Bi-level optimization system for balancing and sequencing of mixed-model assembly lines considering human risk

Abstract

A double-layer optimization system for mixed-flow assembly line balancing and sequencing considering human risk belongs to the technical field of mixed-flow assembly line optimization. Information data of all work tasks in the mixed-flow assembly line is obtained; a double-layer optimization mathematical model is established; the double-layer optimization mathematical model of the mixed-flow assembly line is established according to the production rhythm and constraint conditions of the assembly line and the information data; the upper-layer optimization model is a line balancing model, which aims to minimize the production line cost under the conditions of meeting the priority relationship between tasks and human risk constraints; the lower-layer optimization model is a product launch sequencing model, which aims to minimize the required number of common workers and the maximum number of assembly workstations experiencing work overload in all periods; the double-layer optimization model is optimized and solved by a double-layer optimization algorithm, and the optimal line balancing scheme and launch sequencing scheme are output. The optimization method and system are more likely to obtain a global optimal solution, and have higher optimization efficiency and stability.

Description

Technical Field

[0001] This invention belongs to the field of mixed-flow assembly line optimization technology, and in particular relates to a two-layer optimization method and system that considers human factors and risks in the balancing and sequencing of mixed-flow assembly lines. Background Technology

[0002] Mixed-flow assembly lines are an important production method in modern manufacturing, allowing for the continuous production of different types of products with similar structures and processes on the same production line. While popular among manufacturing companies due to their ability to provide diverse products, mixed-flow assembly lines can also cause workstations to exceed cycle times, leading to overload and, in severe cases, production line shutdowns. Various methods can be used to manage overload and avoid shutdowns in mixed-flow assembly lines, such as increasing the number of assembly workstations to limit the likelihood of overload. While this method reduces the risk of shutdowns due to overload to some extent, it significantly increases the number of workstations and production line space, resulting in increased costs and potentially impacting the layout and optimization of the assembly line.

[0003] The product launch sequence determines the production efficiency of a mixed-flow assembly line. The product launch sequencing process, based on production order requirements, determines the order in which all products enter the production line, representing a short-term optimization problem. The mixed-flow assembly line balancing scheme determines the load on all assembly workstations, while product launch sequencing, based on the line balancing scheme, optimizes the product launch sequence to balance the load on assembly workstations; that is, the product launch sequence also affects the load on assembly workstations. Therefore, the mixed-flow assembly line balancing and product launch sequencing optimization problems are mutually coupled. Existing methods all employ a hierarchical optimization strategy, optimizing the line balancing and product launch sequencing problems separately (performing line balancing optimization first, then product launch sequencing optimization). This hierarchical optimization strategy struggles to obtain globally optimal line balancing and product launch sequencing schemes. Furthermore, while joint optimization methods offer hope of obtaining a globally optimal solution, they introduce a nested structure, making them difficult to solve.

[0004] Currently, some countries have explicit legal requirements mandating that factories consider the ergonomic risks (human factors risks) of work-related musculoskeletal disorders during the design phase, especially for manual assembly lines involving high-frequency repetitive movements. However, existing mixed-flow assembly lines did not consider human factors risks in their initial design, leading to high-risk situations for certain tasks. For example, some parts assembly processes not only require pressing or awkward postures, but workers are also required to use their upper limbs repeatedly at a relatively high frequency, which can lead to musculoskeletal disorders and harm their health. Furthermore, human factors risks also affect the efficiency of the assembly line and the quality of assembled products, while reducing the factory's economic benefits. Moreover, some current methods for assessing human factors risks are non-linear, making it impossible to establish a closed-loop model that incorporates human factors risks into the assembly line balancing problem.

[0005] The existing technology has the following technical problems:

[0006] 1. If a manually designed line balancing scheme does not take into account mixed-flow production, when the production line assembles different products, the different task operation times of different products can easily cause the total operation time of the assembly workstation to exceed the cycle time of the production line (production line takt time), resulting in overload of the assembly workstation and even production line shutdown, thus reducing the efficiency of the production line.

[0007] 2. Mixed-flow assembly lines reduce the risk of overload by increasing the number of assembly workstations. However, this method increases the number of assembly workstations and production line space, significantly increasing costs and even affecting production line efficiency.

[0008] 3. Existing methods do not consider human-cause risks when planning each assembly workstation and assigning tasks. Furthermore, the factory primarily uses post-production analysis to mitigate these risks, meaning that after the production line is operational, work assignments for each position are continuously adjusted to improve their performance. This approach not only increases management costs but also fails to achieve optimal overall results. Moreover, adjusting job tasks during the production launch phase increases the difficulty for workers, reduces work efficiency, and may even lead to a decrease in production line capacity.

[0009] 4. Existing methods optimize the balancing and production scheduling problems of mixed-flow assembly lines in a fragmented manner, using a hierarchical optimization strategy to optimize the line balancing and production scheduling problems separately (first optimizing the line balancing, and then optimizing the production scheduling), which cannot obtain the global optimal solution. Summary of the Invention

[0010] To address the aforementioned technical problems, this invention provides a two-layer optimization method and system for balancing and sequencing mixed-flow assembly lines, considering human factor risks. Specifically, a two-layer optimization model for balancing and sequencing of mixed-flow assembly lines is first constructed. The upper-layer optimization problem is a line balancing optimization problem, whose objective is to minimize production line costs while satisfying human factor risks. The lower-layer optimization problem is a production sequencing optimization problem, whose objective is to minimize the required number of public workers and the maximum number of assembly workstations experiencing overload at all stages. The joint optimization method for balancing and sequencing of mixed-flow assembly lines proposed in this invention is more likely to obtain the global optimum solution, while also exhibiting higher optimization efficiency and stability.

