Scheduling agent and method based on task optimization

Abstract

The invention discloses an intelligent scheduling method based on task optimization. According to the method, firstly, the task load of each time period is predicted through historical data, and then an M / M / c queuing model is established to quantify a task queuing duration expected value as an optimization target. A two-stage optimization strategy is adopted: in the first stage, the optimal number of service desks in each time period is determined by applying dynamic planning, and accurate distribution of human resources is realized; in the second stage, specific employees are distributed to shifts through constraint planning, and meanwhile, complex constraints such as total working time fixing, continuous working duration, shift intervals and skill matching are met. According to the system, a queuing theory, constraint optimization and a prediction model can be combined, and on the premise of ensuring the feasibility of a scheduling scheme, the task processing waiting time is effectively shortened, and the service quality and the human resource utilization rate are improved.

Description

Technical Field

[0001] This invention relates to the field of intelligent office technology, specifically to an intelligent scheduling method based on task optimization. Background Technology

[0002] In labor-intensive industries such as modern service industries and customer service centers, workloads fluctuate, with peaks and valleys, and the specific timing of tasks exhibits a degree of randomness. Therefore, scientific and reasonable staff scheduling is crucial for ensuring service quality, improving operational efficiency, and controlling labor costs. Traditional scheduling methods rely heavily on management experience and are often done manually or semi-automatically, which has the following significant drawbacks:

[0003] First, traditional scheduling methods lack precise quantitative decision-making basis. Managers usually rely on historical experience to roughly estimate the manpower required for each period, making it difficult to accurately cope with random fluctuations in workload. This experience-driven scheduling method often leads to insufficient staff during peak hours, resulting in decreased service quality, or redundant staff during off-peak hours, resulting in wasted resources.

[0004] Secondly, existing scheduling systems struggle to effectively balance multi-objective optimization with complex constraints. Actual scheduling requires considering multiple constraints simultaneously, including fixed total employee hours, continuous work duration limits, shift interval requirements, employee skill matching, and holiday arrangements. Traditional methods often fail to find optimal solutions under these complex constraints, typically only achieving local optimization or feasible solutions, and failing to achieve global optimization. Particularly in multi-server queuing scenarios, the randomness of task arrivals and the variability of service times significantly impact system performance. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a scheduling agent and method based on task optimization.

[0006] Firstly, a task-optimized scheduling method is provided, including the following:

[0007] S1. Estimate the task processing volume for each time period within the scheduled period based on historical data;

[0008] S2. Establish a multi-server queuing model and define system parameters:

[0009] The scheduling cycle is divided into n time periods, T={1,2,...,n}; the length of each time period is Δt hours, Δt>0; the task arrival rate λ in time period t. t >0; Average processing time μ for a single task, 0 < μ < 1;

[0010] S3. Define employee parameters and constraints:

[0011] The employee set E = {1, 2, ..., m}, the total number of employees m is fixed; the total working time H of employee i within the scheduling cycle. i >0; the minimum and maximum continuous working hours for employees are respectively B min B max Satisfying 0 min ≤B max Minimum interval between adjacent trains G min >0 (hours); the set of available time slots A for employee i i The set of skill certificates S belonging to employee i; i Belongs to K;

[0012] S4. Establish an optimization objective function to minimize the expected value of the total task queuing time:

[0013]

[0014] ,

[0015] Where c t x is the number of employees in each position during time period t; i,t P is a decision variable, representing whether employee i works during time period t; q (t) is the queuing probability of the task in time period t.

[0016]

[0017] S4 uses dynamic optimization to determine the optimal number of service counters for each time period;

[0018] S5. Based on constraint programming and the optimal number of service counters for each time period, allocate employee shifts and output employee numbers in the time period correspondence table.

