CN116307629A - Quick evaluation method for flow shop grouping scheduling - Google Patents
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Abstract
The invention discloses a rapid evaluation method for grouped scheduling of a flow shop, which relates to the technical field of workshop scheduling, and takes a distributed flow shop with starting time as an example, and constructs a rapid evaluation method between groups and in groups based on an insertion neighborhood according to the problem characteristics of grouped scheduling; comprising the following steps: step 1: calculating the forward finishing time jc of the workpieces j in group l on machine i [j]，[l]，i The method comprises the steps of carrying out a first treatment on the surface of the Step 2: calculating the backward finishing time js of the workpieces j in the group l on the machine i [j]，[l]，i The method comprises the steps of carrying out a first treatment on the surface of the Step 3: obtaining the maximum finishing time; step 4: updating the forward completion time jc [j]，[l]，i The method comprises the steps of carrying out a first treatment on the surface of the Step 5: updating backward completion time js [j]，[l]，i The method comprises the steps of carrying out a first treatment on the surface of the Wherein l > 0, j > 0, i > 0. The invention solves the problem of quick evaluation of the target value maximum finishing time of the scheduling problem of the flow shop grouping, and reducesThe calculation time is shortened, repeated evaluation can be effectively avoided, the calculation cost is saved, and the scheduling efficiency is improved.
Description
Technical Field
The invention relates to the technical field of workshop scheduling, in particular to a method for rapidly evaluating flow shop grouping scheduling.
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 usually composed of a series of specialized machines, a group of workpieces having similar requirements in terms of tools, setup and sequence of operations, etc. 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 may simplify the scheduling process, shorten the production time, improve the reliability of the production system, which is especially advantageous for highly automated systems. It is becoming one of the most important manufacturing modes in modern enterprises, such as Hua is a limited company, fuji-C technology group, and automobile assembly industry.
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.
Disclosure of Invention
In order to better solve the rapid calculation mode of the target value of the distributed flow shop group scheduling problem with the starting time, an effective rapid evaluation method is provided, namely, the flow shop group scheduling rapid evaluation method is divided into an inter-group insertion acceleration criterion and an intra-group insertion acceleration criterion according to the characteristic of the group scheduling problem.
The invention provides a method for quickly evaluating grouped scheduling of a flow shop, which comprises the following steps: the method comprises the following steps:
step 1: calculating the forward finishing time jc of the workpieces j in group l on machine i [j]，[l]，i ；
Step 2: calculating the backward finishing time js of the workpieces j in the group l on the machine i [j]，[l]，i ；
Step 3: obtaining the maximum finishing time;
step 4: updating the forward completion time jc [j]，[l]，i ；
Step 5: updating backward completion time js [j]，[l]，i ；
Wherein l > 0, j > 0, i > 0.
Further, the fast evaluation method based on the interpolation neighborhood is classified into an inter-group interpolation acceleration criterion and an intra-group interpolation acceleration criterion according to the characteristics of the group problem.
Further, the fast evaluation method based on the interpolation neighborhood is classified into an inter-group interpolation acceleration criterion and an intra-group interpolation acceleration criterion according to the characteristics of the group problem.
Further, the inter-group insertion acceleration criteria include:
suppose that the manufacturing unit k contains delta k Group, try to get delta s Inserting the groups into the manufacturing unit k so that the maximum finishing time obtained is minimized;
step 11: let t=1, consider group l' t Inserting;
step 12: calculating the forward finishing time jc of the workpieces j in group l on machine i [j]，[l]，i ；
Step 13: calculating the backward finishing time js of the workpieces j in the group l on the machine i [j]，[l]，i ；
Step 14: assume group l' t Inserted at q position, q=1, 2, …, δ k +1, calculating the forward completion time after insertion
Step 15: calculating an insertion group l 'according to the forward finishing time and the backward finishing time' t Maximum finishing time C after max (l′ t ，q)；
Step 16: updating forward completion time jc for q-position and thereafter position [j]，[l]，i， Updating the backward completion time js of the q-position and the previous position [j]，[l]，i ；
Step 17: let t=t+1, δ k ＝δ k +1；
Step 18: repeating steps 14, 15, 16, 17 until all delta s The groups are inserted.
Further, in the step 12, a forward finishing time jc of the workpiece j in the group l on the machine i is calculated [j]，[l]，i The calculation formula of (2) is as follows:
jc [j]，[l]，0 ＝0；l＝1，2，…，δ k ；j＝1，2，…，n [l] ；
jc [j]，[l]，i ＝max(jc [j-1]，[l]，i ，jc [j]，[l]，i-1 )+p [j]，[l]，i ；
l＝1，2，…，δ k ，j＝2，3，…，n [l] ，i＝1，2，…，m；
wherein s is [l-1]，[l]，i Representing group l-1 and the preparation time of group l on machine i, p [j]，[l]，i The processing time of the workpieces j in group l on machine i is indicated.