[0011] The objective of this invention is achieved through the following technical solution:

[0012] This invention provides a two-layer optimization method for balancing and sequencing in mixed-flow assembly lines that considers human-caused risks. The method includes first acquiring information data on all tasks in the mixed-flow assembly line, including: 1. Standard working hours of the tasks; 2. Assembly priority relationships between tasks; 3. Data on posture, strength, repetition, and additional risk indicators in the tasks.

[0013] Then, a two-level optimization mathematical model is established: based on the production cycle time and constraints of the assembly line and the information data mentioned above, a two-level optimization mathematical model for the mixed-flow assembly line is established; in this mathematical model, the upper-level optimization model is a line balancing model, the goal of which is to determine the line balancing scheme, aiming to minimize the production line cost under the constraint of human risk; the lower-level optimization model is a product commissioning sequencing model, the goal of which is to formulate the optimal commissioning sequencing scheme based on the given mixed-flow assembly line balancing scheme, aiming to minimize the required number of public workers and the maximum number of assembly workstations experiencing work overload at all times;

[0014] Finally, the established two-level optimization model is optimized and solved using a two-level optimization algorithm, and the optimal line balancing scheme and production scheduling scheme are output.

[0015] Furthermore, the method for calculating the minimum number of assembly workstations is as follows:

[0016]

[0017] Wherein, the parallelization coefficient of task i in product m This indicates the possibility of utility workers and regular workers working together and allocating their work time proportionally to complete tasks; the working hours of utility workers are... The working hours of ordinary workers are

[0018] If parallelism is not possible The working time of an ordinary worker is t.im ;

[0019] When tasks are fully parallelizable The working time for both utility workers and general workers is t. im / 2.

[0020] Furthermore, the objective function and constraints of the line equilibrium model are as follows:

[0021] Objective function:

[0022] MMALB(x * )=min DC (2)

[0023] DC=K×CW+u×DW+Z×DL (3)

[0024]

[0025] Equation (2) is the objective function of the upper-level optimization problem, which minimizes the cost of line balancing; Equation (3) is the cost of the production line after balancing, which mainly includes: the cost of minimizing the number of assembly workstations under the condition of satisfying human risk, the cost of public workers, and the cost of production loss; Equation (4) is the calculation method for the total number of overloads of assembly workstations in all periods, where K is the number of assembly workstations, DC is the total cost of the production line, u is the number of public workers, CW is the cost of a single public worker, Z is the total number of times an assembly workstation is overloaded in all periods, DL is the cost of production loss when a single assembly workstation is overloaded, and S is the total cycle time required to complete all products, S = D + K - 1, z sk The value is defined as follows: if assembly workstation k experiences a work overload within cycle s, it is 1; otherwise, it is zero.

[0026] Constraints:

[0027]

[0028]

[0029] Where, x ik A binary variable indicating whether task i is assigned to assembly workstation k. ER is the average processing time of task i based on task requirements. kFor the human factor risk of workers assigned to assembly workstation k; constraint (5) ensures that each task is assigned to one and only one assembly workstation; constraint (6) ensures that the total processing time of each assembly workstation does not exceed the available cycle time, which is the average time based on historical demand; constraints (7)-(8) ensure that the workload of each assembly workstation is compatible with the time of ordinary workers and utility workers; constraint (9) ensures that the priority relationship between tasks is respected; constraint (11) is a human factor risk constraint that ensures that the human factor risk level of workers in each assembly workstation is acceptable.

[0030] Furthermore, the product launch sequencing model is as follows:

[0031] Define Δ mk For product m, the working overload at assembly workstation k:

[0032]

[0033] Given a set of products M and the short-run demand d for each product m. m Its short-term demand is the total demand. The total cycle time required to complete all products is S = D + K - 1, Δ mk Let y be the overload of product m at assembly workstation k; sm Let y be a binary variable, representing whether product m is allocated to time period s (1≤s≤S), and when s>D, y sm =0; The objective function and constraints of the mixed-flow assembly line sequencing model are:

[0034] Objective function:

[0035] MMALS(K,x * )=min u+v / K (13)

[0036] Equation (13) represents the minimum number of common workers and the maximum number of assembly workstations experiencing work overload in all periods, where v / K≤1; while ensuring the minimum number of common workers, the number of assembly workstations experiencing work overload is minimized to the greatest extent possible, x * The optimal solution for balancing a mixed-flow assembly line is given by v, which is the maximum number of assembly workstations that experience workload overload at all times.

[0037] Constraints:

[0038]

[0039] u,v∈{0,1,...} (21)

[0040] Where B = 100000, constraint (14) ensures that the availability of public workers does not exceed the available time of public workers at any time, ω is the public worker availability coefficient, and y sm This is a binary variable, indicating whether product m is assigned to time period s, and d. m Let m be the short-term demand for product m during the planning period; constraint (15) ensures that all product assembly needs are met; constraint (16) ensures that only one product can be produced at each location; constraint (17) ensures that no product continues to enter the production line during the final transition phase; constraints (18) and (19) make v greater than the maximum number of assembly workstations that experience work overload in all periods; constraint (20) and equation (21) define variables y, z, u, and v, and then calculate the lower bound of the number of public workers:

[0041]

[0042] Furthermore, the two-layer optimization algorithm consists of a hybrid optimization algorithm and a CPLEX solver. The upper-layer optimization model is solved using the hybrid optimization algorithm, which is divided into two stages. The first stage uses the CPLEX solver, and the second stage uses the IGGA algorithm. Specifically, the GA algorithm simultaneously applies the local search function of the IG algorithm.

[0043] (1) In the first stage, the CPLEX solver is called to obtain a solution, that is, a line balance scheme is obtained. This solution and the randomly generated initial solution form the initial population. Neither the solution nor the randomly generated initial solution considers human factors risk.

