A production scheduling method

Abstract

The present invention discloses a production scheduling method. The present invention takes into account two factors, namely the personnel interaction learning effect and the interruptibility of processing, and combines a heuristic rule to design an improved elite genetic algorithm, aiming to obtain an optimal single-workgroup task scheduling scheme, so as to achieve the effective utilization of workers with different skill levels within the workgroup and the optimal scheduling goal. Compared with traditional models and methods, the method of the present invention meets the basic requirements of the actual production situation and can realize the scientific allocation of tasks in a single workgroup.

Description

Technical Field

[0001] The present invention belongs to the technical field of production scheduling, and particularly relates to a production scheduling method. Background Art

[0002] The single workgroup production scheduling problem refers to a scheduling problem with a single workgroup unit composed of multiple workers, which includes how to reasonably arrange the task processing order under a determined personnel structure and reasonably allocate workers to each task to improve the processing efficiency of the entire workgroup. In China, in the fields of high-end equipment manufacturing, software project development, computer resource management, etc., due to factors such as low technical maturity of newly developed projects, large workloads, complex production processes and processing technologies, or limited computing resources and high information exchange frequencies, a task scheduling mode with workgroups as units is widely adopted. Multi-person group processing leads to the generation of personnel interaction learning effects, and periodic breaks lead to interruptions in the personnel processing process. Scheduling research at the workgroup level will effectively solve the problem of low efficiency in fields such as high-end equipment manufacturing scheduling, software project scheduling, and computer resource management.

[0003] Many researchers have carried out research on workgroup-related scheduling problems, from the Seru concept and structure, to the allocation of multi-skilled workers in workgroup production units, and then to labor-intensive production units in recent years. However, there are few studies considering the scheduling constraints and characteristics of single workgroup personnel. There are many models and methods in the research on the scheduling problem of learning effects, but the influence of individuals on the overall learning effect is often ignored. There is an interactive learning effect among team members when the workgroup completes work tasks. Considering factors such as workgroup size and personnel structure can better allocate resources to achieve optimal scheduling. Summary of the Invention

[0004] Aiming at the deficiencies of the above-mentioned existing technologies, the purpose of the present invention is to provide a production scheduling method to solve the problem of inaccurate scheduling schemes caused by the lack of consideration of learning effects and personnel processing interruptions in the existing technology for single workgroup production scheduling.

[0005] To achieve the above purpose, the technical solution provided by the present invention is: a production scheduling method, including the following steps:

[0006] 1) Investigate the production scheduling scenario. First, obtain the basic information of workers and the basic information of tasks, then divide the workgroup personnel into grades, and initialize and generate a problem object;

[0007] 2) Define problem parameters and variables, and establish a mathematical model with minimizing the makespan (minC max ) as the scheduling objective;

[0008] 3) Implement the mathematical model using the elite genetic algorithm, encode the task processing sequence, generate an initial population of scheduling plans, and randomly generate an initial population with N individuals within the range specified by the encoding;

[0009] 4) Calculate the fitness by personnel allocation and identification of personnel processing breakpoints, and retain the individual with the best fitness value;

[0010] 5) Generate a new population, select, cross, and mutate to generate an offspring population through elite retention, and calculate the fitness values of the individuals in the offspring population;

[0011] 6) Update the elite individuals. If the best individual in the offspring is better than the elite individual, it proves that the offspring population has completed evolution. At this time, replace the worst individual in the offspring with the elite individual of the parent generation, and the best individual in the offspring becomes the new elite individual;

[0012] 7) If the number of genetic generations is greater than the initial number of evolutionary generations, terminate the iteration, exit the optimization, and output the elite individuals and scheduling information; otherwise, continue to execute step 4).

