Double-layer optimization system considering human factor risk mixed flow assembly line balancing and sequencing

Abstract

The invention discloses a double-layer optimization system considering human factor risk mixed flow assembly line balancing and sequencing, and belongs to the technical field of mixed flow assembly line optimization. Acquiring information data of all operation tasks in the mixed flow assembly line; establishing a double-layer optimization mathematical model: establishing the double-layer optimization mathematical model of the mixed flow assembly line according to the production takt and constraint conditions of the assembly line and the information data; the upper-layer optimization model is a line balance model, and aims to achieve the minimum production line cost under the condition of meeting the priority relationship between tasks and human factor risk constraints; the lower-layer optimization model is a product commissioning sorting model and aims to minimize the number of required public workers and the maximum number of assembly workstations experiencing working overload in all periods; and performing optimization solution on the established double-layer optimization model through a double-layer optimization algorithm, and outputting an optimal line balance scheme and a production sorting scheme. According to the optimization method and system provided by the invention, a globally optimal solution is expected to be obtained, and meanwhile, the optimization efficiency and the stability are higher.

Description

Technical Field

[0001] The present invention belongs to the technical field of mixed-flow assembly line optimization, and in particular relates to a double-layer optimization method and system for balancing and sequencing mixed-flow assembly lines taking into account human risk. Background Art

[0002] Mixed-flow assembly line is an important production method in modern manufacturing. It can continuously produce different types of products with similar structures and similar processes on the same production line. Mixed-flow assembly line is popular with a series of manufacturing companies because of its ability to provide diversified products, but it may also cause the assembly workstation operation time to exceed the cycle time, resulting in work overload at the assembly workstation, and even cause the production line to stop in severe cases. Mixed-flow assembly line can avoid production stoppage by dealing with work overload in a variety of ways, such as limiting the possibility of work overload by increasing the number of assembly workstations. Although this method reduces the risk of production stoppage due to work overload at the assembly workstation to a certain extent, it greatly increases the number of assembly workstations and production line space, which means that costs need to be increased and may even affect the layout and optimization of the assembly line.

[0003] The order of product launch determines the production efficiency of the mixed-flow assembly line. The product launch sequencing process needs to determine the order in which all products enter the production line according to the production order requirements, which is a short-term optimization problem. The mixed-flow assembly line balancing plan determines the load of all assembly workstations, while the product launch sequencing is based on the line balancing plan. By optimizing the product launch sequence, the load of the assembly workstation is balanced, that is, the product launch sequence also affects the load of the assembly workstation. Therefore, there is a mutual coupling relationship between the mixed-flow assembly line balancing and production sequencing optimization problems. The existing methods all adopt a hierarchical optimization strategy to optimize the line balance and production sequencing problems separately (first perform line balance optimization, then perform production sequencing optimization). This hierarchical optimization strategy is difficult to obtain the global optimal line balance and production sequencing solution. In addition, although the joint optimization method can hopefully obtain the global optimal solution, it also introduces a nested structure, which makes it difficult to solve.

[0004] At present, some countries have clear legal provisions requiring factories to consider the ergonomic risks (human risk) of work-related musculoskeletal diseases during the design phase, especially for manual assembly lines with high-frequency repetitive work movements. However, the existing mixed-flow assembly lines did not consider the human risk factor at the beginning of the design, resulting in high human risk in some work tasks. For example, some parts assembly processes not only require pressing operations or awkward working postures, but workers are also required to use their upper limbs to repeatedly perform work movements at a relatively high frequency, which may cause workers to suffer from musculoskeletal diseases and endanger their health. In addition, human risk will affect the efficiency of the assembly line and the quality of the assembled products, while also reducing the economic benefits of the factory. In addition, some current methods for evaluating human risk are nonlinear, which makes it impossible to establish a closed model that incorporates human risk into the assembly line balance problem.

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

[0006] 1. If the manually formulated line balancing plan does not take mixed-flow production into consideration, when the production line assembles different products, due to the different task operation times of different products, it is easy for the total operation time of the assembly workstation to exceed the cycle time of the production line (production line beat time), resulting in an overload of the assembly workstation workload, and even causing the production line to stop, reducing the efficiency of the production line.

[0007] 2. The mixed-flow assembly line reduces the occurrence of work overload on the assembly line by increasing the number of assembly workstations. However, this method increases the number of assembly workstations and production line space, greatly increasing costs and even affecting the efficiency of the production line.

