Method for minimizing maximum finishing time for curing and post processing operations in aerospace composite manufacturing

Abstract

The present application relates to a kind of aviation composite manufacturing curing and post-processing operation maximum completion time minimization method, including aviation composite manufacturing curing and post-processing operation is modeled as parallel and series two-stage batch processing operation scheduling problem, all operations are grouped batch processing, the to-be-scheduled operation set of aviation composite manufacturing curing and post-processing is constructed, and all operations are sorted in ascending order according to its first stage unit processing time, judge whether all groups batch can be full batch, different batch rules are designed for different judgment results, the minimum maximum completion time of each group batch rule is calculated, and the optimal operation scheduling scheme is selected to carry out aviation composite manufacturing curing and post-processing operation.The present application effectively shortens the maximum completion time of all operations under the premise of meeting strict non-waiting flow constraint, improves line synergy efficiency, equipment utilization and task delivery capacity.

Description

Technical Field

[0001] This invention relates to the field of aerospace composite material manufacturing technology, and in particular to a method for minimizing the maximum completion time of curing and post-processing operations in aerospace composite material manufacturing. Background Technology

[0002] In the manufacturing process of aerospace composite materials, curing and post-treatment typically constitute consecutive production stages, exhibiting a two-stage heterogeneous batch processing characteristic. Taking the manufacturing of aerospace composite components as an example, multiple parts can be simultaneously loaded into an autoclave for curing. Since parts within the same batch share the autoclave space, and process parameters such as temperature and pressure operate according to a uniform curve, the curing stage exhibits typical parallel batch processing characteristics. That is, multiple parts within the batch begin and end processing simultaneously, and the batch processing time generally depends on the part with the most stringent process requirements or the longest curing time within the batch.

[0003] After curing, the parts enter the post-processing stage. Post-processing typically includes demolding, trimming, drilling, polishing, and non-destructive testing. These operations mostly require specialized equipment or workstations to be completed piece by piece, thus exhibiting serial batch processing characteristics. Parts can be transferred from the curing stage to the post-processing stage in batches, but each part within a batch still needs to be processed sequentially during post-processing. The processing time is usually the cumulative processing time of each part within the batch, and may include necessary preparation and changeover time.

[0004] For batch scheduling optimization problems in such continuous processes, existing research and practical applications mostly rely on heuristic rules or experience-based scheduling methods. When faced with complex batch capacity constraints and no waiting constraints, these methods often fail to yield high-quality or even optimal scheduling solutions, easily leading to increased equipment idle time, prolonged production cycles, and decreased overall operating efficiency. The problem of minimizing the maximum completion time in a two-stage batch processing environment mainly involves the following two core technical issues: (1) Batching scheme for the job: The batching scheme needs to determine the number of batches and the job composition of each batch. Since the parallel batch processing time in the first stage is limited by the maximum processing time within the batch, while the serial batch processing time in the second stage increases linearly with the job size, the batching decision needs to find the optimal balance between alleviating the "barrel effect" in the first stage and reducing the cumulative processing load in the second stage. Therefore, under the constraint of batch capacity, the key to determining a reasonable batching scheme is to coordinately optimize the allocation strategy of heterogeneous processing characteristics in the two stages.

[0005] (2) Batch processing sequence optimization: Due to the strong coupling and lack of waiting constraints between the two stages, the system is prone to blockage and idleness due to machine capacity mismatch. Therefore, how to accurately arrange the batch processing sequence based on the specific batch distribution attributes in the optimal scheduling scheme to minimize the waiting time across stages is the core technical challenge to achieve the minimization of the maximum completion time. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a method for minimizing the maximum completion time of curing and post-processing operations in aerospace composite manufacturing. This method solves the problems of traditional methods relying on heuristic rules or experience-based scheduling, lacking optimality guarantees, failing to effectively balance the heterogeneous processing characteristics of the two stages, ignoring the strong coupling relationship between the two stages under no-wait constraints, and being unable to accurately optimize the batch processing sequence. This invention models the curing and post-processing process of aerospace composite manufacturing as a parallel-serial two-stage batch processing flow shop scheduling problem with no-wait constraints. It aims to minimize the maximum completion time under stringent process constraints by collaboratively deciding on batching schemes and processing sequences, thereby significantly improving the production line collaboration efficiency and scheduling automation level of aerospace composite manufacturing.