[0044] The second stage, namely the IGGA algorithm steps, are as follows:

[0045] (2) Initialization: The initial population of the first stage is converted into permutation-based encoding vectors; each encoding is decoded, and the task is assigned to a specific assembly workstation. Human risk is considered, and solutions that satisfy both task priority constraints and human risk are identified as feasible solutions; otherwise, they are identified as infeasible solutions. Infeasible solutions are gradually eliminated through multiple iterations by selecting steps.

[0046] (3) Each solution in the initial population calls the CPLEX solver of the lower-level optimization algorithm to solve the production ordering optimization model, and obtains the optimal lower-level solution corresponding to each upper-level solution, i.e. the production ordering scheme, and calculates the upper-level objective function value (DC) of each initial solution through formula (3).

[0047] (4) Evolution, including crossover and mutation: The initial population is selected for the mating pool using a competitive selection method. Then, a set of solutions is selected from the mating pool. Offspring are generated through the action of sequential crossover and micro-mutation operators. Each solution of the offspring is solved by calling the lower-level optimization algorithm to solve the production sorting optimization model, and the optimal lower-level solution corresponding to each solution of the offspring is obtained, i.e. the production sorting scheme. The upper-level objective function value (DC) of each solution of the offspring is calculated by formula (3).

[0048] (5) Local search: Improve the current optimal solution, that is, the optimal solution in the current initial population and offspring, to obtain a better solution. This solution will also call the lower-level algorithm to obtain the corresponding optimal lower-level solution, and then solve the upper-level objective function value.

[0049] (6) Selection: Select the better individuals, i.e. "promising" solutions, from the initial population and the offspring population to form the next generation population;

[0050] (7) Perform the above evolution, local search and selection steps on the next generation population until the stopping condition is met;

[0051] (8) For all the solutions obtained in the above steps, select the optimal individual, that is, the optimal solution among all the solutions obtained in the selection step, to obtain the optimal line balance scheme and production ordering scheme.

[0052] The lower-level optimization model is solved by calling the CPLEX solver. Based on the input upper-level solution, it finds the corresponding lower-level optimal solution and outputs the corresponding optimal production sequencing scheme.

[0053] Furthermore, the encoding vector contains an array of integers representing the task allocation order. <x1,x2,…,x i The decoding method is as follows:

[0054] Step 1: Initialize the current task index i = 1 and the assembly workstation number k = 0;

[0055] Step 2: Create a new assembly workstation k, and set the assembly workstation time to: Total processing time for assembly workstation k: WT k =0; Total working time for ordinary workers at assembly workstation k: WT1 mk =0; Total working time of assembly workstation k utilities: WT2 mk =0;

[0056] Step 3: Based on the order of task assignment, select the task x at the i-th position in that order. i ;

[0057] Step 4: Determine the task x assigned to the current assembly workstation k. i Processing time;

[0058] Step 5: If the WT of the current assembly workstation k is... k WT1 mk WT2 mk If / ω does not exceed the loop time, corresponding to the constraints in equations (6), (7), and (8) respectively, then task i is assigned to the current assembly workstation k, and at the same time, let i = i + 1; otherwise, k = k + 1, return to step 2;

[0059] Step 6: Check if there are any unassigned tasks; if so, return to step 3; otherwise, proceed to step 7.

[0060] Step 7: Check whether the current solution satisfies the priority relationship between tasks and the human factor risk constraint; if it does, the solution is feasible; otherwise, the solution is not feasible.

[0061] Step 8: Calculate the number of assembly workstations for the current solution.

[0062] Furthermore, the selection specifically refers to:

[0063] If any of the following conditions are met, then solution seq1 is considered superior to solution seq2, and seq1 is set as the better solution in the subsequent solution selection process: (1) seq1 is feasible, seq2 is not feasible; (2) both seq1 and seq2 are feasible, but the objective function value of seq1 is smaller; (3) both seq1 and seq2 are not feasible, but the degree of constraint violation of seq1 is smaller.

[0064] Furthermore, an iterative greedy algorithm is used to improve the optimal solutions of all current populations. Specifically, the optimal solution of the current population is used as the initial solution. In the destruction step, 30%-35% of the encoding vector elements are extracted from the initial solution to obtain a partial sequence. In the construction step, the extracted elements are randomly reinserted into different positions in the partial sequence to form a new sequence. A new sequence is generated in each reinsertion process. Then, the new sequence with the best objective value, i.e., the smallest upper-level objective function value formula (3) and the constraint condition, is selected to replace the current sequence. The above steps are repeated until all elements are reinserted, and finally a new upper-level solution is obtained, i.e., the line-balanced scheme is obtained. The obtained line-balanced scheme is substituted into the lower-level algorithm to obtain the corresponding optimal production sorting scheme, and then its upper-level objective function value DC is solved.

[0065] Furthermore, the ER index of the OCRA method, a concise index for assessing upper limb repetitive movement exposure, was used to evaluate this. kThe OCRA index represents the erroneous risk of workers assigned to assembly workstation (k), aiming to assess whether the workers' erroneous risk is at a low level. It comprehensively assesses erroneous risk factors including posture, strength, repetitive motion, and additional risk, and the specific formula is as follows:

[0066]

[0067] RF=OS×PM×FoM×RM×AdM (25)

[0068] Wherein, AF is the actual frequency, RF is the recommended frequency, Nt represents the number of actions performed in one cycle, OS is a specific parameter with a value of 18; PM is the posture multiplication factor; FoM is a force multiplication factor; RM is the action repeatability multiplication factor; and AdM is the additional factor multiplication factor.

[0069] The criteria for setting human factors risk assessment are:

[0070]

[0071] Among them, the human factor risk for each position is selected from the maximum human factor risk value among all assembly lines.

