CN116629509A - Flow shop grouping scheduling rapid evaluation method based on key machine - Google Patents
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Abstract
The invention discloses a quick evaluation method for flow shop group scheduling based on a key machine, which relates to the technical field of shop scheduling, and takes a distributed flow shop with preparation time as an example, and constructs a quick evaluation method for workpieces in groups and groups based on the insertion neighborhood of the key machine according to the problem characteristics of group scheduling; comprising the following steps: step 1: calculating the forward finishing time of all workpieces in all groups on the machine; step 2: calculating the backward finishing time of all workpieces in all groups on the machine; step 3: inserting groups or workpieces and obtaining key machines; step 4: obtaining the finishing time of the workpiece on the last machine according to the key machine; step 5: and calculating the total delay time according to the result of the step 4. The method solves the problem that the target value is quickly evaluated as the total delay time in the scheduling problem of the flow shop, reduces the calculation time, can effectively avoid repeated evaluation, saves the calculation cost and improves the optimal scheduling efficiency.
Description
Technical Field
The invention relates to the technical field of workshop scheduling, in particular to a method for rapidly evaluating flow workshop grouping scheduling based on key machines.
Background
With the development of economy, manufacturing has become an important support for national economy. The development and application of cell fabrication and grouping techniques has a significant impact on efficient mass production systems. In a cell manufacturing system, resources are divided into smaller organizational units, called manufacturing units. A manufacturing unit is typically composed of a series of specialized machines, and a group is composed of workpieces having similar requirements in terms of tools, setup and order of operation, etc., which creates a group scheduling problem. Group scheduling has proven to be relevant in various fields of unit manufacturing development, reflecting various practical applications such as automotive paint, furniture production, semiconductor industry, metal part punching, centrifugal pump manufacturing, printed circuit board or general electronics manufacturing, etc. The manufacturing unit can simplify the material flow, shorten the production time, improve the flexibility of the production system, and is particularly suitable for highly-automated systems. Along with the optimization of the structure of the production line, more and more enterprises adopt the production mode of the unit manufacturing system, such as Huacheng, fushikang technology, automobile assembly industry and the like.
In existing research for flow shop team scheduling problems, an insert-based neighborhood search operation is generally considered as a method of obtaining a high quality scheduling sequence. However, solving the target value after performing the insertion operation results in a large amount of computation and consumes a large amount of optimal scheduling time, so that the optimal scheduling method cannot be fully utilized, and unreasonable scheduling sequences are caused, which may cause idle production lines, increase production time and reduce production efficiency. Insufficient or wasteful use of resources may be caused, increasing production costs. And the processing precision of certain procedures can be reduced, and the product quality is affected. However, few studies have considered designing a corresponding rapid evaluation method for this problem to reduce the time complexity of target value solution. Therefore, the method has important practical significance and is a problem to be solved urgently.
Based on the analysis, in order to better solve the problem of rapid evaluation of the target value of the scheduling problem of the flow shop grouping, the invention digs the hidden problem characteristics, analyzes the relation between the group and the workpiece in the inserting process, defines the concept of the key machine, and respectively proposes the inserting acceleration criterion based on the key machine for the group and the workpiece. Compared with the traditional calculation mode, the method provided by the invention reduces the calculation time complexity, greatly shortens the calculation time, improves the calculation efficiency, fully digs the potential of the optimal scheduling method, and can perform repeated iterative optimization on the scheduling scheme in the same optimization time, thereby obtaining a more accurate scheduling scheme and avoiding errors in the scheduling process; the workshop tasks can be efficiently scheduled and optimized according to the production requirements, and enterprises are helped to improve the production efficiency; meanwhile, the optimized scheduling scheme can reduce the idle time of materials and equipment, improve the stability and reliability of a production line, reduce the resource waste and further reduce the production cost.
Disclosure of Invention
In order to solve the defects in the prior art, the invention provides a rapid evaluation method for inserting neighborhood group scheduling based on a key machine, which takes a distributed running water workshop with preparation time as an example, improves the calculation modes of workpieces in groups, reduces the calculation or evaluation time of target values and improves the scheduling efficiency of the workshop.
