A workshop human resource allocation optimization method based on personnel dynamic assembly work hour estimation

Abstract

The application discloses a workshop human resource allocation optimization method based on personnel dynamic assembly work hour estimation, solves the problem of inaccurate personnel allocation based on experience in the existing production scene, and the problem of inflexible personnel allocation based on fixed standard assembly work hour in the existing research. Based on learning and fatigue-recovery effect theory, the application estimates dynamic work hours in the assembly process of average technical level workers, and obtains relative work efficiency of multi-level technicians. Then, a mathematical model with the target of minimizing assembly workshop human resource cost is constructed. Finally, the particle swarm algorithm is improved from the aspects of coding mode and dynamic adjustment mode of inertia factor, and the model is solved.

Description

Technical Field

[0001] This invention belongs to the field of assembly manufacturing technology, specifically relating to a method for optimizing workshop human resource allocation by combining multi-factor estimation of dynamic assembly time. Background Technology

[0002] Currently, many manufacturing enterprises in my country choose to expand their factories, hire more employees, and upgrade production equipment and technology to improve efficiency and survive in a fiercely competitive market. These changes may result in many large enterprises having more resources than actually needed for production, meaning they have surplus resources. Meanwhile, in semi-automated assembly systems for large and complex products, personnel are typically the dominant resource, responsible for more than 80% of the assembly tasks. The rationality of personnel allocation directly determines the production capacity of the assembly system. Therefore, finding a balance between human resource costs and production efficiency in production workshops is the key to this research.

[0003] Currently, while research on workshop staffing in the assembly manufacturing field is gradually incorporating the differences in personnel skills (multi-skilled workers), most studies treat personnel's work capacity as a constant value, neglecting the dynamic changes in personnel skill levels during the assembly process. Furthermore, in actual assembly scenarios, assembly personnel cannot maintain consistently high efficiency without any errors. Existing research has included considerations of the impact of learning, forgetting, fatigue, recovery, and their combinations on productivity, and some have explored the probability of human error based on these factors. However, few studies comprehensively consider the impact of these factors on assembly time and apply them to workshop human resource allocation research. This results in existing human resource allocation research failing to adequately reflect the dynamic changes in the actual assembly process. Summary of the Invention

[0004] To address the shortcomings of the aforementioned background technologies, this invention provides a workshop human resource allocation optimization method based on dynamic personnel assembly time estimation. On one hand, by considering the impact of learning and fatigue recovery effects on personnel skill levels, assembly efficiency, and error probability, the necessary working hours required by personnel during the assembly process are estimated. On the other hand, for the current research scenario—a component assembly production unit supplying parts to the assembly line under a hybrid layout mode—the method considers assembly line cycle time constraints and supply requirements, analyzes the personnel combination requirements based on component assembly relationships, and, combined with the estimated dynamic working hours, uses a particle swarm optimization algorithm to calculate the number of work teams and personnel allocation.

[0005] The objective of this invention can be achieved through the following technical solutions.

[0006] A method for optimizing workshop human resource allocation based on dynamic assembly time estimation includes the following steps:

[0007] Step 1: For each component, accumulate the labor time of completing each process under suitable operating conditions and with appropriate operating methods at the normal speed of workers with average experience and skill level to obtain the theoretical working time T of each component; then, combine the learning effect, fatigue recovery effect and probability of human error to estimate the dynamic assembly working time under the average experience and skill level.

[0008] Step 2: Establish a human resource cost optimization model for the assembly workshop and determine the corresponding constraints;

[0009] Step 2.1: Establish the objective function as follows

[0010]

[0011] Where j represents the component type number, j = 1, 2, ..., J; T ja This represents the time, in days, required for team A, responsible for assembling component j to complete the delivery of the component, where A represents the team and n represents the work group. j The total number of work groups is represented by k, which represents the worker's skill level number, k = 0, 1, 2, s jak W represents the number of workers at each skill level. k This represents the daily wage for workers with skill level k.

