Multi-parameter fusion load balancing scheduling adaptation system and method

Abstract

The present application relates to the field of data processing, and discloses a multi-parameter fusion load balancing scheduling adaptation system and method, wherein the multi-parameter fusion load balancing scheduling adaptation method comprises: predicting the demand and the actual available capacity in the future period in a rolling time domain, and calculating the disturbance intensity; constructing a resource department network, calculating the influence intensity and the comprehensive disturbance influence; calculating the over-allocation degree, and constructing a conflict over-allocation graph; generating an initial feasible solution; constructing a multi-objective optimization model, and solving to obtain a resource allocation scheme; the present application can accurately identify and quantify the propagation effect of the disturbance in the resource department network by establishing a three-layer progressive conduction mechanism, realizes accurate prediction and evaluation of the disturbance influence; the problem decomposition is realized through the Lagrange relaxation framework, can handle large-scale scheduling problems containing complex rules, realizes multi-parameter fusion load balancing scheduling adaptation in a cross-department collaborative scenario, and provides a complete technical solution for enterprise-level resource management.

Description

Technical Field

[0001] This invention relates to the field of data processing, and more specifically, to a load balancing scheduling adaptation system and method that integrates multiple parameters. Background Technology

[0002] As modern corporate structures become increasingly complex, cross-departmental collaboration has become a key factor in improving overall operational efficiency. In complex organizations such as large enterprise groups, medical consortia, and logistics networks, there are numerous resource-sharing needs and business collaboration relationships between departments, and traditional single-department scheduling methods can no longer meet the actual needs of modern enterprises.

[0003] Chinese Patent CN118966731B discloses a method, apparatus, medium, and equipment for multi-department duty roster scheduling. The method first sorts the duty personnel by department on an average basis to obtain a duty personnel sequence, and then arranges them into time segments according to the cyclical order of the duty personnel sequence to form a duty roster table. When sorting by department on an average basis, the personnel are first sorted according to the number of duty personnel in each department, and then the insertion ordinal number is calculated. The insertion ordinal number is used to determine the position of each duty personnel in the duty personnel sequence, ultimately forming the duty personnel sequence.

[0004] Existing technologies primarily focus on the even distribution of on-duty personnel among departments, using insertion ordinal algorithms to ensure a uniform distribution of personnel across departments within the sequence. However, these technologies fail to consider resource competition issues arising when multiple departments simultaneously require the same critical resources (such as specialized equipment, core technical personnel, and special facilities). When the scheduling plans of multiple departments involve shared resources, existing methods cannot identify or warn of potential resource conflicts, nor can they establish effective conflict detection and intelligent mediation mechanisms, often leading to resource over-allocation or idleness, thus impacting overall efficiency. Summary of the Invention

[0005] The purpose of this invention is to provide a multi-parameter fusion load balancing scheduling adaptation system and method to solve the above-mentioned problems.

[0006] This invention provides a multi-parameter fusion-based load balancing scheduling adaptation method, comprising the following steps:

[0007] Based on the triggering conditions, the scheduling optimization is initiated. Within the rolling time domain, the demand forecasting model and the capacity correction model are used to predict the demand and actual available capacity for future periods. The disturbance intensity is calculated based on the demand and actual available capacity.

[0008] Construct a resource sector network, determine the number of transmission layers and calculate the impact intensity based on the resource sector network and the disturbance intensity, and calculate the comprehensive disturbance impact based on the impact intensity;

[0009] The over-allocation degree is calculated based on the demand and actual available capacity. A conflict over-allocation diagram is constructed based on the over-allocation degree. The priority score of the department is calculated in combination with the comprehensive disturbance impact.

[0010] Based on the conflict overmap and priority scores, a constraint set is constructed and an initial feasible solution is generated.

[0011] A multi-objective optimization model is constructed using the initial feasible solution as the starting point. The multi-objective optimization model solves the resource allocation scheme based on the constraint set.

[0012] Furthermore, the calculation of the combined disturbance effects includes:

[0013] The disturbance intensity is divided into slight disturbance, moderate disturbance, and severe disturbance;

[0014] Minor disturbances are propagated through the first layer, moderate disturbances through the first and second layers, affecting directly dependent departments and their collaborating departments, and severe disturbances through the first, second, and third layers.

[0015] The first layer of transmission directly affects the departments in the resource department network that directly depend on the resource. The influence strength of the department is the direct influence strength, which is the disturbance strength of the resource multiplied by the resource's dependence on the department weight, and then multiplied by a preset time decay factor.

[0016] The second layer of transmission involves the directly affected departments transmitting disturbances to collaborating departments through cooperation. The influence strength of the collaborating departments is the indirect influence strength, which is the direct influence strength of the directly affected departments multiplied by a preset inter-departmental cooperation strength coefficient, and then multiplied by a preset transmission attenuation factor.

[0017] The third layer of transmission calculates the system-level adjustment influence intensity. The system-level adjustment influence intensity of a department is the overall system disturbance intensity multiplied by the preset department system importance weight, and then multiplied by the preset system adjustment intensity factor.

[0018] The overall disturbance impact of a department is the sum of the department's direct impact intensity multiplied by the preset direct transmission weight, the department's indirect impact intensity multiplied by the preset indirect transmission weight, and the department's system-level adjustment impact intensity multiplied by the preset system adjustment weight.

[0019] Furthermore, the resource sector network includes resource nodes, sector nodes, and connecting edges, where resource nodes represent various types of resources, sector nodes represent various sectors, and connecting edges represent the dependencies of sectors on resources and the weights of those dependencies.

[0020] The intensity of influence includes the intensity of direct influence, the intensity of indirect influence, and the intensity of system-level regulation influence;

[0021] The overall system disturbance intensity is the sum of the products of the disturbance intensity of multiple resources in multiple time periods and the corresponding preset resource weight coefficients, divided by the sum of the preset resource weight coefficients.

[0022] Furthermore, the resource over-allocation during a given period is the greater of zero and the resource demand over-limit, where the resource demand over-limit is the sum of all departments' demand for the resource during that period minus the actual available capacity.

[0023] When the over-provisioning degree is greater than the preset over-provisioning threshold, it is marked as a conflicting resource and a conflict over-provisioning graph is constructed. In the conflict over-provisioning graph, the application node represents the department's demand application, the resource node represents the shared resource, and the hyperedge connects the application nodes competing for the same resource and the hyperedge weight is equal to the over-provisioning degree.

[0024] The department's priority score for a given period is the sum of the basic priority score and the disturbance impact adjustment item. The basic priority score is calculated by multiplying the preset first weight coefficient by the standardized value of the key performance indicator, adding the preset second weight coefficient by the urgency level, adding the preset third weight coefficient by the compliance score, subtracting the preset fourth weight coefficient by the change cost, and adding the preset fifth weight coefficient by the collaboration level. The disturbance impact adjustment item is equal to the preset disturbance impact weight coefficient multiplied by the department's total disturbance impact for the given period.

[0025] Furthermore, calculating the disturbance strength includes:

[0026] The supply and demand difference of resources during a period is the total demand for resources during that period minus the actual available capacity, where the total demand is the sum of the demand for the resource by all departments during that period;

[0027] The disturbance intensity of resources during a given period is the ratio of the absolute value of the supply-demand difference of resources during that period to the preset standard capacity of resources, multiplied by a preset disturbance sensitivity coefficient.

[0028] Furthermore, the constraint set includes capacity constraints and time constraints, where the capacity constraint limits the total resource allocation to no more than the actual available capacity, and the time constraint limits the total resource allocation to no more than the time limit.

[0029] The initial feasible solution is generated using a greedy algorithm, which includes: sorting all departments in descending order based on their priority scores to form a department priority queue; allocating resources to each department in the order of the department priority queue; and when encountering conflicting resources, referring to the conflict over-allocation graph, prioritizing the needs of departments with higher priority scores.

[0030] Furthermore, constructing a multi-objective optimization model for solving includes:

[0031] Construct a multi-objective optimization function. The multi-objective optimization function is: a preset first objective weight coefficient multiplied by the sum of the utility terms of all departments in all time periods, plus a preset second objective weight coefficient multiplied by the fairness term, minus a preset third objective weight coefficient multiplied by the sum of the over-allocation of all resources in all time periods, minus a preset fourth objective weight coefficient multiplied by the sum of the stability terms of all departments in all time periods, and finally minus a preset fifth objective weight coefficient multiplied by the load balancing term.

[0032] A method based on the Lagrange relaxation framework is used to solve the multi-objective optimization function and obtain the resource allocation scheme.

[0033] Furthermore, the utility term is the inner product of the preset utility coefficient vector and the resource allocation vector of the department in the time period, minus the utility loss of the department in the time period. The utility loss is the preset utility sensitivity coefficient multiplied by the comprehensive disturbance effect of the department in the time period. The fairness term is the sum of squares of the negative differences between the total utility of each department and the average utility. The total utility of the department is the sum of the utility terms of the department in all time periods. The average utility is the arithmetic mean of the total utility of all departments. The stability term is the L1 norm of the difference between the resource allocation vector of the department in the current time period and the previous time period. The load balancing term is the variance of the total allocation of each resource in each time period.

[0034] Furthermore, the resource allocation scheme includes a resource quantity allocation matrix, a personnel shift schedule, and an equipment usage time sequence diagram; wherein, the resource quantity allocation matrix includes the number of resources allocated by the department to the department during the time period; the personnel shift schedule includes job position, shift type, working hours, and skill matching; and the equipment usage time sequence diagram includes equipment number, using department, usage time period, and load level.

[0035] This invention provides a multi-parameter fusion load balancing scheduling adaptation system, which stores computer-readable instructions and, when read, can execute the aforementioned multi-parameter fusion load balancing scheduling adaptation method; the system includes:

[0036] The demand and supply module initiates scheduling optimization based on triggering conditions. Within the rolling time domain, it uses a demand forecasting model and a capacity correction model to predict the demand and actual available capacity for future periods, and calculates the disturbance intensity based on the demand and actual available capacity.

[0037] The disturbance impact module constructs a resource sector network, determines the number of propagation layers and calculates the impact intensity based on the resource sector network and the disturbance intensity, and calculates the comprehensive disturbance impact based on the impact intensity.

[0038] The conflict identification module calculates the over-allocation degree based on the demand and actual available capacity, constructs a conflict over-allocation map based on the over-allocation degree, and combines the overall disturbance impact to calculate the priority score of the department.

[0039] The initial constraint module constructs a constraint set and generates an initial feasible solution based on the conflict overfit graph and priority score;

[0040] The resource allocation module constructs a multi-objective optimization model with the initial feasible solution as the starting point. The multi-objective optimization model solves the resource allocation scheme based on the set of constraints.

[0041] The beneficial effects of this invention are as follows: By establishing a three-layer progressive transmission mechanism of direct transmission, collaborative transmission, and system regulation, this invention can accurately identify and quantify the propagation effect of disturbances in resource sector networks, and achieve accurate prediction and assessment of the impact of disturbances; through real-time calculation of the resource supply and demand difference matrix and the disturbance intensity vector, it can quickly identify the initial disturbance source and quantify the severity of the disturbance, providing accurate basic data for subsequent optimization decisions.

[0042] By employing a solution strategy combining Mixed Integer Programming (MIP) and Constrained Programming (CP), and decomposing the problem using a Lagrange relaxation framework, large-scale scheduling optimization problems involving complex rules can be efficiently handled. A multi-objective optimization function incorporating utility, fairness, over-allocation penalty, stability, and load balancing terms is constructed to achieve a coordinated balance among multiple objectives, including resource utilization, departmental satisfaction, and system stability. The shadow prices of each resource are calculated using Lagrange duality theory to reflect their marginal value and scarcity, enabling intelligent resource allocation and adjustment based on market mechanisms. A dual constraint mechanism of quota caps and minimum guaranteed quotas prevents excessive concentration of resources, ensuring that the basic needs of each department are met, thus achieving an organic unity of efficiency and fairness.

[0043] By introducing a disturbance robustness term calculation, the optimal solution is sought under worst-case disturbance conditions, significantly improving the system's resistance to uncertainty and stability. By establishing three types of buffer resource pools—personnel, equipment, and workstations—and adopting a tiered allocation strategy, elastic resource reserves are provided for sudden disturbances, ensuring the system's continuous operation capability under abnormal circumstances.

