Parallel flow-shop batch scheduling method considering preventive maintenance of equipment

Abstract

The application discloses a parallel flow shop job shop scheduling method considering equipment preventive maintenance, relates to a parallel flow shop scheduling integrated optimization model and a solving method thereof. The application takes less system downtime, relatively high equipment utilization and relatively small influence of equipment unexpected failure as the target; by considering the characteristics of the serial flow line "one-stop-all-stop" in the parallel flow shop scheduling process, taking the minimization of the maximum completion time as the objective function, adopting the trial method and the flexible batch division method to solve the batch quantity of the workpiece, and designing the improved discrete fruit fly algorithm to solve the workpiece scheduling sequence and the maintenance plan, the system downtime can be reduced, the equipment utilization is improved, and a feasible and efficient solution is provided for the stability and efficiency improvement of the production system.

Description

Technical Field

[0001] This invention relates to the field of integrated preventive maintenance and batch scheduling in parallel production lines, specifically an integrated optimization method that simultaneously considers preventive maintenance and intelligent batch scheduling in the production scheduling of parallel production lines. Technical Background

[0002] In parallel production line scheduling, preventative maintenance is necessary to prevent excessive equipment deterioration. However, overly frequent preventative maintenance can disrupt smooth production scheduling. Furthermore, actual production involves a wide variety of workpieces with varying demand volumes. Therefore, a reasonable batching strategy must be adopted to appropriately divide the workpieces into batches. Otherwise, uneven workloads on the production line, excessively long production cycles, and significantly reduced production efficiency will result. Thus, considering preventative maintenance and workpiece batching is crucial in production scheduling.

[0003] Current research on the integrated optimization of preventive maintenance and production scheduling in parallel assembly lines fails to consider the "one stop, all stop" characteristic of serial assembly lines, neglecting to assess the maintenance of other equipment when one piece of equipment is shut down for maintenance, thus saving maintenance time. Furthermore, existing research on integrated optimization of scheduling in parallel assembly lines does not consider batching of workpieces, relying solely on workpiece sequence-based encoding, ignoring batch coding. In addition, many existing parallel assembly line studies use metaheuristic algorithms for solving problems, but these algorithms are prone to getting trapped in local optima and are unstable. Therefore, to address the shortcomings of existing models and algorithms for preventive maintenance and batch scheduling in parallel assembly lines, this paper proposes an integrated optimization method for preventive maintenance and batch scheduling in parallel assembly lines based on an improved hybrid discrete fruit fly algorithm. Summary of the Invention

[0004] To address the shortcomings of existing methods for joint decision-making on preventive maintenance and batch scheduling in parallel production lines, this invention proposes a batch scheduling method for parallel production lines that considers preventive maintenance. This method addresses the problems of existing methods neglecting the serial nature of production lines, unreasonable encoding methods, and the tendency for algorithms to get trapped in local optima. It establishes a mathematical model with the optimization objective of minimizing the maximum completion time and combines it with an improved discrete fruit fly algorithm to perform joint decision-making on preventive maintenance and batch scheduling in parallel production lines.

[0005] The technical solution of this invention is a batch scheduling method for parallel production line workshops that considers preventive maintenance of equipment. The method includes the following steps:

[0006] Step 1: Based on the service life thresholds for preventive maintenance and opportunistic maintenance of equipment, establish an integrated optimization model for batch scheduling of parallel flow workshops that considers preventive maintenance of equipment;

[0007] Step 1.1: Determine the constraints of the integrated optimization model;

[0008] (1) The total number of workpieces remains unchanged after being divided into batches.

[0009]

[0010] Where, N ju Indicates the sub-batch size, A j B represents the required quantity of each type of workpiece. j The sub-batch number is represented by j, the workpiece number is represented by n, the number of workpiece types is represented by u, and the batch number is represented by u.

[0011] (2) All processing positions in f production lines must correspond one-to-one with each batch of workpieces, and the types of workpieces that f production lines can process...

[0012] The classes are restricted;

[0013]

[0014] Where m represents the number of devices, X k,l,j,u This indicates that sub-batch u of workpiece j is processed at position l on the production line k, β j,k This indicates whether workpiece j can be processed on production line k. The expression can be arbitrary, and k represents the pipeline number;

[0015] (3) The production line cannot begin processing the next batch of workpieces until the current batch has been processed.