[0012] Step 2.2: Constraints include

[0013] (1) At the takt delivery node, the existing cumulative number of component workstations must reach the required value;

[0014] M ij ≥D ij (2)

[0015] Among them, M ij D represents the cumulative total output of component j at the end of the i-th beat. ij This represents the total demand for component j on the assembly line at the end of the i-th cycle.

[0016] (2) Junior technicians cannot assemble independently;

[0017] S ja ≠[s ja0 [,0,0] (3)

[0018] Among them, S ja This indicates the personnel configuration of team A, which is responsible for assembling component j. ja =[s ja0 ,s ja1 ,s ja2 ];

[0019] (3) The number of personnel in each shift assembling each component has upper and lower limits;

[0020]

[0021] Among them, L j H represents the minimum number of personnel required for each tooling component j. j This indicates the maximum number of personnel required for each tooling component j;

[0022] (4) The number of employees used for component assembly shall not exceed the number of employees in the production system;

[0023]

[0024] Where N2 represents the number of workers at skill level 2, N kj This represents the number of k-level technicians who have mastered the assembly skills of j-type components, where k = 1, 2;

[0025] Step 3: Using the assembly efficiency of intermediate-level skilled personnel as a benchmark, solve for the effectiveness of personnel at all skill levels, as well as the combination effectiveness under different personnel combination modes;

[0026] Step 4: Improve the particle swarm algorithm by considering the adaptive inertia factor and dynamic particle encoding, and use the improved algorithm to solve the human resource cost optimization model.

[0027] Furthermore, the estimation process for the actual assembly time required by personnel in step 1 is as follows:

[0028] Step 1.1: Use statistical methods to obtain the theoretical assembly time T for each component;

[0029] Step 1.2: For each type of component, statistically analyze the changes in assembly ability of unskilled workers under the guidance of skilled workers during the assembly of X products, where X≥X2, and X2 represents the output required for a junior technician to become a senior technician. The data is recorded in the form of the cumulative number of assembled products and assembly time. Based on the data collected in this process, the least squares method is used to fit the learning curve and obtain the values ​​of each parameter in f(X). f(X) is the learning rate after correction based on the traditional learning rate.

[0030] T X =T1·X f(X) (6)

[0031]

[0032] Among them, T X Let T1 represent the time required to produce the Xth product, and T1 represent the accumulated output required for a junior technician to become a mid-level technician. f(X) This represents the trend of assembly time as a function of X, b0 represents the initial learning rate, and c represents the distribution coefficient, which is used to control the distribution range during the steep phase of the curve.

[0033] The learning effect of personnel with average skill levels is calculated, with the level of newly promoted intermediate technicians representing the average skill level:

[0034]

[0035]

[0036] Among them, t X X represents the trend of assembly time for workers with increasing experience output X, where X1 represents the output required for a junior technician to become an intermediate technician, and γ represents the learning effect coefficient.

[0037] The learning effect coefficient γ used to estimate dynamic working hours is expressed as follows:

[0038]

[0039] Step 1.3: Construct a fatigue recovery model based on the work-rest schedule;

[0040] Morning work fatigue accumulation:

[0041]

[0042] Lunch break resumes:

[0043] R(τ)=F1(t1)e -μτ ,0≤τ≤τ1 (12)

[0044] Afternoon work fatigue accumulation

[0045]

[0046] Effective utilization rate of working hours:

[0047]

[0048] Where λ1 and λ2 represent fatigue parameters, μ represents recovery parameters, t represents time, ξ represents the influence coefficient of fatigue accumulation on efficiency, t1 represents the morning working hours stipulated in the work-rest arrangement, τ1 represents the lunch break duration, and t2 represents the afternoon working hours. It is assumed that the fatigue value accumulated on the day after the get off work-rest period is fully recovered the next day.