[0007] To achieve the above technical objectives, the present invention provides the following technical solution: a method for minimizing the maximum completion time of curing and post-processing operations in aerospace composite manufacturing, comprising the following steps: S1. Model the solidification and post-processing operations of aerospace composite manufacturing as a two-stage batch processing scheduling problem involving parallel and serial processes, and perform batch processing on all operations. S2. Construct a set of scheduled jobs for solidification and post-processing of aerospace composite manufacturing, and read the total number of jobs, batch capacity, unit processing time of the first stage, unit processing time of the second stage, and preparation time of the second stage for each job. S3. Sort all jobs in the set of jobs to be scheduled in ascending order according to their first stage unit processing time, reset the job numbers according to the sorting results, and construct the sequence of jobs to be scheduled. S4. Consider the case of starting with full batches, and determine whether all batches can be full based on the total number of jobs and batch capacity. If all batches can be fully completed, the maximum completion time of the full batch batching operation scheduling scheme shall be used as the minimum maximum completion time when starting with full batch batching. If there are non-full batches, enumerate all job scheduling schemes that start with the last batch as a non-full batch, calculate and select the smallest maximum completion time among them, and use it as the smallest maximum completion time when starting with a full batch. S5. Considering the case of starting with a non-full batch, enumerate the work scheduling schemes that are divided into several non-full batches, several full batches, and special batches in sequence, calculate and select the minimum maximum completion time when starting with a non-full batch; the special batch is either a full batch or a non-full batch. S6. Compare the minimum maximum completion time when starting with full batch and the minimum maximum completion time when starting with non-full batch, and select the smaller time value as the minimum maximum completion time for the current aerospace composite manufacturing curing and post-processing operation. The operation scheduling scheme corresponding to this time value is the optimal operation scheduling scheme.

[0008] Optionally, the step of modeling the aerospace composite manufacturing curing and post-processing operations as a two-stage batch processing scheduling problem involving parallel and serial processes, and performing batch processing on all operations, includes: The solidification process is treated as the first stage in parallel, and the post-processing process is treated as the second stage in serial order. The unit processing time for the second stage of each job is the same constant. The batch processing is subject to a uniform batch capacity limitation; The batch capacity is a preset value.

[0009] Optionally, in the first stage, the processing time of each batch in the first stage is determined by the operation with the longest unit processing time in the first stage within that batch, as mathematically represented below: ; in Indicates batch The first stage of processing time; Indicates the first One batch; Indicates batch The Middle The first stage of each task's unit processing time; Indicates batch retrieval The processing time of the operation with the longest unit processing time in the first stage among all operations; In the second stage, the second-stage processing time for each batch is equal to the sum of the second-stage unit processing times of all jobs within that batch and the second-stage preparation time, mathematically represented as follows: ; in, Indicates batch The second stage of processing time; This indicates the preparation time for the second phase; For module length calculation, the above formula is used to calculate the number of jobs within a batch; This indicates the unit processing time for the second stage of the operation.

[0010] Optionally, the batch job scheduling problem follows a no-wait constraint, meaning that each job immediately enters the preparation process for the second stage after the completion of the first stage, and other completed jobs in each batch cannot leave the current stage before the last job in each batch is completed in the second stage.

[0011] Optionally, the step of determining whether all batches can be fully processed based on the total number of jobs and batch capacity includes: The mathematical representation of the number of non-full batch jobs is as follows: ; in This indicates the number of non-full batch operations. The total number of assignments. For batch capacity, Indicates rounding down; like Then all batches can be fully processed; if Then there are batches that are not full.

[0012] Optionally, the full-batch grouping job scheduling scheme includes: Based on batch capacity To determine the batch size, all jobs in the job sequence to be scheduled are divided into several full batches according to the sequence order, forming a job scheduling scheme with full batches. The maximum completion time of the full-batch grouping job scheduling scheme is calculated as follows: ; in, Indicates the maximum completion time; Indicates batch The first stage of processing time, This is the first batch; Represents the total number of batches, satisfying ; Indicates the batch number. Indicates batch The first stage of processing time, For the first One batch; This indicates the operation of finding the maximum value.

[0013] Optionally, the step of enumerating all job scheduling schemes that group non-full batches with the last batch as the grouping point, and calculating and selecting the minimum maximum completion time among them, includes: Number of batch operations with non-full batches To enumerate the length, enumerate all jobs with a length of in the sequence of jobs to be scheduled. The continuous operating range; For each enumerated consecutive job interval, the remaining jobs in the job sequence to be scheduled are batched according to capacity. To determine the batch size, divide the batch into several full batches according to sequence order to form a preceding batch, and set the current length to [missing information]. The continuous work intervals are taken as the last batch, forming the work scheduling scheme corresponding to the continuous work interval; For each consecutive work interval obtained through enumeration, the maximum completion time is calculated using the following method: ; in, Indicates the maximum completion time; Indicates batch The first stage of processing time, This is the first batch; Represents the total number of batches, satisfying ; Indicates the batch number. Indicates batch The first stage of processing time, For the first One batch; This indicates the operation to find the maximum value; Select the maximum completion time of the job scheduling scheme corresponding to each consecutive job interval obtained by enumeration. The minimum value in.