[0019] 2. The task-optimized scheduling method according to claim 1, characterized in that: the method for dynamically optimizing and determining the optimal number of on-duty personnel for each time period includes:

[0020] Calculate the total available working hours:

[0021] ;

[0022] Calculate the minimum number of service units c for each time period t. t min and maximum number of service units c t max ;

[0023]

[0024] ​Where ε is a small positive number, ensuring ρ t <1;

[0025] Initialize the dynamic programming table: dp[0][0] = 0; for s > 0, dp[0][s] = ∞;

[0026] Dynamic programming recursive calculation:

[0027] For t=1 to n, and for s=0 to S:

[0028]

[0029]

[0030] Where c t Satisfy: c t min ≤ct≤c t max , ρt=λ t / c t μ<1, the remaining working hours meet the minimum requirements of the subsequent time period;

[0031] Backtracking yields the optimal server allocation:

[0032] Backtracking from dp[n][S], we obtain the optimal c. t ∗ sequence.

[0033] 3. The task-optimized scheduling method according to claim 1, characterized in that:

[0034] Construct an employee-time period matching matrix to mark the availability status of each employee in each time period;

[0035] Generate an initial shift allocation scheme that satisfies all constraints;

[0036] Resource conflicts, time conflicts, and skill conflicts are detected and resolved through a constraint propagation mechanism.

[0037] A systematic search strategy is employed to optimize shift allocation, minimizing the difference between the actual number of service stations served in each time period and the target value c. t ∗ Deviation;

[0038] Output the final employee-time shift schedule.

[0039] 4. The task-optimized scheduling method according to claim 3, characterized in that: the estimation of task processing volume for each time period within the scheduling period based on historical data includes:

[0040] (a) Data preprocessing stage: Cleaning, outlier handling, and time period alignment of historical task volume data; aggregating data to the scheduling time period granularity. Constructing a complete historical task volume sequence {y1,y2,...,y...} N}, where y τ This represents the task volume in the τ-th historical time period, where N is the total number of historical time periods.

[0041] (b) Time series decomposition stage: An additive model is used to decompose the historical task quantity sequence (Y) τ Decomposed into trend term (T) τ Seasonal item (S) τ ), Event Item (E) τ ) and residual term (R τ ), where Yτ=T τ +S τ +E τ +R τ The trend term reflects the long-term direction of change, while the seasonal term includes daily, weekly, and annual cycle patterns. The event term characterizes the impact of specific events. The residual term represents the random fluctuations after removing the above factors.

[0042] (c) Feature Engineering Stage: Constructing a feature set X that includes time features, historical features, and external event features. t The time features include time period number, day of the week, month, and whether it is a holiday; the external event features include promotional activities, weather data, and special event information; and the historical features include sliding window statistics.

[0043] (d) Probability prediction model stage: Probability prediction is performed using quantile regression gradient boosting trees.

[0044]

[0045] in: This represents the predicted q-quantile value of the task quantity in time period t; q∈Q, Q={q1,q2,...,q M} represents the set of quantile points; Θ represents the model parameters, which are learned by minimizing the quantile loss function;

[0046] (e) For known future events, calculate their impact coefficients:

[0047]

[0048] Establish an event impact coefficient library {β1,β2,...,β K} is used to adjust the baseline forecast;

[0049] (f) Probability distribution generation stage

[0050]

[0051] Where f t (λ) is the probability density function of the task quantity in time period t; Interpolate represents a mathematical process of "constructing a continuous probability distribution function from discrete quantile points", which is to convert several discrete quantile points obtained by model prediction into a complete and continuous probability density function.

[0052] (g) Mathematical expectation calculation stage

[0053] Calculate the expected value of the task volume for each time period:

[0054]

[0055] Through discrete approximation:

[0056]

[0057] Where, {λ t ,j} represents the discrete values ​​of the task quantity, and the corresponding probabilities are calculated by the probability density function;

[0058] Finally: Output the expected task volume for each time period t.

[0059] Secondly, a task-optimized scheduling agent is provided, on which a computer program is stored, which, when executed by a processor, implements the method described in the first aspect.