The invention provides a flow shop group scheduling rapid evaluation method based on a key machine, which comprises the following steps:
dividing an insertion neighborhood rapid evaluation method based on a key machine into a group insertion acceleration criterion and a workpiece insertion acceleration criterion according to the characteristics of the group problems;
further, the group insertion acceleration criteria are described as follows:
in factory k, slave group sequence pi k Group with the first' position removedObtaining a new group sequenceAnd a new factory k complete scheduling sequence +.>Try to insert group->To all delta in the factory k Delta is obtained at each position k Schedule sequences, all delta k The rapid evaluation of the individual sequences is as follows;
step 1: for the scheduling sequence σ' k Forward calculating to obtain forward finishing time
Step 2: for the scheduling sequence σ' k Back calculating to obtain back finishing time
Step 3: hypothesis groupInserted at position t to obtain a new group sequence +.> And a new factory k complete scheduling sequence +.> For the scheduling sequence sigma k Forward calculating to obtain forward finishing time
Step 4: obtaining a positionCritical machine of (2)>Calculating the maximum finishing time of plant k +.>
Step 5: for the scheduling sequence sigma k Calculating an insertion groupThe finishing time of each workpiece in each group on the last machine is later;
step 6: in the scheduling sequence sigma k In the first position group, the expiration date isCalculate the scheduling sequence sigma k Is a function of the total delay time of (a);
step 7: repeating steps 3,4,5,6 until all positions are considered.
Further, the workpiece insertion acceleration criteria are described as follows:
in factory k, from a sequence of workpiecesThe workpiece in the j' th position is removed +.>Obtaining a new work scheduling sequenceAnd a new factory k complete scheduling sequence +.>Attempting to insert a workpieceAll->In the individual positions, is obtained->Schedule sequences, all->The rapid evaluation of the individual sequences is as follows;
step 1: for the scheduling sequence σ' k Forward calculating to obtain forward finishing time
Step 2: for the scheduling sequence σ' k Back calculating to obtain back finishing time
Step 3: assume a workpieceInserting into q position to obtain new workpiece sequence +.> And a new factory k complete scheduling sequence +.> For the scheduling sequence sigma k Forward calculation gives forward finishing time +.>
Step 4: obtaining a positionCritical machine of (2)>Calculating the maximum finishing time of plant k +.>
Step 5: for the scheduling sequence sigma k Calculating an insert workpieceThe finishing time of each workpiece in each group on the last machine is later;
step 6: in the scheduling sequence sigma k In the first position group, the expiration date isCalculate the scheduling sequence sigma k Is a function of the total delay time of (a);
step 7: repeating steps 3,4,5,6 until all positions are considered.
The flow shop group scheduling rapid evaluation method based on the key machine provided by the invention has the following technical effects:
(1) Compared with the traditional calculation mode, the method provided by the invention reduces the calculation time complexity, greatly shortens the calculation time and improves the calculation efficiency;
(2) The scheduling scheme can be subjected to repeated iterative optimization within the same optimization time, and the potential of the optimal scheduling method is fully mined so as to obtain a more accurate scheduling scheme, and errors in the scheduling process are avoided;
(3) The workshop tasks can be efficiently scheduled and optimized according to the production requirements, and enterprises are helped to improve the production efficiency;
(4) The optimized scheduling scheme can reduce the idle time of materials and equipment, improve the stability and reliability of a production line, reduce the resource waste and further reduce the production cost.
In summary, the method and the system can well solve the calculation process of the target value in the grouping problem, and can provide a good solution for quickly calculating the target value for the grouped scheduling of the flow shop.
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FIG. 1 is a comparison of confidence intervals for the present invention.
Detailed Description
Embodiments of the present invention will now be described more fully hereinafter with reference to the accompanying drawings, in which embodiments of the invention are shown. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. Like numbers refer to like elements throughout.
Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms used herein should be interpreted as having a meaning that is consistent with their meaning in the context of this specification and the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
The present invention is described below with reference to flowchart illustrations and/or block diagrams of methods, systems, and computer program products according to embodiments of the invention. It will be understood that some blocks of the flowchart illustrations and/or block diagrams, and combinations of some blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be stored or implemented in a microcontroller, microprocessor, digital Signal Processor (DSP), field Programmable Gate Array (FPGA), state machine, programmable Logic Controller (PLC) or other processing circuit, general purpose computer, special purpose computer. The use computer or other programmable data processing apparatus (e.g., a production machine) to create means or block diagrams for implementing the functions/acts specified in the flowchart and/or block diagrams by the instructions being executed by the processor of the computer or other programmable data processing apparatus.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means. The functions/acts specified in the flowchart and/or block diagram block or blocks are implemented.
The computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus. Other programmable devices provide steps for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. It should be understood that the functions/acts noted in the blocks may occur out of the order noted in the operational illustrations. For example, two blocks shown in succession may in fact be executed substantially concurrently or the blocks may sometimes be executed in the reverse order, depending upon the functionality/acts involved. Although some of the figures include arrows on the communication paths to illustrate the primary direction of communication, it should be understood that communication may occur in a direction opposite to the depicted arrows.
The specific implementation process of the invention is as follows:
taking a printed circuit board PCB as an example, the PCB is an important component in electronic products. During PCB manufacturing, different types of PCB parts need to be scheduled. First, the PCB parts are grouped by type, e.g. the PCB parts are divided into a first PCB group and a second PCB group, and the number of chips that need to be loaded on the machine to process the two different PCB groups is also different. Specifically, the number of chips loaded on the machine is constant when the first PCB set is processed, and when the first PCB set is processed and the second PCB set is required to be switched, the machine is cleaned and maintained to meet the conditions required for processing the second PCB set, so that the switching time is different from one PCB set to another depending on the order of the PCB sets. In this case, the scheduling problem is a flow shop team scheduling problem with a sequence dependent preparation time.
Therefore, the method for rapidly evaluating the flow shop group scheduling based on the key machine comprises the following implementation processes:
in factory k, for a sequence of workpiecesIn total->Positions, defining the q-th position in the work sequence as +.> Define position->Key machine of (2) is->Key machine->The following calculation formula is satisfied;
meanwhile, the maximum finishing time of the factory k can be obtained more quickly through the following calculation formula
Dividing a rapid evaluation method based on the critical machine insertion neighborhood into a group insertion acceleration criterion and a workpiece insertion acceleration criterion according to the characteristics of the group problems;
the group insertion acceleration criteria are described as follows:
in factory k, the slave group sequence pi k Group with the first' position removedObtaining a new group sequenceAnd a new factory k complete scheduling sequence +.>Try to insert group->To all delta in the factory k Delta is obtained at each position k Schedule sequences, all delta k The rapid evaluation of the individual sequences is as follows;
step 1: for the scheduling sequence σ' k Forward calculating to obtain forward finishing timeThe calculation formula is as follows:
step 2: for the scheduling sequence σ' k Back calculating to obtain back finishing timeThe calculation formula is as follows:
step 3: hypothesis groupInserted at position t to obtain a new group sequence +.> And a new factory k complete scheduling sequence +.> For the scheduling sequence sigma k Forward calculating to obtain forward finishing timeThe calculation formula is as follows:
step 4: obtaining a positionCritical machine of (2)>Calculating the maximum finishing time of plant k +.>The calculation formula is as follows:
step 5: for the scheduling sequence sigma k Calculating an insertion groupThe finishing time of each workpiece in each group on the last machine is calculated as follows:
step 5.1: traversing the remaining groups in sequence starting from the group at the t+1st position;
step 5.2: traversing all the workpieces in the current group in sequence;
step 5.3: starting from the critical machine to the last machine;
step 5.4: calculating the finishing time of the current workpiece;
step 5.5: finding a key machine at a next position according to the fact that the maximum factory finishing time on a machine with the largest serial number is equal to the sum of the forward finishing time and the backward finishing time;
step 5.6: traversing the residual workpieces and the residual groups in the current group in sequence according to the modes of steps 5.3, 5.4 and 5.5 until the residual workpieces are traversed;
step 6: in the scheduling sequence sigma k In the first position group, the expiration date isCalculate the scheduling sequence sigma k The calculation formula is as follows:
step 7: repeating steps 3,4,5,6 until all positions are considered.
