number of working teams within the t period on the d - th day, and μ is the service rate of the team.

[0019] Optionally, convert the personnel allocation model into a mixed - integer programming model to obtain the calculation formula for the number of personnel requirements in each period:

[0020]

[0021] In the formula, p d,t,k indicates whether there are k teams working in the t period, ρ d,t,k,v indicates the value of ρ d,t in the interval v when there are k teams working, R k,vDenote the length of interval v when there are k groups working, E is the total number of groups, k is the number of working groups, and y d,t is the number of working groups in the t-th period of the d-th day, and L d,t is the queue length of the system at the end of the t-th period of the d-th day, V is the number of intervals, and S k,v is the slope of the linear function on interval v when there are k groups working, and ρ d,t,k,v is ρ when there are k groups working d,t at interval v. μ is the service rate of the group, Δ is the length of the time period, and L d,t-1 is the queue length of the system at the end of the (t - 1)-th period of the d-th day, and λ d,t is the passenger arrival rate information for each period of each day.

[0022] Optionally, the expression of the security personnel scheduling model considering the randomness of personnel requirements is:

[0023]

[0024]

[0025] In the formula, represents the expectation of the cost required to adjust personnel, and the decision variable y d,t represents the number of groups working in the t-th period of the d-th day, respectively represent the number of groups increased and decreased in the t-th period of the d-th day, and h d,t (ξ) represents the number of groups after adjustment in the t-th period of the d-th day, and R d,t (ξ) represents the number of group requirements after change in the t-th period of the d-th day. The parameter c represents the labor cost of the group going to work, and the parameter c + , c - respectively represent the unit costs of the number of groups increased and decreased.

[0026] Optionally, the constraint conditions that the decision variable also satisfies include: Each group is arranged at most one shift per day, the weekly working hours of each group do not exceed the maximum working hours, the number of groups going to work in each period of each day is greater than the number of groups required, the time interval of each shift of each group is greater than the shortest interval time period, and the maximum number of working days per week of each group is less than the maximum number of working days.

[0027] Optionally, the process of converting the security personnel scheduling model considering the randomness of personnel requirements into a deterministic model includes converting the expectation of the cost required to adjust personnel into a deterministic form;

[0028] Among them, the expression for converting the expectation of the cost required to adjust personnel into a deterministic form is:

[0029]

[0030] In the formula, respectively represent the number of increased teams and the number of decreased teams in the t period of day d under scenario k, and h d,t (ξ k ) represents the adjusted number of teams in the t period of day d under scenario k, and R d,t (ξ k ) represents the changed team demand quantity in the t period of day d under scenario k. The parameter c represents the labor cost of the teams going to work, and the parameters c + , c - respectively represent the unit costs of the increased number of teams and the decreased number of teams.

[0031] Compared with the prior art, the present invention has the following advantages and technical effects:

[0032] In the process of generating the security inspection personnel scheduling plan, the present invention considers the randomness of personnel requirements. The constructed model can effectively cope with the changes in personnel requirements and avoid excessive personnel redundancy and personnel shortage;

[0033] When constructing the constraint conditions of the personnel model, the present invention considers the constraint of the security inspection queue length. The constructed model can intuitively reflect the operation state of the security inspection queue channel;

[0034] The present invention provides a security inspection personnel scheduling method considering the randomness of personnel requirements, which can provide a scientific basis and suggestions for the terminal manager to generate a scheduling plan. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] The drawings constituting a part of this application are used to provide a further understanding of this application. The schematic embodiments of this application and their descriptions are used to explain this application and do not constitute an improper limitation to this application. In the drawings:

[0036] Figure 1 is a flowchart of a security inspection personnel scheduling method for a terminal considering the randomness of personnel requirements according to an embodiment of the present invention;

[0037] Figure 2 is a schematic diagram of the passenger arrival rate at each time period within a week according to an embodiment of the present invention;

[0038] Figure 3 is a schematic diagram of the number of working teams at each time period within a week according to an embodiment of the present invention;

[0039] Figure 4 is a schematic diagram of the security inspection queue length at each time period within a week according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0040] It should be noted that, without conflict, the embodiments in the present application and the features in the embodiments may be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0041] It should be noted that the steps shown in the flowchart of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although the logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in a different order than here.

[0042] Embodiment 1

[0043] As Figure 1 shown, in this embodiment, a method for scheduling security inspection personnel in a terminal considering the randomness of personnel requirements is provided, including the following steps:

[0044] Step 1: Obtain security inspection employee information and divide the employees into groups.

[0045] Six security inspection employees are required to work simultaneously at one security inspection channel. Six security inspection employees are divided into one group, and each group is numbered. The security inspection employee group is represented by the set ε = {1, 2,..., |E|}.