[0060] Beneficial Effects: The intelligent scheduling method and system based on task optimization proposed in this application, through the deep integration of multi-server queuing theory and a two-stage optimization algorithm, achieves a transformation from localized experience-based scheduling to a globally data-driven systematic optimization. It achieves global optimization within the scheduling cycle, fundamentally improving overall service levels and reducing task processing incidents. By using a dynamic programming algorithm for global resource allocation, its objective function directly minimizes the expected total queuing time of all tasks throughout the cycle, ensuring that the allocation of human resources in the spatiotemporal dimensions reaches global optimization rather than a simple superposition of multiple local optima. By shifting employee working hours from off-peak periods to peak periods, it avoids resource misallocation problems such as localized congestion and idle resources, thereby significantly reducing the system's average queuing time and maximum queuing length while keeping total labor costs constant, thus improving service response speed and quality.

[0061] By systematically addressing complex constraints such as employee skill matching, continuous work hours, shift intervals, and holiday arrangements through constraint programming techniques, the scheduling scheme fully complies with laws, regulations, and company policies, demonstrating strong practical feasibility. A two-stage optimization strategy is employed: first, the optimal number of employees for each time period is determined, and then specific employees are allocated. This achieves precise matching of people to positions while satisfying all hard constraints, effectively enhancing human capital value and reducing waste caused by unreasonable scheduling.

[0062] This solution enhances the system's adaptability and stability through probabilistic prediction and robust modeling. By employing quantile regression to output the complete probability distribution of task volume instead of single-point prediction, scheduling optimization can fully consider the uncertainty of business volume, enhance the ability to cope with sudden fluctuations, and avoid system performance degradation due to prediction bias. The system can also integrate external features such as promotional weather and continuously learn from historical data, enabling the scheduling strategy to dynamically adapt to changes in business models. Attached Figure Description

[0063] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0064] Figure 1 This is a flowchart of this application. Detailed Implementation

[0065] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application. Unless otherwise defined, the technical or scientific terms used in this application should have the ordinary meaning understood by those skilled in the art. The words "first," "second," and similar terms used in this application do not indicate any order, quantity, or importance, but are only used to distinguish different components. The words "comprising" or "including," etc., mean that the element or object preceding the word covers the element or object listed after the word and its equivalents, but do not exclude other elements or objects. The words "connected," "coupled," or "connected," etc., are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. "Up," "down," "left," "right," etc., are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0066] The intelligent scheduling method in this application, such as Figure 1 As shown, it includes the following steps:

[0067] First, the task processing volume for each time period within the scheduled period is estimated based on historical data. Models such as ARIMA, RandomForest, LightGBM, and Prophe can be used to predict the workload. The specific prediction method in this embodiment is as follows:

[0068] (a) Data preprocessing stage: Cleaning, outlier handling, and time period alignment of historical task volume data; aggregating data to the scheduling time period granularity. Constructing a complete historical task volume sequence {y1,y2,...,y...} N}, where y τ Let N represent the task volume in the τ-th historical time period, and N be the total number of historical time periods.

[0069] (b) Time series decomposition stage: An additive model is used to decompose the historical task quantity sequence (Y) τ Decomposed into trend term (T) τ Seasonal item (S) τ ), Event Item (E) τ ) and residual term (R τ ), where Yτ=T τ +S τ +E τ +R τThe trend term reflects the long-term direction of change, while the seasonal term includes daily, weekly, and annual cycle patterns. The event term characterizes the impact of specific events. The residual term represents the random fluctuations after removing the above factors.

[0070] (c) Feature Engineering Stage: Constructing a feature set X that includes time features, historical features, and external event features. t The time features include time period number, day of the week, month, and whether it is a holiday, etc.; the external event features include promotional activities, weather data, and special event information; and the historical features include sliding window statistics (mean, variance, etc.).

[0071] (d) Probability prediction model stage: Probability prediction is performed using quantile regression gradient boosting trees.

[0072]

[0073] in: This represents the predicted q-quantile value of the task quantity in time period t; q∈Q, Q={q1,q2,...,q M} represents the set of quantile points, typically Q = {0.05, 0.25, 0.50, 0.75, 0.95}; Θ represents the model parameters, learned by minimizing the quantile loss function.