[0014] Optionally, the enumeration is sequentially divided into several non-full batch groupings, several full batch groupings, and special batching scheduling schemes. The minimum maximum completion time is calculated and selected when starting with a non-full batch grouping, including: Select special batches, several full batches, and several non-full batches from the sequence of jobs to be scheduled, and form a job scheduling scheme that is divided into several non-full batches, several full batches, and special batches. Calculate the maximum completion time and select the minimum value among them as the minimum maximum completion time when starting with non-full batches.

[0015] Optionally, the step of sequentially selecting special batches, several full batches, and several non-full batches from the sequence of jobs to be scheduled, forming a job scheduling scheme that is sequentially divided into several non-full batches, several full batches, and special batches, and calculating the maximum completion time, selecting the minimum value among them as the minimum maximum completion time when starting with non-full batches, includes: When selecting a special batch from the sequence of jobs to be scheduled, there are two cases: one where there is a single full batch before the selected batch, and the other where all the batches before the selected batch are non-full batches. The minimum maximum completion time for each of these two cases is calculated and compared. The smaller of the two values ​​is selected as the minimum maximum completion time when starting with a non-full batch.

[0016] Optionally, the step of calculating and comparing the minimum maximum completion time in the two cases, and selecting the smaller value as the minimum maximum completion time when starting with a non-full batch, includes: If there is a unique full batch before the selected batch, perform the following steps S511-S518: S511. Select the final operation for a special batch, satisfying the following: ; in This indicates the end of a special batch, i.e., the first job in the sequence of jobs to be scheduled. One assignment, This is the index of the final job in the sequence of jobs to be scheduled for a special batch. The total number of assignments. Batch capacity; Indicates the total number of batches in the full batch; This indicates a round-down operation; S512. Select the starting job for a special batch based on the ending job, satisfying: ; in, This indicates the start of a special batch of jobs, i.e., the first job in the sequence of jobs to be scheduled. One assignment, The index of the starting job in the sequence of jobs to be scheduled for a special batch; S513, Constructing Special Batch for: , Indicates the total number of batches; S514. For job sequences in the job sequence to be scheduled that are located after a special batch. According to batch capacity To determine the batch size, divide the batch into several full batches according to sequence order. The resulting sequence is denoted as . , This refers to the total number of batches that are not at full capacity. S515. The job sequence in the job sequence to be scheduled... A full batch is formed by grouping the components into a sequence, denoted as […]. ; S516, When the sequence of remaining jobs in the job sequence to be scheduled is... satisfy At that time, the initial state is as follows: ; in, Indicates the first The number of jobs in a non-full batch; This indicates the number of jobs that have not yet been assigned to any batch. This indicates the operation of retrieving the maximum value; Indicates full batch grouping The first stage of processing time; This indicates the preparation time for the second phase; This indicates the unit processing time for the second stage of the operation; Indicates the first The idle time of a non-full batch is the sum of the idle time of the previously divided batches; This represents the idle time of the currently divided batches, calculated as follows: ; in, Indicates the first Idle time of each pre-divided batch; The sequence of remaining jobs in the job sequence to be scheduled satisfy At that time, the following state transition equation holds: ; in, Indicates the requirement to satisfy Under the conditions The minimum value of the inner expression; S517, For different non-full batch total number of batches Calculate the minimum total idle time of the generated job scheduling scheme. : ; in, ; S518. Calculate the minimum maximum completion time assuming there is only one full batch before the selected batch. The calculation formula is as follows: Simultaneously record the total number of non-full batches corresponding to the maximum completion time. Construct a sequence consisting of non-full batches, denoted as . ; If all previous batches before the selected batch were not full batches, proceed with the following steps S521-S527: S521. Select the final job for a special batch that satisfies: ; S522. Select the starting job for a special batch based on the ending job, satisfying: ; S523, Constructing Special Batch for: ; S524. For job sequences in the job sequence to be scheduled that are located after a special batch. According to batch capacity To determine the batch size, divide the batch into several full batches according to sequence order. The resulting sequence is denoted as . ; S525, When the sequence of remaining jobs in the job sequence to be scheduled is... satisfy At that time, the initial state is as follows: ; in ; The sequence of remaining jobs in the job sequence to be scheduled satisfy At that time, the state transition equation is as follows: ; S526, For different non-full batch total number of batches Calculate the minimum total idle time of the generated job scheduling scheme. : ; S527. Calculate the minimum maximum completion time assuming all previous batches are non-full batches. The calculation formula is as follows: Simultaneously record the total number of non-full batches corresponding to the maximum completion time. Construct a sequence consisting of non-full batches, denoted as . ; The minimum maximum completion time is compared with the minimum maximum completion time when there is only one full batch before the selected batch and the minimum maximum completion time when all batches before the selected batch are non-full batches. The smaller value of the two is selected as the minimum maximum completion time when starting with a non-full batch.