The workpiece insertion acceleration criteria are described as follows:
in factory k, from a sequence of workpiecesThe workpiece in the j' th position is removed +.>Obtaining a new work scheduling sequenceAnd a new factory k complete scheduling sequence +.>Attempting to insert a workpieceAll->In the individual positions, is obtained->Schedule sequences, all->The rapid evaluation of the individual sequences is as follows;
step 1: for the scheduling sequence σ' k Forward calculating to obtain forward finishing timeThe calculation formula is as follows:
step 2: for the scheduling sequence σ' k Back calculating to obtain back finishing timeThe calculation formula is as follows:
step 3: assume a workpieceInserting into q position to obtain new workpiece sequence +.> And a new factory k complete scheduling sequence +.> For the scheduling sequence sigma k Forward calculation gives forward finishing time +.>The calculation formula is as follows:
step 4: obtaining a positionCritical machine of (2)>Calculating the maximum finishing time of plant k +.>Calculation ofThe formula is as follows:
step 5: for the scheduling sequence sigma k Calculating an insert workpieceThe finishing time of each workpiece in each group on the last machine is calculated as follows:
step 5.1: traversing the remaining groups sequentially from the group of the first' position;
step 5.2: if the current group is l', traversing the rest workpieces in sequence from the q+1 position, and if not, traversing all the workpieces in the group in sequence;
step 5.3: starting from the critical machine to the last machine;
step 5.4: calculating the finishing time of the current workpiece;
step 5.5: finding a key machine at a next position according to the fact that the maximum factory finishing time on a machine with the largest serial number is equal to the sum of the forward finishing time and the backward finishing time;
step 5.6: traversing the residual workpieces and the residual groups in the current group in sequence according to the modes of steps 5.3, 5.4 and 5.5 until the residual workpieces are traversed;
step 6: in the scheduling sequence sigma k In the first position group, the expiration date isCalculate the scheduling sequence sigma k The calculation formula is as follows:
step 7: repeating steps 3,4,5,6 until all positions are considered.
By recording the forward finishing time and the backward finishing time, when the maximum finishing time is calculated after the inserting group or the workpiece is operated, the maximum finishing time is obtained by summing the forward finishing time and the backward finishing time, and meanwhile, by updating the inserted position and the key machine at the later position, the calculated amount is reduced, the time complexity is reduced, the target value is solved efficiently, repeated iterative optimization can be carried out on the scheduling scheme in the same optimizing time, the potential of the optimizing scheduling method is fully excavated, so that a more accurate scheduling scheme is obtained, and the scheduling efficiency of workshops is improved.
FIG. 1 is a comparison graph of confidence intervals of the present invention, wherein IG applies the proposed fast evaluation method and IG_NR does not apply the proposed fast evaluation method; the relative deviation index Relative deviation indexRDI is used as an evaluation index of performance, and the RDI is calculated according to the formula of RDI i ＝(TT i -TT best )/(TT worst -TT best ) Wherein TT i Indicating the total delay time obtained when a particular algorithm solves a particular case, while TT best Sum TT worst Respectively representing the minimum and maximum total delay time obtained when solving the same calculation example in all the used algorithms; specifically, as can be seen from the RDI values of fig. 1, the RDI results of IG are significantly better than ig_nr. The method of the invention accelerates the calculation time of the target value, fully exerts the performance of the optimal scheduling method, and can converge to the best value at a higher convergence rate.
Claims (4)
1. A key machine-based flow shop group scheduling rapid evaluation method is characterized by comprising the following steps:
step 1: calculating the forward finishing time of all workpieces in all groups on the machine;
step 2: calculating the backward finishing time of all workpieces in all groups on the machine;
step 3: inserting groups or workpieces and obtaining key machines;
step 4: obtaining the finishing time of the workpiece on the last machine according to the key machine;
step 5: and calculating the total delay time according to the result of the step 4.