[0074] (e) For known future events, calculate their impact coefficients:

[0075]

[0076] Establish an event impact coefficient library {β1,β2,...,β K} is used to adjust the basic forecast.

[0077] (f) Probability distribution generation stage

[0078]

[0079] Where f t (λ) is the probability density function of the task quantity in time period t. Interpolate represents a mathematical process of "constructing a continuous probability distribution function from discrete quantile points". Several discrete quantile points obtained by model prediction are transformed into a complete and continuous probability density function.

[0080] (g) Mathematical expectation calculation stage

[0081] Calculate the expected value of the task volume for each time period:

[0082]

[0083] Through discrete approximation:

[0084]

[0085] Where, {λ t ,j} represents the discrete values ​​of the task quantity, and the corresponding probabilities are calculated by the probability density function.

[0086] Finally: Output the expected task volume for each time period t, which serves as the core input to the scheduling agent; the complete probability distribution, used for uncertainty quantification and risk analysis; and the prediction interval, based on the confidence interval of quantile prediction.

[0087] The second step involves characterizing the scheduling scenario, defining system parameters, and establishing a multi-server queuing model, which includes the following steps:

[0088] Time period parameters: The scheduling cycle is divided into n time periods, T={1,2,...,n}, each time period is Δt hours long, Δt>0, and the value of Δt is usually one hour, i.e., Δt=1; the task arrival rate λ in time period t. t λ is the number of tasks achieved per hour. t >0, λ t Evaluated from historical data;

[0089] Task parameters: Average processing time μ for a single task, 0 < μ < 1. Within time interval t, the task arrival process follows a Poisson process, and the arrival time is randomly and uniformly distributed within time interval t.

[0090] Employee parameters: Employee set E = {1, 2, ..., m}, total number of employees m is fixed; total working time H of employee i within the scheduling cycle. i >0; the minimum and maximum continuous working hours for employees are respectively B min B max Satisfying 0 min ≤B max Minimum interval between adjacent trains G min >0 (hours); the set of available time slots A for employee i i The set of skill certificates S belonging to employee i; i Belongs to K;

[0091] Business constraint: The number of employees with skill k required during time period t is Rt,k.

[0092] Establish the optimization objective function: minimize the expected value of the total task queuing time. The total queuing time refers to the sum of the time spent by all tasks in the system.

[0093] For the M / M / c_t queuing system: the probability that a task needs to be queued upon arrival is:

[0094] ​

[0095] Where, ρ t =λ t / c t μ, ρ t For system utilization, ρ t <1 to ensure system stability.

[0096] The average system time for the task (wait time + service time) is:

[0097]

[0098] The expected total queuing time is:

[0099]

[0100] because Since it is a constant (total service time), the optimization problem is equivalent to:

[0101]

[0102] Where c t x is the total number of service counters in time period t; i,t It is a decision variable, representing whether employee i works during time period t, x i,t∈ {0,1},x i,t =1 indicates going to work, x i,t =0 indicates no work. If one service desk corresponds to one employee, then:

[0103] .

[0104] The constraints are:

[0105] Total working hours are fixed:

[0106]

[0107] The total number of employees is fixed.

[0108]

[0109] For each employee i, the length of any consecutive work period sequence satisfies:

[0110]

[0111] Shift interval constraint: If employee i works during time period t, then:

[0112]

[0113] G minThe minimum interval between two shifts for an employee; the shortest continuous rest period an employee must take after finishing a shift; ⌈G min / Δ t ⌉ represents the minimum number of rest periods; s is an index variable, a loop variable used to iterate through the periods. It starts from t+1 and continues until min(n, t+⌈G). min / Δt⌉) End. x i,s =1 indicates that the employee started work on event s, x i,s =0 means not working.

[0114] For employee i, if he / she works in time period t, then starting from the next time period t+1, until the future ⌈G min The employee must rest during each of the following time periods (up to / Δt⌉, but not beyond the end of the work cycle): / Δt⌉.