Further, in the step 13, a backward finishing time js of the workpiece j on the machine i in the group l is calculated [j]，[l]，i Is of the meter(s)The calculation formula is as follows:
js [j]，[l]，m+1 ＝0；l＝δ k ，δ k -1，…，1；j＝n [l] ，n [l] -1，…，1；
js [j]，[l]，i ＝max(js [j+1]，[l]，i ，js [j]，[l]，i +1)+p [j]，[l]，i ；
l＝δ k ，δ k -1，…，1；j＝n [l] -1，n [l] -2，…，1；i＝m，m-1，…，1；
wherein n is [l] Indicating the number of work pieces in group l, n [l] ＞0。
Further, in the step 14, the calculation of the inserted forward completion time
The calculation formula of (2) is as follows:
further, in the step 15, the maximum finishing time C max (l′ t The calculation formula of q) is as follows:
further, the intra-group insertion acceleration criteria includes:
assume that in group l', n [l′] -1 work piece has been scheduled to completion, where n [l′] For all work pieces in a group, n [l′] > 0; attempting to insert the workpiece t into the group l' such that the maximum finishing time obtained is minimized, where t > 0;
step 21: calculating the forward finishing time jc of the workpieces j in the group l' on the machine i [j]，[l′]，i ；
Step 22: calculating the backward finishing time js of the workpieces j in the group l' on the machine i [j]，[l′]，i ；
Step 23: assuming that the workpiece t is inserted to the q position, q=1, 2, …, n [l′] Calculating the forward completion time jc after insertion t，[l′]，i ；
Step 24: calculating a maximum finishing time c after inserting the work t in the group l' based on the forward finishing time and the backward finishing time max (t，q，[l′])；
Step 25: updating forward completion time jc for q-position and thereafter position [j]，[l′]，i Updating the backward completion time js of the q-position and the previous position [j]，[l′]，i 。
Further, in the step 23, the forward completion time jc after the insertion is calculated t，[l′]，i The calculation formula is as follows:
jc t，[l′]，0 ＝0；
further, in the step 24, the maximum finishing time C max (t，q，[l′]) The calculation formula is as follows:
the method for quickly evaluating the grouped scheduling of the flow shop has the following technical effects:
the method comprises the following steps:
(1) The method is used for excavating hidden problem characteristics, analyzing the relation between groups and workpieces in the groups in the inserting process, and dividing a rapid evaluation method based on the inserting neighborhood into an inter-group inserting acceleration criterion and an intra-group inserting acceleration criterion according to the characteristics of the group problems;
(2) Temporal complexity is driven by using inter-group acceleration criteria
Reduced to->
(3) Temporal complexity is driven by using intra-group acceleration criteria
Reduced to->
(4) By recording the forward finishing time and the backward finishing time at any time, when the maximum finishing time needs to be calculated, the target value is quickly obtained according to the forward finishing time and the backward finishing time.
Application level:
(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.
Therefore, the invention provides a quick evaluation method for grouped scheduling of a flow shop, which takes a distributed flow shop with starting time as an example, improves the calculation modes among groups and in groups, reduces the calculation or evaluation time of target values, and improves the efficiency of workshop scheduling. In addition, 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.
Drawings
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.
The invention provides a method for rapidly evaluating grouped scheduling of a flow shop, which comprises the following steps:
step 1: calculating the forward finishing time jc of the workpieces j in group l on machine i [j]，[i]，i ；
Step 2: calculating the backward finishing time js of the workpieces j in the group l on the machine i [j]，[l]，i ；
Step 3: obtaining the maximum finishing time;
step 4: updating the forward completion time jc [j]，[l]，i ；
Step 5: updating backward completion time js [j]，[l]，i ；
Wherein l > 0, j > 0, i > 0.