[0049] Step 1.4: Considering the effects of learning and fatigue recovery on human error, estimate the error probability of personnel with average skill levels:

[0050]

[0051] u l =β1·NLS (16)

[0052]

[0053] u f =β2·NFS (18)

[0054] HEP(X,t)=w l ·u l +w f ·u f (19)

[0055] Where NLS represents the learning score, NFS represents the fatigue score, and u l Represents standardized learning scores, u f F represents the standardized fatigue fraction. max The maximum value of fatigue level is represented by F(t), the fatigue curve is represented by β1 and β2, and the normalization coefficients are represented by w. l w f They represent u respectively l u f The weights that contribute to human error, HEP(X,t) represents the human error rate;

[0056] Step 1.5: Estimate the dynamic working hours of workers with average skill levels during the assembly process based on the above factors:

[0057]

[0058] Where b% represents the proportion of assembly rework time to theoretical working time, and T represents the theoretical working time for component assembly.

[0059] Furthermore, the detailed method for step 3 is as follows:

[0060] Step 3.1: Analyze the personnel requirements for each process of the component and the serial and parallel operation of the process, and determine the upper and lower limits of the number of people to assemble each component in combination with the assembly environment constraints;

[0061] Step 3.2: Use a learning curve to simulate changes in personnel skill levels, and divide the learning curve into segments based on experience. The segmentation point X1 represents the output required to advance from junior technician to intermediate technician, and the segmentation point X2 represents the output required to advance to senior technician.

[0062] Step 3.3: Let θ(x,k) represent the dynamic efficiency ratio between skilled workers at each level and intermediate skilled workers, as shown in the following formula:

[0063]

[0064] Step 3.4: Calculate the assembly efficiency of each level of technicians, with intermediate technicians as the benchmark;

[0065] pk =θ(X,k)·p1 (22)

[0066] Where, p k This represents the assembly efficiency of workers with skill level k.

[0067] Step 3.5: Based on the characteristics of each assembly operation, for processes where the work content is completed by a single person in parallel, the efficiency increases with the number of personnel; for processes where the work content is completed by a single person in sequence, the efficiency is the average efficiency of the assigned personnel; for processes where the work content needs to be completed in sequence by cooperation, the efficiency increases with the number of personnel, and is then divided by the number of personnel required for cooperation.

[0068] Furthermore, the detailed method for step 4 is as follows:

[0069] Step 4.1: Calculate t for each component j value;

[0070] Step 4.2: Set the values ​​of each parameter of the particle swarm optimization algorithm, the target output of the product, the number of assembly lines to start, the iteration level, the number of iterations at each level, and the number of technicians at each level, etc.

[0071] Step 4.3: Initialize the number of work groups for each component;

[0072] Step 4.4: Initialize the particle swarm, with the position and velocity of each particle represented by a two-dimensional array;

[0073] Step 4.5: Using the combined efficiency solution method described in Step 3.5 and the theoretical time ratio of specific component process types, calculate the dynamic time of assembling components under this specific personnel allocation mode;

[0074] Step 4.6: Calculate the particle fitness value, which is the sum of the objective function value and the three penalty terms;

[0075] Step 4.7: For each particle, compare its fitness value with the best position it has ever reached, pbest. If it is better, then take it as the current best position, pbest.

[0076] Step 4.8: Compare the historical best position pbest of all particles with the global best position gbest of the particle swarm. If pbest is better than gbest, then update gbest with pbest; otherwise, do not update gbest. Accumulate the number of times the fitness value of gbest remains unchanged and use it as the number of optimization attempts c.

[0077] Step 4.9: Determine if the jump condition has been met. The jump condition is: the number of iterations has reached the upper limit. If the jump condition has not been met, proceed to step 4.10; otherwise, proceed to step 4.11.

[0078] Step 4.10: Update the position and velocity of each particle in each region, and return to step 4.5. The inertia factor ω(t) is determined by the penalty term value in gbest, the number of algorithm iterations t, and the number of times the overall optimal solution of the population remains unchanged, c.