[0044] By establishing an anomaly detection mechanism based on statistical control charts, a three-tiered dynamic fine-tuning mechanism is implemented, encompassing time offset adjustment, alternative resource allocation, and buffer resource activation, ensuring the real-time adaptability of the solution execution. Through the mirror descent algorithm and the method of minimizing prediction error, online learning updates of weight parameters and disturbance propagation model parameters are achieved, continuously improving the system's prediction accuracy and decision-making quality.

[0045] By constructing a conflict overlay map to describe resource competition relationships and combining it with dynamic priority scoring of departments based on disturbance impact calculations, intelligent identification and coordinated resolution of cross-departmental resource conflicts are achieved. A two-tiered compliance verification system, consisting of hard constraint checks and soft constraint assessments, ensures that scheduling plans strictly meet mandatory conditions such as regulatory requirements and safety regulations, while also taking into account preferences and comfort requirements.

[0046] Perturbation scenarios are generated through Monte Carlo sampling, and robustness verification is performed in a digital twin simulation sandbox to ensure the stability and reliability of the solution under various perturbation scenarios. A committed scheduling contract is generated, including elements such as the optimal allocation plan, shadow price information, and a set of alternative plans, ensuring the consistency and executability of the solution across various business systems.

[0047] This invention realizes load balancing scheduling adaptation with multi-parameter fusion in cross-departmental collaboration scenarios, significantly improving resource allocation efficiency, system stability and decision-making intelligence, and providing a complete technical solution for enterprise-level resource management. Attached Figure Description

[0048] Figure 1 This is a flowchart illustrating the multi-parameter fusion-based load balancing scheduling adaptation method of the present invention.

[0049] Figure 2 This is an example diagram illustrating the calculation of the comprehensive disturbance impact of the multi-parameter fusion load balancing scheduling adaptation method of the present invention.

[0050] Figure 3 This is an example diagram illustrating the calculation priority score of the multi-parameter fusion load balancing scheduling adaptation method of the present invention;

[0051] Figure 4 This is a module example diagram of the multi-parameter fusion load balancing scheduling adaptation system of the present invention. Detailed Implementation

[0052] The subject matter described herein will now be discussed with reference to exemplary embodiments. It should be understood that these embodiments are discussed only to enable those skilled in the art to better understand and implement the subject matter described herein, and changes may be made to the function and arrangement of the elements discussed without departing from the scope of this specification. Various processes or components may be omitted, substituted, or added as needed in the examples. Furthermore, features described in some examples may be combined in other examples.

[0053] A multi-parameter fusion-based load balancing scheduling adaptation system and method, including the following embodiments:

[0054] Example 1

[0055] Multi-parameter fusion load balancing scheduling adaptation methods, such as Figure 1 As shown, it includes the following steps:

[0056] Step 100: Start scheduling optimization according to the triggering conditions. In the rolling time domain, use the demand forecasting model and the capacity correction model to predict the demand and actual available capacity for future periods, and calculate the disturbance intensity based on the demand and actual available capacity.

[0057] The scheduling optimization process is initiated through a trigger mechanism, and the fusion calculation of demand forecasting and capacity correction is completed within a rolling time domain framework, providing basic data for subsequent disturbance propagation modeling.

[0058] The scheduling optimization process is initiated based on preset trigger conditions, including periodic triggers such as daily or weekly scheduled start-ups; disturbance event triggers such as equipment failures or staff absences; emergency order insertion triggers such as temporary task requests; and triggers when preset threshold parameters of key indicators exceed limits, such as abnormal indicators like resource utilization or task delay rates.

[0059] Upon triggering, it enters the rolling time-domain control mode. This time domain extends from the current moment to the current moment plus the time domain length, where the current moment is the starting point of optimization, and the time domain length is the time span between prediction and optimization, typically set to 1-7 days. Rolling time-domain control is a predictive control method that executes only the decision made at each moment and then rolls to the next moment for re-optimization, ensuring the dynamic and adaptive nature of the decision-making.

[0060] Within a defined rolling timeframe, a demand forecasting model is used to predict and calculate the resource requirements of each department. The method for constructing the demand forecasting model is as follows:

[0061] The demand forecasting model adopts an architecture that combines a multi-layer long short-term memory network (LSTM) with an attention mechanism. The inputs of the demand forecasting model include historical demand sequences, external signal feature vectors, time feature encodings, and departmental feature embeddings. The historical demand sequence is a time series of the demand for each resource by each department over the past T time periods. The default length T of the historical demand sequence is 14 time periods, determined through the decay characteristics of the autocorrelation function and business periodicity analysis in time series analysis, which can effectively capture daily and weekly demand patterns. The external signal feature vector includes numerical representations of external environmental information such as market fluctuation indicators and seasonal factors. The default dimension of the external signal feature vector is 32 dimensions, determined through principal component analysis and feature importance assessment. The time feature encoding is a one-hot encoding of the periodic features of the time period. Periodic features include hours, days of the week, and months. The default dimension of the time feature encoding is 168 dimensions, determined through time pattern analysis and a balance between encoding efficiency and time period. The department feature embedding is a low-dimensional dense vector representation of the static attributes of each department. Static attributes include department size, business type, and historical average demand level. The default dimension of the department feature embedding is 64 dimensions, determined through embedding learning theory and a balance between computational complexity and time period.

[0062] The demand forecasting model outputs the predicted demand of each department for each resource over the next H time periods. The output dimension is the number of departments multiplied by the number of resource types multiplied by the number of forecast periods.

[0063] The training steps for the demand forecasting model include: a data preprocessing stage, which involves collecting historical demand data, external signal data, and departmental attribute data; standardizing numerical features and encoding categorical features; using the Z-score method for data standardization; and setting a default threshold of 5% for missing value imputation, where features exceeding this threshold are discarded. A feature engineering stage involves constructing a sliding time window to extract historical demand sequences, with a default sliding window step size of one time period; calculating the statistical characteristics and trends of external signals, with a default statistical window length of seven time periods; and generating periodic codes for time features. A model building stage involves designing a multi-layer LSTM network to extract temporal features, with a default LSTM layer count of three layers and a default number of hidden units per layer of 128. An attention mechanism is introduced to capture the importance of different time periods and features. The default weight coefficients and number of attention heads are set to 8. A fully connected layer is added for feature fusion and output mapping, with a default number of 256 neurons in the fully connected layer. During model training, mean squared error is used as the loss function, and the Adam optimizer is used to update the preset parameters. The default initial learning rate is 0.001. A preset learning rate decay strategy is set, with a default decay factor of 0.95 and a default decay interval of 10 rounds. An early stopping mechanism is added to prevent overfitting, with a default early stopping patience value of 15 rounds. During model validation, the prediction accuracy is evaluated on the validation set. The default ratio of the training set to the validation set is 8:2. Mean absolute percentage error (MAPE) and root mean square error (RMSE) are used as evaluation metrics. The preset hyperparameters are optimized through grid search, with a default number of grid search iterations of 50.

[0064] Among them, the department's demand for resources in a time period represents the actual quantity of resources required by the department in different time periods. The length of the historical demand sequence T is usually set to 7-30 time periods. The number of predicted time periods H is determined according to the length of the rolling time domain. The dimension of the external signal feature vector is set according to the number of external factors in the actual business scenario.

[0065] Corresponding to demand forecasting, a capacity correction model is used to correct the actual available capacity of various resources. The construction method of the capacity correction model is as follows:

[0066] The capacity correction model employs a hybrid architecture combining convolutional neural networks (CNN) and recurrent neural networks (RNN). The inputs to the capacity correction model include a resource status feature matrix, a sequence of preset equipment operating parameters, maintenance plan information, and an environmental factor vector. The resource status feature matrix comprises a matrix representation of the current operating status, historical fault records, and usage frequency of each resource. The sequence of preset equipment operating parameters is a time series of key operating indicators for the equipment over the past S time periods, including temperature, pressure, speed, and load rate. The maintenance plan information includes structured data such as planned maintenance time, maintenance type, and estimated downtime. The environmental factor vector includes numerical representations of external environmental conditions such as temperature, humidity, and power supply stability.

[0067] The capacity correction model outputs the predicted actual available capacity of each resource over the next H time periods, with the output dimension being the number of resources multiplied by the number of prediction time periods.

[0068] The training steps of the capacity correction model include: Data acquisition phase, collecting heterogeneous data from multiple sources from equipment monitoring systems, maintenance management systems, and environmental monitoring systems (default data acquisition frequency is once every 5 minutes), establishing unified data standards and quality control mechanisms, with a default data quality threshold of 95%; Data fusion phase, performing time alignment and spatial matching on data from different sources (default time alignment accuracy is 1 minute), handling missing and outlier values ​​(outlier detection uses the 3σ criterion), and constructing a multidimensional feature tensor; Network design phase, using one-dimensional convolutional layers to extract local feature patterns based on preset equipment operation parameters (default kernel size is 3, default number of convolutional layers is 2, default number of kernels per layer is 64), using LSTM layers to capture temporal dependencies (default number of LSTM hidden units is 128), and fusing preset weight coefficients for the contributions of different types of features through an attention mechanism. The default value for the attention mechanism dimension is 64. In the loss function design phase, a composite loss function is constructed by combining regression loss and ranking loss. The default value for the regression loss weight coefficient is 0.8, and the default value for the ranking loss weight coefficient is 0.2. The regression loss measures the difference between the predicted and actual capacity values, while the ranking loss ensures the correctness of the relative order of capacity predictions among different resources. In the training and optimization phase, the batch gradient descent algorithm is used for model training. The default batch size is 64. A preset adaptive learning rate adjustment strategy is used, with an initial learning rate of 0.0005. The learning rate decay strategy uses cosine annealing. Dropout and batch normalization techniques are introduced to improve the model's generalization ability, with a default Dropout ratio of 0.3. In the model evaluation phase, the accuracy of capacity prediction is evaluated on the test set, with a default test set ratio of 20%. The mean absolute error (MAE) and preset coefficient of determination parameters are used. Using 5-fold cross-validation as an evaluation metric, model stability is ensured.

[0069] Among them, the actual available capacity of resources in a time period represents the actual available capacity of resources in a time period. The dimension of the resource status feature matrix is ​​determined according to the resource type and the number of monitoring indicators. The length S of the preset parameter sequence for equipment operation is usually set to 24-168 time periods to capture daily and weekly cycle features. The number of predicted time periods H is consistent with the demand forecasting model.

[0070] After completing demand forecasting and supply correction, demand-supply matching analysis is performed to identify potential resource shortages or surpluses. By comparing the total demand for each resource with the actual available capacity in each time period, a resource supply-demand discrepancy matrix is ​​obtained. This matrix is ​​a two-dimensional matrix, with its dimension being the product of the resource quantity and the forecast period quantity. Rows represent various resource types, such as equipment, personnel, and workstations, while columns represent the time periods within the rolling time domain, typically the next H time periods. The method for calculating the resource supply-demand discrepancy matrix is ​​as follows:

[0071] The supply-demand difference of a resource during a given period is equal to the total demand for that resource during that period minus the actual available capacity, where the total demand is the sum of the demand for that resource from all departments during that period.

[0072] Among them, the difference between supply and demand of resources in a given period indicates the degree of imbalance between supply and demand of resources in that period. A positive value indicates that demand exceeds supply, resulting in a resource shortage, while a negative value indicates that supply exceeds demand, resulting in a resource surplus.

[0073] Based on the resource supply and demand difference matrix, the initial disturbance source is identified and the disturbance intensity is quantified. The disturbance intensity calculation method is as follows:

[0074] The disturbance intensity of a resource during a given period is equal to the ratio of the absolute value of the supply-demand difference of the resource during that period to the preset standard capacity of the resource, multiplied by a preset disturbance sensitivity coefficient.

[0075] Among them, the disturbance intensity of a resource during a time period indicates the severity of the disturbance to the resource during that time period, the preset standard capacity of a resource is the standardized capacity benchmark value of the resource, and the preset disturbance sensitivity coefficient is a preset weighted coefficient parameter that reflects the sensitivity of the resource to disturbances. Its default value is 1.0, and it is determined through statistical analysis of historical disturbance data and expert experience.