[0008] 3. The existing methods do not consider the human risk of the work tasks when planning each assembly workstation and assigning work tasks. In addition, the factory mainly uses the method of post-analysis to reduce the human risk of the position, that is, after the production line is put into production, the human risk of the position is improved by continuously adjusting the work task plan of each position. This method not only increases management costs but also makes it difficult to achieve a better overall effect. In addition, the adjustment of job tasks at the production stage increases the difficulty of workers' work, reduces work efficiency, and even leads to a reduction in the production capacity of the production line.

[0009] 4. Existing methods separately optimize the mixed-flow assembly line balance and production sequencing problems, and adopt a hierarchical optimization strategy to optimize the line balance and production sequencing problems separately (first optimize the line balance, and then optimize the production sequencing), which cannot obtain the global optimal solution. Summary of the invention

[0010] In view of the above-mentioned technical problems, the present invention provides a two-layer optimization method and system for balancing and sorting mixed-flow assembly lines taking into account human risks. Specifically, a two-layer optimization model for balancing and sorting mixed-flow assembly lines is first constructed. Among them, the upper-level optimization problem is a line balance optimization problem, and its optimization goal is to minimize the production line cost under the premise of satisfying human risks; and the lower-level optimization problem is a production sorting optimization problem, and its optimization goal is to minimize the number of common workers required and the maximum number of assembly workstations that experience work overload at all stages. The joint optimization method of two-layer optimization of mixed-flow assembly line balancing and sorting proposed in the present invention is more likely to obtain a global optimal solution, and also has higher optimization efficiency and stability.

[0011] The objective of the present invention is achieved through the following technical solutions:

[0012] The present invention provides a two-layer optimization method for balancing and sorting a mixed-flow assembly line considering human risk, comprising first obtaining information data of all work tasks in the mixed-flow assembly line, including: 1. standard working hours of the work tasks; 2. assembly priority relationships between the work tasks; 3. posture, strength, repeatability and additional risk indicator data in the work tasks;

[0013] Then, a two-layer optimization mathematical model is established: a two-layer optimization mathematical model of a mixed-flow assembly line is established according to the production rhythm and constraints of the assembly line and the above-mentioned information data; in this mathematical model, the upper optimization model is a line balance model, whose goal is to determine the line balance plan, aiming to minimize the production line cost under the constraints of human risk; the lower optimization model is a product production sequencing model, whose goal is to develop an optimal production sequencing plan based on a given mixed-flow assembly line balance plan, aiming to minimize the number of common workers required and the maximum number of assembly workstations experiencing work overload in all periods;

[0014] Finally, the double-layer optimization model established above is optimized and solved through the double-layer optimization algorithm, and the optimal line balance plan and production sequencing plan are output.

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

[0016]

[0017] Among them, the parallelization coefficient of task i in product m is It indicates the possibility of public workers and ordinary workers working together and allocating working time in proportion to complete the task; the working time of public workers is The working hours of ordinary workers are

[0018] If parallelism is not possible The working time of an average worker is tim ;

[0019] When tasks are fully parallelizable The working time of public workers and ordinary workers is t im / 2.

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

[0021] Objective function:

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

[0023] DC=K×CW+u×DW+Z×DL (3)

[0024]

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

[0026] Constraints:

[0027]

[0028]

[0029] Among them, x ik is a binary variable indicating whether task i is assigned to assembly workstation k, is the average processing time of task i based on task requirements, ER kis the human risk of the worker 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, and the total processing time 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 public workers; constraint (9) ensures that the priority relationship between tasks is observed; constraint (11) is a human risk constraint, which ensures that the human risk level of workers in each assembly workstation is an acceptable level;

[0030] Furthermore, the product production sequencing model:

[0031] Definition Δ mk The work overload for product m at assembly workstation k is:

[0032]

[0033] Given a set of products M and the short-term demand d for each product m m , and its total short-term demand is The total cycle time required to complete all products is S = D + K-1, Δ mk is the work overload of product m at assembly workstation k; let y sm is a binary variable, indicating 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] Formula (13) represents the minimized number of common workers and the maximum number of assembly workstations that experience work overload in all periods, where v / K≤1; while minimizing the number of common workers, the number of assembly workstations that experience work overload is minimized, x * is the optimal solution for the mixed-flow assembly line balance optimization, v is the maximum number of assembly workstations that experience work overload in all periods;

[0037] Constraints:

[0038]

[0039] u,v∈{0,1,...} (21)