[0079] When the penalty term is not zero, it indicates that the particle is still far from the target position. Therefore, global optimization becomes the particle's main task. During this stage, the particle maintains the maximum inertia factor ω = ω max When the penalty term is zero, the particles should gradually strengthen their local search ability as the objective function value decreases. If the optimal position obtained by the particle swarm remains unchanged after multiple searches, it can be considered that the particle swarm has reached the global optimum or is trapped in a local optimum. At this point, the global search ability of the inertia factor ω should be restored to give the particles a mutation velocity to escape the local optimum. That is:

[0080] When c < C, ω(t) = (ω max -ω min (G) k -t) / G k +ω min t is the number of iterations in the current layer, G k Let ω be the total number of iterations for the current layer, and C be the upper limit set for the number of iterations at which the overall optimal solution of the population remains unchanged; otherwise, when c≥C, activate the global search capability of the particles, and let ω=(ω max -ω min (G) k -g) / G k +ω min Where g = [(cC)modC]·(G k modC);

[0081] Step 4.11: Determine if the sum of the penalty terms at the position gbest is 0. If it is, output gbest and exit the program. The obtained gbest is the optimal human resource allocation; otherwise, calculate based on the time penalty term P. 3j Increase the particle length, increase the number of work groups corresponding to component j, return to step 4.4, and perform a new round of calculation.

[0082] This invention is based on actual production scenarios. First, it estimates the working hours consumed by personnel during the actual assembly process based on the learning and fatigue recovery effects, making it closer to the real-world scenario, i.e., the higher the skill level of the employee, the shorter the assembly time, and vice versa. Then, it constructs a cost-minimizing personnel configuration model with constraints such as the number of deliveries and cycle time. Finally, it improves the particle swarm optimization algorithm to make it suitable for solving the model of this problem, and finally obtains the optimal solution to the problem. Attached Figure Description

[0083] Figure 1This is a schematic diagram of the dynamic expansion of particle encoding;

[0084] Figure 2 This is a flowchart of the improved particle swarm optimization algorithm;

[0085] Figure 3 It is a comparison of the optimization process of particle swarm under different inertia coefficients (the whole process);

[0086] Figure 4 It is a comparison of the optimization process of particle swarms under different inertia coefficients (final stage). Detailed Implementation

[0087] This invention pertains to a derivative problem of the Resource Constrained Projects Scheduling Problem (RCPSP)—the Resource Investment Problem (RIP). Based on a fixed project duration and flexible resources, it investigates how to allocate resources to minimize costs. To address the problem, firstly, it estimates dynamic assembly time under average experienced technical levels using multi-factor estimation. Secondly, it establishes an optimization model for personnel allocation with cost minimization as the objective function, defining its constraints. Finally, it improves the particle swarm optimization algorithm to adapt to the problem's solution, introducing a penalty function as a mapping of the constraints and dynamically adjusting the particle swarm inertia factor to impart different search capabilities at different search stages. The obtained optimal solution determines the appropriate number of work teams and the personnel configuration for each team.

[0088] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. The specific steps are as follows:

[0089] Step 1: Workshop survey. Break down each task into multiple simple processes, and calculate the operation time of each basic process under average intensity and proficiency. Summate the standard operation time of all processes to obtain the theoretical working time T for the complete operation of each component;

[0090] For each component, the changes in the assembly ability of junior technicians during the assembly of approximately X = 1 to 100 products are recorded, with the cumulative number of assembled products and assembly time as the record format. To reduce errors, multiple sets of sample data can be collected by random sampling and the average value is taken.

[0091] An exponential learning curve is used to fit the processed data. To improve the fit, the learning factor is adjusted to adapt to the changing patterns of the data.

[0092] T X =T1·X f(X)

[0093]

[0094] The following formula is derived to obtain the learning effect coefficient γ used to estimate dynamic working hours at the average skill level:

[0095]

[0096]

[0097]

[0098] Based on the fatigue recovery function and the company's work-rest scheduling system, calculate the effective utilization rate of working hours α (fatigue recovery effect):

[0099]

[0100] Based on the learning effect and fatigue recovery effect, the probability of human error for each component at different assembly stages is estimated as HEP(X,t), thus obtaining the maximum error probability hep. To simplify the problem, it is assumed that an assembly defect may occur only when the maximum error probability exceeds 75%, and that a product undergoes at most one rework during assembly.