[0017] By employing the above technical solution, the present invention provides a method for minimizing the maximum completion time of curing and post-processing operations in the manufacturing of aerospace composite materials, which has at least the following beneficial effects: (1) This invention optimizes the batching method of the work and improves the resource utilization level of the parallel batch processing stage. In view of the parallel batch processing characteristics of the solidification process, by reasonably dividing the batching scheme, the processing time of the parts in the same batch is more matched, thereby reducing the redundancy of batch processing time and improving the space utilization and processing coordination of the pressure tank equipment. (2) The present invention optimizes the batch processing sequence and reduces the risk of waiting and blockage during the process of process connection. By making reasonable arrangements for the batch processing sequence, a smoother connection relationship is formed between the upstream solidified batch and the downstream post-processing operation, reducing idle time and production blockage between processes, thereby improving the operational stability of the two-stage continuous manufacturing system. Attached Figure Description

[0018] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart of a method for minimizing the maximum completion time of curing and post-processing operations in the manufacturing of aerospace composite materials according to the present invention. Detailed Implementation

[0019] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. This will allow for a full understanding of how the present application uses technical means to solve technical problems and achieve technical effects, and to facilitate its implementation.

[0020] Those skilled in the art will understand that all or part of the steps in the implementation of the methods of the embodiments can be implemented by a program instructing related hardware. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0021] Please refer to Figure 1This illustration shows a specific implementation of the present embodiment. This embodiment models the solidification and post-processing operations of aerospace composite manufacturing as a two-stage no-wait pipeline scheduling problem consisting of a parallel batch processor and a serial batch processor. The first-stage batch processing time is determined by the maximum processing time within the batch, and the second-stage batch processing time is composed of the sum of the processing times of each operation within the batch and a fixed preparation time. The optimization objective is to effectively shorten the maximum completion time of all operations and improve production line collaboration efficiency, equipment utilization, and task delivery capability under the condition of no-wait constraints by jointly optimizing the batching scheme and batch processing sequence.

[0022] This embodiment proposes a method for minimizing the maximum completion time of curing and post-processing operations in aerospace composite manufacturing. The method includes the following steps: S1. Model the solidification and post-processing operations of aerospace composite manufacturing as a two-stage batch processing scheduling problem involving parallel and serial processes, and perform batch processing on all operations.

[0023] As a preferred embodiment of step S1, it specifically includes: The solidification process is treated as the first stage in parallel, and the post-processing process is treated as the second stage in serial order. The unit processing time for the second stage of each job is the same constant. The batch processing is subject to a uniform batch capacity. The limitations, satisfy , This represents the total number of assignments. The batch capacity This is the default value.

[0024] S2. Construct a set of scheduled tasks for the curing and post-processing of aerospace composite materials manufacturing. Total number of read jobs Batch capacity The first stage of each operation's unit processing time Second stage unit processing time and the preparation time for the second phase .

[0025] As a preferred embodiment of step S2, it specifically includes: In the first stage, the first stage processing time for each batch The processing time is determined by the longest unit processing time in the first stage within this batch, as expressed mathematically below: ; in Indicates batch The first stage of processing time; Indicates the first One batch; Indicates batch The Middle The first stage of each task's unit processing time; Indicates batch retrieval The processing time of the operation with the longest unit processing time in the first stage among all operations; In the second stage, there is a fixed preparation period before each batch processing. The preparation time for the second stage is... This refers to the time required for the preparation process; In the second stage, the second-stage processing time for each batch Equal to the second stage unit processing time of all operations within this batch. Total and preparation time for Phase 2 The sum, mathematically represented as follows: ; in, Indicates batch The second stage of processing time; This indicates the preparation time for the second phase; For module length calculation, the above formula is used to calculate the number of jobs within a batch; This indicates the unit processing time for the second stage of the operation.

[0026] More specifically, the batch job scheduling problem follows a no-wait constraint, meaning that each job immediately enters the preparation process for the second stage after the first stage is completed, and other completed jobs in each batch cannot leave the current stage before the last job in each batch is completed in the second stage.

[0027] S3. Arrange all jobs in the set of jobs to be scheduled according to their first-stage unit processing time. Sort the jobs in ascending order, reset the job numbers based on the sorting results, and construct a sequence of jobs to be scheduled. ,satisfy ( Indicates the number of jobs in the sequence to be scheduled. The first stage of each task's unit processing time.

[0028] S4. Considering the case of starting with full batches, calculate the minimum maximum completion time under the case of starting with full batches.

[0029] As a preferred embodiment of step S4, the specific process includes: S41. Determine whether all batches can be fully processed based on the total number of jobs and batch capacity. Specifically: ; in This indicates the number of non-full batch operations. The total number of assignments. For batch capacity, Indicates rounding down; like Then all batches can be fully processed; if Then there exists a number of jobs. Non-full batch (i.e., the last batch in the generated job scheduling plan) Inside (One assignment).