[0046] Step 2: Obtain the dates of a week for which a scheduling plan needs to be generated, divide each day into time periods of equal length, and obtain the passenger arrival rate information for each time period of each day.

[0047] Each day within the entire week is represented by the set where |D| = 7. Each day is divided into 24 time periods of equal length, each time period is 1 h, the length of the time period is represented by Δ, and the set represents each time period within a day, |T| = 24, and the passenger arrival rate information for each time period of each day is obtained. The symbol λ d,t represents the passenger arrival rate at the t-th time period on the d-th day, with the unit of person / hour.

[0048] Step 3: Given the assumptions for simplifying the calculation of the security inspection queue length.

[0049] The arrival of passengers at the security inspection channel is a random and non-stationary process. Assume: (1) The passenger arrival rate does not change within half an hour, and the passenger arrival is a non-stationary Poisson process with the arrival rate changing over time; (2) Passengers undergoing security inspection follow the first-come, first-served principle, and passengers leave the security inspection system after passing through the security inspection; (3) The security inspection service time follows an exponential distribution.

[0050] Step 4: Establish a method for calculating the security inspection queue length.

[0051] For an M / M / s queuing system, ρ represents the service intensity and s represents the number of servers. The queuing length in the steady state of the system is calculated as follows:

[0052]

[0053] For the security check queuing system, the system state is calculated using the point-by-point stationary fluid approximation method. For time period t, the flow balance equation is as follows:

[0054] L t-1 +λ t ·Δ=L t +ρ t ·s t ·μ·Δ

[0055] In the equation, L t represents the system queue length at the end of time period t, λ t represents the passenger arrival rate during time period t, λ t ·Δ represents the number of passengers entering the system during time period t, ρ t represents the service intensity during time period t, with a value between 0 and 1, s t represents the number of working groups during time period t, and the parameter μ represents the service rate of each group. ρ t ·s t ·μ·Δ represents the number of passengers leaving the system during time period t.

[0056] Assume that the queuing system can reach a steady state at the end of each time period t. Then L t can be calculated using the steady-state system queue length formula l(ρ, s). The flow balance equation can be rewritten as:

[0057] L t-1 +λ t ·Δ=l(ρ t ,s t )+ρ t ·s t ·μ·Δ

[0058] where L t-1 is the system queue length at the end of time period t - 1, λ t ·Δ is the number of passengers entering the system during time period t, ρ t ·s t ·μ·Δ is the number of passengers leaving the system during time period t, and l(ρ t ,s t ) is the queuing length in the steady state of the system. Δ is the length of the time period. The system queue length L t at the end of time period t can be calculated through this equation.

[0059] This equation is about ρ tThe non-linear equation can be quickly solved by the bisection method.

[0060] Step 5: Construct a staffing model.

[0061] The objective function of the staffing model is to minimize the total working hours of all teams within a week, and its mathematical expression is as follows:

[0062]

[0063] Among them, the decision variable q d,t represents the number of teams working in the t-th period on the d-th day, taking positive integer values, and Δ is the length of the time period.

[0064] The constraint condition of the staffing model is to control the queue length in each period within a week within a given range, and its mathematical expression is as follows:

[0065]

[0066] Among them, L d,t represents the system queue length at the end of the t-th period on the d-th day, which can be calculated by the method in Step 4. L d,0 = 0 sets the queue length at the first period of each day to zero. ρ d,t represents the service intensity within the t-th period on the d-th day. The parameter L max represents the maximum security check queue length. L max is the maximum security check queue length. L d,t-1 is the system queue length at the end of the (t - 1)-th period on the d-th day. Δ is the length of the time period, l is the calculation formula for the steady-state queue length, q d,t is the number of working teams within the t-th period on the d-th day, and μ is the service rate of the team.

[0067] Step 6: Linearize the security check queue length calculation formula, transform the staffing model into a mixed-integer linear programming model, and call the solver to solve the mixed-integer linear programming model to obtain the number of working teams q required for the d-th day and t-th period within a week d,t .

[0068] Consider introducing some variables and rewrite the queue length calculation formula in the constraint condition in Step 5 into the following form.

[0069]

[0070] ρ d,t,k,v ≤ p d,t,k R k,v

[0071]

[0072] Among them, p d,t,kIndicates whether there are k groups working in the t period, with values of 0 and 1, ρ d,t,k,v Indicates ρ when there are k groups working d,t The value on the interval v, R k,v Indicates the length of the interval v when there are k groups working, E is the total number of groups, k is the number of working groups, y d,t Is the number of working groups in the t period of the dth day, L d,t Is the queue length of the system at the end of the t period of the dth day, V is the number of intervals, S k,v Is the slope of the linear function on the interval v when there are k groups working, ρ d,t,k,v Is ρ when there are k groups working d,t The value on the interval v, μ is the service rate of the group, Δ is the length of the time period, L d,t-1 Is the queue length of the system at the end of the t-1 period of the dth day, λ d,t Is the passenger arrival rate information for each time period of each day.