[0072] The optimization system of this invention employs the aforementioned two-layer optimization method for balancing and sequencing mixed-flow assembly lines considering human factors and risks, and includes:

[0073] The information data acquisition module is used to acquire information data of all work tasks in the mixed-flow assembly line;

[0074] The two-layer optimization mathematical model building module establishes a two-layer optimization mathematical model for the mixed-flow assembly line based on the production cycle time and constraints of the assembly line, as well as the aforementioned information data. The upper-layer optimization model module is the line balancing model module, used to determine the line balancing scheme, aiming to minimize production line costs while satisfying the priority relationships between tasks and human risk constraints. The lower-layer optimization model module is the production scheduling model module, whose objective is to formulate the optimal production scheduling scheme based on a given mixed-flow assembly line balancing scheme, aiming to minimize the required number of public workers and the maximum number of assembly workstations experiencing overload at all times.

[0075] The two-layer optimization algorithm module includes an upper-layer optimization algorithm module and a lower-layer optimization algorithm module. The upper-layer optimization algorithm module obtains the solution of the line balance scheme by solving the problem through a hybrid optimization algorithm based on the established upper-layer optimization model module.

[0076] The lower-level optimization algorithm module uses the CPLEX solver to solve the production ranking optimization model for all solutions obtained by the upper-level optimization algorithm, and obtains the optimal lower-level solution corresponding to each upper-level solution, i.e. the production ranking scheme. Then, the upper-level optimization model module solves the upper-level objective function value for each solution.

[0077] By performing evolution, local search, and selection on the initial population to obtain better solutions, a next-generation population is formed. This next-generation population is then used as a new initial population to undergo the same evolution, local search, and selection steps until a stopping condition is met. The optimal line-balanced scheme and production sequencing scheme are then output. The beneficial effects of this invention are:

[0078] The optimization method and system of the present invention are more likely to obtain the global optimal solution, and also have higher optimization efficiency and stability. Attached Figure Description

[0079] Figure 1 This is a schematic diagram illustrating the working principle of the present invention.

[0080] Figure 2 This is a flowchart of the overall algorithm of the present invention.

[0081] Figure 3 This is a system block diagram of the present invention. Detailed Implementation

[0082] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0083] Example: Figures 1-3 As shown, the present invention provides a two-layer optimization method for balancing and sequencing in a mixed-flow assembly line that considers human factors and risks. The method includes first acquiring information data of all tasks in the mixed-flow assembly line, including: 1. Standard working hours of the tasks; 2. Assembly priority relationship between tasks; 3. Posture, strength, repetition and additional risk index data of the tasks.

[0084] Then, a two-level optimization mathematical model is established: based on the production cycle time and constraints of the assembly line and the information data mentioned above, a two-level optimization mathematical model for the mixed-flow assembly line is established; in this mathematical model, the upper-level optimization model is a line balancing model, the goal of which is to determine the line balancing scheme, aiming to minimize the production line cost under the constraint of human factors risk; the lower-level optimization model is a line sequencing model, the goal of which is to formulate the optimal production sequencing scheme based on the given mixed-flow assembly line balancing scheme, aiming to minimize the required number of public workers and the maximum number of assembly workstations experiencing work overload at all times;

[0085] Finally, the mathematical model established above is optimized and solved using a two-level optimization algorithm, and the optimal line balancing scheme and production scheduling scheme are output.

[0086] Since the number of assembly workstations is directly proportional to production costs, the fewer the number of assembly workstations, the lower the cost. The calculation method for the minimum number of assembly workstations is as follows:

[0087]

[0088] Wherein, the parallelization coefficient of task i in product m This indicates the possibility of utility workers and regular workers working together and allocating their work time proportionally to complete tasks; the working hours of utility workers are... The working hours of ordinary workers are

[0089] If parallelism is not possible The working time of an ordinary worker is t. im ;

[0090] When tasks are fully parallelizable The working time for both utility workers and general workers is t. im / 2.

[0091] The objective function and constraints of the line equilibrium model are as follows:

[0092] Objective function:

[0093] MMALB(x * )=min DC (2)

[0094] DC=K×CW+u×DW+Z×DL (3)

[0095]

[0096] Equation (2) is the objective function of the upper-level optimization problem, which minimizes the cost of line balancing; Equation (3) is the cost of the production line after balancing, which mainly includes: the cost of minimizing the number of assembly workstations under the condition of satisfying human risk, the cost of public workers and the cost of production loss; Equation (4) is the calculation method for the total number of overloads of assembly workstations in all periods.

[0097] Constraints:

[0098]

[0099] Where, x ik A binary variable indicating whether task i is assigned to assembly workstation k. The average processing time of task i is based on task requirements; constraint (5) ensures that each task is assigned to one and only one assembly workstation; constraint (6) ensures that the total processing time of each assembly workstation (average time based on historical requirements) does not exceed the available cycle time; constraints (7)-(8) ensure that the workload of each assembly workstation is compatible with the time of ordinary workers and utility workers; constraint (9) ensures that the priority relationship between tasks is respected; constraint (11) is a human factor risk constraint, ensuring that the human factor risk level of workers in each assembly workstation is acceptable.

[0100] The product launch sequencing model:

[0101] Define Δ mk For product m, the working overload at assembly workstation k:

[0102]

[0103] Given a set of products M and the short-run demand d for each product m. m Its short-term demand is the total demand. The total cycle time required to complete all products is S = D + K - 1; let y sm Let y be a binary variable, representing whether product m is allocated to time period s (1≤s≤S), and when s>D, y sm =0; The objective function and constraints of the mixed-flow assembly line sequencing model are:

[0104] Objective function:

[0105] MMALS(K,x * )=min u+v / K (13)

[0106] Equation (13) is the objective function of the lower-level optimization problem, representing minimizing the number of public workers and the maximum number of assembly workstations experiencing work overload in all periods.