[0013] Further, the parameters and variables in step 2) specifically include: a group of workers M process a group of workpieces J, h represents the worker number, h = 1, 2, ……, l, k represents the workpiece number, k = 1, 2, ……, n, highly skilled workers have a learning rate α h , h = 1, 2, ……, m H , low-skilled workers have a learning rate β h , h = m H + 1, m H + 2, ……, l; workpiece J k Basic required number of processing personnel JM k , [P k is the average total man-hours, P k is the actual processing time, is the complete processing time considering the learning effect at any time, S k is the start processing time, C k is the completion time, is the number of allocated high-level workers, is the number of allocated low-level workers, a eh , b eh is the e-th start interruption time and the e-th end interruption time of worker M h , e = 1, 2, …, θ h , t represents the moment of change in the state of production personnel, F represents the rank after rearranging the interruption times, a [F] represents all a eh , b eh of the workers producing the workpiece arranged in non-decreasing order, a[0] is the starting machining time of the workpiece, a [f] is the moment when the last personnel status change occurs before the workpiece is completed. The constructed single-workgroup scheduling model has the following three decision variables:

[0014] Worker M h The total time for machining workpiece J k where

[0015] f = max{e|a eh ·[y kh ≤ C k};

[0016]

[0017]

[0018] Furthermore, the mathematical model established in step 2) is as follows:

[0019] The single-workgroup scheduling mixed-integer programming model is as follows:

[0020] (21) Objective function: Minimize the makespan

[0021] min C max

[0022] (22) Constraint 1: Restrict each worker to machining only one workpiece at the same time:

[0023]

[0024] (23) Constraint 2: Restrict worker M h to be assigned to workpiece J k , and this worker cannot be assigned other workpieces before workpiece J k is completed:

[0025]

[0026] (24) Constraint 3: Restrict each workpiece to be machined only once, and the number of machining workers is equal to the number of workpiece demand workers:

[0027]

[0028] (25) Constraint 4: Restrict the number of high-level workers in the machining state of workpiece J k at the same time t not to exceed the total number of assigned high-level workers:

[0029]

[0030] (26) Constraint 5: Restrict workpiece J k The number of low-level workers in the processing state at the same moment t cannot exceed the total number of allocated low-level workers:

[0031]

[0032] (27) Constraint 6: Define the calculation formula of the processing time P of workpiece J k Processing time P k of:

[0033]

[0034] (28) Constraint 7: Restrict the completion time to be equal to the sum of the start time and the actual processing time of the workpiece:

[0035] C k = S k + P k , k = 1, 2, …, n

[0036] (29) Constraint 8: Restrict the total time for a worker to process workpiece J k not to be greater than the actual processing time of the workpiece:

[0037] x kh ≤ P k , k = 1, 2, …, n; h = 1, 2, …, l

[0038] (210) Constraint 9: Restrict the start processing time of workpiece J k to be greater than the completion time of the previous workpiece J k-1 :

[0039] C k-1 ≤ S k , k = 1, 2, …, n

[0040] (211) Constraint 10: When the same worker is assigned to process other workpieces, the start time for the worker to process this workpiece is not less than the end time of the original workpiece:

[0041] S i [y ih + P i [y ih + P i+1 [y i+1,h + … + P j [y j-1,h ≤ S j [y jh , i = 1, 2, …, n; j = 1, 2, …, n; i < j; h = 1, 2, …, l

[0042] Compared with the traditional scheduling model considering the learning effect, the model has the following characteristics. First, the personnel interaction learning effect characterization model proposed based on Jiang's model of representing the standard processing time and the learning effect of workers is a non-linear function of the basic man-hours [P h when worker M processes workpiece J independently k , and Constraints 6 - 10 are non-linear constraints; Second, due to the existence of the interruption interval, calculating the processing time P kh defined based on Constraint 6 requires multiple judgments and iterations to find the moment a k when the last personnel status change occurs before the workpiece is completed, where f = max{e|a [f] ·[y eh ≤ C kh}; Finally, the premise of multi-person group processing and the interruptibility of personnel processing in the present invention determines that personnel allocation needs to be carried out first to calculate the workpiece processing time, adding decision variables x k and y kh for identifying the workpiece processing information at the interruption point. Both decision variables are related to the processing personnel actually assigned to the workpiece. The number of x kht is equal to max{e|a kh ·[y eh ≤ C kh}, that is, f, and the number of y k is equal to kht The total number of constraints is equal to: Therefore, this mathematical model is not easy to solve, and the present invention proposes an e-GA solution method based on heuristic rules.