[0073] By introducing the above symbols, the scheduling model is transformed into a mixed integer linear programming model, and the optimization solver can be called to directly solve it to obtain the number of security inspection personnel q required for the dth day and t period within a week d,t 。

[0074] Step 7: Construct a security inspection personnel scheduling model considering the randomness of personnel requirements.

[0075] In practice, the passenger arrival rate is uncertain, and the demand for security inspection personnel is uncertain. Denote the change in personnel demand as event ξ. The security inspection personnel scheduling model considering the randomness of personnel requirements takes the minimum of the total labor cost of all groups within a week plus the expected cost of adjusting personnel as the objective function. The mathematical expression is as follows:

[0076]

[0077] Among them, Represents the expected cost of adjusting personnel, decision variable y d,t Represents the number of groups working in the t period of the dth day, taking positive integer values, Represent the number of increased groups and the number of decreased groups in the t period of the dth day respectively, taking positive integer values, h d,t (ξ) represents the number of adjusted groups in the t period of the dth day, taking positive integer values, R d,t (ξ) represents the changed group demand quantity in the t period of the dth day, parameter c represents the labor cost of the group going to work, parameter c + ,c - Represent the unit costs of the number of increased groups and the number of decreased groups respectively.

[0078] In addition, the decision variable y d,t needs to satisfy the following constraints:

[0079] (1) Each group can be assigned at most one shift per day.

[0080]

[0081] Among them, the decision variable x e,d,n indicates whether group e is assigned to shift n on day d, taking values of 0 and 1, N is the number of shifts, e is any group, ε is the set of all groups, d is any day within a week, is the set of each day within the entire week.

[0082] (2) The weekly working hours of each group do not exceed H.

[0083]

[0084] Among them, the parameter a n,t indicates whether to work in the t period of the nth shift, a n,t equals 0 means not working, a n,t equals 1 means working, the parameter H represents the maximum weekly working hours, x e,d,n is whether group e is assigned to shift n on day d, Δ is the length of the time period, D is a preset natural number, and N is the number of shifts.

[0085] (3) The number of groups working in each time period per day is greater than the number of required groups.

[0086]

[0087] Among them, the parameter R d,t is the number of groups required in the t period of day d, and its value is equal to the q d,t value obtained by solving in step 5.

[0088] (4) The time interval between each shift of each group is greater than R.

[0089]

[0090] Among them, the decision variable z e,d indicates whether group e works on day d, the parameter R represents the shortest interval time period between the shifts of two groups working, the parameter f n represents the end time period of shift n, the parameter s n represents the start time period of shift n, x e,d,n is whether group e is assigned to shift n on day d, s n is the start time period of shift n, xe,d+1,n Whether group e is assigned to shift n on day d + 1, z e,d+1 Whether group e goes to work on day d + 1, R is the shortest interval between shifts of two groups, and D is a preset natural number.

[0091] (5) The maximum number of working days per week for each group is less than D max .

[0092]

[0093] Among them, the parameter D max represents the maximum number of working days per week.

[0094] Step 8: Use the method of sample mean to convert the expectation of the cost required to adjust personnel in Step 7 into a deterministic form.

[0095] Let ξ k be a scenario of ξ, p k be the probability of the occurrence of scenario ξ k , then can be written as:

[0096]

[0097] Among them, respectively represent the number of increased groups and the number of decreased groups at time period t on day d under scenario k, taking positive integer values, h d,t (ξ k ) represents the number of adjusted groups at time period t on day d under scenario k, taking positive integer values, R d,t (ξ k ) represents the changed group demand quantity at time period t on day d under scenario k, the parameter c represents the labor cost of the group going to work, and the parameter c + , c - respectively represent the unit costs of the number of increased groups and the number of decreased groups.

[0098] Step 9: Call the solver to solve the deterministic model transformed in Step 8 to obtain the shift n for which group e goes to work on day d.

[0099] Combining Step 7 and Step 8, the specific form of the deterministic model is as follows:

[0100] The objective function is:

[0101]

[0102] The constraint conditions are:

[0103]

[0104] The above model belongs to an integer programming model. By invoking the solver, it can be quickly solved to obtain the shift n of group e on day d.