[0107] Constraints:

[0108]

[0109]

[0110] u,v∈{0,1,...}(21)

[0111] Where B = 100000, constraint (14) ensures that the available time of utilities does not exceed the limit at any time; constraint (15) ensures that all product assembly requirements are met; constraint (16) ensures that only one product can be produced at each position; constraint (17) ensures that no product continues to enter the production line during the final transition phase; constraints (18) and (19) make v greater than the maximum number of assembly workstations that experience work overload in all periods; constraint (20) and equation (21) define variables y, z, u, and v, and then calculate the lower bound of the number of utilities:

[0112]

[0113] Furthermore, such as Figure 2 As shown, the two-layer optimization algorithm consists of a hybrid optimization algorithm and a CPLEX solver. The upper-layer optimization model is solved using the hybrid optimization algorithm, which is divided into two stages. The first stage consists of the CPLEX solver, and the second stage consists of the IGGA algorithm. Specifically, the GA algorithm simultaneously applies the local search of the IG algorithm.

[0114] (1) In the first stage, the CPLEX solver is called to obtain a solution, that is, a line balance scheme is obtained. This solution and the randomly generated initial solution form the initial population. Neither the solution nor the randomly generated initial solution considers human factors risk.

[0115] The second stage, namely the IGGA algorithm steps, are as follows:

[0116] (2) Initialization: The initial population of the first stage is converted into permutation-based encoding vectors; each encoding is decoded, and the task is assigned to a specific assembly workstation. Human risk is considered, and solutions that satisfy both task priority constraints and human risk are identified as feasible solutions; otherwise, they are identified as infeasible solutions. Infeasible solutions are gradually eliminated through multiple iterations by selecting steps.

[0117] The encoding vector contains an array of integers representing the task allocation order. <x1,x2,…,x i The decoding method is as follows:

[0118] Step 1: Initialize the current task index i = 1 and the assembly workstation number k = 0;

[0119] Step 2: Create a new assembly workstation k, and set the assembly workstation time to: Total processing time for assembly workstation k: WT k =0; Total working time for ordinary workers at assembly workstation k: WT1 mk =0; Total working time of assembly workstation k utilities: WT2 mk =0;

[0120] Step 3: Based on the order of task assignment, select the task x at the i-th position in that order. i ;

[0121] Step 4: Determine the task x assigned to the current assembly workstation k. i Processing time;

[0122] Step 5: If the WT of the current assembly workstation k is... k WT1 mk WT2 mk If / ω does not exceed the loop time, corresponding to the constraints in equations (6), (7), and (8) respectively, then task i is assigned to the current assembly workstation k, and at the same time, let i = i + 1; otherwise, k = k + 1, return to step 2;

[0123] Step 6: Check if there are any unassigned tasks; if so, return to step 3; otherwise, proceed to step 7.

[0124] Step 7: Check whether the current solution satisfies the priority relationship between tasks and the human factor risk constraint; if it does, the solution is feasible; otherwise, the solution is not feasible.

[0125] Step 8: Calculate the number of assembly workstations for the current solution.

[0126] (3) Each solution in the initial population calls the CPLEX solver of the lower-level optimization algorithm to solve the production ordering optimization model, and obtains the optimal lower-level solution corresponding to each upper-level solution, i.e. the production ordering scheme, and calculates the upper-level objective function value (DC) of each initial solution through formula (3).

[0127] (4) Evolution, including crossover and mutation: The initial population is selected for the mating pool using a competitive selection method. Then, a set of solutions is selected from the mating pool. Offspring are generated through the action of sequential crossover and micro-mutation operators. Each solution of the offspring is solved by calling the lower-level optimization algorithm to solve the production sorting optimization model, and the optimal lower-level solution corresponding to each solution of the offspring is obtained, i.e. the production sorting scheme. The upper-level objective function value (DC) of each solution of the offspring is calculated by formula (3).

[0128] (5) Local search, using the iterative greedy algorithm, abbreviated as IG algorithm: improve the current optimal solution, that is, the optimal solution in the current initial population and offspring, to obtain a better solution. This solution will also call the lower-level algorithm to obtain the corresponding optimal lower-level solution, and then solve the upper-level objective function value.

[0129] The iterative greedy algorithm is as follows: the optimal solution of all current populations is used as the initial solution. In the destruction step, 30%-35% of the encoding vector elements are extracted from the initial solution. In this example, 30% is extracted, and then a partial sequence is obtained. In the construction step, the extracted elements are randomly reinserted into different positions in the partial sequence to form a new sequence. A new sequence is generated in each reinsertion process. Then, the new sequence with the best objective value, i.e. the smallest upper objective function value formula (3) and the constraint condition, is selected to replace the current sequence. The above steps are repeated until all elements are reinserted, and finally a new upper solution is obtained, i.e., the line balance scheme is obtained. The obtained line balance scheme is substituted into the lower algorithm to obtain the corresponding optimal production sorting scheme, and then its upper objective function value DC is solved.

[0130] (6) Selection: Select the better individuals, i.e. the "promising" solutions, from the initial population and the offspring population to form the next generation population; for example, sort the solutions from the best to the worst according to the specific selection steps, and then select the top 100 (the number of solutions to be selected depends on the size of the specific population) better solutions to form the next generation population.

[0131] Specifically, if any of the following conditions are met, then solution seq1 is considered superior to solution seq2, and seq1 is set as the better solution in the subsequent solution selection process: (1) seq1 is feasible, seq2 is not feasible; (2) both seq1 and seq2 are feasible, but the objective function value of seq1 is smaller; (3) both seq1 and seq2 are not feasible, but the degree of constraint violation of seq1 is smaller.