[0076] The resource supply and demand difference matrix and the disturbance intensity vector are used as the basic input data for disturbance transmission modeling, providing quantitative initial conditions for the disturbance transmission analysis in step 200.

[0077] Step 200: Construct a resource sector network; determine the number of transmission layers and calculate the impact intensity based on the resource sector network and the disturbance intensity; calculate the comprehensive disturbance impact based on the impact intensity, specifically as follows: Figure 2 As shown.

[0078] Based on the resource supply and demand difference matrix and disturbance intensity vector identified in step 100, this step constructs a disturbance transmission model, analyzes the propagation mechanism of disturbances in the resource sector network, quantifies the degree of impact on each sector, and provides basic data for subsequent conflict identification and priority scoring.

[0079] A resource department network is a network structure that describes the dependencies between resources and departments, including resource nodes, department nodes, and connecting edges. Resource nodes represent various resources, such as equipment, personnel, and workstations; department nodes represent various business departments; and connecting edges represent the dependencies between departments and resources, as well as the weights of these dependencies.

[0080] Maintaining a resource department dependency table serves as the foundational data for constructing the resource department network. This table, built upon business process analysis and expert knowledge, records the dependency strength weight of each resource on each department. Dependency strength weights are categorized into four levels: no dependency, slight dependency, moderate dependency, and severe dependency. The default value for no dependency is 0, for slight dependency is 0.2, for moderate dependency is 0.5, and for severe dependency is 0.8. These default values ​​are determined based on business process analysis and expert knowledge assessment. The threshold for slight dependency is determined by a resource usage frequency below 20%, for moderate dependency by a resource usage frequency between 20% and 60%, and for severe dependency by a resource usage frequency above 60%.

[0081] In a resource department network, a department directly dependent on a resource refers to a department with a non-zero dependency weight in the resource department dependency relationship table. This means that the normal operation of this department directly requires the use of the resource, categorized into three levels: slight dependency, moderate dependency, and severe dependency. Collaborating departments refer to other departments that have business collaboration relationships with directly dependent departments. These departments form collaborative working relationships with directly dependent departments through workflow integration, information sharing, and resource complementarity. Their business performance is indirectly affected by changes in the operational status of directly dependent departments. Collaboration relationships are quantified using an inter-departmental collaboration strength coefficient. This coefficient is determined based on a comprehensive evaluation of indicators such as historical collaboration frequency, business relevance, and information interaction density. The default values ​​for the historical collaboration frequency weight coefficient, business relevance weight coefficient, and information interaction density weight coefficient are 0.4 and 0.2 respectively. The collaboration strength coefficient is calculated as a weighted average of the three indicator scores, ranging from 0 to 1, determined through historical data statistics and expert evaluation.

[0082] Based on the disturbance intensity vector calculated in step 100, the disturbance is categorized into three severity levels: minor, moderate, and severe. A minor disturbance has a disturbance intensity less than 0.3, a moderate disturbance has a disturbance intensity between 0.3 and 0.7, and a severe disturbance has a disturbance intensity greater than 0.7. The number of layers in which the disturbance propagates is automatically determined based on the disturbance level.

[0083] Minor disturbances propagate only at the first level, limiting their impact to sectors within the resource sector network that directly depend on that resource. Moderate disturbances propagate at the first and second levels, extending their impact to directly dependent sectors and their collaborating sectors. Severe disturbances propagate at all three levels, potentially triggering systemic propagation effects. The intensity of the impact includes the intensity of direct impact, indirect impact, and system-level moderating impact.

[0084] Based on the resource sector dependency table, calculate the intensity of the direct impact of resource disturbances on sectors:

[0085] The direct impact intensity of a department during a given time period is equal to the disturbance intensity of the resource during that time period multiplied by the resource's dependence intensity on the department, and then multiplied by a preset time decay factor.

[0086] Among them, the direct impact intensity of a department during a time period represents the degree of direct impact of resource disturbances on the department during that time period. The resource dependence intensity weight is the dependence coefficient of that resource on that department. The preset time decay factor is used to reflect the decay characteristics of the disturbance impact over time. The calculation formula is an exponential function with the natural constant as the base. The power of the exponential function is the product of the preset time decay coefficient and the time interval. The default value of the preset time decay coefficient is 0.1, which is obtained through time series analysis and empirical data fitting.

[0087] The disturbance propagation adopts a three-layer progressive propagation mechanism, calculating the propagation effect of the disturbance in the resource sector network layer by layer according to the disturbance level:

[0088] The first layer of transmission is direct transmission, where resource disturbances directly affect sectors that depend on that resource, and the intensity of the impact is determined according to the direct impact intensity calculation results mentioned above. All levels of disturbances will undergo the first layer of transmission.

[0089] The second layer of transmission is collaborative transmission, which is activated only when the disturbance level is moderate or severe. Directly affected departments transmit the disturbance to collaborating departments through collaborative relationships. The method for calculating the indirect impact intensity of collaborating departments is as follows:

[0090] The indirect influence intensity of the collaborating department during a given time period is equal to the direct influence intensity of the source department during that time period multiplied by the preset inter-departmental collaboration intensity coefficient, and then multiplied by the preset transmission attenuation factor.

[0091] Among them, the indirect influence intensity of the collaborating departments during the time period represents the degree of disturbance influence transmitted through the departmental collaboration relationship. The preset inter-departmental collaboration intensity coefficient reflects the closeness of collaboration between two departments, with a value range of 0 to 1. Its default value is determined based on the historical collaboration frequency and business relevance between departments. The preset transmission attenuation factor is used to reflect the attenuation of influence during the transmission process. The default value is 0.7, which is determined through network propagation theory and empirical analysis.

[0092] The third layer of transmission is the system-level regulation transmission, which is activated only when the disturbance level is severe. The third layer of transmission calculates the intensity of system-level regulation impact, used to quantify the degree of impact of the overall system's buffer regulation on each sector. The calculation method for the intensity of system-level regulation impact is as follows:

[0093] The intensity of a department's system-level adjustment influence during a given time period is equal to the overall system disturbance intensity multiplied by the preset department system importance weight coefficient, and then multiplied by the preset system adjustment intensity factor.

[0094] The overall system disturbance intensity is the weighted average of the disturbance intensities of all resources. Specifically, it is calculated as follows: the overall system disturbance intensity equals the sum of the products of the disturbance intensities of multiple resources over multiple time periods and their corresponding preset resource weight coefficients, divided by the sum of all preset resource weight coefficients. The resource weight coefficients are determined based on the resource's system criticality and scope of influence; the weight coefficient for critical resources is set to 1.0, for important resources to 0.7, and for general resources to 0.3. The departmental system importance weight coefficient reflects the department's importance within the entire system and is quantified using the analytic hierarchy process (AHP) in conjunction with three dimensions: departmental business criticality, resource dependence, and scope of collaborative influence. The evaluation uses a weighting factor of 0.5 for business criticality, 0.3 for resource dependence, and 0.2 for the scope of collaboration impact. Each dimension is scored on a scale of 1-5, and the final importance weighting factor is obtained by weighted averaging and normalization. A system adjustment intensity factor controls the degree of impact of system-level adjustments. Its calculation method is as follows: when the overall system disturbance intensity is less than or equal to 0.3, the system adjustment intensity factor is 0.2; when the overall system disturbance intensity is between 0.3 and 0.6, the system adjustment intensity factor is 0.5; and when the overall system disturbance intensity is greater than 0.6, the system adjustment intensity factor is 0.8, reflecting an adaptive mechanism where the greater the disturbance, the stronger the system adjustment. When the overall system disturbance intensity exceeds the system adjustment threshold of 0.7, a system-level buffer adjustment mechanism is activated. This mitigates the impact of the disturbance by calling up the backup resource pool or adjusting the priority of non-critical tasks. The backup resource pool has a higher priority than task priority adjustment. The adjustment effect is evaluated by the reduction in disturbance intensity.

[0095] Based on the calculation results of the three-layer transmission mechanism, the comprehensive disturbance impact on each sector is summarized, and the corresponding utility changes are predicted.

[0096] The calculation method for the comprehensive disturbance impact of a department is as follows:

[0097] The overall disturbance impact of a department during a given period is equal to the weighted sum of the department's direct impact intensity, indirect impact intensity, and system-level regulatory impact intensity during that period, with the weighting coefficients being preset direct transmission weighting coefficients, preset indirect transmission weighting coefficients, and preset system-level regulatory impact weighting coefficients, respectively. Specifically, the overall disturbance impact of a department during a given period is the sum of the department's direct impact intensity multiplied by the preset direct transmission weighting coefficient, the department's indirect impact intensity multiplied by the preset indirect transmission weighting coefficient, and the department's system-level regulatory impact intensity multiplied by the preset system-level regulatory weighting coefficient.

[0098] Among them, the comprehensive disturbance impact of a department during a time period represents the overall disturbance impact on the department during that time period. The default value of the direct transmission weight coefficient is 0.6, the default value of the indirect transmission weight coefficient is 0.3, and the default value of the system adjustment weight coefficient is 0.1, reflecting the dominant role of direct impact. These weight coefficients are determined through impact transmission mechanism analysis and historical data verification.

[0099] Based on the combined effects of disturbances, a piecewise linear mapping function is used to predict sectoral utility loss:

[0100] The utility loss of a department during a given period is equal to the preset utility sensitivity coefficient multiplied by the overall disturbance impact of the department during that period. When the overall disturbance impact is less than the preset tolerance threshold parameter, the utility loss is zero.

[0101] The utility loss of a department during a given period represents the reduction in utility caused by disturbances during that period. This utility loss will be used as a negative adjustment factor for the utility term in the multi-objective optimization in step 500. The preset utility sensitivity coefficient reflects the department's sensitivity to disturbances, with a default value of 2.0, which is determined through the department's historical performance data and sensitivity analysis. The preset tolerance threshold parameter is the minimum level of disturbance impact that the department can tolerate, with a default value of 0.1, which is set based on the department's risk tolerance assessment and business continuity requirements.

[0102] This step outputs disturbance level classification results, departmental comprehensive disturbance impact vector, and departmental utility loss vector, providing quantitative disturbance impact data and risk level information for conflict identification, overfitting calculation, and dynamic priority scoring in step 300.

[0103] Step 300: Calculate the oversizing degree based on the demand and actual available capacity; construct a conflict oversizing graph based on the oversizing degree; and combine this with the priority score of the department calculating the overall disturbance impact, specifically as follows... Figure 3 As shown.

[0104] Based on the departmental comprehensive disturbance impact vector and departmental utility loss vector output in step 200, this step identifies resource competition conflicts, constructs a conflict overlay graph, and calculates the departmental dynamic priority score in conjunction with the disturbance impact, providing a priority ranking basis for constructing the initial feasible solution in step 400.

[0105] First, based on the resource supply-demand difference matrix, the time periods and resource types where resource competition exists are identified. For each resource in each time period, the method for calculating resource oversupply is as follows:

[0106] The over-allocation of resources during a period is equal to the greater of zero and the excess of resource demand, where the excess of resource demand equals the sum of the demand for the resource by all departments during that period minus the actual available capacity of the resource during that period.

[0107] Among them, the over-allocation of resources during a time period indicates the degree to which resources are excessively demanded during that time period, and the demand of a department for resources during a time period is the specific quantity of resources that the department demands during that time period.

[0108] When the over-allocation of a resource exceeds the preset over-allocation threshold parameter during a time period, the resource is marked as a conflicting resource and resource allocation adjustment is required. The default value of the preset over-allocation threshold parameter is 0.05, which is determined through analysis of historical resource utilization data and capacity planning requirements.

[0109] For identified conflicting resources, a conflict overspending graph is constructed to describe the resource competition relationship. In the conflict overspending graph, request nodes represent departments' requests for resources during a given time period, resource nodes represent shared resources, and hyperedges connect multiple request nodes competing for the same resource. The hyperedge has a preset weight coefficient equal to the overspending degree of that resource.