[0030] S42. If all batches can be fully completed, then the maximum completion time of the job scheduling scheme with all batches fully completed is taken as the minimum maximum completion time when starting with full batches. Specifically: Based on batch capacity To determine the batch size, include all jobs in the job sequence to be scheduled. Divide into several full batches according to sequence order. , This forms a full-batch batch operation scheduling scheme.

[0031] The maximum completion time for a full-batch job scheduling scheme is calculated as follows: ; in, Indicates the maximum completion time; Indicates batch The first stage of processing time, This is the first batch; Indicates the total number of batches; Indicates the batch number. Indicates batch The first stage of processing time, For the first One batch; This indicates the operation of finding the maximum value.

[0032] S43. If there are non-full batches, enumerate all job scheduling schemes that start with the last batch as a non-full batch, calculate and select the smallest maximum completion time among them, and use it as the smallest maximum completion time when starting with a full batch. Specifically: S431, Using non-full batch batch number of jobs To enumerate the length, enumerate all jobs with a length of in the sequence of jobs to be scheduled. The continuous work interval is mathematically represented as: ;in, For the job index set for enumeration, in any Take the length as Continuous operating range As a non-full batch batch.

[0033] S432. For each enumerated consecutive job interval, batch the remaining jobs in the job sequence to be scheduled. To determine the batch size, divide the batch into several full batches according to the sequence order to form a preceding batch. , , will the current length be Continuous operating range As the final batch, it forms the work scheduling scheme corresponding to the continuous work interval.

[0034] S433. For each consecutive work interval obtained through enumeration, calculate the maximum completion time for the corresponding work scheduling scheme. The calculation method is the same as in step S42, that is: .

[0035] S434. Select the maximum completion time of the job scheduling scheme corresponding to each consecutive job interval obtained by enumeration. The minimum value in the range is used as the minimum maximum completion time when starting with a full batch.

[0036] S5. Considering the case of starting with a non-full batch, enumerate the job scheduling schemes that are divided into several non-full batches, several full batches, and special batches in sequence, and calculate and select the minimum maximum completion time when starting with a non-full batch.

[0037] Next, consider the case of "starting with non-full batches." The optimal scheduling scheme in this case has structural characteristics: several non-full batches + several full batches + special batches (full batches or non-full batches). The overall approach is as follows: first enumerate the last batch, then determine the middle full batches, and finally perform dynamic programming to solve for the preceding non-full batches. After solving, establish a recursive equation... This represents the minimum total idle time for partial scheduling, and this state must meet the following conditions: (1) From the sequence of jobs to be scheduled The assignments in the assignments were considered; (2) The system contains A batch that is not fully loaded; (3) and These correspond to the job indices with the maximum and minimum unit processing times in the first stage of the special batch within the current job scheduling scheme; (4) Indicates the first The number of jobs in a non-full batch; (5) This indicates the number of jobs that have not yet been assigned to any batch.

[0038] As a preferred embodiment of step S5, it specifically includes: From the sequence of jobs to be scheduled, special batches, several full batches, and several non-full batches are selected sequentially to form a job scheduling scheme that is sequentially divided into several non-full batches, several full batches, and special batches. The maximum completion time is calculated, and the minimum value is selected. Specifically, when selecting special batches from the sequence of jobs to be scheduled, there are two cases: (1) Special batching The first stage of minimum unit processing time Previously, there was only one full batch grouping. Before that All batches were not full-batch batches; (2) Special batching The first stage of minimum unit processing time Previous batch All batches are not full batches; there are no full batches.

[0039] Calculate the minimum maximum completion time for each of the two cases and compare them. Select the smaller value as the minimum maximum completion time for the case where the batch starts with a non-full batch.