[0016] S k,l ≥C k,l-1

[0017] Among them, S k,l C represents the start time of processing of the workpiece at processing position l in production line k. k,l-1 This indicates the completion time of the workpiece at processing position l-1 on the production line k.

[0018] (4) The relationship between the start time and finish time of the process for workpieces on the same production line;

[0019]

[0020] Where, C i,k,l The completion time S of the workpiece at position l on equipment i in production line k. i,k,l The start time of processing of the workpiece at processing position l on equipment i in production line k, P j.k (5) The workpiece must complete the current processing step before entering the next processing step on the next processing step.

[0021] Ci,k,l ≤S i+1,k,l

[0022] (6) Constraints on decision variables;

[0023] X k,l,j,u ∈{0,1}

[0024] (7) Equipment preventive maintenance service life threshold and opportunistic maintenance threshold constraints;

[0025] T o ≤T p

[0026] Among them, T o T represents the opportunity maintenance age threshold. p This indicates the service life threshold for preventive maintenance of equipment.

[0027] Step 1.2: Perform preventative maintenance modeling;

[0028] when Sometimes, Then, production line k undergoes its r-th maintenance shutdown, denoted as Z. rk =1,Z r,ki =1,t kr =t, perform opportunistic maintenance judgments on other equipment in the production line:

[0029]

[0030] Where t represents the time of the r-th preventive maintenance of the production line k. Z represents the service life of device i on production line k at time t. rk Z indicates that production line k is undergoing its r-th maintenance shutdown. r,ki This indicates whether equipment i needs maintenance when production line k undergoes its r-th maintenance shutdown.

[0031] Considering maintenance capacity limitations, a maximum of `limit` devices can be maintained simultaneously during a maintenance shutdown of a certain production line. Therefore, the maintenance time for the r-th maintenance shutdown of the production line is:

[0032]

[0033] Among them, T kr This represents the maintenance time for the r-th preventive maintenance of production line k, where n is the maintenance time. kr T represents the number of maintenance devices for the r-th preventive maintenance of production line k, and limit represents the limit on the number of devices that can be maintained simultaneously during a certain shutdown. m Indicates the average maintenance time of the equipment;

[0034] A virtual service life model is used to model the maintenance effect. After the r-th downtime maintenance of pipeline k, according to Z... r,ki After the r-th maintenance shutdown of pipeline k, t+T m Virtual service age of time device, T m Mean time between maintenance (MTBG) for equipment:

[0035] (1)Z r,ki =0, meaning that during the r-th maintenance of production line k, equipment E ki No maintenance required:

[0036] (2)Z r,ki =1, meaning that during the r-th maintenance of production line k, equipment E ki Perform maintenance:

[0037] Where, ε i The service life improvement factor describes the change in service life of equipment after imperfect maintenance; 0 < ε i <1 and is a constant;

[0038] Step 1.3: Update start and finish times:

[0039]

[0040] Step 1.4: Construct the objective function of the ensemble optimization model;

[0041] min(C max )

[0042] Among them, C max This represents minimizing the maximum completion time;

[0043] Step 2: Divide the workpieces into batches and lots based on workpiece type, workpiece quantity, and sub-batch limit;

[0044] Step 2.1: Calculate the optimal batch partitioning result using a trial-and-error method;

[0045] Step 2.1.1: Determine the upper limit of each type of workpiece sub-batch and randomly generate the quantity of each type of workpiece sub-batch;

[0046] Step 2.1.2: Use a trial-and-error method to determine the optimal batch size for each workpiece;

[0047] First, a type of workpiece is randomly selected and its sub-batch quantity is incremented by 1, where the sub-batch quantity must not exceed the sub-batch upper limit; then, based on the batch division result, the batch size of each sub-batch is divided using the flexible batch division method described in step 2.2, and the scheduling is performed using the method described in step 3. If the scheduling result is improved, the sub-batch quantity is increased; if it is not improved, the sub-batch quantity is decreased by 1 and the next type of workpiece is selected to determine the batch quantity.