[0101] HEP(X,t)=w l ·u l +w f ·u f

[0102] The dynamic assembly time under average technical level is estimated using the learning effect coefficient, fatigue recovery coefficient, and probability of human error during a certain production period. The estimation formula is as follows:

[0103]

[0104] Step 2: Establish a mathematical model for human resource allocation, with the objective of minimizing the labor costs invested in assembling each component. The formula is as follows. The calculation of labor costs uses the daily wage of different skilled workers and the assembly day length as factors;

[0105]

[0106] The constraints on component delivery quantity and personnel allocation are established, expressed by the following formula. Specifically, each component production unit must produce a sufficient number of components before the start of the next cycle; simultaneously, each shift must have at least one skilled worker (intermediate or advanced level); due to the limited assembly area of ​​each component, the upper and lower limits of personnel in each component shift are defined; and because there are multiple skilled workers (generally advanced level), the number of advanced workers in each unit cannot exceed the existing number of advanced workers, and the total number of employees allocated cannot exceed the total number of employees in the production system.

[0107] a、M ij ≥Dij

[0108] b、S ja ≠[x0,0,0]

[0109]

[0110]

[0111] Step 3: The learning curve expression is shown in Equation (1). Based on the classification criteria for multi-skilled personnel, the learning curve is divided into three segments to describe the three learning stages of the worker. Let X1 and X2 be the dividing points, and their values ​​are set by the management. When a junior technician completes more than X1 assembly stands, the worker transitions to an intermediate skill level. Similarly, when an intermediate technician completes more than X2 assembly stands, the worker transitions to an advanced skill level.

[0112] Since the learning effect and fatigue recovery effect are the dominant factors influencing the assembly ability (duration) of different personnel, this ratio is used to calculate the efficiency level of different skill levels, with intermediate-level workers as the benchmark. The fatigue recovery effect coefficient is the same for all skill levels, thus canceling each other out. Therefore, the efficiency ratios of personnel at different skill levels are calculated as follows:

[0113]

[0114] p k =θ(X,k)·p1

[0115] Based on the characteristics of each assembly operation, for processes where the work content is completed by a single person in parallel, the efficiency increases with the number of personnel; for processes where the work content is completed by a single person in sequence, the efficiency is the average efficiency of the assigned personnel; for processes where the work content needs to be completed in sequence by cooperation, the efficiency increases with the number of personnel, and is then divided by the number of personnel required for cooperation.

[0116] Step 4: Solve the model using the improved particle swarm optimization algorithm. The main process of this algorithm is as follows: Figure 2 As shown, the specific process includes the following steps:

[0117] Step 4.1: Calculate t for each component j value;

[0118]

[0119] Step 4.2: Set the values ​​of each parameter of the particle swarm optimization algorithm, the target output of the product, the number of assembly lines in operation, the iteration level (equal to the number of assembly lines in operation), and the number of iterations for each level;

[0120] Step 4.3: Set the number of skilled workers at each level, and represent the skills of senior skilled workers using a 0-1 matrix. The sum of the 1-elements in the j-th column of the matrix is ​​the number of advanced workers capable of assembling component j.

[0121] Step 4.4: Initialize the number of groups for each component, and mark them as component numbers in the last column of each particle X;

[0122] Step 4.5: Initialize the particle swarm. The position and velocity of each particle are represented by a two-dimensional array, i.e. The first three columns represent the number of junior workers, intermediate workers, and senior workers respectively.

[0123] Step 4.6: Using the combined efficiency solution method described in Step 3 and the theoretical working time ratio of specific component process types, calculate the dynamic working time of the assembly components under the specific personnel allocation mode X.