[0043] Furthermore, the encoding method in step 3) is as follows: permutation encoding is adopted, and the workpieces to be processed are encoded in sequence. All workpieces to be processed are arranged in a column as a chromosome, and each workpiece corresponds to a gene on the chromosome.

[0044] Furthermore, the process of calculating the individual fitness by personnel allocation and identifying the personnel processing interruption point in step 4) is as follows:

[0045] (41) Update the total learning duration of the workgroup personnel and group the workers according to the learning level;

[0046] (42) Determine k and according to the basic required number of personnel JM for the workpiece, and calculate the ideal processing time when there is no interruption in personnel processing;

[0047]

[0048] (43) Judge a eh [y​kh or b eh [y kh and relationship, where

[0049]

[0050] (44) Find the interrupted workers according to the interruption interval, update the set of interruption points, recalculate the ideal processing

[0051] time, and repeat step (42);

[0052] (45) When count = f = max{e|a eh ·[y kh ≤ C k} is satisfied, update the processing time of the workers and update the list of interruption intervals.

[0053] (46) During the actual processing of the workpiece with the starting processing time a [0] = S k = C k-1 of the workpiece, a [0] is equal to the starting processing time of workpiece J k and is equal to the ending processing time of the (k - 1)-th workpiece. a [f] represents the moment of the last personnel status change before the workpiece is completed. It can be deduced that the total processing time of this workpiece is

[0054] (47) Repeat steps (41) - (46) to calculate the completion time of the workpieces in each individual solution, and then obtain the individual fitness;

[0055] In step (44) Calculate based on the standard processing time and the learning effect characterization model of the workers as the basis, and deduce the complete processing time of workpiece J k at any time considering the learning effect:

[0056]

[0057] Furthermore, step 5) specifically includes: performing a selection operation using the elitist selection strategy method; performing a crossover operation using the partially matched crossover method; performing a mutation operation using the inverse mutation method

[0058] Furthermore, the selection operation in step 5) is as follows:

[0059] (51) Assume that by the t-th generation, a(t) in the population is the optimal individual;

[0060] (52) Let A(t + 1) be the new generation population, and select the optimal individual in A(t + 1).

[0061] (53) If there is no individual in A(t + 1) that is superior to a(t), then a(t) is added to A(t + 1) as the (n + 1)-th individual (n is the population size).

[0062] Furthermore, the crossover operation in step 5) is as follows:

[0063] (54) Determine the initial parent population.

[0064] (55) Randomly generate a number less than the length of the parent chromosome.

[0065] (56) Swap the segments corresponding to this length and position in the chromosome.

[0066] (57) Keep the swapped segments unchanged, find duplicate values in the unswapped segments, and then replace the elements at the corresponding positions in the part of the parent that has been swapped away.

[0067] Furthermore, the mutation operation in step 5) is as follows: Randomly select two points on the parent chromosome coding as reverse points, and reverse the order of the genes between the two reverse points to obtain the mutated chromosome.

[0068] The beneficial effects of the present invention are as follows: The present invention takes into account the learning effect phenomenon and the processing interruptibility phenomenon existing in actual production. The invention proposes a single workgroup scheduling problem considering the personnel interaction learning effect, constructs a single workgroup scheduling model considering the personnel interaction learning effect and processing interruptibility for this problem, gives a solution method of the e-GA model based on heuristic rules, and finally demonstrates the effectiveness of the constructed model and algorithm through simulation of examples of different scales. First, it analyzes and characterizes the personnel interaction learning effect in the workgroup unit, takes into account the processing interruptibility phenomenon in actual problems, and realizes the reduction of errors in relevant data such as working hours of the single workgroup scheduling problem and the optimal matching of key resources in the workgroup; secondly, it constructs a single workgroup scheduling model and algorithm considering the personnel interaction learning effect and processing interruptibility, realizes the organic combination of personnel allocation and workpiece scheduling in the single workgroup, improves the processing efficiency of the production system with the workgroup as the processing unit, and makes up for the problem of ignoring the difference in learning levels between people by treating the workgroup as a whole in the past; finally, it uses python to implement the example simulation based on e-GA, analyzes in detail the influence of the personnel structure of the workgroup on the scheduling results, and provides guidance for the determination of the replacement ratio in actual production. Description of the Drawings

[0069] Figure 1 It is a flowchart of the method of the present invention.