[0048] Step 2.2: Calculate the batch size of each sub-batch based on the optimal batch partitioning result obtained in Step 2.1 using the flexible batch partitioning method;

[0049] Step 2.2.1: Based on the number of sub-batches B j Randomly generate sub-batch size N ju , let u=1;

[0050] Step 2.2.2: Determine N ju +B j -u≤A j If yes, proceed to step 2.2.3; otherwise, return to step 2.2.1.

[0051] Step 2.2.3: Let A j =A j -N ju , u = u + 1;

[0052] Step 2.2.4: Determine if u = B j If so, then let N ju =A j Otherwise, return to step 2.2.1;

[0053] Step 3: Use the improved discrete fruit fly algorithm to calculate the workpiece scheduling order and maintenance plan when the objective function is minimized;

[0054] Step 3.1: Encoding the solution;

[0055] Using a two-dimensional array π = {π1, π2, ... π} k …,π f} represents the allocation and processing sequence of workpieces in various production lines; where π1 records the batching results of each workpiece obtained in step 2, and each one-dimensional array π k It contains sub-batch workpieces assigned to this production line. The numbers in the array represent the workpiece sub-batch index numbers. The workpieces are processed sequentially in the order in the array. The workpiece processing sequence determines the equipment maintenance time based on the adopted equipment preventive maintenance strategy.

[0056] Step 3.2: Population initialization;

[0057] The initial population consists of n individuals, two of which are constructed using heuristic methods, and the remaining individuals are generated randomly.

[0058] Step 3.3: Population segmentation and olfactory search;

[0059] A population of n individuals is divided into 7 subpopulations, each with a relatively uniform number of individuals and employing different olfactory search strategies.

[0060] Step 3.4: Visual search;

[0061] Step 3.5: Merge all subpopulations;

[0062] Step 3.6: Determine if the current population has reached the maximum number of iterations. If yes, proceed to step 3.7; otherwise, proceed to step 3.3.

[0063] Step 3.7: Obtain the optimal workpiece scheduling sequence and maintenance time point.

[0064] Furthermore, the specific method of step 3.2 is as follows:

[0065] Step 3.2.1: Generate an individual using the following heuristic algorithm;

[0066] All workpiece batches are classified according to the different types of workpieces processed on the production line. The classified workpiece batches are first sorted in descending order of total processing time, and then workpiece batches are taken out from the sequence one by one and inserted into the optimal position in the processing sequence of the production line that can be processed, so as to minimize the completion time of the current production line.

[0067] Step 3.2.2: Generate an individual using the following heuristic algorithm;

[0068] All workpiece batches are classified according to the different types of workpieces processed on the production line. The classified workpiece batches are first sorted in descending order of total processing time. Then, workpiece batches are taken out from the sequence one by one and inserted into the optimal position in the processing sequence of the production line to minimize the completion time of the current production line. After each new workpiece batch is inserted, a workpiece batch is randomly removed from before or after the insertion position and inserted again into the optimal position in the current production line to reduce the completion time of the production line.

[0069] Step 3.2.3: Random generation method;

[0070] First, classify all workpiece batches according to the different types of workpieces processed on the production line; then, take the first n workpieces from each classified workpiece batch and insert them into n production lines in sequence, and insert the (n+1)th workpiece and subsequent workpieces into the production line with the shortest completion time.

[0071] Furthermore, the specific method of step 3.3 is as follows:

[0072] Step 3.3.1: Classify the production lines according to the different types of workpieces processed on the production line, and group the production lines that can process the same workpieces into one category;

[0073] Step 3.3.2: Perform pipeline insertion operation in subpopulation 1; randomly select two pipelines from the same type of pipeline. If the selected pipelines are the same, perform pipeline insertion operation; otherwise, perform pipeline insertion operation; randomly select an initial workpiece batch and a target workpiece batch. The initial workpiece will be moved to the back of the target workpiece.

[0074] Step 3.3.3: Perform a pipeline exchange operation in subpopulation 2. Randomly select two pipelines from the same type. If the selected pipelines are the same, perform an intra-pipeline exchange operation; otherwise, perform an inter-pipeline exchange operation. Randomly select two workpiece batches and exchange their positions.

[0075] Step 3.3.4: Perform a pipeline reversal operation within subpopulation 3, randomly select N positions from the same type of pipeline, and invert the batch of workpieces at these N positions;

[0076] Step 3.3.5: In subpopulations 4 to 7, combine insertion and swap, insertion and reverse, swap and reverse, and insertion, swap and reverse to achieve multi-level search operations.