[0040] More specifically, for the case where there is a unique full batch before the selected batch, perform the following steps S511-S518: S511. Select the final operation for a special batch, satisfying the following: ; in This indicates the end of a special batch, i.e., the first job in the sequence of jobs to be scheduled. One assignment, This is the index of the final job in the sequence of jobs to be scheduled for a special batch. The total number of assignments. Batch capacity; Indicates the total number of batches in the full batch; This indicates a round-down operation; S512. Select the starting job for a special batch based on the ending job, satisfying: ; in, This indicates the start of a special batch of jobs, i.e., the first job in the sequence of jobs to be scheduled. One assignment, The index of the starting job in the sequence of jobs to be scheduled for a special batch; S513, Constructing Special Batch for: ; S514. For job sequences in the job sequence to be scheduled that are located after a special batch. According to batch capacity To determine the batch size, divide the batch into several full batches according to sequence order. The resulting sequence is denoted as . ; S515. The job sequence in the job sequence to be scheduled... A full batch is formed by grouping the components into a sequence, denoted as […]. ; S516, When the sequence of remaining jobs in the job sequence to be scheduled is... satisfy At that time, the initial state is as follows: ; Otherwise, it is: ; in, Indicates the first The number of jobs in a non-full batch; This indicates the number of jobs that have not yet been assigned to any batch. This indicates the operation of retrieving the maximum value; Indicates full batch grouping The first stage of processing time; This indicates the preparation time for the second phase; This indicates the unit processing time for the second stage of the operation; Indicates infinity; Indicates the first The idle time of a non-full batch is the sum of the idle time of the previously divided batches; This represents the idle time of the currently divided batches, calculated as follows: ; in, Indicates the first Idle time of each pre-divided batch; The sequence of remaining jobs in the job sequence to be scheduled satisfy At that time, the following state transition equation holds: ; in, Indicates the requirement to satisfy Under the conditions The minimum value of the inner expression; S517, For different non-full batch total number of batches Calculate the minimum total idle time of the generated job scheduling scheme. : ; in, ; S518. Calculate the minimum maximum completion time assuming there is only one full batch before the selected batch. The calculation formula is as follows: Simultaneously record the total number of non-full batches corresponding to the maximum completion time. Construct a sequence consisting of non-full batches, denoted as . ; If all previous batches before the selected batch were not full batches, proceed with the following steps S521-S527: S521. Select the final job for a special batch that satisfies: ; S522. Select the starting job for a special batch based on the ending job, satisfying: ; S523, Constructing Special Batch for: ; S524. For job sequences in the job sequence to be scheduled that are located after a special batch. According to batch capacity To determine the batch size, divide the batch into several full batches according to sequence order. The resulting sequence is denoted as . ; S525, When the sequence of remaining jobs in the job sequence to be scheduled is... satisfy At that time, the initial state is as follows: ; Otherwise, it is: ; in ; The sequence of remaining jobs in the job sequence to be scheduled satisfy At that time, the state transition equation is as follows: ; S526, For different non-full batch total number of batches Calculate the minimum total idle time of the generated job scheduling scheme. : ; S527. Calculate the minimum maximum completion time assuming all previous batches are non-full batches. The calculation formula is as follows: Simultaneously record the total number of non-full batches corresponding to the maximum completion time. Construct a sequence consisting of non-full batches, denoted as . ; The minimum maximum completion time is compared with the minimum maximum completion time when there is only one full batch before the selected batch and the minimum maximum completion time when all batches before the selected batch are non-full batches. The smaller value of the two is selected as the minimum maximum completion time when starting with a non-full batch.

[0041] S6. Compare the minimum maximum completion time when starting with a full batch with the minimum maximum completion time when starting with a non-full batch, and select the smaller time value as the minimum maximum completion time for the current aerospace composite manufacturing curing and post-processing operation. The operation scheduling scheme corresponding to this time value is taken as the optimal operation scheduling scheme, and the aerospace composite manufacturing curing and post-processing operation is carried out to minimize the maximum completion time of the aerospace composite manufacturing curing and post-processing operation.

[0042] This invention optimizes the batch processing method, improving resource utilization in the parallel batch processing stage. Targeting the parallel batch processing characteristics of the curing process, it rationally divides the batch processing scheme to better match the processing times of parts within the same batch, thereby reducing batch processing time redundancy and improving the space utilization and processing coordination of the pressure vessel equipment. Furthermore, this invention optimizes the batch processing sequence, reducing the risk of waiting and blockages during process transitions. By rationally arranging the batch processing sequence, it creates a smoother connection between upstream curing batches and downstream post-processing operations, reducing idle time and production blockages between processes, thus improving the operational stability of the two-stage continuous manufacturing system.

[0043] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0044] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus or device (such as a computer-based system, a processor-included system or other system that can fetch and execute instructions from, an instruction execution system, apparatus or device).

[0045] The above embodiments provide a detailed description of the present invention. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for minimizing the maximum completion time of curing and post-processing operations in the manufacturing of aerospace composite materials, characterized in that, include: S1. Model the solidification and post-processing operations of aerospace composite manufacturing as a two-stage batch processing scheduling problem involving parallel and serial processes, and perform batch processing on all operations. S2. Construct a set of scheduled jobs for solidification and post-processing of aerospace composite manufacturing, and read the total number of jobs, batch capacity, unit processing time of the first stage, unit processing time of the second stage, and preparation time of the second stage for each job. S3. Sort all jobs in the set of jobs to be scheduled in ascending order according to their first stage unit processing time, reset the job numbers according to the sorting results, and construct the sequence of jobs to be scheduled. S4. Consider the case of starting with full batches, and determine whether all batches can be full based on the total number of jobs and batch capacity. If all batches can be fully completed, the maximum completion time of the full batch batching operation scheduling scheme shall be used as the minimum maximum completion time when starting with full batch batching. If there are non-full batches, enumerate all job scheduling schemes that start with the last batch as a non-full batch, calculate and select the smallest maximum completion time among them, and use it as the smallest maximum completion time when starting with a full batch. S5. Considering the case of starting with a non-full batch, enumerate the work scheduling schemes that are divided into several non-full batches, several full batches, and special batches in sequence, calculate and select the minimum maximum completion time when starting with a non-full batch; the special batch is either a full batch or a non-full batch. S6. Compare the minimum maximum completion time when starting with full batch and the minimum maximum completion time when starting with non-full batch, and select the smaller time value as the minimum maximum completion time for the current aerospace composite manufacturing curing and post-processing operation. The operation scheduling scheme corresponding to this time value is the optimal operation scheduling scheme.