2. The rapid evaluation method for key machine-based flow shop group scheduling according to claim 1, further characterized in that the rapid evaluation method based on the key machine insertion neighborhood is classified into a group insertion acceleration criterion and a workpiece insertion acceleration criterion according to the characteristics of the group problem and described by a specific numbering scheme,
factory k contains delta k Grouping, the scheduling sequence isWherein->For the first position processed group, l ε {1,2, …, δ k Definitions->For the number of workpieces in the group processed in the first position, group +.>Is->The scheduling sequence of each workpiece is Wherein->For the workpiece processed in the j-th position +.> Combining the group scheduling sequence and the workpiece scheduling sequence to obtain a complete scheduling sequence of the factory k>
In the scheduling sequence sigma k In the machine M, the workpiece at the j-th position in the first group i The earliest finishing time is defined asThe duration between the latest start time and the maximum finish time is defined as +.>Group l and group l+1 in machine M i The preparation time between is defined as +.>Wherein (1)>Representative of the preparation time of the first processed group, the workpieces in the j-th position of the first group being in the machine M i The processing time is defined as->
In factory k, for a sequence of workpiecesIn total->Positions, defining the q-th position in the work sequence as +.> But->And->Obviously a position, define position +.>Key machine of (2) is->
3. The rapid assessment method for key machine-based flow shop group scheduling of claim 2, the group insertion acceleration criteria being described as follows:
in factory k, slave group sequence pi k Group with the first' position removedObtaining a new group sequenceAnd a new factory k complete scheduling sequence +.>Try to insert group->To all delta in the factory k Delta is obtained at each position k Schedule sequences, all delta k The rapid evaluation of the individual sequences is as follows;
step 1: for the scheduling sequence σ' k Forward calculating to obtain forward finishing time
Step 2: for the scheduling sequence σ' k Back calculating to obtain back finishing time
Step 3: hypothesis groupInserted at position t to obtain a new group sequence +.> And a new factory k complete scheduling sequence +.> For the scheduling sequence sigma k Forward calculation gives forward finishing time +.>
Step 4: obtaining a positionCritical machine of (2)>Calculating the maximum finishing time of plant k +.>
Step 5: for the scheduling sequence sigma k Calculating an insertion groupThe finishing time of each workpiece in each group on the last machine is later;
step 6: in the scheduling sequence sigma k In the first position group, the expiration date isCalculate the scheduling sequence sigma k Is a function of the total delay time of (a);
step 7: repeating steps 3,4,5,6 until all positions are considered.
4. The rapid assessment method for key machine-based flow shop team scheduling of claim 2, wherein the workpiece insertion acceleration criteria is described as follows:
in factory k, from a sequence of workpiecesThe workpiece in the j' th position is removed +.>Obtaining a new work scheduling sequenceAnd a new factory k complete scheduling sequence +.>Attempting to insert a workpieceAll->In the individual positions, is obtained->Schedule sequences, all->The rapid evaluation of the individual sequences is as follows;
step 1: for the scheduling sequence σ' k Forward calculating to obtain forward finishing time
Step 2: for the scheduling sequence σ' k Back calculating to obtain back finishing time
Step 3: assume a workpiece And a new factory k complete scheduling sequence +.> For the scheduling sequence sigma k Forward calculation gives forward finishing time +.>
Step 4: obtaining a positionCritical machine of (2)>Calculating the maximum finishing time of plant k +.>
Step 5: for the scheduling sequence sigma k Calculating an insert workpieceThe finishing time of each workpiece in each group on the last machine is later;
step 6: in the scheduling sequence sigma k In the first position group, the expiration date isCalculate the scheduling sequence sigma k Is a function of the total delay time of (a);
step 7: repeating steps 3,4,5,6 until all positions are considered.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117371769A (en) * | 2023-12-08 | 2024-01-09 | 聊城大学 | Scheduling acceleration evaluation method for distributed blocking flow shop |
| CN117787476A (en) * | 2023-12-07 | 2024-03-29 | 聊城大学 | Quick evaluation method for blocking flow shop scheduling based on key machine |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117787476A (en) * | 2023-12-07 | 2024-03-29 | 聊城大学 | Quick evaluation method for blocking flow shop scheduling based on key machine |
| CN117371769A (en) * | 2023-12-08 | 2024-01-09 | 聊城大学 | Scheduling acceleration evaluation method for distributed blocking flow shop |
| CN117371769B (en) * | 2023-12-08 | 2024-03-12 | 聊城大学 | Scheduling acceleration evaluation method for distributed blocking flow shop |
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