[0040] where B = 100,000, constraint (14) ensures that the available time of the public workers is not exceeded in any period, ω is the public worker availability coefficient, y sm is a binary variable, indicating whether product m is assigned to period s, d m is the short-term demand for product m during the planning period; constraint (15) ensures that all product assembly requirements are met; constraint (16) ensures that each position can only produce one product; 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 the variables y, z, u, and v, and then calculate the lower bound of the number of common workers:

[0041]

[0042] Furthermore, the two-layer optimization algorithm is composed of a hybrid optimization algorithm and a CPLEX solver, wherein the upper optimization model is solved using the hybrid optimization algorithm, which is divided into two stages. The first stage is composed of the CPLEX solver, and the second stage is composed of the IGGA algorithm. Specifically, the local search of the IG algorithm is simultaneously applied in the GA algorithm, specifically:

[0043] (1) In the first stage, the CPLEX solver is called to obtain a solution, that is, a line equilibrium solution. The solution and the randomly generated initial solution constitute the initial population. The solution and the randomly generated initial solution do not consider human risk.

[0044] The second stage, i.e. the IGGA algorithm steps are as follows:

[0045] (2) Initialization: Convert the initial population of the first stage into a permutation-based encoding vector; each encoding will be decoded, and the task will be assigned to a specific assembly workstation. At the same time, considering the human risk, the solution that meets the task priority constraint and human risk will be marked as a feasible solution, otherwise, it will be an infeasible solution. After multiple iterations, the infeasible solution will be gradually eliminated through the selection step;

[0046] (3) Each solution in the initial population calls the CPLEX solver of the lower-level optimization algorithm to solve the production scheduling optimization model, obtain the optimal lower-level solution corresponding to each upper-level solution, that is, the production scheduling solution, and calculate 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 the competitive selection method, and then a set of solutions is selected from the mating pool. The offspring is 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, that is, the production sorting scheme, and 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: Selecting better individuals from the initial population and the offspring population, i.e., “promising” solutions to form the next generation population;

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

[0051] (8) For all the solutions obtained in the above steps, the best individual is selected, that is, the best solution among all the solutions obtained in the selection step, to obtain the optimal line balancing plan and production sequencing plan;

[0052] The lower-level optimization model is solved by calling the CPLEX solver, which solves the corresponding lower-level optimal solution based on the input upper-level solution and outputs the corresponding optimal production sequencing plan.

[0053] Furthermore, the encoding vector contains an integer array, which indicates that the task allocation order is <x1,x2,…,x i >, the decoding method is as follows:

[0054] Step 1: Initialize the current task index to be assigned 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 of assembly workstation k: WT k =0; Total working time of ordinary workers at assembly workstation k: WT1 mk = 0; Total working time of common workers at assembly workstation k: WT2 mk =0;

[0056] Step 3: According to the order of task assignment, select task x at the i-th position in the 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 k 、WT1 mk 、WT2 mk / ω does not exceed the cycle time, corresponding to the constraints in equations (6), (7), and (8), respectively. Then, task i is assigned to the current assembly workstation k. At the same time, i=i+1; otherwise, k=k+1, return to step 2;

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

[0060] Step 7: Check whether the current solution satisfies the priority relationship between tasks and the human risk constraints; if so, the solution is feasible; otherwise, the solution is infeasible;

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

[0062] Further, the selection is specifically:

[0063] If any of the following conditions is met, solution seq1 is considered better than solution seq2, and seq1 is set as the better solution in the subsequent solution selection process: (1) seq1 is feasible and 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.

[0064] Furthermore, an iterative greedy algorithm is used to improve the optimal solution of all current populations, specifically: the optimal solution of the current population is used as the initial solution, and in the destruction step, 30%-35% of the coding vector elements are extracted from the initial solution, 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 set of new sequences is generated during each reinsertion process, and then a new sequence with the best target value, that is, the minimum upper layer objective function value formula (3) and satisfying the constraints is selected to replace the current sequence; the above steps are repeated until all elements are reinserted, and finally a new upper layer solution is obtained, that is, a line balance solution is obtained, and the obtained line balance solution is brought into the lower layer algorithm to obtain the corresponding optimal production sorting solution, and then its upper layer objective function value DC is solved.

[0065] Furthermore, the OCRA index ER was used to evaluate the exposure to upper limb repetitive motions. kIt indicates the human risk of workers assigned to the assembly workstation (k). The purpose is to assess whether the human risk of workers is at a low risk level. The OCRA index comprehensively evaluates the human risk factors of posture, strength, repetitiveness and additional risk. The specific formula is as follows:

[0066]

[0067] RF=OS×PM×FoM×RM×AdM (25)

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

[0069] The human risk assessment criteria are:

[0070]

[0071] Among them, the human risk of each position selects the maximum human risk value among all assembly lines.