[0077] Furthermore, the specific method of step 3.4 is as follows:

[0078] Step 3.4.1: Visually search for the best individual in each type of production line for each subpopulation, select a batch of workpieces from the production lines with longer completion times, and exchange it with a batch of workpieces from another production line of the same type.

[0079] Step 3.4.2: Repeat step 3.4.1. If the maximum completion time of the best individual cannot be improved after two consecutive swaps, then select the best individual from the swaps that have been performed to replace the worst individual in the subpopulation.

[0080] Building upon traditional fruit fly optimization algorithms, a multi-strategy initialization method effectively improves the overall quality and diversity of the population, thereby enhancing algorithm performance. Furthermore, by implementing different olfactory search strategies for each subpopulation, each subpopulation can cover a wider solution space, increasing the likelihood of finding the global optimum. In addition, different olfactory search strategies guide subpopulations to explore in diverse directions, increasing population diversity and reducing the risk of getting trapped in local optima. Improvements to the visual search strategy ensure the discovery of closer, better local solutions around the global optimum, further improving solution quality. Attached Figure Description

[0081] Figure 1 Flowchart for batch / group division;

[0082] Figure 2 To improve the flowchart of the discrete fruit fly algorithm;

[0083] Figure 3 This is a flowchart illustrating a specific implementation of the method of the present invention;

[0084] Figure 4 A Gantt chart showing the batch scheduling results for preventative maintenance as an example. Detailed Implementation

[0085] The embodiments of the present invention are described in detail below. Figure 3 This embodiment is implemented based on the technical solution of the present invention, and provides detailed implementation methods and specific operation processes. However, the scope of protection of the present invention is not limited to the following embodiment.

[0086] The implementation procedure can be mainly divided into the following steps:

[0087] Step 1: Based on the service life thresholds for preventive maintenance and opportunistic maintenance of equipment, establish an integrated optimization model for batch scheduling of parallel flow workshops that considers preventive maintenance of equipment;

[0088] Step 1.1: Determine the constraints of the integrated optimization model;

[0089] (1) The total number of workpieces remains unchanged after being divided into batches.

[0090]

[0091] (2) All processing positions in f production lines must correspond one-to-one with each batch of workpieces.

[0092]

[0093] The j-th type of workpiece, the u-th sub-batch, is at the l-th position on the k-th production line.

[0094] (3) The production line cannot begin processing the next batch of workpieces until the current batch has been processed.

[0095] S k,l ≥C k,l-1

[0096] (4) The relationship between the start time and finish time of the process for workpieces on the same production line;

[0097]

[0098] (5) Before a workpiece can enter the next machine for processing the next step, it must complete the process that the current machine is currently processing.

[0099] C i,k,l ≤S i+1,k,l

[0100] (6) Constraints on decision variables

[0101] X k,l,j,u ∈{0,1}

[0102] (7) Equipment preventive maintenance service life threshold and opportunistic maintenance threshold constraints

[0103] T o ≤T p

[0104] Among them, X k,l,j,u This indicates that sub-batch u of workpiece j is processed at position l on the production line k, S i,k,l C represents the start time of processing the workpiece at processing position l of equipment i in production line k. i,k,l This represents the completion time of the workpiece at position l in equipment i of the production line k.

[0105] Step 1.2: Perform preventative maintenance modeling;

[0106] Let the service life threshold for preventive maintenance of equipment be T. p The opportunity maintenance age threshold is T. o ,when Sometimes, Then, production line k undergoes its r-th maintenance shutdown, denoted as Z. rk =1,Z r,ki =1,t kr =t, perform opportunistic maintenance judgments on other equipment in the production line:

[0107]

[0108] Among them, t kr This indicates the time of the r-th preventive maintenance of production line k. This represents the service life of device i on production line k at time t.

[0109] Considering maintenance capacity limitations, a maximum of `limit` devices can be maintained simultaneously during a maintenance shutdown of a certain production line. Therefore, the maintenance time for the r-th maintenance shutdown of the production line is:

[0110]

[0111] Among them, T kr This represents the maintenance time for the r-th preventive maintenance of production line k, where n is the maintenance time. kr T represents the number of maintenance devices for the r-th preventive maintenance of production line k, and limit represents the limit on the number of devices that can be maintained simultaneously during a certain shutdown.m This indicates the average maintenance time for the equipment.