[0070] Figure 2 Schematic diagram for calculating the man-hour when the machining of workpiece k is interrupted by personnel during the task processing in a certain factory.

[0071] Figure 3 Gantt chart of the optimal scheduling under different personnel structures during the task processing in a certain factory after the calculation by this method.

[0072] Figure 4 Iteration diagram of the calculation results when the personnel ratio is 0:10 during the task processing in a certain factory after the calculation by this method.

[0073] Figure 5 Iteration diagram of the calculation results when the personnel ratio is 2:8 during the task processing in a certain factory after the calculation by this method.

[0074] Figure 6 Iteration diagram of the calculation results when the personnel ratio is 5:5 during the task processing in a certain factory after the calculation by this method.

[0075] Figure 7 Iteration diagram of the calculation results when the personnel ratio is 8:2 during the task processing in a certain factory after the calculation by this method.

[0076] Figure 8 Iteration diagram of the calculation results when the personnel ratio is 10:0 during the task processing in a certain factory after the calculation by this method. Detailed implementation manner

[0077] For the convenience of understanding by those skilled in the art, the present invention will be further described below in conjunction with examples and schematic diagrams. The content mentioned in the implementation manner does not limit the present invention.

[0078] Refer to Figure 1 As shown, a single-workgroup production scheduling method considering personnel interactive learning effect and machining interruptibility of the present invention is described by constructing an example of the task processing in a certain factory, including the following steps:

[0079] (1) Investigate the production background of the enterprise. The task processing in a certain factory uses a 10-person workgroup as the scheduling unit. The basic man-hours for workers to independently machine workpieces are randomly distributed in [30, 80]. The learning rate of high-level workers is 30% (learning factor = -0.3), and the learning rate of low-level workers is 10% (learning factor = -0.1). Each worker has 3 interruption intervals, which are distributed at a fixed step of 0.5 within [0, 41]. Machine parts numbered 1 - 10, and there are currently 10 workpieces J of the same part family k , JM k and [P k as shown in Table 1.

[0080] Table 1 Basic required number of personnel and basic man-hours of workpieces

[0081]

[0082] (2) Define the problem parameters and variables, and establish a mathematical model with minimizing the makespan (minC max ) as the scheduling objective. The parameters and variables in the corresponding example specifically include: A group of workers M processes a group of workpieces J. h represents the worker number, h = 1, 2, ……, l, k represents the workpiece number, k = 1, 2, ……, n. Highly skilled workers have a learning rate of α h , h = 1, 2, ……, m H , and low - skilled workers have a learning rate of β h , h = m H + 1, m H + 2, ……, l; The workpiece J k The basic required number of processing workers JM k , [P k is the average total man - hours, P k is the actual processing time, is the complete processing time considering the learning effect at any time, S k is the start processing time, C k is the completion time, is the number of allocated high - level workers, is the number of allocated low - level workers, a eh , b eh are the e - th start interruption time and the e - th end interruption time of the worker M h , e = 1, 2, …, θ h , t represents the moment of change in the state of production personnel, F represents the rank after rearranging the interruption times, a [F] represents a eh , b eh of all workers processing the workpiece arranged in non - decreasing order, a [0] is the start processing time of the workpiece, a [f] is the moment of the last change in the state of personnel before the completion of the workpiece. In the constructed single - workgroup scheduling model, there are the following three decision variables:

[0083] The total time for the worker M h to process the workpiece J k , where

[0084] f = max{e|a eh ·[y kh ≤ C k};

[0085]

[0086]

[0087] The single-workgroup scheduling mixed-integer programming model is as follows:

[0088] (21) Objective function: Minimize the makespan

[0089] min C max

[0090] (22) Constraint 1: Restrict that each worker can only process one workpiece at the same time:

[0091]

[0092] (23) Constraint 2: Restrict worker M h from being assigned to other workpieces before workpiece J k is completed: k

[0093]

[0094] (24) Constraint 3: Restrict that each workpiece can only be processed once, and the number of processing workers is equal to the number of workpiece demand workers:

[0095]

[0096] (25) Constraint 4: Restrict that the number of high-level workers in the processing state of workpiece J k at the same time t cannot exceed the total number of high-level workers assigned:

[0097]

[0098] (26) Constraint 5: Restrict that the number of low-level workers in the processing state of workpiece J k at the same time t cannot exceed the total number of low-level workers assigned:

[0099]

[0100] (27) Constraint 6: Define the calculation formula for the processing time P k of workpiece J k :

[0101]

[0102] (28) Constraint 7: Restrict that the completion time is equal to the sum of the start time and the actual processing time of the workpiece:

[0103] C k = S k + P k , k = 1, 2, …, n​

[0104] (29) Constraint 8: Restrict the total time for worker to process workpiece J k not to exceed the actual processing time of the workpiece:

[0105] x kh ≤P k , k = 1, 2, …, n; h = 1, 2, …, l

[0106] (210) Constraint 9: Restrict the start processing time of workpiece J k to be greater than the completion time of the previous workpiece J k-1 :

[0107] C k-1 ≤S k , k = 1, 2, …, n

[0108] (211) Constraint 10: When restricting the same worker to be assigned to other workpieces for processing, the start time for the worker to process this

[0109] workpiece is not less than the end time of the original workpiece:

[0110] S i [y ih +P i [y ih +P i+1 [y i+1,h +…+P j [y j-1,h ≤S j [y jh , i = 1, 2, …, n; j = 1, 2, …, n; i < j; h = 1, 2, …, l

[0111] (3) Number the natural numbers for the workpiece processing sequence. According to the precedence relationship of workpiece processing, arrange the processes in a column as a chromosome. Taking the chromosome [10, 2, 1, 6, 9, 5, 7, 3, 4, 8] as an example, this chromosome indicates that workpiece 10 is processed first, workpiece 2 is processed after workpiece 1 is completed, workpiece 1 is processed after workpiece 2 is completed…, and workpiece 8 is processed last.

[0112] (31) Generate chromosomes according to the above rules to reach the pre-set population size and complete the initialization.

[0113] (32) Calculate the fitness through personnel allocation and personnel processing breakpoint identification: Taking a certain chromosome [1, 2, 10, 6, 9, 3, 7, 5, 4, 8] in the initial population as an example, first process workpiece 1, and calculate the fitness value according to the following steps:

[0114] a) Update the total learning duration of the personnel, and group the processing workers required for workpiece 1 according to the learning level;

[0115] b) According to the basic required number of personnel JM for workpiece 1 k Determine and and calculate the ideal processing time when personnel processing does not interrupt;

[0116] c) Judge a eh [y kh or b eh [y kh and the relationship of, where

[0117] d) Find the interrupted processing workers according to the interruption interval, update the set of interruption points, recalculate the ideal processing time, and repeat step (42);

[0118] e) When count = f = max{e|a eh ·[y kh ≤ C k}, update the processing time of the workers and update the list of interruption intervals.

[0119] f) During the actual processing of the workpiece with the start processing time a [0] = S k = C k-1 , a [0] is equal to the start processing time of workpiece J k , is equal to the end processing time of the (k - 1)-th workpiece, a [f] represents the moment of the last personnel status change before the workpiece is completed, and it can be derived from Figure 2 that the total processing time of this workpiece is

[0120] g) Repeat steps (41)--(46) to calculate the completion time of the workpiece in each individual solution, and then obtain the individual fitness;

[0121] (33) Selection: The operation of selecting population individuals according to the elite retention strategy is as follows:

[0122] a) Assume that by the t-th generation, a(t) in the population is the optimal individual;

[0123] b) Assume that A(t + 1) is the new generation population, and select the optimal individual in A(t + 1);

[0124] c) If there is no individual in A(t + 1) that is better than a(t), then a(t) is added to A(t + 1) as the (n + 1)-th individual (n is the population size).