[0072] The present invention adopts the optimization system of the double-layer optimization method for balancing and sequencing mixed-flow assembly lines considering human risk, including:

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

[0074] A two-layer optimization mathematical model building module is used to build a two-layer optimization mathematical model module for a mixed-flow assembly line according to the production rhythm and constraints of the assembly line and the above-mentioned information data; wherein the upper-layer optimization model module is a line balancing model module, which is used to determine the line balancing plan, aiming 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 module is a production sequencing model module, whose goal is to develop an optimal production sequencing plan based on a given mixed-flow assembly line balancing plan, aiming to minimize the number of common workers required and the maximum number of assembly workstations that experience work overload in all periods;

[0075] The double-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 a solution of the line balancing solution by solving the established upper-layer optimization model module through a hybrid optimization algorithm.

[0076] The lower-level optimization algorithm module uses the CPLEX solver to solve the production order optimization model of all solutions obtained by the upper-level optimization algorithm, and obtains the optimal lower-level solution corresponding to each upper-level solution, that is, the production order scheme, and then solves the upper-level optimization model module to obtain the upper-level objective function value of each solution;

[0077] By evolving, locally searching and selecting the initial population to obtain a better solution to form the next generation population, the next generation population is used as a new initial population to perform the above evolution, local search and selection steps until the stop condition is met, and the optimal line balance solution and production sequencing solution are output. The beneficial effects of the present invention are:

[0078] The optimization method and system of the present invention are more likely to obtain a global optimal solution, and also have higher optimization efficiency and stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 It is a working principle diagram of the present invention.

[0080] Figure 2 It is the overall algorithm flow chart of the present invention.

[0081] Figure 3 It is a system block diagram of the present invention. DETAILED DESCRIPTION

[0082] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0083] Example: Figure 1-Figure 3 As shown, the present invention provides a two-layer optimization method for balancing and sorting mixed-flow assembly lines considering human risk, including first obtaining information data of all work tasks in the mixed-flow assembly line, including: 1. Standard working hours of work tasks; 2. Assembly priority relationships between work tasks; 3. Posture, strength, repeatability and additional risk indicator data in work tasks;

[0084] Then, a two-layer optimization mathematical model is established: according to the production rhythm and constraints of the assembly line and the above information data, a two-layer optimization mathematical model of the mixed-flow assembly line is established; in this mathematical model, the upper optimization model is a line balancing model, whose goal is to determine the line balancing plan, aiming to minimize the production line cost under the constraints of human risk; the lower optimization model is a line sequencing model, whose goal is to develop the optimal production sequencing plan based on a given mixed-flow assembly line balancing plan, aiming to minimize the number of common workers required and the maximum number of assembly workstations experiencing work overload in all periods;

[0085] Finally, the mathematical model established above is optimized and solved through a double-layer optimization algorithm, and the optimal line balance plan and production sequencing plan are output.

[0086] Since the number of assembly workstations is proportional to the production cost, the fewer the number of assembly workstations, the lower the cost; the calculation method of the minimum number of assembly workstations is as follows:

[0087]

[0088] Among them, the parallelization coefficient of task i in product m is It indicates the possibility of public workers and ordinary workers working together and allocating working time in proportion to complete the task; the working time of public workers is The working hours of ordinary workers are

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

[0090] When tasks are fully parallelizable The working time of public workers and ordinary workers is t im / 2.

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

[0092] Objective function:

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

[0094] DC=K×CW+u×DW+Z×DL (3)

[0095]

[0096] Formula (2) is the objective function of the upper optimization problem, which minimizes the cost of line balancing; Formula (3) is the cost of the production line after the production line is balanced, which mainly includes: the cost of minimizing the number of assembly workstations under the condition of human risk, the cost of common workers and the cost of production loss; Formula (4) is the calculation method of the total overload times of assembly workstations in all periods;

[0097] Constraints:

[0098]

[0099] Among them, x ik is a binary variable indicating whether task i is assigned to assembly workstation k, is the average processing time of task i based on task demand; 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 (the average time based on historical demand) 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 public workers; constraint (9) ensures that the priority relationship between tasks is observed; constraint (11) is a human risk constraint, which ensures that the human risk level of workers in each assembly workstation is acceptable;

[0100] The product production sequencing model:

[0101] Definition Δ mk The work overload for product m at assembly workstation k is:

[0102]