[0115] Skill matching constraints:

[0116]

[0117] In this embodiment, the optimization solution is performed in two stages. The first stage involves optimizing the number of service counters, determining the optimal number of service counters c for each time period. t ∗ The optimized model is:

[0118]

[0119] Determine the minimum number of service units c for each time period t. t min and maximum number of service units c t max Determine the feasible domain for the number of servers in each time period t;

[0120] ,

[0121] Where ε is a small positive number, which can be 0.01, to ensure ρ t <1. It is the minimum number of people required to meet the skill requirements.

[0122] Create a two-dimensional array dynamic programming table dp[t][s] and its corresponding selection record table choice[t][s], where s represents the total number of working hours consumed in the first t time periods. The value of dp[t][s] represents the minimum cumulative queuing cost that can be achieved under the premise that "a total of s working hours are allocated to the first t time periods".

[0123] Initialize the dynamic programming table: dp[0][0] = 0; for s > 0, dp[0][s] = ∞;

[0124] Dynamic programming recursive calculation:

[0125] Perform recursive calculation through a triple loop. The outer layer is the time period t from 1 to n, processing each time period in chronological order; the middle layer is the cumulative working hours from 0 to S, traversing all possible total working hour consumption situations. s must be traversed from 0 to S to ensure that no possible resource allocation plan is missed. The inner layer is the number of service desks c that can be allocated in the current time period, enumerating all possible numbers of service desks in the current time period t. S is the sum of the total number of service desks in each time period, that is, the total working hours of the employees.

[0126] Feasibility check:

[0127] 1. Calculate the previous state, prev s = s - cΔt. If prev s < 0, skip.

[0128] 2. Check the validity of the previous state: If dp[t - 1][prevs] = ∞, skip.

[0129] 3. Check the system stability: ρ t = λ t / (cμ) ≥ 1, skip;

[0130] 4. Feasibility check (looking ahead): Ensure that the remaining working hours meet the minimum requirements of the subsequent time periods.

[0131] State transition calculation:

[0132] If all checks pass, for t = 1 to n, for s = 0 to S:

[0133] Then calculate:

[0134]

[0135]

[0136] State update:

[0137] If new_value < dp[t][s], then update the value of dp[t][s] to new_value, and at the same time update its corresponding selection record table.

[0138] Backtracking to obtain the optimal service desk allocation:

[0139] After the recursion is completed, the total cost of the global optimal solution is stored in dp[n][S]. Starting from the final state (t = n, s = S), using the choice[t][s] table, trace back step by step to restore each decision (that is, the number of people allocated in each time period) made to achieve the optimal cost, forming a complete optimal solution sequence {c* 1,c * 2,...,c * n}

[0140] After determining the number of service counters for each stage, assign corresponding staff to the service counters for each time period. Transform the abstract target for the number of service counters into concrete staff arrangements, aiming to approach the optimal target of the first stage as closely as possible while satisfying all complex constraints. The specific process is as follows:

[0141] Construct an employee-time period matching matrix: mark time period availability based on employee vacation data, mark skill availability based on the matching relationship between employee skill certificates and time period skill requirements, pre-calculate the set of available employees for each time period, and identify time periods that must be allocated due to rigid skill requirements.

[0142] Generate an initial shift allocation scheme that satisfies all constraints; sort by the number of target service counters in descending order for each time period, prioritize time periods with a high number of target service counters, and allocate available employees with the highest skill matching to each time period to ensure that the allocation results meet the continuous working time constraint and shift interval constraint.

[0143] Resource conflicts, time conflicts, and skill conflicts are detected and resolved through a constraint propagation mechanism. This constraint propagation mechanism includes:

[0144] Forward check: Once it is determined that an employee works during a certain time period, immediately deduce the impact of this assignment on adjacent time periods;

[0145] Constraint propagation: By propagating constraints through constraint networks, potential conflicts can be detected in advance;

[0146] Domain reduction: Gradually narrowing the possible value space of each decision variable.