[0110] Based on the comprehensive disturbance impact calculated in step 200, the dynamic priority score of each department is calculated for each time period. The method for calculating the dynamic priority score of a department is as follows:

[0111] The department's priority score for a given period is equal to the weighted sum of the basic priority score and the disturbance impact adjustment item. The basic priority score is a linear combination of five weighted items, specifically: the preset first weight coefficient multiplied by the standardized value of the key performance indicator, plus the preset second weight coefficient multiplied by the urgency, plus the preset third weight coefficient multiplied by the compliance score, minus the preset fourth weight coefficient multiplied by the change cost, and plus the preset fifth weight coefficient multiplied by the collaboration degree. The disturbance impact adjustment item is equal to the preset disturbance impact weight coefficient multiplied by the department's total disturbance impact for the given period.

[0112] Among them, the department's priority score in a time period represents the department's resource allocation priority value in that time period. The preset first to fifth preset weight coefficients correspond to the importance of different evaluation dimensions, and the sum of all preset weight coefficients is equal to 1. Their default values ​​are 0.3, 0.25, 0.2, 0.15, and 0.1, respectively, and are determined through the analytic hierarchy process and expert review. The standardized value of the key performance indicators is the value of the department's key performance indicators after standardization. The urgency is an indicator of the degree of urgency calculated based on the task deadline and current progress. The compliance score is a score reflecting the degree of compliance with regulatory requirements. The change cost is a cost indicator reflecting the cost required to adjust the current arrangement. The cooperation is a cooperation indicator reflecting the degree of support the department provides to other departments. The preset disturbance impact weight coefficient is a parameter that controls the importance of disturbance impact in the priority score. Its default value is 0.2 and is determined based on disturbance impact analysis and decision sensitivity testing.

[0113] The standardized values ​​of key performance indicators (KPIs) are obtained by first collecting raw data on departmental KPIs, including core business indicators such as task completion rate, quality compliance rate, customer satisfaction, cost control rate, and innovation contribution. Task completion rate equals the number of completed tasks divided by the total number of planned tasks; quality compliance rate equals the number of qualified outputs divided by the total output; customer satisfaction is obtained through customer evaluation questionnaires and quantified using a five-point Likert scale; cost control rate equals one minus the percentage by which actual costs exceed budgeted costs; and innovation contribution is calculated as a weighted average of the number of innovation projects, patent applications, and process improvement suggestions. Then, each indicator is further analyzed... Standardization is performed using Z-score standardization, where the standardized value of an indicator equals the original value of the indicator minus its historical mean, and then divided by its historical standard deviation. The historical mean and standard deviation are calculated based on historical data from the past twelve months. Finally, each standardized indicator is weighted and averaged according to preset weight coefficients to obtain the standardized value of the key performance indicator. The default values ​​for the weight coefficients are 0.3 for task completion rate, 0.25 for quality compliance rate, 0.2 for customer satisfaction, 0.15 for cost control rate, and 0.1 for innovation contribution. These weight coefficients are determined through the analytic hierarchy process and expert review.

[0114] The urgency level is calculated based on the task deadline and current progress. The specific formula is: urgency equals 1 minus the ratio of remaining time to total time, multiplied by a task importance coefficient. Remaining time equals the task deadline minus the current time, and total time equals the task deadline minus the task start time. The task importance coefficient is determined based on the task's business impact and is divided into four levels: 0.5 for general tasks, 0.7 for important tasks, 0.9 for critical tasks, and 1.0 for urgent tasks. When the remaining time is negative, it indicates the task is overdue, and the urgency level is set to the maximum value of 1.0. When a task has not yet started, the urgency level is estimated based on its time urgency within the overall plan. The estimation method is: urgency equals the task priority coefficient multiplied by a time pressure coefficient. The task priority coefficient is determined based on business importance assessment, and the time pressure coefficient is calculated based on the tension of the task's time window.

[0115] The compliance score is obtained by assessing the department's compliance with regulatory requirements, policy provisions, industry standards, and internal systems. The specific calculation steps include: establishing a compliance assessment indicator system, comprising four dimensions: regulatory compliance, policy compliance, standard compliance, and system compliance. Each dimension includes several specific compliance inspection items. Each compliance inspection item is scored on a 100-point scale, with full compliance scoring 100 points, basic compliance scoring 80 points, partial compliance scoring 60 points, and non-compliance scoring 0 points. Scoring is based on compliance audit results, regulatory inspection reports, and internal compliance assessment reports. Finally, the compliance score for each dimension is calculated. The dimensional compliance score is equal to the weighted average of the scores of all inspection items within that dimension. The weighting coefficients are determined based on the importance and risk level of the inspection items. The comprehensive compliance score is calculated as the weighted average of the compliance scores across the four dimensions. The default weighting coefficients for regulatory compliance are 0.4, policy compliance 0.3, standards compliance 0.2, and institutional compliance 0.1. These weighting coefficients are determined through risk assessment and compliance importance analysis. The comprehensive compliance score is then standardized by dividing the compliance score by 100, resulting in a standardized compliance score ranging from 0 to 1.

[0116] The method for calculating change costs is to quantify the various costs required to adjust the current resource allocation arrangement, including both direct and indirect costs. The specific calculation formula is that change cost equals the weighted sum of direct and indirect change costs. Direct change costs include directly quantifiable cost items such as personnel transfer costs, equipment relocation costs, workstation reconfiguration costs, and training costs. Indirect change costs include cost items that are difficult to quantify but do exist, such as production interruption losses, coordination and communication costs, increased risk costs, and morale impact costs. The calculation method for direct change costs is a simple summation of various direct costs. Specifically, personnel transfer cost equals the number of personnel transferred multiplied by the unit transfer cost, equipment relocation cost equals the number of equipment relocated multiplied by the unit relocation cost, workstation reconfiguration cost equals the number of workstations reconfigured multiplied by the unit configuration cost, and training cost equals the number of personnel requiring training multiplied by the unit training cost.

[0117] The unit cost is determined using activity-based costing (ABC) combined with parametric estimation.

[0118] The unit transfer cost is calculated based on activity-based costing (ABC), breaking down the personnel transfer process into various operational activities, including transfer approval, personnel procedures, work handover, relocation, and adaptation period. The cost of each activity equals the activity time multiplied by the activity unit price. The activity time is determined through time analysis and historical data statistics, while the activity unit price is calculated based on personnel wage levels and management costs. Specifically, the unit transfer cost equals the transfer approval cost plus personnel procedure costs plus work handover costs plus relocation costs plus adaptation period loss costs. The transfer approval cost equals the approval time multiplied by the number of management personnel... Average hourly wage; the default approval time is 4 hours; HR procedure cost equals procedure processing time multiplied by the average hourly wage of HR specialists, with a default procedure processing time of 2 hours; work handover cost equals handover time multiplied by the average hourly wage of the transferred personnel, with a default handover time of 8 hours; relocation cost includes transportation and moving expenses, with transportation expenses calculated based on the transfer distance and transportation standards, and moving expenses calculated based on the quantity of items and handling standards; adaptation period loss cost equals adaptation period duration multiplied by the efficiency loss ratio multiplied by the average hourly wage of the transferred personnel, with a default adaptation period duration of 40 hours and an default efficiency loss ratio of 30%.

[0119] The unit relocation cost is calculated using a full life-cycle cost analysis method. The equipment relocation process is broken down into standard work units such as dismantling, transportation, installation, commissioning, and acceptance. The cost of each work unit is calculated using standard labor hour quotas and resource consumption quotas. Specifically, the unit relocation cost equals the dismantling cost plus transportation cost plus installation cost plus commissioning cost plus acceptance cost plus downtime loss cost. The dismantling cost equals the dismantling time multiplied by the average hourly wage of technical personnel. The dismantling time is determined based on the equipment complexity level; the default dismantling time for simple equipment is 4 hours, and for complex equipment, it is 12 hours. Transportation costs are calculated using a transportation cost function based on equipment weight, volume, and transportation distance. The transportation cost function is the base freight plus a weight coefficient multiplied by the equipment weight plus a distance coefficient multiplied by the transportation distance. Installation costs are equal to installation hours multiplied by the average hourly wage of technicians. Installation hours are typically 1.2 times the dismantling hours. Commissioning costs are equal to commissioning hours multiplied by the average hourly wage of technicians. The default value for commissioning hours is 0.5 times the installation hours. Acceptance costs are equal to acceptance hours multiplied by the average hourly wage of quality inspectors. The default value for acceptance hours is 2 hours. Downtime loss costs are equal to downtime multiplied by the hourly output value of the equipment. Downtime is the sum of dismantling, transportation, installation, commissioning, and acceptance times.

[0120] The unit configuration cost is calculated using the standard cost method based on a standardized workstation configuration list and market price information. Workstation configuration includes three parts: hardware configuration, software configuration, and environmental configuration. Hardware configuration costs include the procurement or allocation costs of office desks and chairs, computer equipment, communication equipment, and special tools. Procurement costs are calculated based on market prices, and allocation costs are calculated based on equipment depreciation and transportation costs. Software configuration costs include license fees and installation and configuration fees for operating systems, application software, and professional software. License fees are calculated based on software vendor quotations, and installation and configuration fees are calculated based on technicians' working hours and hourly wages. Environmental configuration costs include the allocated costs of infrastructure such as network access, power supply, air conditioning and ventilation, and security protection. Allocated costs are calculated based on the workstation area and the unit area cost of infrastructure. The specific calculation formula is: unit configuration cost equals hardware configuration cost plus software configuration cost plus environmental configuration cost plus configuration implementation cost, where configuration implementation cost equals configuration working hours multiplied by the average hourly wage of technicians, with a default value of 6 hours for configuration working hours.

[0121] The unit training cost is calculated using a training cost accounting model, breaking down training costs into direct and indirect costs. Direct training costs include trainer fees, training material costs, training venue costs, and training equipment costs. Trainer fees are calculated based on training duration and the trainer's daily wage; training material costs are calculated based on the average material cost per person; training venue costs are calculated based on venue rental standards and usage duration; and training equipment costs are calculated based on equipment rental or depreciation costs. Indirect training costs include trainee wage costs and opportunity costs. Wage costs equal training duration multiplied by the trainee's average hourly wage, and opportunity costs... The cost equals the output loss caused by trainees being unable to perform normal work during the training period. The specific calculation formula is that the unit training cost equals the direct training cost divided by the number of trainees plus the indirect training cost. The direct training cost equals the trainer's fee plus the training material cost plus the training venue cost plus the training equipment cost. The default value for the trainer's daily wage is 1200 yuan, the default value for the average material cost per person is 150 yuan, and the default value for the daily venue rental is 800 yuan. The indirect training cost equals the training duration multiplied by the average hourly wage of the trainees multiplied by the opportunity cost coefficient. The default value for the opportunity cost coefficient is 1.2, which reflects the loss of productivity during the training period.

[0122] The indirect change cost is calculated using a cost estimation model. This model is constructed using multiple regression analysis combined with neural network technology, and is trained and calibrated based on historical change data and expert experience. The model input features include multi-dimensional feature vectors such as change scale indicators, change complexity indicators, change time urgency indicators, and organizational adaptability indicators. The change scale indicator is calculated using quantitative indicators such as the number of affected personnel, the number of departments involved, and the number of business processes affected. The change complexity indicator is determined through assessments of dimensions such as technical complexity, coordination complexity, and risk complexity. The change time urgency indicator is calculated as the ratio of available time to standard time. The organizational adaptability indicator is comprehensively assessed through factors such as organizational change capability, employee acceptance, and management support. The model employs a three-layer feedforward neural network. The network structure is as follows: the number of neurons in the input layer equals the dimension of the feature vector; the default number of neurons in the hidden layer is 1.5 times the number of neurons in the input layer; and the output layer outputs a single neuron's estimated indirect change cost. Model training uses the backpropagation algorithm, with mean squared error as the loss function and ReLU as the activation function. The default learning rate is 0.001, and the default number of training epochs is 1000. Model calibration employs an expert evaluation method, collecting cost estimation opinions from domain experts on typical change scenarios using the Delphi method. These expert estimations are used as a benchmark to calibrate and adjust the model output, with calibration coefficients determined through least squares fitting. The model output is an estimated indirect change cost, and the estimation accuracy is evaluated using the mean absolute percentage error (MAPE), with a target MAPE value within 15%.