[0103] Given a set of products M and the short-term demand d for each product m m , and its total short-term demand is The total cycle time required to complete all products is S = D + K-1; let y sm is a binary variable, indicating 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] Formula (13) is the objective function of the lower optimization problem, which represents the minimization of the number of common workers and the maximum number of assembly workstations that experience 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 the common workers is not exceeded in any period; 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 the variables y, z, u, and v, and then calculate the lower bound of the number of common workers:

[0112]

[0113] Furthermore, if Figure 2 As shown in FIG. 1 , the two-layer optimization algorithm is composed of a hybrid optimization algorithm and a CPLEX solver. The upper optimization model is solved using the hybrid optimization algorithm, which is divided into two stages. The first stage is composed of the CPLEX solver, and the second stage is composed of the IGGA algorithm. Specifically, the local search of the IG algorithm is applied simultaneously in the GA algorithm, specifically:

[0114] (1) In the first stage, the CPLEX solver is called to obtain a solution, that is, a line equilibrium solution. The solution and the randomly generated initial solution constitute the initial population. The solution and the randomly generated initial solution do not consider human risk.

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

[0116] (2) Initialization: Convert the initial population of the first stage into a permutation-based encoding vector; each encoding will be decoded, and the task will be assigned to a specific assembly workstation. At the same time, considering the human risk, the solution that meets the task priority constraint and human risk will be marked as a feasible solution, otherwise, it will be an infeasible solution. After multiple iterations, the infeasible solution will be gradually eliminated through the selection step;

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

[0118] Step 1: Initialize the current task index to be assigned 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 of assembly workstation k: WT k =0; Total working time of ordinary workers at assembly workstation k: WT1 mk = 0; Total working time of common workers at assembly workstation k: WT2 mk =0;

[0120] Step 3: According to the order of task assignment, select task x at the i-th position in the 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 k 、WT1 mk 、WT2 mk / ω does not exceed the cycle time, corresponding to the constraints in equations (6), (7), and (8), respectively. Then, task i is assigned to the current assembly workstation k. At the same time, i=i+1; otherwise, k=k+1, return to step 2;

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

[0124] Step 7: Check whether the current solution satisfies the priority relationship between tasks and the human risk constraints; if so, the solution is feasible; otherwise, the solution is infeasible;

[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 scheduling optimization model, obtain the optimal lower-level solution corresponding to each upper-level solution, that is, the production scheduling solution, and calculate 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 the competitive selection method, and then a set of solutions is selected from the mating pool. The offspring is 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, that is, the production sorting scheme, and 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, referred to as the IG algorithm: the current optimal solution, that is, the optimal solution in the current initial population and offspring, is improved to obtain a better solution, which 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 specifically as follows: the optimal solution of all current populations is used as the initial solution. In the destruction step, 30%-35% of the coding vector elements are extracted from the initial solution, and 30% is extracted in this example, 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 set of new sequences is generated during each reinsertion process, and then a new sequence with the best target value, that is, the upper layer objective function value formula (3) is minimized while satisfying the constraints, is selected to replace the current sequence; the above steps are repeated until all elements are reinserted, and finally a new upper layer solution is obtained, that is, a line balance solution is obtained, and the obtained line balance solution is brought into the lower layer algorithm to obtain the corresponding optimal production sorting solution, and then its upper layer objective function value DC is solved.

[0130] (6) Selection: Selecting better individuals, i.e., "promising" solutions, from the initial population and the offspring population to form the next generation population; for example, sorting the solutions from the highest to the lowest in terms of excellence according to the specific selection steps, and then selecting the first 100 (the number is selected according to the specific population size) better solutions to form the next generation population;

[0131] Specifically, if any of the following conditions is met, solution seq1 is considered better than solution seq2, and seq1 is set as the better solution in the subsequent solution selection process: (1) seq1 is feasible, and 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.

[0132] (7) subjecting the next generation population to the above-mentioned evolution, local search and selection steps until a stopping condition is met; the stopping condition set in the present invention is: whether a set number of iterations is met;

[0133] (8) For all the solutions obtained in the above steps, the best individual is selected, that is, the best solution among all the solutions obtained in the selection step, to obtain the optimal line balancing plan and production sequencing plan;

[0134] The lower-level optimization model is solved by calling the CPLEX solver, which solves the corresponding lower-level optimal solution based on the input upper-level solution and outputs the corresponding optimal production sequencing plan.