[0124] Step 4.7: Calculate the particle fitness value. The fitness value is the sum of the objective function value and three penalty terms. The expressions for the three penalty terms are as follows:

[0125]

[0126]

[0127]

[0128] In the calculation of P3, the cycle time (CT) is used as the time segment node for cumulative output verification. The calculation of cumulative output needs to be combined with the preparation time (t) obtained in step 1. j Step 2 calculates the efficiency level and the personnel configuration represented by the current particle.

[0129] Step 4.8: For each particle, compare its fitness value with the best position it has passed through, pbest. If it is better, then take it as the current best position, pbest.

[0130] Step 4.9: Compare the historical best position pbest of all particles with the global best position gbest of the particle swarm, update gbest, and accumulate the number of optimization attempts c for gbest to remain unchanged in fitness value.

[0131] Step 4.10: Determine if the jump condition (maximum number of iterations) has been met. If not, proceed to step 4.11; otherwise, proceed to step 4.12.

[0132] Step 4.11: Update the position and velocity of each particle in each region, and return to step 4.6.

[0133]

[0134] The inertia factor ω(t) is determined by the penalty term value of gbest, the number of algorithm iterations, and the number of times c, the overall optimal solution of the population remains unchanged.

[0135] (1) If the penalty items in gbest and Then the population maintains ω max ;

[0136] (2) Otherwise, when c < C, ω(t) = (ω max -ω min (G) k -t) / G k +ω min G k C represents the total number of iterations for the current layer, and C is the upper limit set for the number of times the overall optimal solution of the population remains unchanged.

[0137] (3) Otherwise, when c≥C, activate the global search capability of the particle, let ω=(ω max -ω min (G) k -g) / G k +ω min Where g = [(cC)modC]·(G k modC).

[0138] Step 4.12: Determine if the sum of the penalty terms at position gbest is 0. If it is, output gbest and exit the program; otherwise, calculate based on the time penalty term P. 3j Increasing the particle length increases the number of workgroups corresponding to component j, such as... Figure 1 As shown, return to step 4.4.

[0139] Below, we will use some workshop data to verify the improved particle swarm optimization algorithm through an example. Taking the production of some components shown in Table 1 as an example, Table 2 shows the number of employees at each level and their salary levels. Senior technicians possess multiple skills, which can be represented by an m×n skill 0-1 matrix S, where m is the number of senior technicians and n is the component category. By accumulating the values ​​of each column, we can obtain the number of senior technicians corresponding to each component in Table 1. Furthermore, the assembly line's pulse rate is CT = 8, and a preparation time of Δt = 10 days is given for each component before the assembly line officially starts operation.

[0140] The improved particle swarm optimization algorithm is set to use 25 particles, a maximum of 120 × N (number of assembly lines), a particle velocity range of (-1, 1), an inertia weight range of (0.6, 1.4), and a maximum of 30 iterations for the current optimal value. The overall optimal result generated in a particular iteration is shown in Table 3. Since the fitness value during algorithm execution is the result of assigning weights to the objective function, the output optimal particle fitness value needs to be transformed to obtain the final objective function value.

[0141] Table 1 Component Assembly Information

[0142]

[0143] Table 2 Employee Information

[0144]

[0145] Table 3 shows the team and personnel allocation for the example.

[0146]

[0147] To verify the superiority of the improved particle swarm optimization algorithm, comparative experiments were conducted using a particle swarm optimization algorithm with a fixed inertia factor, a particle swarm optimization algorithm with a linearly decreasing inertia factor, and a particle swarm optimization algorithm with an adaptive inertia factor. Figure 3 , Figure 4 To compare the optimization processes of the three methods above, the objects represented by the curves are shown in the legend in the table. They all use the same input environment and output the optimal particle fitness of the population in each execution.

[0148] from Figure 3 and Figure 4 The particle swarm optimization algorithm with a fixed inertia factor exhibits poor convergence, with an average convergence speed lower than the other two algorithms and a worse local search capability. The particle swarm optimization algorithm with a linearly decreasing inertia factor has a fast convergence speed but suffers from getting trapped in local optima. In contrast, the particle swarm optimization algorithm with an adaptive inertia factor, which is improved to suit the characteristics of the model, has a faster convergence speed and the ability to escape local optima, resulting in better algorithm stability.