[0123] The final change cost is converted into a standardized value between 0 and 1 through standardization. The standardization method is to divide the change cost by a preset maximum change cost threshold parameter, which is determined based on statistical analysis of historical change cost data. The default value is the 95th percentile of historical change costs.

[0124] The calculation method for collaboration degree is to quantify the degree of support and collaborative contribution of a department to other departments. Specifically, the calculation includes a comprehensive evaluation of three dimensions: collaboration frequency, collaboration quality, and collaboration impact. The formula is: Collaboration degree = Collaboration frequency score multiplied by a preset collaboration frequency weighting coefficient, plus Collaboration quality score multiplied by a preset collaboration quality weighting coefficient, plus Collaboration impact score multiplied by a preset collaboration impact weighting coefficient. The collaboration frequency score is calculated by dividing the number of collaborations between the department and other departments by a preset collaboration frequency benchmark. The number of collaborations is obtained by statistically analyzing the frequency of collaborative activities such as project cooperation, information sharing, resource sharing, and technical support between departments. The preset collaboration frequency benchmark is determined based on the industry average and organizational collaboration goals. The collaboration quality score is obtained through a collaboration effectiveness evaluation questionnaire and collaboration outcome evaluation, with evaluation dimensions including... The collaboration evaluation includes timeliness, effectiveness, satisfaction, and innovation. Each dimension is scored using a five-point scale, and the collaboration quality score is the weighted average of the scores for each dimension. The collaboration impact score is calculated by assessing the positive impact of departmental collaboration on the performance of other departments and the overall organization. Impact assessment includes the contribution to improving the performance of collaborating departments, the promotion of the achievement of overall organizational goals, and the driving effect on cross-departmental process optimization. A comprehensive evaluation is conducted through a combination of quantitative analysis and qualitative assessment. The default values ​​for the collaboration frequency weight coefficient, collaboration quality weight coefficient, and collaboration impact weight coefficient are 0.4 and 0.2, respectively. These weight coefficients are determined through collaboration value analysis and organizational synergy theory. Finally, the collaboration degree is converted into a standardized value between 0 and 1 through standardization.

[0125] Step 400: Construct a constraint set and generate an initial feasible solution based on the conflict overmap and priority score.

[0126] Based on the conflict overmap and departmental dynamic priority scores, this step constructs a constraint set and uses a priority-driven greedy algorithm to quickly generate an initial feasible solution, providing a high-quality hot start point for the multi-objective optimization in step 500.

[0127] Based on the conflicting resources and business rules identified in step 300, a complete set of constraints is established to ensure that the generated initial solution satisfies all hard constraints. The constraint set includes:

[0128] The capacity constraint stipulates that for each resource in each time period, the total amount allocated to that resource by all departments during that time period must not exceed the actual available capacity of that resource during that time period. This constraint ensures that resource allocation does not exceed physical limits.

[0129] The time constraint stipulates that for each department, the total amount of all resources allocated to that department in each time period must not exceed the department's time limit for that time period. This constraint ensures that the department's workload remains within a reasonable range.

[0130] The compliance constraint stipulates that for each department, the allocation of each resource in each time period must not exceed the department's available capacity limit for that resource in that time period. This constraint reflects regulatory and policy requirements.

[0131] The skills matching constraint requires that personnel resources allocated to a department must possess the skill levels and certifications required by that department. This constraint ensures that personnel capabilities match task requirements.

[0132] The delivery window constraint requires that departmental tasks be completed within a specified time window, and that corresponding resource allocation support the time requirements. This constraint ensures that tasks are delivered on time.

[0133] An initial feasible solution is generated using a greedy algorithm based on dynamic departmental priority scores. The algorithm flow is as follows:

[0134] All departments are sorted in descending order of their priority scores calculated in step 300 for the time period, forming a department priority queue. Departments with higher priority scores receive resource allocation opportunities first.

[0135] Resources are allocated to each department sequentially according to the department priority queue. For the current department, the matching degree of the department with each resource is calculated, taking into account resource utility, availability, and conflict level.

[0136] When encountering conflicting resources, refer to the conflict over-allocation diagram constructed in step 300, prioritize the needs of departments with higher priority scores, and for departments with lower priority, find alternative resources or adjust the time slot schedule.

[0137] After each resource allocation, check whether any constraints in the above constraint set are violated. If a constraint violation occurs, roll back and try a suboptimal allocation scheme.

[0138] After completing the resource allocation for all departments, verify the integrity and feasibility of the initial solution to ensure that the basic needs of all departments are met and there are no constraint violations.

[0139] The generated initial feasible solution includes the specific allocation quantity of each resource for each department in each time period, forming a three-dimensional allocation matrix. The initial solution is then evaluated for quality, and key indicators such as overall utility, resource utilization, and constraint satisfaction are calculated.

[0140] This initial feasible solution serves as the hot start point for the multi-objective optimization model in step 500, providing a good search starting point for subsequent precise optimization and significantly improving optimization efficiency and solution quality.

[0141] Step 500: Construct a multi-objective optimization model with the initial feasible solution as the hot start point. The multi-objective optimization model solves the resource allocation scheme based on the constraint set inherited by the model.

[0142] Based on the three-dimensional allocation matrix of the initial feasible solution generated in step 400, this step uses the initial solution as a hot start point to construct a multi-objective optimization model and perform accurate solution to achieve global optimization of resource allocation and load balancing.

[0143] Receive the initial feasible solution three-dimensional allocation matrix output from step 400. This matrix includes the specific allocation quantity of each resource for each department in each time period. Starting from this initial solution, construct a multi-objective optimization model to further improve the quality of the solution while ensuring its feasibility.

[0144] The multi-objective optimization model constructs a multi-objective optimization function. The method for constructing the multi-objective optimization function is as follows:

[0145] The goal of the multi-objective optimization function is to maximize the linear combination of five weighted terms. Specifically, it is to multiply the first objective weight coefficient by the sum of the utility terms of all departments in all time periods, add the second objective weight coefficient by the fairness term, subtract the third objective weight coefficient by the sum of the over-allocation of all resources in all time periods, subtract the fourth objective weight coefficient by the sum of the stability terms of all departments in all time periods, and then subtract the fifth objective weight coefficient by the load balancing term.

[0146] The meanings of each term are as follows: the utility term equals the inner product of the preset utility coefficient vector and the department's resource allocation vector during the time period, minus the department's utility loss during the time period. Mathematically, the department's utility term during the time period equals the sum of the products of the department's preset utility coefficients for each resource and the corresponding resource allocation amounts, minus the department's utility loss during the time period. Here, the preset utility coefficient vector is the set of preset utility coefficients for each resource by the department during the time period, and the preset utility coefficients represent the satisfaction or value generated by the department using a unit of resource. The department's resource allocation vector during the time period is the set of allocation amounts for all resources by the department during the time period. The department's utility loss during the time period is the reduction in utility caused by the disturbance calculated in step 200. The equivalence term equals the sum of squares of the negative differences between total utility and average utility of each sector. Mathematically, it is the sum of squares of the negative differences between total utility and average utility of all sectors. The total utility of a sector equals the sum of its utility terms across all time periods, representing the overall satisfaction or value that the sector gains from resource allocation throughout the entire time domain. Average utility equals the arithmetic mean of the total utility of all sectors. The over-allocation penalty term is the sum of the over-allocation degrees of all resources across all time periods, used to penalize resource over-allocation. The stability term is the L1 norm of the difference between the resource allocation vector of a sector in the current time period and the previous time period, used to penalize frequent changes. The load balancing term is the variance of the total allocation of each resource in each time period, used to penalize uneven load distribution.

[0147] The multi-objective optimization model inherits the constraint set established in step 400, including capacity constraints, time constraints, compliance constraints, skill matching constraints, and delivery window constraints, to ensure that the feasibility of the solution is always guaranteed during the optimization process.

[0148] The multi-objective optimization model employs a hierarchical decomposition solution strategy, breaking down the multi-objective optimization problem into two levels: a resource allocation subproblem and a shift sequence generation subproblem. The first level, the resource allocation subproblem, uses a mixed-integer programming (MIP) solver to handle resource quantity allocation problems primarily based on linear objectives and capacity constraints. The decision variables are the number of resources allocated to departments during a given time period. The objective function is a weighted combination of utility, fairness, and over-allocation penalty terms, with constraints including capacity constraints, work hour constraints, and delivery window constraints. The second level, the shift sequence generation subproblem, uses a constrained programming (CP) solver to efficiently handle shift sequence arrangement problems involving complex rules. The decision variables are specific personnel shift arrangements and equipment usage sequences. The objective function is a weighted combination of stability and load balancing terms, with constraints including compliance constraints, skill matching constraints, and sequence constraints.

[0149] The two subproblems are coordinated using a Lagrange relaxation framework. The specific coordination mechanism is as follows: First, initialize the Lagrange multiplier vector, which corresponds to the shadow price of each coupled constraint. Second, fix the Lagrange multipliers and solve the resource allocation subproblem and the scheduling sequence generation subproblem respectively to obtain their optimal solutions. Third, based on the consistency check results of the solutions to the two subproblems, update the Lagrange multipliers using the subgradient method. The update formula is: the Lagrange multiplier equals the current Lagrange multiplier plus a preset step size coefficient multiplied by the constraint violation amount. The default value of the preset step size coefficient is 0.1, determined through convergence analysis and numerical stability testing. Fourth, repeat steps two and three until the convergence condition is met or the maximum number of iterations is reached.

[0150] Based on the initial feasible solution three-dimensional allocation matrix output in step 400, the final first resource allocation scheme is generated through the following complete process:

[0151] The first stage is the initial solution preprocessing and quality assessment. The initial feasible solution is subjected to integrity checks and quality assessments to verify whether the initial solution meets all hard constraints. The objective function value of the initial solution is calculated as the optimization benchmark, and resource allocation bottlenecks and improvement space in the initial solution are identified to provide directional guidance for subsequent optimization.

[0152] The second stage is the hierarchical optimization solution execution. Following the aforementioned hierarchical decomposition strategy, the resource allocation subproblem is solved first. Under the condition of fixed Lagrange multipliers, the resource allocation quantity of departments in time periods is optimized by a mixed integer programming solver to obtain the optimal solution for resource quantity allocation. Then, the shift sequence generation subproblem is solved. Based on the determined resource quantity allocation, the specific personnel shift arrangements and equipment usage sequence are optimized by a constraint programming solver to obtain a detailed shift sequence arrangement.

[0153] The third stage is the consistency coordination and iterative optimization of the solution. It checks the consistency between the solutions of the two subproblems. When there is inconsistency, it coordinates through the Lagrange multiplier update mechanism and repeats the hierarchical solution process of the second stage until the solutions of the two subproblems meet the consistency requirements or the convergence conditions.

[0154] The fourth stage is the final solution integration and output, which integrates the optimal solutions of the resource allocation subproblem and the scheduling sequence generation subproblem to generate a first resource allocation scheme that includes complete resource allocation information and scheduling sequence information.

[0155] The first resource allocation scheme, as the output of multi-objective optimization, includes the following core components:

[0156] The resource allocation matrix is ​​a three-dimensional structure, with the dimensions being the number of departments multiplied by the number of time periods multiplied by the number of resource types. The matrix elements represent the number of resources allocated by departments during the time period. This matrix inherits from and optimizes the initial feasible solution's three-dimensional allocation matrix, ensuring the accuracy of resource allocation and constraint satisfaction.

[0157] The personnel shift schedule is a detailed record of each person's specific work arrangements for each time period, including job position, shift type, working hours, skill matching, and other information. The personnel shift schedule is generated based on the personnel resource allocation results in the resource quantity allocation matrix to ensure consistency between personnel arrangements and resource allocation.

[0158] The equipment usage sequence diagram describes the usage status and allocation of each piece of equipment in each time period, including equipment number, user department, usage time period, load level, maintenance window, and other information. The equipment usage sequence diagram is generated based on the equipment resource allocation results in the resource quantity allocation matrix to ensure the rationality of equipment usage sequence and the satisfaction of capacity constraints.