[0125] (34) Crossover: The operation of performing crossover on the population individuals according to the partial matching crossover method is as follows:

[0126] a) Determine the initial parent populations, Parent 1 and Parent 2, as shown in Table 2 and Table 3, as follows:

[0127] Table 2

[0128]

[0129] Table 3

[0130]

[0131] b) If a number randomly generated is less than the length of the parent chromosome and is 4, the two parents exchange the gene order at the 3rd to 6th gene positions with each other;

[0132] c) Exchange the segments corresponding to this length and position in the chromosomes. The order of the genes in the gene segment [1, 6, 9, 5] in Parent 1 in Parent 2 is [6, 5, 7, 2]. Replace the original gene segment in Parent 1 with this. The un-revised Offspring 1 is shown in Table 4, as follows:

[0133] Table 4

[0134]

[0135] Similarly, recombine the gene segment [6, 5, 7, 2] in Parent 2 according to the order in Parent 1 to obtain the un-revised Offspring 2, as shown in Table 5, as follows:

[0136] Table 5

[0137]

[0138] d) Revise the duplicate elements. In the un-revised Offspring 1, both [7, 2] have duplicate elements with the swapped [6, 5, 7, 2]. Keep the swapped segment unchanged, find the duplicate values in the non-swapped segment, and then find the elements at the corresponding positions in the part swapped away from the parent to replace them to obtain Offspring 1, as shown in Table 6, as follows:

[0139] Table 6

[0140]

[0141] Similarly, perform operations on the un-revised Offspring 2 to obtain Offspring 2, as shown in Table 7, as follows:

[0142] Table 7

[0143]

[0144] The parent will be replaced only when the fitness of the offspring is higher than that of the parent; otherwise, crossover will be performed again.

[0145] (35) Mutation: Randomly select two points on the chromosome encoding of the parent as reversal points, and reverse the genes between the two reversal points to obtain the mutated chromosome. Replace the original operation sequence according to the mutation probability. If the fitness of the new individual is higher than that of the original individual, it will be replaced; otherwise, mutation will be performed again.

[0146] (36) Termination criterion: When the maximum number of iterations of the genetic algorithm is reached, the algorithm ends, and the workpiece scheduling plan and personnel allocation plan with the highest current fitness value are output.

[0147] It should be noted here that in this embodiment, the algorithm solving program is written in Python. In the scenario of 10 workpieces and 10 workers, 11 sets of examples with different personnel structures are set, and the personnel ratios are 0:10, 1:9, 2:8, 3:7, 4:6, 5:5, 6:4, 7:3, 8:2, 9:1, 10:0 respectively. To improve the solving efficiency, the e-GA algorithm (population size = 20; number of iterations = 200; XOVR = 0.9; Pm = 0.2) is designed for solving. All 11 sets of examples converge within the set number of iterations. The processing sequence and processing time of each optimal scheduling plan are as Figure 3 shown in the figure. In the figure, the proportion of high-level workers in scheme1 to scheme11 gradually increases, and the makespan of the optimal plan gradually shortens as the proportion of high-level workers increases. Analyze the number of iterations for the algorithm to obtain the optimal solution under the personnel ratios of 0:10, 2:8, 5:5, 8:2, 10:0. From Figures 4-8 it can be seen that the examples under the above different personnel structures can all converge within 100 generations, indicating that the method of the present invention can achieve convergence relatively quickly and the solving results are stable when solving small and medium-sized problems, and can be used in the production scheduling problems of actual enterprises.

[0148] In addition, the embodiment of the present invention also provides a computer-readable storage medium. Among them, the computer-readable storage medium can store a program, and when the program is executed, it includes some or all of the steps of any production scheduling method recorded in the above method embodiment.

[0149] In addition, in each embodiment of the present invention, each functional unit can be integrated in a processing unit, or each unit can exist physically alone, or two or more units can be integrated in one unit. The above integrated unit can be implemented in the form of hardware or in the form of a software functional unit.