2. The method for minimizing the maximum completion time of curing and post-processing operations in the manufacturing of aerospace composite materials according to claim 1, characterized in that: The process of modeling the curing and post-processing operations of aerospace composite manufacturing as a two-stage batch processing scheduling problem involving parallel and serial processes, involves batch processing of all operations, including: The solidification process is treated as the first stage in parallel, and the post-processing process is treated as the second stage in serial order. The unit processing time for the second stage of each job is the same constant. The batch processing is subject to a uniform batch capacity limitation; The batch capacity is a preset value.

3. The method for minimizing the maximum completion time of curing and post-processing operations in the manufacturing of aerospace composites according to claim 2, characterized in that: In the first stage, the processing time of each batch in the first stage is determined by the operation with the longest unit processing time in the first stage within that batch, as expressed mathematically below: ； in Indicates batch The first stage of processing time; Indicates the first One batch; Indicates batch The Middle The first stage of each task's unit processing time; Indicates batch retrieval The processing time of the operation with the longest unit processing time in the first stage among all operations; In the second stage, the second-stage processing time for each batch is equal to the sum of the second-stage unit processing times of all jobs within that batch and the second-stage preparation time, mathematically represented as follows: ； in, Indicates batch The second stage of processing time; This indicates the preparation time for the second phase; For module length calculation, the above formula is used to calculate the number of jobs within a batch; This indicates the unit processing time for the second stage of the operation.

4. The method for minimizing the maximum completion time of curing and post-processing operations in the manufacturing of aerospace composites according to claim 3, characterized in that: The batch job scheduling problem follows a no-wait constraint, meaning that each job immediately enters the preparation process for the second stage after the first stage is completed, and other completed jobs in each batch cannot leave the current stage before the last job in each batch is completed in the second stage.

5. The method for minimizing the maximum completion time of curing and post-processing operations in the manufacturing of aerospace composite materials according to claim 3, characterized in that: The method of determining whether all batches can be fully processed based on the total number of jobs and batch capacity includes: The mathematical representation of the number of non-full batch jobs is as follows: ； in This indicates the number of non-full batch operations. The total number of assignments. For batch capacity, Indicates rounding down; like Then all batches can be fully processed; if Then there are batches that are not full.

6. The method for minimizing the maximum completion time of curing and post-processing operations in aerospace composite manufacturing according to claim 5, characterized in that: The full-batch batching job scheduling scheme includes: Batch capacity To determine the batch size, all jobs in the job sequence to be scheduled are divided into several full batches according to the sequence order, forming a job scheduling scheme with full batches. The maximum completion time of the full-batch grouping job scheduling scheme is calculated as follows: ； in, Indicates the maximum completion time; Indicates batch The first stage of processing time, This is the first batch; Represents the total number of batches, satisfying ; Indicates the batch number. Indicates batch The first stage of processing time, For the first One batch; This indicates the operation of finding the maximum value.

7. The method for minimizing the maximum completion time of curing and post-processing operations in aerospace composite manufacturing according to claim 5, characterized in that: The process of enumerating all job scheduling schemes that group non-full batches with the last batch as the grouping point, calculating and selecting the minimum maximum completion time among them, includes: Batch number of non-full batches To enumerate the length, enumerate all jobs with a length of in the sequence of jobs to be scheduled. The continuous operating range; For each enumerated consecutive job interval, the remaining jobs in the job sequence to be scheduled are batched according to capacity. To determine the batch size, divide the batch into several full batches according to sequence order to form a preceding batch, and set the current length to [missing information]. The continuous work intervals are taken as the last batch, forming the work scheduling scheme corresponding to the continuous work interval; For each consecutive work interval obtained through enumeration, the maximum completion time is calculated using the following method: ； in, Indicates the maximum completion time; Indicates batch The first stage of processing time, This is the first batch; Represents the total number of batches, satisfying ; Indicates the batch number. Indicates batch The first stage of processing time, For the first One batch; This indicates the operation to find the maximum value; Select the maximum completion time of the job scheduling scheme corresponding to each consecutive job interval obtained by enumeration. The minimum value in.

8. The method for minimizing the maximum completion time of curing and post-processing operations in the manufacturing of aerospace composites according to claim 3, characterized in that: The enumeration is sequentially divided into several non-full batches, several full batches, and special batches of job scheduling schemes. The minimum maximum completion time is calculated and selected when starting with a non-full batch, including: Select special batches, several full batches, and several non-full batches from the sequence of jobs to be scheduled, and form a job scheduling scheme that is divided into several non-full batches, several full batches, and special batches. Calculate the maximum completion time and select the minimum value among them as the minimum maximum completion time when starting with non-full batches.