[0159] The workstation allocation configuration table records the allocation status and usage arrangements of each workstation in each time period, including information such as workstation number, allocating department, user, configuration requirements, and environmental conditions. The workstation allocation configuration table is generated based on the workstation resource allocation results in the resource quantity allocation matrix, ensuring the spatial rationality and functional matching of workstation allocation.

[0160] The resource scheduling execution instruction set includes specific resource scheduling operation instructions to guide each execution system in the actual operation of resource allocation. The instruction content includes detailed information such as resource allocation time, allocation quantity, allocation path, execution priority, and exception handling method to ensure the executability and standardization of the resource allocation plan.

[0161] Among them, the resource quantity allocation matrix, as the core component of the first resource allocation scheme, requires that the values ​​of its matrix elements satisfy non-negative integer constraints and capacity limit constraints. The rows and columns of the matrix correspond to the department dimension, time period dimension, and resource type dimension, respectively. Through three-dimensional indexing, the allocation quantity of any resource for any department at any time period can be accurately located. The personnel scheduling sequence table and equipment usage time sequence diagram, as specific expansions of the resource quantity allocation matrix in the personnel and equipment dimensions, provide more detailed operational information. The workstation allocation configuration table, as a specific description of spatial resource allocation, ensures the rational allocation of physical space resources. The resource scheduling execution instruction set, as an operational guide for scheme execution, bridges the implementation gap between optimization results and actual execution.

[0162] An iterative algorithm based on Lagrange relaxation is employed to solve the multi-objective optimization function. This algorithm gradually approximates the global optimum by iteratively updating the Lagrange multipliers. Multiple convergence criteria are used to determine the convergence of the algorithm, ensuring the stability of the solution process and the quality of the solution.

[0163] The specific criteria for convergence determination include: The objective function convergence criterion: when the relative change in the objective function value within a preset number of convergence check rounds is less than a preset target convergence threshold parameter, the objective function is considered convergent. The default value for the preset number of convergence check rounds is 5 rounds, and the default value for the preset target convergence threshold is 0.001, determined through numerical optimization theory and computational accuracy requirements. The Lagrange multiplier convergence criterion: when the change in the L2 norm of the Lagrange multiplier vector is less than a preset multiplier convergence threshold parameter, the Lagrange multiplier is considered convergent. The default value is 0.01, determined through duality theory and numerical stability analysis; the constraint violation convergence criterion is that the constraint is considered to be convergent when the sum of the violations of all constraints is less than the preset constraint violation threshold parameter. The default value of the preset constraint violation threshold is 0.05, determined through a balance between feasibility requirements and fault tolerance; the subgradient norm convergence criterion is that the algorithm is considered to have converged to the neighborhood of the optimal solution when the L2 norm of the subgradient vector is less than the preset subgradient threshold parameter. The default value of the preset subgradient threshold is 0.1, determined through a balance between optimality conditions and computational complexity.

[0164] The algorithm stops when all four convergence criteria mentioned above are met simultaneously, or when the preset maximum number of iterations is reached. The default value for the preset maximum number of iterations is 1000, determined based on computational resource constraints and solution time requirements. When the maximum number of iterations is reached but the convergence criteria are not met, the current optimal solution is output as an approximate solution, and convergence status information is recorded for subsequent analysis.

[0165] To enhance robustness, a perturbation robustness term is introduced. The calculation method is to find the scheme that minimizes the Lagrange function value under the worst perturbation condition among all feasible resource allocation schemes, and obtain the first resource allocation scheme. The worst perturbation condition refers to the perturbation that maximizes the Lagrange function value under the constraint that the norm of the perturbation vector does not exceed the preset robustness parameter.

[0166] The Lagrange function is a composite function including the original objective function and constraints. The disturbance vector is a vector representing uncertainty. The preset robustness parameter is a parameter that controls the tolerance to disturbances, with a default value of 0.15, determined through statistical analysis and risk assessment of historical disturbance data. The default values ​​of the preset first objective weight coefficient to the preset fifth objective weight coefficient are 0.4, 0.2, 0.2, 0.1, and 0.1, respectively. The first objective weight coefficient of 0.4 reflects the principle of prioritizing utility and is determined through business value analysis; the second objective weight coefficient of 0.2 reflects the importance of fairness and is determined through organizational equity theory; the third objective weight coefficient of 0.2 reflects the need for operational stability and is determined through stability analysis; the fourth objective weight coefficient of 0.1 reflects the need for load balancing and is determined through resource utilization optimization; and the fifth objective weight coefficient of 0.1 reflects the requirement for cost control and is determined through cost-benefit analysis. The balancing logic of the five weight coefficients follows a hierarchical principle of prioritizing utility, balancing fairness and stability, and considering both load and cost.

[0167] In the multi-objective optimization solution process, the shadow price of each resource at each time period is calculated using Lagrange duality theory. The method for calculating shadow prices is as follows:

[0168] The shadow price of a resource in a given period is equal to the partial derivative of the Lagrange function with respect to the capacity constraint of that resource in that period, reflecting the marginal value and scarcity of that resource in that period.

[0169] In this context, the shadow price of a resource during a given time period represents the improvement in the objective function when the resource's capacity is increased by one unit during that time period. The Lagrangian function is a composite function that includes the original objective function and all constraints. The capacity constraint is a condition that limits resource allocation to no more than the actual available capacity. The magnitude of the shadow price directly reflects the scarcity of the resource; the higher the shadow price, the scarcer the resource is during that time period, and the more significant the improvement in overall utility from increasing the resource's capacity.

[0170] Simultaneously, the marginal utility estimate of the resource by the department is calculated. The method for calculating the marginal utility estimate of the resource by the department over a given period is as follows:

[0171] The marginal utility estimate of a department for a resource during a given period is equal to the partial derivative of the department's utility function with respect to the allocated amount of the resource during that period. Specifically, it is calculated as the first partial derivative of the department's utility term with respect to the allocated amount of the resource during that period. The steps for calculating the marginal utility estimate are as follows: First, determine the mathematical form of the department's utility function, which is equal to the sum of the products of the department's pre-defined utility coefficients for each resource and the corresponding allocated amounts, minus the department's utility loss during that period. Next, calculate the first partial derivative of the utility function with respect to the allocated amount of the resource. Since the utility function is linear, the partial derivative result is the department's pre-defined utility coefficient for that resource. Considering the impact of constraints, when the allocated amount of the resource is within the feasible region, the marginal utility estimate equals the pre-defined utility coefficient. When the allocated amount of the resource reaches the constraint boundary, it needs to be corrected using Lagrange multiplier theory. The corrected marginal utility estimate equals the pre-defined utility coefficient minus the Lagrange multipliers of the relevant constraints. Finally, output the final marginal utility estimate, which reflects the department's true marginal value assessment of the resource.

[0172] Among them, the marginal utility estimate of a department for a resource during a given time period represents the incremental utility that a department can obtain when the allocation of a resource increases by one unit during that time period, reflecting the department's assessment of the marginal value of that resource; the utility function is a mathematical function describing the satisfaction or value that a department obtains from resource allocation, and its specific form is the inner product of the preset utility coefficient vector and the department's resource allocation vector during the time period minus the department's utility loss during the time period; the utility term is the function value of the utility function under the current resource allocation state, representing the department's overall satisfaction with the current resource allocation; the first-order partial derivative is the derivative of the utility function with respect to the resource allocation amount, which is equal to the department's preset utility coefficient for that resource in the unconstrained case; the Lagrange multiplier is the dual variable reflecting the tightness of the constraint in the constrained optimization problem. When the constraint is in an active state, the Lagrange multiplier is positive, indicating the marginal impact of the constraint on the objective function.

[0173] This step outputs the optimized first resource allocation scheme, the shadow price vector of each resource in each time period, and the marginal utility valuation matrix of each resource for each department in each time period, providing the optimal solution and a complete price information basis for the price-based intelligent adjustment in step 600.

[0174] Step 600: Based on the optimized first resource allocation scheme, the shadow price vector of each resource in each time period, and the marginal utility valuation matrix of each resource for each department in each time period output in step 500, this step uses a pricing mechanism to carry out intelligent adjustment to achieve fair allocation and compliance verification of resources.

[0175] Based on a comparison of shadow prices and sectoral marginal utility estimates, a price-based adjustment strategy is implemented. The adjustment decision rule is as follows:

[0176] When a department's marginal utility estimate of a resource in a given time period is less than the shadow price of that resource in that time period, the department's demand for that resource is determined to be of low priority. The department is then guided to release some of its resource allocation, and the released resources are reallocated to departments with higher marginal utility estimates. When a department's marginal utility estimate of a resource in a given time period is greater than or equal to the shadow price of that resource in that time period, the department's current allocation to that resource is maintained, and an optimized solution is searched for for the department within the neighborhood time window or in the set of alternative resources.

[0177] Among them, the neighborhood time window is the set of time periods within the preset time window range parameters before and after the current time period. The default value of the preset time window range is 2 time periods, which is determined by balancing business flexibility requirements and scheduling complexity. The alternative resource set is the set of resources that are similar in function to the current resource and can be substituted for each other. It is established based on resource attribute analysis and business process compatibility assessment.

[0178] To prevent excessive concentration of resources and ensure that the basic needs of all departments are met, a fair quota adjustment mechanism will be established. The quota setting method is as follows:

[0179] The upper limit of a department's resource quota is equal to the department's historical average demand multiplied by the preset upper limit coefficient, and the minimum guaranteed quota of a department's resources is equal to the department's basic operational demand multiplied by the preset guarantee coefficient.

[0180] Among them, the department's resource quota upper limit represents the maximum allowable allocation of resources to the department, the department's minimum guaranteed resource quota represents the minimum guaranteed allocation of resources to the department, the department's historical average demand is the average demand for the resource by the department in the historical period, and the department's basic operating demand is the amount of resources necessary for the department to maintain basic operations. The default value of the preset quota upper limit coefficient is 1.2, which is determined through historical demand fluctuation analysis, allowing the department to have a 20% flexibility based on the average demand; the default value of the preset guarantee coefficient is 0.8, which is determined through basic operating demand assessment, ensuring that the department obtains a minimum guarantee of 80% of its basic operating demand.

[0181] During the resource allocation process, quota constraints are checked simultaneously to ensure that the resource allocation of any department neither exceeds the quota limit nor falls below the minimum guaranteed quota, thus forming a dual regulation mechanism of price guidance and quota constraints.

[0182] After price-based adjustment and quota adjustment are completed, a comprehensive compliance verification of the adjustment results is conducted. The verification process consists of two levels: hard constraint checks and soft constraint assessments.

[0183] Hard constraint checks ensure that the initial resource allocation plan after mediation strictly meets mandatory conditions such as legal requirements, safety regulations, and labor laws. Each hard constraint is verified individually; any violation of a hard constraint will trigger a plan rollback and re-mediation.

[0184] Soft constraint assessment evaluates non-mandatory conditions such as preference requirements, comfort conditions, and efficiency goals. The method for calculating penalties for violating soft constraints is as follows:

[0185] The soft constraint penalty term is equal to the sum of all soft constraint violation penalties, where each soft constraint violation penalty is equal to the larger of zero and the degree of soft constraint violation multiplied by the corresponding preset penalty coefficient.

[0186] Among them, the degree of soft constraint violation refers to the severity of the soft constraint violation, and the preset penalty coefficient is the penalty weight coefficient for the corresponding soft constraint violation. Its default value is set according to the type of soft constraint: the preference constraint is 10.0, which is determined through employee satisfaction survey and preference violation cost analysis; the comfort constraint is 5.0, which is determined through work environment assessment and comfort impact analysis; and the efficiency constraint is 15.0, which is determined through production efficiency loss assessment and business impact analysis. The efficiency constraint has the highest weight coefficient, which reflects its key impact on business performance.

[0187] Identify highly sensitive changes and implement a human factors review mechanism. This mechanism involves manual intervention and control for highly sensitive changes. It automatically identifies changes that may significantly impact employee work experience, safety risks, and business continuity, and submits them to management for manual review and decision-making to ensure the rationality and acceptability of scheduling adjustments. Highly sensitive changes include adjustments to night shift arrangements, frequent job changes, and the reassignment of key skilled personnel—any adjustments that significantly impact employee work experience and safety risks.