Specifically, taking a distributed flow shop with a start time as an example, the method mainly comprises the following implementation processes:
dividing a rapid evaluation method based on the interpolation neighborhood into an inter-group interpolation acceleration criterion and an intra-group interpolation acceleration criterion according to the characteristics of the group problems;
in some embodiments of the present application, the inter-group insertion acceleration criteria include:
suppose that PCB manufacturing unit k contains delta k Group, try to get delta s Inserting the groups into the PCB manufacturing unit k so that the maximum finishing time obtained is minimized; wherein k > 0, delta k ＞0；
Step 11: let t=1, consider group l' t Inserting;
step 12: calculating the forward finishing time jc of the workpieces j in group l on machine i [j]，[l]，i Wherein s is [l-1]，[l]，i Representing group l-1 and the preparation time of group l on machine i, p [j]，[l]，i The processing time of the workpiece j in the group l on the machine i is represented by the following calculation formula:
jc [j]，[l]，0 ＝0；l＝1，2，…，δ k ；j＝1，2，…，n [l] ；
jc [j]，[l]，i ＝max(jc [j-1]，[l]，i ，jc [j]，[l]，i-1 )+p [j]，[l]，i ；
l＝1，2，…，δ k ，j＝2，3，…，n [l] ，i＝1，2，…，m；
wherein m is an integer;
step 13: calculating the backward finishing time js of the workpieces j in the group l on the machine i [j]，[l]，i Wherein n is [l] Indicating the number of work pieces in group l, n [l] > 0, the calculation formula is as follows:
js [j]，[l]，m+1 ＝0；l＝δ k ，δ k -1，…，1；j＝n [l] ，n [l] -1，…，1；
js [j]，[l]，i ＝max(js [j+1]，[l]，i ，js [j]，[l]，i+1 )+p [j]，[l]，i ；
l＝δ k ，δ k -1，…，1；j＝n [l] -1，n [l] -2，…，1；i＝m，m-1，…，1；
step 14: assume group l' t Inserted at q position, q=1, 2, …, δ k +1, calculating the forward completion time after insertion
step 15: calculating an insertion group l 'according to the forward finishing time and the backward finishing time' t Maximum finishing time C after max (l′ t ，q)；
Step 16: updating forward completion time jc for q-position and thereafter position [j]，[l]，i Updating the backward completion time js of the q-position and the previous position [j]，[l]，i ；
Step 17: let t=t+1, δ k ＝δ k +1；
Step 18: repeating steps 14, 15, 16, 17 until all delta s The groups are inserted.
Some embodiments of the present application slave time complexity by using an inter-group acceleration criterion
Is reduced to
In some embodiments of the present application, the intra-group insertion acceleration criteria include:
assume that in group l', n [l′] -1 work piece has been scheduled to completion, where n [l′] For all work pieces in group l', n [l′] > 0; attempting to insert the workpiece t into the group l' such that the maximum finishing time obtained is minimal, where t > 0;
step 21: calculating the forward finishing time jc of the workpieces j in the group l' on the machine i [j]，[l′]，i ；
Step 22: calculating the backward finishing time js of the workpieces j in the group l' on the machine i [j]，[l′]，i ；
Step 23: assuming that the workpiece t is inserted to the q position, q=1, 2, …, n [l′] Calculating the forward completion time jc after insertion t，[l′]，i The calculation formula is as follows:
jc t，[l′]，0 ＝0；
wherein m is an integer;
step 24: calculating a maximum finishing time C after inserting the work t in the group l' based on the forward finishing time and the backward finishing time max (t，q，[l′]) The calculation formula is as follows:
step 25: updating forward completion time jc for q-position and thereafter position [j]，[l′]，i Updating the backward completion time js of the q-position and the previous position [j]，[l′]，i 。
Some embodiments of the present application slave time complexity by using intra-group acceleration criteria
Reduced to->
By recording the forward finishing time and the backward finishing time at any time, when the maximum finishing time is required to be calculated, a target value is obtained according to the forward finishing time and the backward finishing time, so that the calculating time is reduced, and the scheduling efficiency of the workshop is improved.
FIG. 1 is a comparison graph of confidence intervals of the present invention, wherein tIGA applies the proposed rapid assessment method and tIGA_nr does not apply the proposed rapid assessment method; RPI represents relative percentage deviation (Relative percentage increase) as an evaluation index of performance, and the calculation formula of RPI is RPI= (Ci-Cbest)/Cbest multiplied by 100, wherein Ci represents the maximum finishing time obtained when a specific algorithm solves a specific example, and Cbest represents the minimum maximum finishing time obtained when the same example is solved in all the used algorithms; specifically, as can be seen from the RPI values of fig. 1, the RPI results of tIGA are significantly better than tiga_nr. The method of the invention accelerates the calculation time of the target value, fully exerts the algorithm performance, and can converge to the best value with a faster convergence rate.
Finally, it should be noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and those skilled in the art, after reading the present application, may make various modifications or alterations to the present invention with reference to the above embodiments, all falling within the scope of the appended claims.
Claims (10)
1. A method for quickly evaluating grouped scheduling of a flow shop is characterized by comprising the following steps:
step 1: calculating the forward finishing time jc of the workpieces j in group l on machine i [j]，[li]，i ；
Step 2: calculating the backward finishing time js of the workpieces j in group k on machine i [j]，[l]，i ；
Step 3: obtaining the maximum finishing time;
step 4: updating the forward completion time jc [j]，[l]，i ；
Step 5: updating backward completion time js [j]，[l]，i ；
Wherein l > 0, j > 0, i > 0.