[0112] A virtual service life model is used to model the maintenance effect. After the r-th downtime maintenance of pipeline k, according to Z... r,ki After the r-th maintenance shutdown of pipeline k, t = t + T m Virtual service age of time device, T m Mean time between maintenance (MTBG) for equipment:

[0113] (1)Z r,ki =0, meaning that during the r-th maintenance of production line k, equipment E ki No maintenance required:

[0114] (2)Z r,ki =1, meaning that during the r-th maintenance of production line k, equipment E ki Perform maintenance:

[0115] Where, ε i The service life improvement factor describes the change in service life of equipment after imperfect maintenance; 0 < ε i <1 and is a constant value

[0116] Step 1.3: Update start and finish times:

[0117]

[0118] Step 1.4: Construct the objective function of the ensemble optimization model;

[0119] min(C max )

[0120] Step 2: Divide the workpieces into batches and lots based on workpiece type, workpiece quantity, and sub-batch limit. Figure 1 The following is relevant production data for a TV assembly workshop, where each production line has 12 machines, and the processing time is the processing time of the workpiece on a certain machine.

[0121] Table 1 Workpiece Machining Information

[0122] <![CDATA[j1]]> 9000 <![CDATA[k1-k2]]> 45s 20 <![CDATA[j2]]> 7000 <![CDATA[k1-k2]]> 45s 20 <![CDATA[j3]]> 8000 <![CDATA[k3-k7]]> 57s 20 <![CDATA[j4]]> 6000 <![CDATA[k3-k7]]> 57s 20 <![CDATA[j5]]> 7000 <![CDATA[k3-k7]]> 57s 20 <![CDATA[j6]]> 6000 <![CDATA[k3-k7]]> 57s 20 <![CDATA[j7]]> 2000 <![CDATA[k8-k9]]> 142s 20 <![CDATA[j8]]> 3000 <![CDATA[k8-k9]]> 142s 20

[0123] Step 2.1: Calculate the optimal batch partitioning result using a trial-and-error method;

[0124] Step 2.1.1: Determine the maximum limit of each type of workpiece sub-batch, and randomly generate the quantity of each type of workpiece sub-batch;

[0125] Step 2.1.2: Use a trial-and-error method to determine the optimal batch size for each workpiece;

[0126] First, a type of workpiece is randomly selected and its sub-batch quantity is incremented by 1, where the sub-batch quantity must not exceed the sub-batch upper limit; then, based on the batch division result, the batch size of each sub-batch is divided using the flexible batch division method described in 2.2, and the scheduling is performed using the method described in step 3. If the scheduling result is improved, the sub-batch quantity is increased; if it is not improved, the sub-batch quantity is decreased by 1 and the next type of workpiece is selected to continue determining the batch quantity.

[0127] Step 2.2: Calculate the batch size of each sub-batch based on the batch size generated in 2.1 using the flexible batch partitioning method;

[0128] Step 2.2.1: Determine the number of sub-batches B according to 3.1 j And randomly generate sub-batch N ju , let u=1;

[0129] Step 2.2.2: Determine N ju +B j -u≤A j If yes, proceed to step 2.2.3; otherwise, return to step 2.2.1.

[0130] Step 2.2.3: Let A j =A j -N ju , u = u + 1;

[0131] Step 2.2.4: Determine if u = B j If so, then let N ju =A j Otherwise, return to step 2.2.1.

[0132] The batch size division results obtained according to this method are as follows:

[0133] Table 2 Batch Size Division Results

[0134]

[0135] Step 3: Use the improved discrete fruit fly algorithm to calculate the workpiece scheduling order and maintenance plan when the objective function is minimized. Figure 2 );

[0136] Step 3.1: Encoding the solution;

[0137] Using a two-dimensional array π = {π1, π2, ..., π} f} represents the allocation and processing sequence of workpieces in various production lines. Here, π1 records the batching results for each type of workpiece obtained in step 3, and each one-dimensional array π... kThis array contains sub-batch workpieces assigned to the production line. The numbers in the array represent the sub-batch index numbers of the workpieces, which are processed sequentially in the order shown in the array. The workpiece processing sequence determines the equipment's maintenance time based on the adopted preventative maintenance strategy. Therefore, it is not desirable to represent equipment maintenance tasks in a two-dimensional array.