Claims

1. A method for optimizing workshop human resource allocation based on dynamic assembly time estimation, comprising the following steps: Step 1: For each component, accumulate the labor time required to complete each process under suitable operating conditions and using appropriate operating methods at the normal speed of workers with average experience and skill level, to obtain the theoretical working time for each component. Then, by combining the learning effect, fatigue recovery effect, and probability of human error, the dynamic assembly time under the average experience and skill level is estimated. Step 2: Establish a human resource cost optimization model for the assembly workshop and determine the corresponding constraints; Step 2.1: Establish the objective function as follows in, Indicates the component type number. ; Indicates responsibility Class component assembly The time, in days, required for a work team to complete the deliverable components; 'a' represents the work team. This indicates the total number of work groups. Indicates the worker's skill level number. , This indicates the number of workers at each skill level. express Daily wage for workers with advanced skill levels; Step 2.2: Constraints include (1) At the cycle delivery node, the existing cumulative number of component workstations must reach the required value; in, Indicates the first The last component of each beat The cumulative total output, Indicates the first At the end of each cycle, the assembly line assembles the components. Total demand; (2) Junior technicians cannot assemble independently; in, Indicates responsibility Class component assembly Staffing of the work team ; (3) The number of personnel in each shift assembling each component has upper and lower limits; in, Representation Component The minimum number of personnel required for each piece of equipment. Representation Component The maximum number of personnel required for each piece of equipment; (4) The number of employees used for component assembly shall not exceed the number of employees in the production system; in, This indicates the number of workers at skill level 2. Indicates mastery Class component assembly skills The number of skilled workers, ; Step 3: Using the assembly efficiency of intermediate-level skilled personnel as a benchmark, solve for the effectiveness of personnel at all skill levels, as well as the combination effectiveness under different personnel combination modes; Step 3.1: Analyze the personnel requirements for each process of the component and the serial and parallel operation of the process, and determine the upper and lower limits of the number of people to assemble each component in combination with the assembly environment constraints; Step 3.2: Simulate changes in personnel skill levels using a learning curve, and segment the learning curve based on experience, identifying the segmentation points. The dividing point represents the accumulated output required to advance from a junior technician to an intermediate technician. This represents the output required to advance to the level of a senior technician; Step 3.3: with The dynamic performance ratio of skilled workers at each level to intermediate-level skilled workers is expressed by the following formula: Step 3.4: Calculate the assembly efficiency of each level of technicians, with intermediate technicians as the benchmark; in, express Assembly efficiency of workers with advanced skill levels; Step 3.5: Based on the characteristics of each assembly operation, for processes where the work content is completed by a single person in parallel, the efficiency increases with the number of personnel; for processes where the work content is completed by a single person in sequence, the efficiency is the average efficiency of the assigned personnel; for processes where the work content needs to be completed in sequence by cooperation, the efficiency increases with the number of personnel, and is then divided by the number of personnel required for cooperation. Step 4: Improve the particle swarm optimization algorithm by considering the adaptive inertia factor and dynamic particle encoding, and use the improved algorithm to solve the human resource cost optimization model; Step 4.1: Calculate the values ​​of each component. value; Step 4.2: Set the values ​​of each parameter of the particle swarm optimization algorithm, the target output of the product, the number of assembly lines to start, the iteration level, the number of iterations at each level, and the number of technicians at each level; Step 4.3: Initialize the number of work groups for each component; Step 4.4: Initialize the particle swarm, with the position and velocity of each particle represented by a two-dimensional array; Step 4.5: Using the combined efficiency solution method described in Step 3.5 and the theoretical time ratio of specific component process types, calculate the dynamic time of assembling components under this specific personnel allocation mode; Step 4.6: Calculate the particle fitness value, which is the sum of the objective function value and the three penalty terms; Step 4.7: For each particle, correlate its fitness value with the best position it has traversed. Make a comparison, and if it is better, then take it as the current best position. ; Step 4.8: Find the best historical position of all particles With the global optimal position of the particle swarm In comparison, if Compare Better yet, adopt renew Otherwise, no update. ;Grand total The number of times the fitness value remains unchanged is taken as the number of optimization attempts. ; Step 4.9: Determine if the jump condition has been met. The jump condition is: the number of iterations has reached the upper limit. If the jump condition has not been met, proceed to step 4.10; otherwise, proceed to step 4.