[0105] To verify the effect of the shift scheduling plan generated by the present invention, the passenger arrival rate on the first day of a week as shown Figure 2 is selected as the input of the model, and the passenger arrival rates for the remaining six days are similar to Figure 2 this. The present invention divides 348 employees into 58 groups, sets the service rate μ of all groups to 100 people per hour, sets the maximum weekly working hours H to 40h, the maximum weekly working days D max to 6 days, the maximum security check queue length L max to 10 people, and the shortest interval period R between shifts to 14.

[0106] The present invention invokes the Gurobi solver to solve the personnel allocation model and obtains the number of staff in each time period of a week. Figure 3 It is a schematic diagram of the number of working groups in each time period within a week. The present invention also obtains the security check queue lengths in each time period of a week. Figure 4 It is a schematic diagram of the security check queue lengths in each time period within a week. The queue length in each time period is controlled within 10 people. By inputting the result of the personnel allocation model into the shift scheduling model, the shift of each employee in a week can be obtained by solving the shift scheduling model.

[0107] The above is only a preferred specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present application should be covered by the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A scheduling method for terminal security inspection personnel considering the randomness of personnel requirements, characterized in that, Including the following steps: Grouping security inspection employees to obtain the grouped security inspection employees; Obtaining the passenger arrival rate information for each time period of each day on a weekly basis; Determining the security inspection queue length based on the passenger arrival rate information; Constructing a staffing model based on the security inspection queue length and the grouped security inspection employees; Constructing the staffing model with the goal of minimizing the total working hours of all groups within a week; The expression of the staffing model is: In the formula, represents the system queue length at the end of the th time period on the th day. Set the queue length of the first time period of each day to zero. represents the service intensity within the th time period on the th day. The parameter represents the maximum security check queue length. is the maximum security check queue length. is the system queue length at the end of the th time period on the th day. is the calculation formula for the steady-state queue length. is the number of work teams within the th time period on the th day. is the service rate of the team. is the passenger arrival rate information for each time period of each day. Converting the staffing model into a mixed-integer programming model to obtain the number of personnel required for each time period; Constructing a security inspection personnel scheduling model considering the randomness of personnel requirements based on the number of personnel required; The expression of the security inspection personnel scheduling model considering the randomness of personnel requirements is: In the formula, represents the expectation of the cost required for personnel adjustment, and the decision variable represents the number of teams working in the th time period on the th day, respectively represent the number of teams increased and the number of teams decreased in the time period on the th day, represents the number of teams after adjustment in the time period on the th day, represents the number of teams required after change in the time period on the th day. The parameter represents the labor cost of a team going to work, and the parameters The constraint conditions that the decision variables also satisfy include: Each group is arranged at most one shift per day, the weekly working hours of each group do not exceed the maximum working hours, the number of groups going to work at each time period every day is greater than the required number of groups, the time interval between each shift of each group is greater than the shortest interval time period, and the maximum number of working days per week of each group is less than the maximum number of working days; Converting the security inspection personnel scheduling model considering the randomness of personnel requirements into a deterministic model to obtain a personnel scheduling plan.

2. The method for scheduling security check personnel in the terminal building considering the randomness of personnel requirements according to claim 1, characterized in that The calculation formula for the security inspection queue length is: Wherein, is the system queue length at the end of the time period, is the number of passengers entering the system during the time period, is the number of passengers leaving the system during the time period, is the steady-state queue length of the system, is the length of the time period.

3. The method for scheduling security personnel at the terminal considering the randomness of personnel requirements according to claim 1, characterized in that, The calculation formula for converting the staffing model into a mixed-integer programming model to obtain the number of personnel required for each time period is: Wherein, represents whether there are groups working during the time period. represents that there are groups working, and the value of in the interval ; represents that there are groups working, and the length of the interval ; is the total number of groups, is the number of working groups, is the number of the th day and the number of working groups during the time period; is the number of the th day, and is the queue length of the system at the end of the time period; is the number of intervals, is the slope of the linear function when there are groups working in the interval ; is the number of groups working, and the value of in the interval ; is the service rate of the groups, is the length of the time period, is the number of the th day, and is the queue length of the system at the end of the is the passenger arrival rate information for each time period of each day.

4. The method for scheduling security personnel at the terminal considering the randomness of personnel requirements according to claim 1, characterized in that, The process of converting the security inspection personnel scheduling model considering the randomness of personnel requirements into a deterministic model includes converting the expectation of the cost required to adjust personnel into a deterministic form; Among them, the expression for converting the expectation of the cost required to adjust personnel into a deterministic form is: Wherein, respectively represent the number of increased groups and the number of decreased groups in the scenario on the day during the period; represents the number of groups after adjustment on the day during the period in the scenario; represents the number of group requirements after change during the day in the scenario. The parameter represents the labor cost of the groups at work, and the parameters respectively represent the unit costs of the increased number of groups and the decreased number of groups.

Images