[0138] Step 3.2: Population initialization;

[0139] The initial population consists of n individuals, two of which are constructed using heuristic methods, and the remaining individuals are generated randomly.

[0140] Step 3.2.1: Generate an individual using a heuristic algorithm; classify all workpiece batches according to the different types of workpieces processed on the production line; sort the classified workpiece batches first in descending order of total processing time, and then take out workpiece batches from the sequence one by one and insert them into the optimal position in the processing sequence of the processable production line to minimize the completion time of the current processable production line.

[0141] Step 3.2.2: Generate an individual using a heuristic algorithm; classify all workpiece batches according to the different types of workpieces processed on the production line; sort the classified workpiece batches in descending order of total processing time, then take out workpiece batches from the sequence one by one and insert them into the optimal position in the processing sequence of the processable production line to minimize the completion time of the current processable production line; after each new workpiece batch is inserted, randomly remove a workpiece batch before or after the insertion position and insert it again into the optimal position in the current production line to reduce the completion time of the production line.

[0142] Step 3.2.3: Random generation method; First, classify all workpiece batches according to the different types of workpieces processed on the production line; then, take the first n workpieces from the classified workpiece batches and insert them into the n production lines in sequence, and insert the (n+1)th workpiece and the workpieces thereafter into the production line with the shortest completion time.

[0143] Step 3.3: Population segmentation and olfactory search;

[0144] A population of n individuals is divided into 7 subpopulations, each with a relatively uniform number of individuals and employing different olfactory search strategies.

[0145] Step 3.3.1: Classify the production lines according to the different types of workpieces processed on the production line, and group the production lines that can process the same workpieces into one category;

[0146] Step 3.3.2: Perform pipeline insertion operation in subpopulation 1. Randomly select two pipelines from the same type. If the selected pipelines are the same, perform intra-pipeline insertion; otherwise, perform inter-pipeline insertion. Randomly select an initial workpiece batch and a target workpiece batch. The initial workpiece will be moved to the end of the target workpiece batch.

[0147] Step 3.3.3: Perform a pipeline exchange operation in subpopulation 2. Randomly select two pipelines from the same type. If the selected pipelines are the same, perform an intra-pipeline exchange operation; otherwise, perform an inter-pipeline exchange operation. Randomly select two workpiece batches and exchange their positions.

[0148] Step 3.3.4: Perform a pipeline reversal operation within subpopulation 3, randomly select N positions from the same type of pipeline, and invert the batch of workpieces at these N positions;

[0149] Step 3.3.5: In subpopulations 4 to 7, combine insertion and swap, insertion and reverse, swap and reverse, and insertion, swap and reverse to achieve multi-level search operations;

[0150] Step 3.4: Visual search;

[0151] Step 3.4.1: Visually search for the best individual in each type of production line for each subpopulation, select a batch of workpieces from the production lines with longer completion times, and exchange it with a batch of workpieces from other similar production lines.

[0152] Step 3.4.2: Repeat step 3.4.1. If the maximum completion time of the best individual cannot be improved after two consecutive swaps, then select the best individual from the swaps that have been performed to replace the worst individual in the subpopulation.

[0153] Step 3.5: Merge all subpopulations;

[0154] Step 3.6: Determine if the current population has reached the maximum number of iterations. If yes, proceed to step 3.7; otherwise, proceed to step 3.3.

[0155] Step 3.7: Obtain the optimal workpiece scheduling sequence and maintenance time point ( Figure 4 ).