11. Step 4.10: Update the position and velocity of each particle in each region, and return to step 4.5, where the inertia factor... Depend on The penalty term value and the number of algorithm iterations in the data. and the number of times the overall optimal solution of the population remains unchanged. Joint decision: When the penalty term is not zero, it indicates that the particle is still far from the target position. Therefore, global optimization becomes the particle's main task, and the particle maintains the maximum inertia factor during this stage. When the penalty term is zero, the particles should gradually increase their local search ability as the objective function value decreases. If the optimal position obtained by the particle swarm remains unchanged after multiple searches, it is considered that the particle swarm has reached the global optimum or is trapped in a local optimum. In this case, the inertia factor should be restored. Its global search capability allows particles to acquire a mutation rate that allows them to escape local optima; that is: when hour, , This represents the number of iterations in the current layer. This represents the total number of iterations for the current layer. The upper limit of the number of times the overall optimal solution of the population remains unchanged; otherwise, when At that time, activate the global search capability of particles, and let: ,in ; Step 4.11: Determine Check if the sum of the penalty terms at the specified position is 0. If so, output the value. Exit the program and get This represents the optimal human resource allocation; otherwise, a time penalty will apply. Increase particle length and add components Given the corresponding number of work groups, return to step 4.4 for a new round of calculation.

2. The workshop human resource allocation optimization method based on dynamic assembly time estimation of personnel as described in claim 1, characterized in that, The estimation process for the necessary man-hours for actual assembly in step 1 is as follows: Step 1.1: Use statistical methods to obtain the theoretical assembly time for each component. ; Step 1.2: For each type of component, calculate the assembly performance of unskilled workers initially guided by skilled workers. Changes in assembly capabilities during the product manufacturing process, among which , This represents the accumulated output required for a junior technician to become a senior technician, recorded in terms of the cumulative number of assembled products and assembly time. Based on the data collected during this process, a learning curve is fitted using the least squares method to obtain... The values ​​of each parameter in the text, This is a modified learning rate based on the traditional learning rate; in, Indicates the production of the first Time required for each product This represents the output required for a junior technician to become a mid-level technician. Indicates assembly time varies The trend of change This represents the initial learning rate. This represents the distribution coefficient, used to control the range of distribution during the steep phase of the curve; The learning effect of personnel with average skill levels is calculated, with the level of newly promoted intermediate technicians representing the average skill level: in, Indicates production based on experience The trend of changes in the cumulative average assembly time of skilled workers. This represents the output required for a junior technician to become a mid-level technician. This represents the learning effect coefficient. Learning effect coefficient used to estimate dynamic working time It is expressed as follows: Step 1.3: Construct a fatigue recovery model based on the work-rest schedule; Morning work fatigue accumulation: Lunch break resumes: Afternoon work fatigue accumulation Effective utilization rate of working hours: in, , Indicates fatigue parameters, Indicates the recovery parameters. Indicates time, This represents the coefficient indicating the impact of fatigue accumulation on efficiency. This indicates the morning working hours stipulated in the work-rest arrangement. Indicates the duration of the lunch break. This indicates the duration of afternoon work, assuming that the fatigue accumulated during the day is fully recovered the following day after resting at the end of the workday. Step 1.4: Considering the effects of learning and fatigue recovery on human error, estimate the human error rate for workers with average skill levels. ; Step 1.5: Estimate the dynamic working hours of workers with average skill levels during the assembly process based on the above factors: in, This indicates the proportion of assembly rework time to theoretical working hours. This represents the theoretical man-hours for component assembly.

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