[0132] (7) Perform the above evolution, local search and selection steps on the next generation population until the stopping condition is met; the stopping condition set in this invention is: whether the set number of iterations is met;

[0133] (8) For all the solutions obtained in the above steps, select the optimal individual, that is, the optimal solution among all the solutions obtained in the selection step, to obtain the optimal line balance scheme and production ordering scheme.

[0134] The lower-level optimization model is solved by calling the CPLEX solver. Based on the input upper-level solution, it finds the corresponding lower-level optimal solution and outputs the corresponding optimal production sequencing scheme.

[0135] The ER index is a concise index for assessing exposure to repetitive movements of the upper limbs. k(Formula (23)) represents the erroneous risk assigned to the worker at the assembly workstation (k). The OCRA index comprehensively assesses erroneous risk factors such as posture, strength, repetitiveness, and additional risk. Its purpose is to assess whether the worker's erroneous risk is at a low level. The specific formula is as follows:

[0136]

[0137] RF=OS×PM×FoM×RM×AdM (25)

[0138] Where AF is the actual frequency, RF is the recommended frequency, and Nt represents the number of actions performed in one cycle. OS This is represented as a specific parameter, and in this invention, the value is 18; PM The multiplication coefficients for the posture; FoM It is a force multiplier; RM The multiplication coefficient for the repetitiveness of the action; AdM The multiplication coefficient is the factor added.

[0139] The criteria for setting human factors risk assessment are:

[0140]

[0141] Since the assembly line proposed in this invention is a mixed-flow production line, this invention stipulates that the human factor risk for each position is selected from the maximum human factor risk value among all assembly lines.

[0142] Table 1 below explains the relevant variables and symbols used in the mathematical model proposed in this invention.

[0143] Table 1:

[0144]

[0145]

[0146] This invention provides an optimization system for a two-layer optimization method considering the balancing and sequencing of mixed-flow assembly lines based on human factors and risks, comprising:

[0147] The information data acquisition module is used to acquire information data of all work tasks in the mixed-flow assembly line;

[0148] The two-layer optimization mathematical model building module establishes a two-layer optimization mathematical model for the mixed-flow assembly line based on the production cycle time and constraints of the assembly line, as well as the aforementioned information data. The upper-layer optimization model module is the line balancing model module, used to determine the line balancing scheme, aiming to minimize production line costs while satisfying the priority relationships between tasks and human risk constraints. The lower-layer optimization model module is the production scheduling model module, whose objective is to formulate the optimal production scheduling scheme based on a given mixed-flow assembly line balancing scheme, aiming to minimize the required number of public workers and the maximum number of assembly workstations experiencing overload at all times.

[0149] The two-layer optimization algorithm module includes an upper-layer optimization algorithm module and a lower-layer optimization algorithm module. The upper-layer optimization algorithm module obtains the solution of the line balance scheme by solving the problem through a hybrid optimization algorithm based on the established upper-layer optimization model module.

[0150] The lower-level optimization algorithm module uses the CPLEX solver to solve the production ranking optimization model for all solutions obtained by the upper-level optimization algorithm, and obtains the optimal lower-level solution corresponding to each upper-level solution, i.e. the production ranking scheme. Then, the upper-level optimization model module solves the upper-level objective function value for each solution.

[0151] By performing evolution, local search, and selection on the initial population to obtain better solutions, a next-generation population is formed. The next-generation population is then used as a new initial population to perform the above evolution, local search, and selection steps until the stopping condition is met, and the optimal line balance scheme and production sorting scheme are output.

[0152] The parts not described in detail in this application are all existing conventional technologies and will not be elaborated here.

[0153] It is understood that the above specific description of the present invention is only for illustrating the present invention and is not limited to the technical solutions described in the embodiments of the present invention. Those skilled in the art should understand that modifications or equivalent substitutions can still be made to the present invention to achieve the same technical effect; as long as the use needs are met, they are all within the protection scope of the present invention.

Claims

1. A two-level optimization method for balancing and sequencing mixed-flow assembly lines considering human factors and risks, characterized in that: This includes first acquiring information data on all tasks in the mixed-flow assembly line, including:

1. Standard working hours of the tasks; 2. Assembly priority relationships between tasks; 3. Posture, force, repetition, and additional risk indicators data of the tasks. Then, a two-level optimization mathematical model is established: based on the production cycle time and constraints of the assembly line and the information data mentioned above, a two-level optimization mathematical model for the mixed-flow assembly line is established; in this mathematical model, the upper-level optimization model is a line balancing model, the goal of which is to determine the line balancing scheme, aiming to minimize the production line cost under the constraint of human risk; the lower-level optimization model is a product commissioning sequencing model, the goal of which is to formulate the optimal commissioning sequencing scheme based on the given mixed-flow assembly line balancing scheme, aiming to minimize the required number of public workers and the maximum number of assembly workstations experiencing work overload at all times; Finally, the established two-level optimization mathematical model is optimized and solved using a two-level optimization algorithm, and the optimal line balancing scheme and production sequencing scheme are output. The objective function and constraints of the line equilibrium model are as follows: Objective function: DC (2) （3） （4） Equation (2) is the objective function of the upper-level optimization problem, which minimizes the cost of line balancing. Equation (3) represents the optimal solution for balancing the mixed-flow assembly line; Equation (4) represents the cost of the production line after balancing, including: the cost of minimizing the number of assembly workstations under the condition of satisfying human risk, the cost of public workers and production loss costs, and CS represents the cost of a single assembly workstation; Equation (5) represents the calculation method for the total number of overloads of assembly workstations in all periods. Where is the number of assembly workstations, and DC is the total cost of the production line. Let CW be the number of public workers, Z be the total number of times the assembly workstations overload over all periods, DL be the production loss cost when a single assembly workstation overloads, and S be the total cycle time required to complete all products, S = D + K−1. The value is defined as follows: if assembly workstation k experiences work overload within cycle s, it is 1; otherwise, it is zero. D is the total demand for short-term demand. Constraints: （5） （6） （7） （8） （9） （10） （11） in, A binary variable indicating whether task i is assigned to assembly workstation k. It is the average processing time of task i based on task requirements. Human-cause risks for workers assigned to assembly workstation k; The availability coefficient of public workers; constraint (5) ensures that each task is assigned to one and only one assembly workstation; constraint (6) ensures that the total processing time of each assembly workstation does not exceed the available cycle time, where the total processing time is the average time based on historical demand, and C is the cycle time; constraints (7)-(8) ensure that the workload of each assembly workstation is compatible with the time of ordinary workers and public workers. Let be the parallelization coefficient of task i in product m. Let be the processing time of task i in product m. The number of tasks; constraint (9) ensures that the priority relationship between tasks is respected. For the previous task directly or passed on to task i; constraint (11) is a human factor risk constraint to ensure that the human factor risk level of workers in each assembly workstation is an acceptable level; The product launch sequencing model: definition For product m, the working overload at assembly workstation k: （12） Given a set of products M and the short-run demand for each product m Its short-term aggregate demand is D= The total cycle time required to complete all products is S = D + K−1. Assume that product m experiences overload at assembly workstation k; Let be a binary variable, representing whether product m is allocated to time period s, where 1 ≤ s ≤ S and when s > D. = 0; The objective function and constraints of the mixed-flow assembly line sequencing model are: Objective function: （13） Equation (13) represents the minimum number of common workers and the maximum number of assembly workstations experiencing work overload in all periods, where v / K≤1; while ensuring the minimum number of common workers, the number of assembly workstations experiencing work overload is minimized. For the optimal solution of mixed-flow assembly line balancing optimization, v is the maximum number of assembly workstations that experience workload overload in all periods. The number of public sector workers; Constraints: （14） （15） （16） （17） （18） （19） （20） （21） Where B = 100000, constraint (14) ensures that the available time of the utility worker does not exceed the limit at any time. The availability coefficient of public workers. This is a binary variable indicating whether product m is assigned to time period s. Let m be the short-term demand for product m during the planning period; constraint (15) ensures that all product assembly needs are met; constraint (16) ensures that only one product can be produced at each location; constraint (17) ensures that no product continues to enter the production line during the final transition phase; constraints (18) and (19) make v greater than the maximum number of assembly workstations that experience work overload in all periods; constraint (20) and equation (21) define variables y, z, u, and v, and then calculate the lower bound of the number of public workers: （22）。 2. The two-layer optimization method for balancing and sequencing mixed-flow assembly lines considering human factors and risks as described in claim 1, characterized in that: The minimum number of assembly workstations is calculated as follows: (1) Wherein, the parallelization coefficient of task i in product m , 0≤ ≤1 indicates the probability that utility workers and ordinary workers will collaborate and allocate their work time proportionally to complete the task; the working time of utility workers is... / 2, the working hours of ordinary workers are (1− / 2) ; If parallelism is not possible = 0, then the working hours of an ordinary worker are ; When tasks are fully parallelizable = 1, the working hours for both utility workers and general workers are 1. / 2; Let be the processing time of task i in product m; i represents the task.

3. The two-layer optimization method for balancing and sequencing mixed-flow assembly lines considering human factors and risks, as described in claim 1, is characterized in that: The two-layer optimization algorithm consists of a hybrid optimization algorithm and a CPLEX solver. The upper-layer optimization model is solved using the hybrid optimization algorithm, which is divided into two stages. The first stage uses the CPLEX solver, and the second stage uses the IGGA algorithm. Specifically, the GA algorithm simultaneously applies the local search of the IG algorithm. (1) In the first stage, the CPLEX solver is called to obtain a solution, that is, a line balance scheme is obtained. This solution and the randomly generated initial solution form the initial population. In this case, neither the solution nor the randomly generated initial solution considers human risk. The second stage, namely the IGGA algorithm steps, are as follows: (2) Initialization: The initial population of the first stage is converted into a permutation-based encoding vector; each encoding will be decoded to assign the task to a specific assembly workstation. At the same time, human factors risk is considered. The solution that satisfies the task priority constraint and human factors risk is labeled as a feasible solution. Otherwise, it is an infeasible solution. Infeasible solutions are gradually eliminated through multiple iterations by selecting steps. (3) Each solution in the initial population calls the CPLEX solver of the lower-level optimization algorithm to solve the production ordering optimization model, and obtains the optimal lower-level solution corresponding to each upper-level solution, i.e. the production ordering scheme, and calculates the upper-level objective function value DC of each initial solution through formula (3). (4) Evolution, including crossover and mutation: The initial population is selected for the mating pool using a competitive selection method. Then, a set of solutions is selected from the mating pool. Offspring are generated through the action of sequential crossover and micro-mutation operators. Each solution of the offspring is solved by calling the lower-level optimization algorithm to solve the production ranking optimization model, and the optimal lower-level solution corresponding to each solution of the offspring is obtained, i.e. the production ranking scheme. The upper-level objective function value DC of each solution of the offspring is calculated by formula (3). (5) Local search: Improve the current optimal solution, that is, the optimal solution in the current initial population and offspring, to obtain a better solution. This solution will also call the lower-level algorithm to obtain the corresponding optimal lower-level solution, and then solve the upper-level objective function value. (6) Selection: Select the better individuals, i.e. "promising" solutions, from the initial population and the offspring population to form the next generation population; (7) Perform the above evolution, local search and selection steps on the next generation population until the stopping condition is met; (8) For all the solutions obtained in steps (2), (4), (5) and (7) above, select the optimal individual, that is, the optimal solution among all the solutions obtained in the selection step, to obtain the optimal line balance scheme and production ordering scheme; The lower-level optimization model is solved by calling the CPLEX solver. Based on the input upper-level solution, it finds the corresponding lower-level optimal solution and outputs the corresponding optimal production sequencing scheme.