Claims

1. A batch scheduling method for a parallel production line considering preventive maintenance of equipment, the method comprising the following steps: Step 1: Based on the service life thresholds for preventive maintenance and opportunistic maintenance of equipment, establish an integrated optimization model for batch scheduling of parallel flow workshops that considers preventive maintenance of equipment; Step 1.1: Determine the constraints of the integrated optimization model; (1) The total number of workpieces remains unchanged after being divided into batches; ； in, Indicates the batch size. This indicates the required quantity of each type of workpiece. Indicates the number of sub-batches. Indicates the workpiece number. Indicates the number of workpiece types. Indicates the batch number; (2) All processing positions in the production line must correspond one-to-one with each batch of workpieces. There are limitations on the types of workpieces that can be processed on a single production line; ； ； in, Indicates the number of devices. Indicates workpiece sub-batch On the assembly line Location Upward processing, Indicates workpiece On the assembly line Is it possible to process it? Indicates any, Indicates the production line number; (3) The production line cannot start processing the next batch of workpieces before the current batch of workpieces has been processed; ； in, Indicates assembly line Processing position The start time of processing the workpiece. Indicates assembly line Processing position The completion time of the workpiece on the workpiece; (4) The relationship between the start and finish times of the processes for workpieces on the same production line; ； in, assembly line equipment in Processing position The completion time of the workpiece on the surface. assembly line equipment in Processing position The start time of processing the workpiece. Indicates workpiece On the assembly line Processing time of each piece of equipment on the machine; (5) Before a workpiece can enter the next machine for processing the next process, it must complete the process that the current machine is currently processing; ； (6) Constraints on decision variables; ； (7) Equipment preventive maintenance service life threshold and opportunistic maintenance threshold constraints; ； in, This indicates the opportunity to maintain the service age threshold. Indicates the service life threshold for preventive maintenance of equipment; Step 1.2: Perform preventative maintenance modeling; when Sometimes, Then the assembly line Conduct the first The maintenance shutdown was recorded. , Perform opportunistic maintenance assessments on other equipment in the production line: ； in, Indicates assembly line No. During the second preventative maintenance period, Indicates assembly line On the equipment exist The length of service at any time Indicates assembly line Conduct the first Second maintenance shutdown Indicates assembly line Conduct the first During the second maintenance shutdown, is it necessary to perform equipment maintenance? Perform maintenance; Considering maintenance capacity limitations, the maximum number of simultaneous maintenance requests during a maintenance shutdown of a certain production line is [number missing]. The equipment is in the first stage of the production line. The maintenance downtime for this maintenance is as follows: ； in, Indicates assembly line No. Maintenance time for preventative maintenance. Indicates assembly line No. The number of maintenance equipment required for preventative maintenance. This indicates the limit on the number of devices that can be maintained during a single downtime. Indicates the average maintenance time of the equipment; A virtual service life model is used to model the maintenance effect on the pipeline. Conduct the first After the first maintenance shutdown, according to Update the production line The After the first shutdown maintenance The virtual service life of the time device Mean time between maintenance (MTBG) for equipment: assembly line No. During the next maintenance, the equipment No maintenance required: ; assembly line No. During the next maintenance, the equipment Perform maintenance: ; in, This is the service life improvement factor, used to describe the change in service life of equipment after imperfect maintenance. And it is a constant value; Step 1.3: Update start and finish times: ； ； Step 1.4: Construct the objective function of the ensemble optimization model: ; This represents minimizing the maximum completion time. ; Step 2: Divide the workpieces into batches and lots based on workpiece type, workpiece quantity, and sub-batch limit; Step 2.1: Calculate the optimal batch partitioning result using a trial-and-error method; Step 2.1.1: Determine the upper limit of each type of workpiece sub-batch and randomly generate the quantity of each type of workpiece sub-batch; Step 2.1.2: Use a trial-and-error method to determine the optimal batch size for each workpiece; First, randomly select a type of workpiece and increment its sub-batch quantity by 1, where the sub-batch quantity must not exceed the sub-batch upper limit; then, based on the batch division result, use the flexible batch division method in step 2.2 to divide the batch size of each sub-batch, and use the method described in step 3 for scheduling. If the scheduling result is improved, continue to increase the sub-batch quantity; if it is not improved, decrease the sub-batch quantity by 1 and select the next type of workpiece to determine the batch quantity. Step 2.2: Calculate the batch size of each sub-batch based on the optimal batch partitioning result obtained in Step 2.1 using the flexible batch partitioning method; Step 2.2.1: Based on the number of sub-batches Randomly generate sub-batch batches ,make ; Step 2.2.2: Determine If yes, proceed to step 2.2.3; otherwise, return to step 2.2.