[0135] The ER index was obtained by using the OCRA method, a concise index for the assessment of exposure to repetitive movements of the upper limbs. k(Formula (23)) is used to represent the human risk of workers assigned to assembly workstation (k). The OCRA index comprehensively evaluates the human risk factors of posture, strength, repetitiveness and additional risk. The purpose is to assess whether the human risk of workers is at a low risk level. The specific formula is as follows:

[0136]

[0137] RF=OS×PM×FoM×RM×AdM (25)

[0138] Among them, AF is the actual frequency, RF is the recommended frequency, Nt represents the number of actions executed in one cycle, OS It is expressed as a specific parameter, and the value of the present invention is 18; PM is the multiplication coefficient of posture; FoM is a force multiplication factor; RM is the multiplication coefficient of the action repeatability; AdM is the multiplication coefficient of the additional factor.

[0139] The human risk assessment criteria are:

[0140]

[0141] The assembly production line proposed in the present invention belongs to a mixed-flow production line. Therefore, the present invention stipulates that the human risk of each position is the maximum human risk value among all assembly lines.

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

[0143] Table 1:

[0144]

[0145]

[0146] The optimization system of the double-layer optimization method for balancing and sequencing mixed-flow assembly lines taking into account human risk of the present invention comprises:

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

[0148] A two-layer optimization mathematical model building module is used to build a two-layer optimization mathematical model module for a mixed-flow assembly line according to the production rhythm and constraints of the assembly line and the above-mentioned information data; wherein the upper-layer optimization model module is a line balancing model module, which is used to determine the line balancing plan, aiming 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 module is a production sequencing model module, whose goal is to develop an optimal production sequencing plan based on a given mixed-flow assembly line balancing plan, aiming to minimize the number of common workers required and the maximum number of assembly workstations that experience work overload in all periods;

[0149] The double-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 a solution of the line balancing solution by solving the established upper-layer optimization model module through a hybrid optimization algorithm.

[0150] The lower-level optimization algorithm module uses the CPLEX solver to solve the production order optimization model of all solutions obtained by the upper-level optimization algorithm, and obtains the optimal lower-level solution corresponding to each upper-level solution, that is, the production order scheme, and then solves the upper-level optimization model module to obtain the upper-level objective function value of each solution;

[0151] The next generation population is formed by evolving, locally searching and selecting the initial population to obtain a better solution. The next generation population is used as a new initial population to perform the above-mentioned evolution, local search and selection steps until the stopping condition is met, and the optimal line balancing plan and production sequencing plan are output.

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

[0153] It can be understood that the above specific description of the present invention is only used to illustrate 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 the present invention can still be modified or replaced by equivalents to achieve the same technical effects; as long as the use requirements are met, they are 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 risk, characterized by: It includes first obtaining the information data of all the work tasks in the mixed-flow assembly line, including:

1. The standard working hours of the work tasks; 2. The assembly priority relationship between the work tasks; 3. The posture, strength, repeatability and additional risk indicator data in the work tasks; Then, a two-layer optimization mathematical model is established: a two-layer optimization mathematical model of a mixed-flow assembly line is established according to the production rhythm and constraints of the assembly line and the above-mentioned information data; in this mathematical model, the upper optimization model is a line balance model, whose goal is to determine the line balance plan, aiming to minimize the production line cost under the constraints of human risk; the lower optimization model is a product production sequencing model, whose goal is to develop an optimal production sequencing plan based on a given mixed-flow assembly line balance plan, aiming to minimize the number of common workers required and the maximum number of assembly workstations experiencing work overload in all periods; Finally, the double-layer optimization model established above is optimized and solved through the double-layer optimization algorithm, and the optimal line balancing plan and production sequencing plan are output.

2. According to claim 1, the two-level optimization method for balancing and sequencing mixed-flow assembly lines taking into account human risk is characterized by: The minimum number of assembly workstations is calculated as follows: Among them, the parallelization coefficient of task i in product m is It indicates the possibility of public workers and ordinary workers working together and allocating working time in proportion to complete the task; the working time of public workers is The working hours of ordinary workers are If parallelism is not possible The working time of an average worker is t im ; When tasks are fully parallelizable The working time of public workers and ordinary workers is t im / 2.