4. The two-layer optimization method for balancing and sequencing mixed-flow assembly lines considering human factors and risks, as described in claim 3, is characterized in that: The encoding vector contains an array of integers representing the task allocation order. <x1, x2,…,x j， x J > where j is the index, and the value of J satisfies J = max i. The decoding method is as follows: Step 1: Initialize the current assigned task index j = 1, and the assembly workstation number k = 0; Step 2: Create a new assembly workstation k, and set the assembly workstation time to: Total processing time for assembly workstation k: Total working hours for ordinary workers at assembly workstation k: Total working hours for assembly workstation k (common workers): ; Step 3: Based on the order of task assignment, select the task x at the j-th position in that order. j ; Step 4: Determine the task x assigned to the current assembly workstation k. j Processing time; Step 5: If the current assembly workstation k , , If / ω does not exceed the loop time, corresponding to the constraints in equations (6), (7), and (8) respectively, then the task order x will be... j The corresponding task is assigned to the current assembly workstation k, and at the same time... = + , = + (1− / 2), = + / 2, j = j + 1; otherwise, k = k + 1, return to step 2; Step 6: Check if there are any unassigned tasks; if so, return to step 3; otherwise, proceed to step 7. Step 7: Check whether the current solution satisfies the priority relationship between tasks and the human factor risk constraint; if it does, the solution is feasible; otherwise, the solution is not feasible. Step 8: Calculate the number of assembly workstations for the current solution.

5. The two-layer optimization method for balancing and sequencing mixed-flow assembly lines considering human factors and risks, as described in claim 3, is characterized in that: The selection specifically refers to: If any of the following conditions are met, then solution seq1 is considered superior to solution seq2, and seq1 is set as the better solution in the subsequent solution selection process: (1) seq1 is feasible, seq2 is not feasible; (2) seq1 and seq2 are both feasible, but the objective function value of seq1 is smaller; (3) seq1 and seq2 are both infeasible, but the degree of constraint violation of seq1 is smaller.

6. The two-layer optimization method for balancing and sequencing mixed-flow assembly lines considering human factors and risks, as described in claim 3, is characterized in that: An iterative greedy algorithm is used to improve the optimal solutions of all current populations. Specifically, the optimal solutions of the current populations are used as the initial solutions. In the destruction step, 30%-35% of the encoding vector elements are extracted from the initial solutions to obtain a partial sequence. In the construction step, the extracted elements are randomly re-inserted into different positions in the partial sequence to form a new sequence. In each re-insertion process, a new sequence is generated, and then the new sequence with the best objective value, i.e. the smallest upper objective function value formula (3) and the constraint condition, is selected to replace the current sequence. The above steps are repeated until all elements are re-inserted, and finally a new upper solution is obtained, i.e. the line balance scheme is obtained. The obtained line balance scheme is brought into the lower algorithm to obtain the corresponding optimal production sorting scheme, and then its upper objective function value DC is solved.

7. The two-layer optimization method for balancing and sequencing mixed-flow assembly lines considering human factors and risks, as described in claim 3, is characterized in that: The ER index, a concise indicator of upper limb repetitive movement exposure, was developed using the OCRA method. k This represents the erroneous risk of worker k assigned to assembly workstation, aiming to assess whether the worker's erroneous risk is at a low level. The OCRA index comprehensively assesses erroneous risk factors such as posture, strength, repetitive motion, and additional risk, with the specific formula as follows: （23） （24） （25） Where AF is the actual frequency, RF is the recommended frequency, and Nt represents the number of actions performed in one cycle. This represents a specific parameter with a value of 18. The multiplication coefficients for the posture; It is a force multiplier; The multiplication coefficient for the repetitiveness of the action; The multiplication coefficient of the additional factor; The criteria for setting human factors risk assessment are: （26） Among them, the human factor risk for each position is selected from the maximum human factor risk value among all assembly lines.

8. An optimization system employing the two-level optimization method for balancing and sequencing mixed-flow assembly lines considering human factors and risks as described in any one of claims 1-7, characterized in that: include: The information data acquisition module is used to acquire information data of all work tasks in the mixed-flow assembly line; The two-layer optimization mathematical model building module establishes a two-layer optimization mathematical model module for the mixed-flow assembly line based on the production cycle time and constraints of the assembly line and the aforementioned information data. Among them, the upper-layer optimization model module is the line balancing model module, which is used to determine the line balancing scheme, aiming to minimize the production line cost while satisfying the priority relationship between tasks and the constraints of human factors and risks. The lower-level optimization model module is the production sequencing model module. Its goal is to formulate the optimal production sequencing scheme based on a given mixed-flow assembly line balancing scheme, aiming to minimize the required number of public workers and the maximum number of assembly workstations experiencing work overload at all times. The two-layer optimization algorithm module includes an upper-layer optimization algorithm module and a lower-layer optimization algorithm module. The upper-layer optimization algorithm module obtains the solution of the line balance scheme by solving the problem through a hybrid optimization algorithm based on the established upper-layer optimization model module. The lower-level optimization algorithm module uses the CPLEX solver to solve the production ranking optimization model for all solutions obtained by the upper-level optimization algorithm, and obtains the optimal lower-level solution corresponding to each upper-level solution, i.e. the production ranking scheme. Then, the upper-level optimization model module solves the upper-level objective function value for each solution. By performing evolution, local search, and selection on the initial population to obtain better solutions, the next generation population is formed. The next generation population is then used as a new initial population to perform the same evolution, local search, and selection steps until the stopping condition is met, and the optimal line balance scheme and production sorting scheme are output.

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