1. Step 2.2.3: Let , ; Step 2.2.4: Judgment If so, then let Otherwise, return to step 2.2.1; Step 3: Use the improved discrete fruit fly algorithm to calculate the workpiece scheduling order and maintenance plan when the objective function is minimized; Step 3.1: Encoding the solution; Using two-dimensional arrays This indicates the distribution and processing sequence of workpieces across different production lines; among which, Record the batching results for each type of workpiece obtained in step 2, for each one-dimensional array. It contains sub-batch workpieces assigned to this production line. The numbers in the array represent the workpiece sub-batch index numbers. The workpieces are processed sequentially in the order in the array. The workpiece processing sequence determines the equipment maintenance time based on the adopted equipment preventive maintenance strategy. Step 3.2: Population initialization; Initializing the population includes There are 10 individuals, two of which are constructed using heuristic methods, and the remaining individuals are generated randomly. Step 3.3: Population segmentation and olfactory search; there will be The population of individuals is divided into 7 subpopulations, with each subpopulation having a relatively even number of individuals and implementing different olfactory search strategies. Step 3.4: Visual search; Step 3.5: Merge all subpopulations; Step 3.6: Determine if the current population has reached the maximum number of iterations. If yes, proceed to step 3.7; otherwise, proceed to step 3.

3. Step 3.7: Obtain the optimal workpiece scheduling sequence and maintenance time point.

2. The parallel flow workshop batch scheduling method considering preventive equipment maintenance as described in claim 1, characterized in that, The specific method for step 3.2 is as follows: Step 3.2.1: Generate an individual using the following heuristic algorithm; All workpiece batches are classified according to the different types of workpieces processed on the production line. The classified workpiece batches are first sorted in descending order of total processing time, and then workpiece batches are taken out from the sequence one by one and inserted into the optimal position in the processing sequence of the production line that can be processed, so as to minimize the completion time of the current production line. Step 3.2.2: Generate an individual using the following heuristic algorithm; All workpiece batches are classified according to the different types of workpieces processed on the production line. The classified workpiece batches are first sorted in descending order of total processing time. Then, workpiece batches are taken out from the sequence one by one and inserted into the optimal position in the processing sequence of the production line to minimize the completion time of the current production line. After each new workpiece batch is inserted, a workpiece batch is randomly removed from before or after the insertion position and inserted again into the optimal position in the current production line to reduce the completion time of the production line. Step 3.2.3: Random generation method; First, all workpiece batches are classified according to the different types of workpieces processed on the assembly line; then, the workpieces are taken out from the classified batches. The workpieces were inserted sequentially into In the production line, the first Each workpiece and subsequent workpieces are inserted into the production line with the shortest completion time.

3. The parallel flow workshop batch scheduling method considering preventive equipment maintenance as described in claim 1, characterized in that, The specific method for step 3.3 is as follows: Step 3.3.1: Classify the production lines according to the different types of workpieces processed on the production line, and group the production lines that can process the same workpieces into one category; Step 3.3.2: Perform pipeline insertion operation in subpopulation 1; randomly select two pipelines from the same type of pipeline. If the selected pipelines are the same, perform pipeline insertion operation; otherwise, perform pipeline insertion operation; randomly select an initial workpiece batch and a target workpiece batch. The initial workpiece will be moved to the back of the target workpiece. Step 3.3.3: Perform pipeline exchange operation in subpopulation 2. Randomly select two pipelines from the same type of pipeline. If the selected pipelines are the same, perform an intra-pipeline exchange operation; otherwise, perform an inter-pipeline exchange operation. Randomly select two workpiece batches and exchange their positions. Step 3.3.4: Perform pipeline reversal operation within subpopulation 3, randomly selecting from the same type of pipeline. This position will Workpieces at each location are inverted; Step 3.3.5: In subpopulations 4 to 7, combine insertion and swap, insertion and reverse, swap and reverse, and insertion, swap and reverse to achieve multi-level search operations.

4. The parallel flow workshop batch scheduling method considering preventive equipment maintenance as described in claim 1, characterized in that, The specific method for step 3.4 is as follows: Step 3.4.1: Visually search for the best individual in each type of production line for each subpopulation, select a batch of workpieces from the production lines with longer completion times, and exchange it with a batch of workpieces from another production line of the same type. Step 3.4.2: Repeat step 3.4.

1. If the maximum completion time of the best individual cannot be improved after two consecutive swaps, then select the best individual from the swaps that have been performed to replace the worst individual in the subpopulation.

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