9. The method for minimizing the maximum completion time of curing and post-processing operations in the manufacturing of aerospace composites according to claim 8, characterized in that: The step of sequentially selecting special batches, several full batches, and several non-full batches from the sequence of jobs to be scheduled, forming a job scheduling scheme that is sequentially divided into several non-full batches, several full batches, and special batches, and calculating the maximum completion time, and selecting the minimum value among them as the minimum maximum completion time when starting with non-full batches, includes: When selecting a special batch from the sequence of jobs to be scheduled, there are two cases: one where there is a single full batch before the selected batch, and the other where all the batches before the selected batch are non-full batches. The minimum maximum completion time for each of these two cases is calculated and compared. The smaller of the two values ​​is selected as the minimum maximum completion time when starting with a non-full batch.

10. The method for minimizing the maximum completion time of curing and post-processing operations in the manufacturing of aerospace composite materials according to claim 9, characterized in that: The step of calculating and comparing the minimum maximum completion time under the two scenarios, and selecting the smaller value as the minimum maximum completion time when starting with a non-full batch, includes: If there is a unique full batch before the selected batch, perform the following steps S511-S518: S511. Select the final operation for a special batch, satisfying the following: ； in This indicates the end of a special batch, i.e., the first job in the sequence of jobs to be scheduled. One assignment, This is the index of the final job in the sequence of jobs to be scheduled for a special batch. The total number of assignments. Batch capacity; Indicates the total number of batches in the full batch; This indicates a round-down operation; S512. Select the starting job for a special batch based on the ending job, satisfying: ； in, This indicates the start of a special batch of jobs, i.e., the first job in the sequence of jobs to be scheduled. One assignment, The index of the starting job in the sequence of jobs to be scheduled for a special batch; S513, Constructing Special Batch for: , Indicates the total number of batches; S514. For job sequences in the job sequence to be scheduled that are located after a special batch. According to batch capacity To determine the batch size, divide the batch into several full batches according to sequence order. The resulting sequence is denoted as . , This refers to the total number of batches that are not at full capacity. S515. The job sequence in the job sequence to be scheduled... A full batch is formed by grouping the components into a sequence, denoted as […]. ; S516, When the sequence of remaining jobs in the job sequence to be scheduled is... satisfy At that time, the initial state is as follows: ； in, Indicates the first The number of jobs in a non-full batch; This indicates the number of jobs that have not yet been assigned to any batch. This indicates the operation of retrieving the maximum value; Indicates full batch grouping The first stage of processing time; This indicates the preparation time for the second phase; This indicates the unit processing time for the second stage of the operation; Indicates the first The idle time of a non-full batch is the sum of the idle time of the previously divided batches; This represents the idle time of the currently divided batches, calculated as follows: ； in, Indicates the first Idle time of each pre-divided batch; The sequence of remaining jobs in the job sequence to be scheduled satisfy At that time, the following state transition equation holds: ； in, Indicates the requirement to satisfy Under the conditions The minimum value of the inner expression; S517, For different non-full batch total number of batches Calculate the minimum total idle time of the generated job scheduling scheme. : ； in, ; S518. Calculate the minimum maximum completion time assuming there is only one full batch before the selected batch. The calculation formula is as follows: Simultaneously record the total number of non-full batches corresponding to the maximum completion time. Construct a sequence consisting of non-full batches, denoted as . ; If all previous batches before the selected batch were not full batches, proceed with the following steps S521-S527: S521. Select the final operation for a special batch that satisfies: ； S522. Select the starting job for a special batch based on the ending job, satisfying: ； S523, Constructing Special Batch for: ; S524. For job sequences in the job sequence to be scheduled that are located after a special batch. According to batch capacity To determine the batch size, divide the batch into several full batches according to sequence order. The resulting sequence is denoted as . ; S525, When the sequence of remaining jobs in the job sequence to be scheduled is... satisfy At that time, the initial state is as follows: ； in ; The sequence of remaining jobs in the job sequence to be scheduled satisfy At that time, the state transition equation is as follows: ； S526, For different non-full batch total number of batches Calculate the minimum total idle time of the generated job scheduling scheme. : ； S527. Calculate the minimum maximum completion time assuming all previous batches are non-full batches. The calculation formula is as follows: Simultaneously record the total number of non-full batches corresponding to the maximum completion time. Construct a sequence consisting of non-full batches, denoted as . ; The minimum maximum completion time is compared with the minimum maximum completion time when there is only one full batch before the selected batch and the minimum maximum completion time when all batches before the selected batch are non-full batches. The smaller value of the two is selected as the minimum maximum completion time when starting with a non-full batch.

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