3. According to claim 1, the two-level optimization method for balancing and sequencing mixed-flow assembly lines taking into account human risk is characterized by: The objective function and constraints of the line balance model are as follows: Objective function: MMALB(x * )=min DC (2) DC=K×CW+u×DW+Z×DL (3) Formula (2) is the objective function of the upper optimization problem, which minimizes the cost of line balancing; Formula (3) is the cost of the production line after the production line is balanced, which mainly includes: the cost of minimizing the number of assembly workstations under the condition of satisfying human risk, the cost of common workers and the cost of production loss; Formula (4) is the calculation method of the total number of overloads of assembly workstations in all periods. K is the number of assembly workstations, DC is the total cost of the production line, u is the number of common workers, CW is the cost of a single common worker, Z is the total number of overloads of assembly workstations in all periods, DL is the production loss cost when a single assembly workstation is overloaded, S is the total cycle time required to complete all products, S = D + K-1, z sk The value of is defined as: 1 if the assembly workstation k experiences work overload in period s, otherwise it is zero; Constraints: Among them, x ik is a binary variable indicating whether task i is assigned to assembly workstation k, is the average processing time of task i based on task requirements, ER k is the human risk of the worker 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, and the total processing time 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 public workers; constraint (9) ensures that the priority relationship between tasks is observed; constraint (11) is the human risk constraint, which ensures that the human risk level of workers in each assembly workstation is acceptable.

4. According to claim 1, the two-level optimization method for balancing and sequencing mixed-flow assembly lines taking into account human risk is characterized by: The product production sequencing model: Definition Δ mk The work overload for product m at assembly workstation k is: Given a set of products M and the short-term demand d for each product m m , and its total short-term demand is The total cycle time required to complete all products is S = D + K-1, Δ mk is the work overload of product m at assembly workstation k; let y sm is a binary variable, indicating 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: Objective function: MMALS(K,x * )=min u+v / K (13) Formula (13) represents the minimized number of common workers and the maximum number of assembly workstations that experience work overload in all periods, where v / K≤1; while minimizing the number of common workers, the number of assembly workstations that experience work overload is minimized, x * is the optimal solution for the mixed-flow assembly line balance optimization, v is the maximum number of assembly workstations that experience work overload in all periods; Constraints: u,v∈{0,1,...} (21) where B = 100,000, constraint (14) ensures that the available time of the public workers is not exceeded in any period, ω is the public worker availability coefficient, y sm is a binary variable, indicating whether product m is assigned to period s, d m is the short-term demand for product m during the planning period; constraint (15) ensures that all product assembly requirements are met; constraint (16) ensures that each position can only produce one product; 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 the variables y, z, u, and v, and then calculate the lower bound of the number of common workers:

5. According to claim 1, the two-level optimization method for balancing and sequencing mixed-flow assembly lines taking into account human risk is characterized by: The two-layer optimization algorithm is composed of a hybrid optimization algorithm and a CPLEX solver. The upper optimization model is solved using the hybrid optimization algorithm, which is divided into two stages. The first stage is composed of the CPLEX solver, and the second stage is composed of the IGGA algorithm. Specifically, the local search of the IG algorithm is applied simultaneously in the GA algorithm, specifically: (1) In the first stage, the CPLEX solver is called to obtain a solution, that is, a line equilibrium solution. The solution and the randomly generated initial solution constitute the initial population. The solution and the randomly generated initial solution do not consider human risk. The second stage, i.e. the IGGA algorithm steps are as follows: (2) Initialization: Convert the initial population of the first stage into a permutation-based encoding vector; each encoding will be decoded, and the task will be assigned to a specific assembly workstation. At the same time, considering the human risk, the solution that meets the task priority constraint and human risk will be marked as a feasible solution, otherwise, it will be an infeasible solution. After multiple iterations, the infeasible solution will be gradually eliminated through the selection step; (3) Each solution in the initial population calls the CPLEX solver of the lower-level optimization algorithm to solve the production scheduling optimization model, obtain the optimal lower-level solution corresponding to each upper-level solution, that is, the production scheduling solution, and calculate 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 the competitive selection method, and then a set of solutions is selected from the mating pool. The offspring is 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, that is, the production sorting scheme, and 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: Selecting better individuals from the initial population and the offspring population, that is, "promising" solutions to form the next generation population; (7) subjecting the next generation population to the above evolution, local search, and selection steps until the stopping condition is met; (8) For all the solutions obtained in the above steps, the best individual is selected, that is, the best solution among all the solutions obtained in the selection step, to obtain the optimal line balancing plan and production sequencing plan; The lower-level optimization model is solved by calling the CPLEX solver, which solves the corresponding lower-level optimal solution based on the input upper-level solution and outputs the corresponding optimal production sequencing plan.