[0188] The method for identifying highly sensitive changes is as follows: when the sensitivity score of any change in the mediation plan exceeds the preset approval threshold parameter, the change is marked as a highly sensitive change. The sensitivity score comprehensively considers factors such as the degree of impact of the change on employees, the level of security risk, and the impact on business continuity. The default value of the preset approval threshold is 0.3, which is determined through historical change risk statistical analysis. This threshold corresponds to a medium risk level, ensuring that more than 30% of sensitive changes require manual review, thus balancing automation efficiency and risk control needs.

[0189] For identified highly sensitive changes, equivalent alternatives are automatically generated for managers to choose from and submitted for manual approval. Alternative generation is based on neighborhood search and resource substitution rules, ensuring that the feasibility and utility of the solutions are maintained while reducing sensitivity.

[0190] This step outputs a second resource allocation scheme that has undergone price adjustment, quota constraints, compliance verification, and human factors review, providing a complete adjustment result for the simulation verification in step 700.

[0191] Step 700: Based on the second resource allocation scheme output from Step 600, which has undergone price adjustment, quota constraints, compliance verification, and human factor review, this step conducts robustness verification in a digital twin simulation sandbox to ensure the stability of the scheme under various disturbance scenarios and completes the formal release and delivery of the scheme.

[0192] The second resource allocation scheme output in step 600 is used as the benchmark scheme for simulation verification. A simulation model consistent with the actual production environment is constructed in the digital twin simulation sandbox. The simulation model includes a resource status simulator, a departmental demand generator, a disturbance event injector, and a performance indicator monitor.

[0193] The disturbance scenario generation employs Monte Carlo sampling, randomly sampling from a predefined disturbance scenario space according to historical disturbance probability distributions. The disturbance scenario space includes typical disturbance types such as equipment failure, staff absence, emergency order insertion, and supply chain disruption. The probability and intensity distribution of each disturbance type are determined based on statistical analysis of historical data.

[0194] Robustness assessment includes two core indicators: expected target value and conditional value of risk. The expected target value is calculated as follows:

[0195] The expected target value is equal to the sum of the products of the objective function value and the corresponding scenario probability under all sampling perturbation scenarios.

[0196] The method for calculating conditional value at risk is as follows:

[0197] The conditional value of risk is equal to the conditional expectation of the objective function value provided that the objective function value does not exceed the value of risk, where the value of risk is the preset alpha quantile parameter of the distribution of the objective function value.

[0198] The default value of the preset alpha quantile is 0.05, which is determined by risk management theory and business risk tolerance. Conditional Value at Risk is used to measure tail risk in extreme situations.

[0199] A robustness compliance standard is set, with the expected target value not lower than 90% of the baseline target value and the conditional value at risk not lower than 70% of the baseline target value. When simulation test results show that the robustness indicators fail to meet the standard, a solution adjustment mechanism is triggered.

[0200] First, revert to step 500 to re-perform multi-objective optimization, adjusting key parameters such as the preset first objective weight coefficient to the preset fifth objective weight coefficient, the preset robustness parameter, and the preset time domain length parameter; second, assess whether it is necessary to increase the buffer resource pool or adjust the resource quota limit; finally, re-execute the price adjustment and compliance verification process of step 600.

[0201] The buffer resource pool is a reserve of flexible resources designed to cope with sudden disturbances and uncertainties, providing emergency support when regular resource allocation cannot meet demand. The buffer resource pool comprises three sub-pools: a personnel buffer pool, an equipment buffer pool, and a workstation buffer pool.

[0202] The personnel buffer pool consists of flexible personnel with multi-skilled capabilities, who can quickly switch between multiple roles to provide temporary support to different departments. The size of the personnel buffer pool is calculated as follows:

[0203] The size of the personnel buffer pool is equal to the sum of the peak personnel demand of each department multiplied by the preset personnel buffer coefficient, where the default value of the preset personnel buffer coefficient is 0.15, which is determined through historical disturbance frequency analysis and emergency response capability assessment.

[0204] The equipment buffer pool consists of rapidly deployable backup and leased equipment, used to replace faulty equipment or meet temporary incremental demand. The capacity of the equipment buffer pool is calculated as follows:

[0205] The capacity of the equipment buffer pool is equal to the standard capacity of each type of equipment multiplied by the corresponding preset equipment buffer ratio. The preset equipment buffer ratio is determined according to the failure rate and criticality of the equipment type. The buffer ratio for critical equipment is 0.20, the buffer ratio for important equipment is 0.15, and the buffer ratio for general equipment is 0.10.

[0206] Workstation buffer zones consist of flexibly configurable temporary work areas, including mobile workstations, shared office areas, and emergency work zones. The number of workstation buffer zones is calculated as follows:

[0207] The number of workstation buffer pools is equal to the sum of the peak demand for workstations in each department multiplied by the preset workstation buffer coefficient, where the default value of the preset workstation buffer coefficient is 0.12, which is determined through space utilization analysis and flexibility demand assessment.

[0208] The activation of buffer resource pools follows a tiered activation mechanism. When the resource over-provisioning exceeds the preset activation threshold parameter of 0.15, the personnel buffer pool is activated first; when the over-provisioning exceeds 0.25, the equipment buffer pool is activated simultaneously; when the over-provisioning exceeds 0.35, all buffer resources, including the workstation buffer pool, are fully activated. The activation cost of buffer resources is higher than that of regular resources, and it is quantified through preset buffer cost coefficients: 1.5 for personnel buffers, 1.3 for equipment buffers, and 1.2 for workstation buffers, ensuring that buffer resources are activated only when necessary.

[0209] The default value for the preset time domain length parameter is 7 days, determined through a balance between business cycle analysis and forecast accuracy. Parameter adjustments follow a gradual strategy, with each adjustment not exceeding 20% ​​of the current value to avoid drastic changes in the solution.

[0210] The second resource allocation scheme, having passed robustness verification, proceeds to the commitment processing stage. A commitment-based scheduling contract is generated, which includes the following core elements:

[0211] The second resource allocation plan details the specific allocation quantity and usage arrangements of each resource for each department at each time period; the shadow price information of key resources at each time period provides a price reference for subsequent dynamic adjustments; the set of alternative plans includes emergency resource allocation plans for common disturbance scenarios; the rollback rule definition clarifies the conditions and procedures for plan rollback in abnormal situations; and the freeze window and unfreeze strategy stipulate the change restrictions and release conditions during the implementation of the plan.

[0212] Commitment-based scheduling contracts are uniformly pushed to all execution terminals through an enterprise-level data bus, including production scheduling systems, human resource management systems, equipment management systems, and other related business systems, ensuring the consistency and executability of the solution across all systems.

[0213] This step outputs a simulation-verified commitment scheduling contract and related execution parameters, providing a stable and reliable execution benchmark for runtime monitoring and fine-tuning in step 800.

[0214] Step 800: Based on the committed scheduling contract and execution benchmark output in Step 700, this step establishes an operational monitoring system to monitor and dynamically fine-tune the execution process of the plan in real time, and continuously optimize system parameters through an online learning mechanism to ensure the effectiveness and adaptability of the scheduling plan in actual operation.

[0215] Establish a monitoring indicator system based on commitment-based scheduling contracts to track the execution of key performance indicators in real time. The monitoring indicators include four core dimensions: resource over-provisioning during time periods, task on-time rate, load variance, and the number of compliance alerts.

[0216] Monitoring data is collected in real time from various execution systems via an enterprise-level data bus, including task execution status from the production scheduling system, employee attendance from the human resources management system, and equipment operating status from the equipment management system. The system uses a sliding window mechanism to analyze the monitoring data in real time, with a window length set to 1 hour and monitoring results updated every 15 minutes.

[0217] Anomaly detection employs a statistical control chart-based approach, triggering anomaly alarms when monitored metrics exceed preset monitoring threshold parameters. These preset monitoring thresholds are set separately for each metric type: resource over-provisioning threshold is 0.1, task on-time performance threshold is 0.85, load variance threshold is 0.2, and the number of compliance alarms is 5. These thresholds are determined based on historical operational data statistical analysis and business service level requirements.

[0218] When an anomaly detection triggers an alarm, a dynamic fine-tuning mechanism is activated. The fine-tuning strategy follows the principle of minimal intervention, prioritizing local adjustments to avoid significant disruption to the overall solution.

[0219] The fine-tuning operation includes three levels. The first level is time offset adjustment, which slightly moves the task execution time forward or backward without changing the total amount of resources allocated. The second level is alternative resource invocation, which activates predefined resource alternative schemes based on the set of alternative plans generated in step 700. The third level is buffer resource pool activation. When the first two levels cannot solve the problem, the buffer resource pool is activated according to the hierarchical invocation mechanism defined in step 700. This includes a personnel buffer pool, an equipment buffer pool, and a workstation buffer pool to provide elastic resource reserves for abnormal situations.

[0220] Local optimization is restricted to the affected subgraph or sub-window to accelerate convergence and reduce computational overhead. The subgraph extent is determined based on the disturbance propagation analysis results and typically includes the directly affected departments and their primary collaborating departments; the sub-window length is set according to the duration of the disturbance's impact, generally ranging from 2 to 6 hours.

[0221] By leveraging online learning mechanisms and continuously optimizing key parameters based on actual operational data, we can improve prediction accuracy and decision-making quality.

[0222] The weight coefficient parameters are updated using a mirror descent algorithm, adjusting the preset weight coefficients of the first objective to the preset weight coefficients of the fifth objective in the multi-objective optimization based on the actual execution results. The weight coefficient update formula is as follows:

[0223] The preset weight coefficient vector is updated to the projection result on the constraint set of the current preset weight coefficient vector minus the preset learning rate multiplied by the gradient with respect to the preset weight coefficient.

[0224] The default value of the preset learning rate is 0.01, which was determined through learning convergence analysis and stability testing. This learning rate ensures the stability and convergence of parameter updates. The adaptive learning rate strategy is as follows: when the improvement of the objective function after 5 consecutive updates is less than 0.001, the learning rate decays to 0.8 times the original value; when the improvement of the objective function is greater than 0.01, the learning rate is restored to the initial value. The gradient of the preset weight coefficients is calculated by the deviation between the actual objective function value and the expected objective function value.

[0225] The parameters of the perturbation propagation model are updated by minimizing the prediction error. The method for updating the preset propagation matrix parameters is as follows:

[0226] Find the preset propagation matrix parameters that minimize the sum of squared Euclidean distances between the predicted perturbations and the actual observed perturbations at all times.

[0227] Parameter updates employ a batch learning approach, performed every 24 hours to ensure the stability and reliability of the model parameters. The sample window length for batch learning is 7 days, maintaining the timeliness of training data through a sliding window mechanism. When the cumulative number of samples falls below 100, the update cycle is extended to 48 hours to ensure the statistical significance of parameter updates. When significant environmental changes are detected, such as the addition of a new department or equipment upgrades, a fast learning mode is triggered, increasing the update frequency to once every 12 hours for 3 days before returning to the normal frequency.

[0228] Regularly evaluate the effectiveness of the scheduling plan, generate an effectiveness report, and provide feedback for the next round of scheduling optimization. Evaluation indicators include comprehensive performance indicators such as resource utilization rate, task completion rate, departmental satisfaction, and compliance rate.

[0229] Based on the evaluation results of the execution effect, the parameter settings for the next round of scheduling optimization are automatically adjusted, including key parameters such as preset time domain length parameters, preset robustness parameters, and preset monitoring thresholds, forming a closed-loop optimization mechanism for continuous improvement.

[0230] Through operational monitoring and fine-tuning, as well as online learning, this step enables the scheduling scheme to remain effective in a dynamically changing environment, achieve continuous optimization of resource allocation in cross-departmental collaboration scenarios, effectively cope with various disturbances and uncertainties, and ensure a stable improvement in overall operational efficiency and service quality.