[0150] When the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable memory. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a memory and includes several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned memory includes: USB flash drives, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), mobile hard disks, magnetic disks, or optical discs, etc., which are various media that can store program codes.

[0151] Those of ordinary skill in the art can understand that all or part of the steps in the various methods of the above embodiments can be completed by instructing relevant hardware through a program. The program can be stored in a computer-readable memory, and the memory can include: flash drives, read-only memories (English: Read-Only Memory, abbreviated: ROM), random access memories (English: Random Access Memory, abbreviated: RAM), magnetic disks, or optical discs, etc.

[0152] The above has described an exemplary flowchart of a method for implementing a service chain according to an embodiment of the present invention with reference to the accompanying drawings. It should be noted that a large number of details included in the above description are only exemplary descriptions of the present invention, rather than limitations on the present invention. In other embodiments of the present invention, the method may have more, fewer, or different steps, and the order, inclusion, function, etc. relationships between the steps may be different from those described and illustrated.

Claims

1. A production scheduling method, characterized in that , it includes the following steps: 1) Obtain the basic information of workers and the basic information of tasks, then classify the personnel in the work group, initialize and generate a problem object; 2) Define problem parameters and variables, and establish a mathematical model with minimizing the makespan as the scheduling objective; 3) Use the elitist genetic algorithm to implement the mathematical model, encode the task processing order, generate an initial population of scheduling schemes, and randomly generate an initial population with N individuals within the range specified by the encoding; 4) Calculate the individual fitness through personnel allocation and identification of personnel processing breakpoints, and retain the individual with the highest fitness value; 5) Generate a new population, generate offspring populations through elitist retention for selection, crossover, and mutation, and calculate the fitness values of the individuals in the offspring populations; 6) Update the elite individuals. If the optimal individual in the offspring is better than the elite individual, it proves that the offspring population has completed evolution. At this time, replace the worst individual in the offspring with the elite individual of the parent generation, and the optimal individual in the offspring becomes the new elite individual; 7) If the number of genetic generations is greater than the initial number of evolutionary generations, the iteration terminates, the optimization is exited, and the elite individuals and scheduling information are output; otherwise, continue to execute step 4); The parameters and variables in step 2) specifically include: A group of workers M process a group of workpieces J. h represents the worker number, h = 1, 2, ……, l, and k represents the workpiece number, k = 1, 2, ……, n. Highly skilled workers have a learning rate of α h , h = 1, 2, ……, m H , and low - skilled workers have a learning rate of β h , h = m H + 1, m H + 2, ……, l; for workpiece J k The basic required number of processing workers JM k , [P k is the average total man - hours, P k is the actual processing time, is the complete processing time considering the learning effect at any time, S k is the start processing time, C k is the completion time, is the number of highly skilled workers assigned, is the number of low - skilled workers assigned, a eh , b eh are the e - th start interruption time and the e - th end interruption time of worker M h , e = 1, 2, …, θ h , t represents the moment of change in the state of production personnel, F represents the rank after re - arranging the interruption times, a [F] represents all a eh , b eh of the workers processing the workpiece arranged in non - decreasing order, a [0] is the start processing time of the workpiece, a [f] is the moment of the last change in the state of personnel before the completion of the workpiece; In the constructed single - work - group scheduling model, there are the following three decision variables: Worker M h Process workpiece J k Total time, where f = max{e|a eh ·[y kh ≤ C k}; The mathematical model established in step 2) is: The single work group scheduling mixed integer programming model is as follows: (21) Objective function: Minimize the makespan min C max (22) Constraint 1: Limit that each worker can only process one workpiece at the same time: (23) Constraint 2: Restrict worker M h from being assigned to workpiece J k until workpiece J k is completed, and this worker cannot be assigned other workpieces: (24) Constraint 3: Limit that each workpiece can only be processed once, and the number of processing personnel is equal to the number of workpiece requirements: (25) Constraint 4: Restrict workpiece J k The number of high-level workers in the machining state at the same moment t cannot exceed the total number of allocated high-level workers: (26) Constraint 5: Restrict workpiece J k The number of low-level workers in the machining state at the same moment t cannot exceed the total number of allocated low-level workers: (27) Constraint 6: Define workpiece J k The calculation formula of the processing time P k is as follows: (28) Constraint 7: Limit that the completion time is equal to the sum of the start time and the actual processing time of the workpiece: C k = S k + P k , k = 1, 2, …, n (29) Constraint 8: Restrict the total time for the worker to process workpiece J k to be no greater than the actual processing time of the workpiece: x kh ≤P k , k = 1, 2, …, n; h = 1, 2, …, l (210) Constraint 9: Restrict workpiece J k The start processing time is greater than the previous workpiece J k-1 Completion time: C k-1 ≤S k , k = 1, 2, …, n (211) Constraint 10: Limit that when the same worker is assigned to process other workpieces, the start time of the worker processing this workpiece is not less than the end time of the original workpiece: S i [y ih +P i [y ih +P i+1 [y i+1,h +…+P j [y j-1,h ≤S j [y jh [y jh ], i = 1, 2, …, n; j = 1, 2, …, n; i < j; h = 1, 2, …, l; The process of calculating the individual fitness through personnel allocation and identification of personnel processing breakpoints in step 4) is as follows: (41) Update the total learning duration of the personnel in the work group, and group the workers according to the learning level; (42) Determine the ideal processing time when the processing of personnel does not interrupt according to the basic required number of personnel JM for the workpiece k Determine and and calculate the ideal processing time when the processing of personnel does not interrupt; (43) Determine a eh [y kh or b eh [y kh and the relationship of, where (44) Find the workers with interrupted processing according to the interruption interval, update the set of breakpoints, recalculate the ideal processing time, and repeat step (42); (45) count = f = max{e|a eh ·[y kh ≤ C k}, update the processing times of all workers and update the list of interrupted intervals; (46) At the start of the processing time a [0] = S k = C k-1 During the actual processing of the workpiece, a [0] is equal to the start processing time of the workpiece J k and is equal to the end processing time of the (k - 1)-th workpiece. a [f] represents the moment of the last change in the personnel status before the workpiece is completed. It can be deduced that the total processing time of this workpiece is (47) Repeat steps (41)--step (46), calculate the completion time of the workpieces in each individual plan, and then obtain the individual fitness; In step (44) Based on the calculation of the characterization model based on the standard processing time and the learning effect of workers As the basis, the complete processing time of workpiece J considering the learning effect at any time is derived k is obtained as follows:

2. The production scheduling method according to claim 1, characterized in that the encoding method in step 3) is: Adopt permutation encoding to encode all workpieces to be processed in the processing order. All workpieces to be processed are arranged in a column as a chromosome, and each workpiece corresponds to a gene on the chromosome.

3. The production scheduling method according to claim 1, characterized in that step 5) specifically includes: Using the elitist selection strategy method for the selection operation; Using the partially mapped crossover method for the crossover operation; Using the inversion mutation method for the mutation operation.

4. The production scheduling method according to claim 3, characterized in that the selection operation in step 5) is as follows: (51) Assume that by the t-th generation, a(t) in the population is the optimal individual; (52) Let A(t + 1) be the new generation population, and select the optimal individual in A(t + 1). (53) If there is no individual in A(t + 1) that is better than a(t), then a(t) is added to A(t + 1) as the (n + 1)-th individual, where n is the population size.

5. The production scheduling method according to claim 1, characterized in that the crossover operation in step 5) is as follows: (54) Determine the initial parent population; (55) Randomly generate a number less than the length of the parent chromosome; (56) Swap the segments corresponding to this length and position in the chromosome; (57) Keep the swapped segments unchanged, find duplicate values in the non-swapped segments, and then replace the elements at the corresponding positions in the part of the parent that was swapped away.

6. The production scheduling method according to claim 1, characterized in that the mutation operation in step 5) is as follows: Randomly select two points on the parent chromosome coding as the reversal points, and reverse the genes between the two reversal points to obtain the mutated chromosome.

7. A computer-readable storage medium storing a computer program, characterized in that when the computer program is executed by a processor, it implements the steps of a production scheduling method according to any one of claims 1 to 6.

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