6. The two-level optimization method for balancing and sequencing mixed-flow assembly lines considering human risk according to claim 5 is characterized by: The encoding vector contains an integer array, indicating the order of task allocation. <x1,x2,…,x i >, the decoding method is as follows: Step 1: Initialize the current task index to be assigned i=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 of assembly workstation k: WT k =0; Total working time of ordinary workers at assembly workstation k: WT1 mk = 0; Total working time of common workers at assembly workstation k: WT2 mk =0; Step 3: According to the order of task allocation, select task x at the i-th position in the order i ; Step 4: Determine the task x assigned to the current assembly workstation k i processing time; Step 5: If the WT of the current assembly workstation k k 、WT1 mk 、WT2 mk / ω does not exceed the cycle time, corresponding to the constraints in equations (6), (7), and (8), respectively. Then, task i is assigned to the current assembly workstation k. At the same time, i=i+1; otherwise, k=k+1, return to step 2; Step 6: Check if there are any tasks that have not been assigned; If it exists, return to step 3; Otherwise, jump to step 7; Step 7: Check whether the current solution satisfies the priority relationship between tasks and the human risk constraints; if so, the solution is feasible; otherwise, the solution is infeasible; Step 8: Calculate the number of assembly workstations for the current solution.

7. The two-level optimization method for balancing and sequencing mixed-flow assembly lines considering human risk according to claim 5 is characterized by: The selections are specifically: If any of the following conditions is met, solution seq1 is considered better than solution seq2, and seq1 is set as the better solution in the subsequent solution selection process: (1) seq1 is feasible and 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.

8. The two-level optimization method for balancing and sequencing mixed-flow assembly lines considering human risk according to claim 5, characterized in that: An iterative greedy algorithm is used to improve the optimal solution of all current populations, specifically: the optimal solution of the current population is used as the initial solution, and 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; During each reinsertion process, a new set of sequences is generated, and then the new sequence with the best target value, that is, the new sequence with the minimum upper-level target function value formula (3) and satisfying the constraints 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, that is, the line balancing solution is obtained. The obtained line balancing solution is brought into the lower-level algorithm to obtain the corresponding optimal production sequencing solution, and then its upper-level target function value DC is solved.

9. The two-level optimization method for balancing and sequencing mixed-flow assembly lines considering human risk according to claim 5, characterized in that: Index ER of the OCRA method using a concise index for assessing upper limb repetitive motion exposure k It indicates the human risk of workers assigned to the assembly workstation (k). The purpose is to assess whether the human risk of workers is at a low risk level. The OCRA index comprehensively evaluates the human risk factors of posture, strength, repetitiveness and additional risk. The specific formula is as follows: RF=OS×PM×FoM×RM×AdM (25) Among them, AF is the actual frequency, RF is the recommended frequency, Nt represents the number of actions performed in one cycle, OS represents a specific parameter with a value of 18; PM is the multiplication coefficient of posture; FoM is a force multiplication coefficient; RM is the multiplication coefficient of action repeatability; AdM is the multiplication coefficient of the additional factor. The human risk assessment criteria are: Among them, the human risk of each position selects the maximum human risk value among all assembly lines.

10. An optimization system using a double-layer optimization method for balancing and sequencing mixed-flow assembly lines taking into account human risk as described in any one of claims 1 to 9, characterized in that: include: An information data acquisition module is used to acquire information data of all operation tasks in the mixed-flow assembly line; A double-layer optimization mathematical model building module is used to build a double-layer optimization mathematical model module for a mixed-flow assembly line according to the production rhythm and constraints of the assembly line and the above-mentioned information data; wherein the upper-layer optimization model module is a line balance model module, which is used to determine the line balance plan, aiming to minimize the production line cost under the conditions of meeting the priority relationship between tasks and human risk constraints; The lower optimization model module is the production sequencing model module, whose goal is to develop the optimal production sequencing plan based on a given mixed-flow assembly line balancing plan, aiming to minimize the number of common workers required and the maximum number of assembly workstations that experience work overload in all periods; The double-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 a solution of the line balancing solution by solving the established upper-layer optimization model module through a hybrid optimization algorithm. The lower-level optimization algorithm module uses the CPLEX solver to solve the production order optimization model of all solutions obtained by the upper-level optimization algorithm, and obtains the optimal lower-level solution corresponding to each upper-level solution, that is, the production order scheme, and then solves the upper-level optimization model module to obtain the upper-level objective function value of each solution; The next generation population is formed by evolving, locally searching and selecting the initial population to obtain a better solution. The next generation population is used as a new initial population to perform the above-mentioned evolution, local search and selection steps until the stopping condition is met, and the optimal line balancing plan and production sequencing plan are output.

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