[0231] Example 2

[0232] See Figure 4 As shown, a multi-parameter fusion load balancing scheduling adaptation system is provided, which stores computer-readable instructions. When the computer-readable instructions are read, the aforementioned multi-parameter fusion load balancing scheduling adaptation method can be executed. The system includes:

[0233] The demand and supply module 101 initiates scheduling optimization based on triggering conditions. It uses a demand forecasting model and a capacity correction model to predict the demand and actual available capacity for future periods within the rolling time domain, and calculates the disturbance intensity based on the demand and actual available capacity.

[0234] The disturbance impact module 102 constructs a resource sector network, determines the number of transmission layers and calculates the impact intensity based on the resource sector network and the disturbance intensity, and calculates the comprehensive disturbance impact based on the impact intensity.

[0235] The conflict identification module 103 calculates the over-allocation degree based on the demand and actual available capacity, constructs a conflict over-allocation map based on the over-allocation degree, and combines the priority score of the department based on the comprehensive disturbance impact.

[0236] The initial constraint module 104 constructs a constraint set and generates an initial feasible solution based on the conflict overfit graph and priority score;

[0237] The resource allocation module 105 constructs a multi-objective optimization model with the initial feasible solution as the hot start point. The multi-objective optimization model solves the resource allocation scheme based on the constraint set inherited by the module.

[0238] The embodiments of the present invention have been described above. However, the embodiments are not limited to the specific implementation methods described above. The specific implementation methods described above are merely illustrative and not restrictive. Those skilled in the art can make more equivalent embodiments under the guidance of the present embodiments, and all of them are within the protection scope of the present embodiments.

Claims

1. A multi-parameter fusion-based load balancing scheduling adaptation method, characterized in that, Includes the following steps: Based on the triggering conditions, the scheduling optimization is initiated. Within the rolling time domain, the demand forecasting model and the capacity correction model are used to predict the demand and actual available capacity for future periods. The disturbance intensity is calculated based on the demand and actual available capacity. A resource sector network is constructed. Based on the resource sector network and the disturbance intensity, the number of transmission layers is determined and the influence intensity is calculated. Based on the influence intensity, the comprehensive disturbance influence is calculated. The resource sector network includes resource nodes, sector nodes, and connecting edges, where resource nodes represent various types of resources, sector nodes represent various sectors, and connecting edges represent the dependence relationship between sectors and resources and the dependence intensity weight. The intensity of the impact includes the intensity of direct impact, the intensity of indirect impact, and the intensity of system-level regulation impact; the calculation of the comprehensive disturbance impact includes: The disturbance intensity is divided into slight disturbance, moderate disturbance, and severe disturbance; Minor disturbances are propagated through the first layer, moderate disturbances through the first and second layers, affecting directly dependent departments and their collaborating departments, and severe disturbances through the first, second, and third layers. The first layer of transmission directly affects the departments in the resource department network that directly depend on the resource. The influence strength of the department is the direct influence strength, which is the disturbance strength of the resource multiplied by the resource's dependence on the department weight, and then multiplied by a preset time decay factor. The second layer of transmission involves the directly affected departments transmitting disturbances to collaborating departments through cooperation. The influence strength of the collaborating departments is the indirect influence strength, which is the direct influence strength of the directly affected departments multiplied by a preset inter-departmental cooperation strength coefficient, and then multiplied by a preset transmission attenuation factor. The third layer of transmission calculates the system-level adjustment influence intensity. The system-level adjustment influence intensity of a department is the overall system disturbance intensity multiplied by the preset department system importance weight, and then multiplied by the preset system adjustment intensity factor. The overall system disturbance intensity is the sum of the products of the disturbance intensity of multiple resources in multiple time periods and the corresponding preset resource weight coefficients, divided by the sum of the multiple preset resource weight coefficients. The overall disturbance impact of a department is the sum of the direct impact intensity of the department multiplied by the preset direct transmission weight, the indirect impact intensity of the department multiplied by the preset indirect transmission weight, and the system-level adjustment impact intensity of the department multiplied by the preset system adjustment weight. The over-allocation degree is calculated based on the demand and actual available capacity. A conflict over-allocation diagram is constructed based on the over-allocation degree. The priority score of the department is calculated in combination with the comprehensive disturbance impact. The over-allocation degree of resources in a time period is the larger of zero and the resource demand excess, where the resource demand excess is the sum of the demand for the resource by all departments in that time period minus the actual available capacity. When the over-provisioning degree is greater than the preset over-provisioning threshold, it is marked as a conflicting resource and a conflict over-provisioning graph is constructed. In the conflict over-provisioning graph, the application node represents the department's demand application, the resource node represents the shared resource, and the hyperedge connects the application nodes competing for the same resource and the hyperedge weight is equal to the over-provisioning degree. The department's priority score for a given period is the sum of the basic priority score and the disturbance impact adjustment item. The basic priority score is calculated by multiplying the preset first weight coefficient by the standardized value of the key performance indicator, adding the preset second weight coefficient by the urgency level, adding the preset third weight coefficient by the compliance score, subtracting the preset fourth weight coefficient by the change cost, and adding the preset fifth weight coefficient by the collaboration level. The disturbance impact adjustment item is equal to the preset disturbance impact weight coefficient multiplied by the department's total disturbance impact for the given period. Based on the conflict overmap and priority scores, a constraint set is constructed and an initial feasible solution is generated. A multi-objective optimization model is constructed using the initial feasible solution as the starting point. The multi-objective optimization model solves the resource allocation scheme based on the constraint set.

2. The multi-parameter fusion load balancing scheduling adaptation method according to claim 1, characterized in that, The calculation of disturbance intensity includes: The supply and demand difference of resources during a period is the total demand for resources during that period minus the actual available capacity, where the total demand is the sum of the demand for the resource by all departments during that period; The disturbance intensity of resources during a given period is the ratio of the absolute value of the supply-demand difference of resources during that period to the preset standard capacity of resources, multiplied by a preset disturbance sensitivity coefficient.

3. The multi-parameter fusion load balancing scheduling adaptation method according to claim 1, characterized in that, The constraint set includes capacity constraints and time constraints. The capacity constraint limits the total resource allocation to no more than the actual available capacity, and the time constraint limits the total resource allocation to each department to no more than the time limit. The initial feasible solution is generated using a greedy algorithm, which includes: sorting all departments in descending order based on their priority scores to form a department priority queue; allocating resources to each department in the order of the department priority queue; and when encountering conflicting resources, referring to the conflict over-allocation graph, prioritizing the needs of departments with higher priority scores.

4. The multi-parameter fusion load balancing scheduling adaptation method according to claim 3, characterized in that, The process of constructing and solving a multi-objective optimization model includes: Construct a multi-objective optimization function. The multi-objective optimization function is: a preset first objective weight coefficient multiplied by the sum of the utility terms of all departments in all time periods, plus a preset second objective weight coefficient multiplied by the fairness term, minus a preset third objective weight coefficient multiplied by the sum of the over-allocation of all resources in all time periods, minus a preset fourth objective weight coefficient multiplied by the sum of the stability terms of all departments in all time periods, and finally minus a preset fifth objective weight coefficient multiplied by the load balancing term. A method based on the Lagrange relaxation framework is used to solve the multi-objective optimization function and obtain the resource allocation scheme.

5. The multi-parameter fusion load balancing scheduling adaptation method according to claim 4, characterized in that, The utility term is the inner product of the preset utility coefficient vector and the department's resource allocation vector in the time period, minus the department's utility loss in the time period. The utility loss is the preset utility sensitivity coefficient multiplied by the department's comprehensive disturbance impact in the time period. The fairness term is the sum of squares of the negative differences between the total utility and the average utility of each department. The total utility of a department is the sum of the utility terms of the department in all time periods. The average utility is the arithmetic mean of the total utility of all departments. The stability term is the L1 norm of the difference between the department's resource allocation vector in the current time period and the previous time period. The load balancing term is the variance of the total allocation of each resource in each time period.

6. The multi-parameter fusion load balancing scheduling adaptation method according to claim 4, characterized in that, The resource allocation scheme includes a resource quantity allocation matrix, a personnel shift schedule, and an equipment usage time sequence diagram. The resource quantity allocation matrix includes the number of resources allocated by the department to the department during the specified time period. The personnel shift schedule includes job positions, shift types, working hours, and skill matching. The equipment usage time sequence diagram includes equipment number, using department, usage time period, and load level.

7. A multi-parameter fusion load balancing scheduling adaptation system, characterized in that, It is used to store computer-readable instructions, which, when read, can execute the multi-parameter fusion load balancing scheduling adaptation method as described in any one of claims 1-6; the system includes: The demand and supply module initiates scheduling optimization based on triggering conditions. Within the rolling time domain, it uses a demand forecasting model and a capacity correction model to predict the demand and actual available capacity for future periods, and calculates the disturbance intensity based on the demand and actual available capacity. The disturbance impact module constructs a resource sector network, determines the number of propagation layers and calculates the impact intensity based on the resource sector network and the disturbance intensity, and calculates the comprehensive disturbance impact based on the impact intensity. The resource sector network includes resource nodes, sector nodes, and connecting edges, where resource nodes represent various types of resources, sector nodes represent various sectors, and connecting edges represent the dependencies of sectors on resources and the dependency intensity weights. The impact intensity includes direct impact intensity, indirect impact intensity, and system-level adjustment impact intensity. The calculation of the comprehensive disturbance impact includes: The disturbance intensity is divided into slight disturbance, moderate disturbance, and severe disturbance; Minor disturbances are propagated through the first layer, moderate disturbances through the first and second layers, affecting directly dependent departments and their collaborating departments, and severe disturbances through the first, second, and third layers. The first layer of transmission directly affects the departments in the resource department network that directly depend on the resource. The influence strength of the department is the direct influence strength, which is the disturbance strength of the resource multiplied by the resource's dependence on the department weight, and then multiplied by a preset time decay factor. The second layer of transmission involves the directly affected departments transmitting disturbances to collaborating departments through cooperation. The influence strength of the collaborating departments is the indirect influence strength, which is the direct influence strength of the directly affected departments multiplied by a preset inter-departmental cooperation strength coefficient, and then multiplied by a preset transmission attenuation factor. The third layer of transmission calculates the system-level adjustment influence intensity. The system-level adjustment influence intensity of a department is the overall system disturbance intensity multiplied by the preset department system importance weight, and then multiplied by the preset system adjustment intensity factor. The overall system disturbance intensity is the sum of the products of the disturbance intensity of multiple resources in multiple time periods and the corresponding preset resource weight coefficients, divided by the sum of the multiple preset resource weight coefficients. The overall disturbance impact of a department is the sum of the direct impact intensity of the department multiplied by the preset direct transmission weight, the indirect impact intensity of the department multiplied by the preset indirect transmission weight, and the system-level adjustment impact intensity of the department multiplied by the preset system adjustment weight. The conflict identification module calculates the over-allocation degree based on the demand and actual available capacity, constructs a conflict over-allocation map based on the over-allocation degree, and calculates the priority score of the department in conjunction with the comprehensive disturbance impact; the over-allocation degree of resources in a time period is the larger of zero and the resource demand excess, where the resource demand excess is the sum of the demand for the resource by all departments in that time period minus the actual available capacity; When the over-provisioning degree is greater than the preset over-provisioning threshold, it is marked as a conflicting resource and a conflict over-provisioning graph is constructed. In the conflict over-provisioning graph, the application node represents the department's demand application, the resource node represents the shared resource, and the hyperedge connects the application nodes competing for the same resource and the hyperedge weight is equal to the over-provisioning degree. The department's priority score for a given period is the sum of the basic priority score and the disturbance impact adjustment item. The basic priority score is calculated by multiplying the preset first weight coefficient by the standardized value of the key performance indicator, adding the preset second weight coefficient by the urgency level, adding the preset third weight coefficient by the compliance score, subtracting the preset fourth weight coefficient by the change cost, and adding the preset fifth weight coefficient by the collaboration level. The disturbance impact adjustment item is equal to the preset disturbance impact weight coefficient multiplied by the department's total disturbance impact for the given period. The initial constraint module constructs a constraint set and generates an initial feasible solution based on the conflict overfit graph and priority score; The resource allocation module constructs a multi-objective optimization model with the initial feasible solution as the starting point. The multi-objective optimization model solves the resource allocation scheme based on the set of constraints.

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