[0147] Sudden resolution includes:

[0148] Resource conflict resolution: When there are not enough available employees in a certain period, adjust the allocation of employees in adjacent periods;

[0149] Time conflict resolution: When continuous work or interval constraints are violated, shift sequences are rescheduled;

[0150] Skill conflict resolution: Prioritize ensuring skill coverage requirements during periods of high skill demand.

[0151] A systematic search strategy is employed to optimize shift allocation, minimizing the difference between the actual number of service stations served in each time period and the target value c. t ∗ The bias is addressed by prioritizing employee-time allocation decisions with the fewest available choices, selecting the assignment that minimizes constraints on subsequent decisions for each decision variable, and pruning infeasible branches through constraint propagation.

[0152] Finally, output the final employee-time shift schedule.

[0153] Based on the same inventive concept, this application also provides a scheduling intelligent agent, which stores a computer program that, when executed by a processor, implements the method of any one of claims 1 to 7.

[0154] Beneficial Effects: The intelligent scheduling method and system based on task optimization proposed in this application, through the deep integration of multi-server queuing theory and a two-stage optimization algorithm, achieves a transformation from localized experience-based scheduling to a globally data-driven systematic optimization. It achieves global optimization within the scheduling cycle, fundamentally improving overall service levels and reducing task processing incidents. By using a dynamic programming algorithm for global resource allocation, its objective function directly minimizes the expected total queuing time of all tasks throughout the cycle, ensuring that the allocation of human resources in the spatiotemporal dimensions reaches global optimization rather than a simple superposition of multiple local optima. By shifting employee working hours from off-peak periods to peak periods, it avoids resource misallocation problems such as localized congestion and idle resources, thereby significantly reducing the system's average queuing time and maximum queuing length while keeping total labor costs constant, thus improving service response speed and quality.

[0155] By systematically addressing complex constraints such as employee skill matching, continuous work hours, shift intervals, and holiday arrangements through constraint programming techniques, the scheduling scheme fully complies with laws, regulations, and company policies, demonstrating strong practical feasibility. A two-stage optimization strategy is employed: first, the optimal number of employees for each time period is determined, and then specific employees are allocated. This achieves precise matching of people to positions while satisfying all hard constraints, effectively enhancing human capital value and reducing waste caused by unreasonable scheduling.

[0156] This solution enhances the system's adaptability and stability through probabilistic prediction and robust modeling. By employing quantile regression to output the complete probability distribution of task volume instead of single-point prediction, scheduling optimization can fully consider the uncertainty of business volume, enhance the ability to cope with sudden fluctuations, and avoid system performance degradation due to prediction bias. The system can also integrate external features such as promotional weather and continuously learn from historical data, enabling the scheduling strategy to dynamically adapt to changes in business models.

[0157] This application describes embodiments of methods, apparatus (systems), and computer program products according to embodiments of this application with reference to flowchart illustrations and / or block diagrams. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0158] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0159] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0160] Although preferred embodiments have been described in this application, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of this application.

[0161] Obviously, those skilled in the art can make various modifications and variations to the embodiments of this application without departing from the spirit and scope of the embodiments of this application. Therefore, if these modifications and variations to the embodiments of this application fall within the scope of the claims in this application and their equivalents, then this application also intends to include these modifications and variations.

Claims

1. A task-optimized scheduling method, characterized in that, Including the following: S1. Estimate the task processing volume for each time period within the scheduled period based on historical data; S2. Establish a multi-server queuing model and define system parameters: The scheduling cycle is divided into n time periods, T={1,2,...,n}; the length of each time period is Δt hours, Δt>0; the task arrival rate λ in time period t. t >0; Average processing time μ for a single task, 0 < μ < 1; S3. Define employee parameters and constraints: The employee set E = {1, 2, ..., m}, the total number of employees m is fixed; the total working time H of employee i within the scheduling cycle. i >0; the minimum and maximum continuous working hours for employees are respectively B min B max Satisfying 0 min ≤B max Minimum interval between adjacent trains G min >0 (hours); the set of available time slots A for employee i i The set of skill certificates S belonging to employee i; i Belongs to K;​ S4. Establish an optimization objective function to minimize the expected value of the total task queuing time: ， Where c t x is the number of employees in each position during time period t; i,t P is a decision variable, representing whether employee i works during time period t; q (t) is the queuing probability of the task in time period t. S4 uses dynamic optimization to determine the optimal number of service counters for each time period; S5. Based on constrained programming and the optimal number of service counters for each time period, allocate employee shifts and output a table of employee IDs and time periods.