2. The method according to claim 1, wherein the method is divided into an inter-group insertion acceleration criterion and an intra-group insertion acceleration criterion according to characteristics of a group problem.
3. The method of claim 2, wherein the inter-group insertion acceleration criteria comprises:
suppose that the manufacturing unit k contains delta k Group, try to get delta s Inserting the groups into the manufacturing unit k so that the maximum finishing time obtained is minimized; wherein k > 0, delta k ＞0；
Step 11: let t=1, consider group l' t Inserting;
step 12: calculating the forward finishing time jc of the workpieces j in group l on machine i [j]，[l]，i ；
Step 13: calculating the backward finishing time js of the workpieces j in the group l on the machine i [j]，[l]，i ；
Step 14: assume group l' t Inserted at q position, q=1, 2, …, δ k +1, calculating the forward completion time after insertion
Step 15: calculating an insertion group l 'according to the forward finishing time and the backward finishing time' t Maximum finishing time C after max (l′ t ，q)；
Step 16: updating forward completion time jc for q-position and thereafter position [j]，[l]，i Updating the backward completion time js of the q-position and the previous position [j]，[l]，i ；
Step 17: let t=t+1, δ k ＝δ k +1；
Step 18: repeating steps 14, 15, 16, 17 until all delta s The groups are inserted.
4. A method for rapid evaluation of a flow shop team schedule according to claim 3, wherein in step 12, the forward finishing time jc of the workpieces j in the team i on machine i is calculated [j]，[l]，i The calculation formula of (2) is as follows:
jc [j]，[l]，0 ＝0；l＝1，2，…，δ k ；j＝1，2，…，n [l] ；
jc [j]，[l]，i ＝max(jc [j-1]，[l]，i ，jc [j]，[l]，i-1 )+p [j]，[l]，i ；
l＝1，2，…，δ k ，j＝2，3，…，n [l] ，i＝1，2，…，m；
wherein s is [l-1]，[l]，i Representing group l-1 and the preparation time of group l on machine i, p [j]，[l]，i The processing time of the workpieces j in group l on machine i is indicated.
5. A method for rapid evaluation of a flow shop team schedule according to claim 3, wherein in step 13, the work pieces j in the computing team i are back on machine iTo the finishing time js [j]，[l]，i The calculation formula of (2) is as follows:
js [j]，[l]，m+1 ＝0；l＝δ k ，δ k -1，…，1；j＝n [l] ，n [l] -1，…，1；
js [j]，[l]，i ＝max(js [j+1]，[l]，i ，js [j]，[l]，i+1 )+p [j]，[l]，i ；
l＝δ k ，δ k -1，…，1；j＝n [l] -1，n [l] -2，…，1；i＝m，m-1，…，1；
wherein n is [l] Indicating the number of work pieces in group l, n [l] ＞0。
6. A method for rapid evaluation of flow shop team scheduling according to claim 3, wherein in step 14, the calculated post-insertion forward completion time jc [j]，l′t，i The calculation formula of (2) is as follows:
7. a method for rapid evaluation of flow shop team scheduling according to claim 3, wherein in step 15 the maximum completion time C max (l′ t The calculation formula of q) is as follows:
8. the method of claim 2, wherein the in-group insertion acceleration criteria comprises:
assume that in group l', n [l′] -1 work piece has been scheduled to completion, where n [l′] For all work pieces in a group, n [l′] > 0; attempting to insert a workpiece t into the set l' such that the maximum finishing time obtained is minimized, where t > 0;
step 21: calculating the forward finishing time jc of the workpieces j in the group l' on the machine i [j]，[l′]，i ；
Step 22: calculating the backward finishing time js of the workpieces j in the group l' on the machine i [j]，[l′]，i ；
Step 23: assuming that the workpiece t is inserted to the q position, q=1, 2, …, n [l′] Calculating the forward completion time jc after insertion t，[l′]，i ；
Step 24: calculating a maximum finishing time c after inserting the work t in the group l' based on the forward finishing time and the backward finishing time max (t，q，[l′])；
Step 25: updating forward completion time jc for q-position and thereafter position [j]，[l′]，i Updating the backward completion time js of the q-position and the previous position [j]，[l′]，i 。
9. The method according to claim 8, wherein in step 23, the forward completion time jc after the insertion is calculated t，[l′]，i The calculation formula is as follows:
jc t，[l′]，0 ＝0；
10. the method for rapid evaluation of flow shop team scheduling of claim 8, wherein in step 24, the maximum completion time C max (t，q，[l′]) The calculation formula is as follows:
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