2. The task-optimized scheduling method according to claim 1, characterized in that: The method for dynamically optimizing and determining the optimal number of on-duty personnel for each time period includes: Calculate the total available working hours: ； Calculate the minimum number of service units c for each time period t. t min and maximum number of service units c t max ; Where ε is a small positive number, ensuring ρ t <1; Initialize the dynamic programming table: dp[0][0] = 0; for s > 0, dp[0][s] = ∞; Dynamic programming recursive calculation: For t=1 to n, and for s=0 to S: Where c t Satisfy: c t min ≤ct≤c t max , ρt=λ t / c t μ<1, the remaining working hours meet the minimum requirements of the subsequent time period; Backtracking yields the optimal server allocation: Backtracking from dp[n][S], we obtain the optimal c. t ∗ sequence.

3. The task-optimized scheduling method according to claim 1, characterized in that: Construct an employee-time period matching matrix to mark the availability status of each employee in each time period; Generate an initial shift allocation scheme that satisfies all constraints; Resource conflicts, time conflicts, and skill conflicts are detected and resolved through a constraint propagation mechanism. A systematic search strategy is employed to optimize shift allocation, minimizing the difference between the actual number of service stations served in each time period and the target value c. t ∗ Deviation; Output the final employee-time shift schedule.

4. The task-optimized scheduling method according to claim 3, characterized in that: The estimated task processing volume for each time period within the scheduled period based on historical data includes: (a) Data preprocessing stage: Cleaning, outlier handling, and time period alignment of historical task volume data; aggregating data to the scheduling time period granularity. Constructing a complete historical task volume sequence {y1,y2,...,y...} N }, where y τ This represents the task volume in the τ-th historical time period, where N is the total number of historical time periods. (b) Time series decomposition stage: An additive model is used to decompose the historical task quantity sequence (Y) τ Decomposed into trend term (T) τ Seasonal item (S) τ ), Event Item (E) τ ) and residual term (R τ ), where Yτ=T τ +S τ +E τ +R τ The trend term reflects the long-term direction of change, while the seasonal term includes daily, weekly, and annual cycle patterns. The event term characterizes the impact of specific events. The residual term represents the random fluctuations after removing the above factors. (c) Feature Engineering Stage: Constructing a feature set X that includes time features, historical features, and external event features. t The time features include time period number, day of the week, month, and whether it is a holiday; the external event features include promotional activities, weather data, and special event information; and the historical features include sliding window statistics. (d) Probability prediction model stage: Probability prediction is performed using quantile regression gradient boosting trees. in: This represents the predicted q-quantile value of the task quantity in time period t; q∈Q, Q={q1,q2,...,q M } represents the set of quantile points; Θ represents the model parameters, which are learned by minimizing the quantile loss function; (e) For known future events, calculate their impact coefficients: Establish an event impact coefficient library {β1,β2,...,β K } is used to adjust the baseline forecast; (f) Probability distribution generation stage Where f t (λ) is the probability density function of the task quantity in time period t; Interpolate represents the mathematical process of constructing a continuous probability distribution function from discrete quantile points. Several discrete quantile points obtained by model prediction are transformed into a complete and continuous probability density function. (g) Mathematical expectation calculation stage Calculate the expected value of the task volume for each time period: Through discrete approximation: Where, {λ t ,j} represents the discrete values ​​of the task quantity, and the corresponding probabilities are calculated by the probability density function; Finally: Output the expected task volume for each time period t.

5. A task-optimized scheduling agent, which stores a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 4.

Images