CN107437121B - Production process control method suitable for simultaneously processing single workpiece by multiple machines - Google Patents

Production process control method suitable for simultaneously processing single workpiece by multiple machines Download PDF

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CN107437121B
CN107437121B CN201610353532.2A CN201610353532A CN107437121B CN 107437121 B CN107437121 B CN 107437121B CN 201610353532 A CN201610353532 A CN 201610353532A CN 107437121 B CN107437121 B CN 107437121B
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workpiece
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CN107437121A (en
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李新宇
肖胜强
高亮
陈鹏
陈羊幸
余傲蓉
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Huazhong University of Science and Technology
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    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
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    • G06Q10/0633—Workflow analysis

Abstract

The invention discloses a production process control method suitable for simultaneously processing single workpieces by multiple machines, which comprises the steps of firstly constructing a problem model of multiple parallel processing machines according to the characteristics of a production workshop, wherein the model comprises the processing situation that multiple machines simultaneously and independently process single workpieces; secondly, a model solving method is constructed based on a DABC algorithm, and an optimal workpiece processing sequence and machine resource allocation mode are sought by taking the minimized maximum completion time and the minimized equipment investment cost as targets; and finally, issuing and storing the production control result scheme, and storing and managing the related workshop data information. The invention can solve the production control problem that a plurality of machines simultaneously process a single workpiece processing scene, comprehensively considers the workpiece processing sequence and the machine resource allocation, improves the model solving efficiency by improving the DABC algorithm, and greatly improves the productivity by the optimized production process control scheme.

Description

Production process control method suitable for simultaneously processing single workpiece by multiple machines
Technical Field
The invention belongs to the technical field of workshop production process control, and particularly relates to a production process control method for simultaneously processing single workpieces by multiple machines, which is suitable for processing single workpieces by multiple machines in a discrete manufacturing workshop.
Background
Aiming at a production process control method, the prior art has mature schemes, so that the problem of relevant process control in workshop production can be better solved, and a better technical effect is obtained. For example, the Chinese patent invention 201210012320.X proposes a workshop production control method based on an improved genetic algorithm, which takes the maximum product satisfaction and the maximum minimum satisfaction as production control targets, and solves the problems of processing parameter nondeterminiseness and complex workshop production control with dynamic interference events. The invention patent 201310202922.6 in China proposes a strategy search genetic method, aims at minimizing the sum of the maximum completion time and the weighted delay time, and solves the production control problem of a multi-stage mixed flow shop with two different equipment types of a dispersion machine and a batch processor. In addition, some process control schemes for specific workshops of different production types exist in the prior art, for example, chinese patent 201510261796.0 discloses a system and a method for controlling and managing production of iron and steel enterprises, and the specification of chinese patent 201510592591.0 discloses a system for monitoring and managing information of a hydraulic support welding workshop.
In the prior art, different intelligent optimization technologies and methods are used for solving the general production process control problem, but from the technical process control method, the method is usually more specific to the classical standard problem and is deficient in the technical method specific to the specific production processing scene; in addition, from the aspect of a production process control system, the construction of a system of emphasis and workshop information is insufficient in the aspect of an intelligent control technical method. In addition, because of the large number of types and production methods of workshops, many other types of workshops lack an effective production control method.
Particularly, in the actual workshop production process, aiming at the production scene that the workpiece has a large body and the machine processes around the workpiece, a production mode that a plurality of machines simultaneously and independently process the same workpiece exists, such as the welding of a large structural member, and the like.
Disclosure of Invention
In view of the above defects or improvement requirements of the prior art, the present invention provides a method for controlling a generation process of a single workpiece processed by multiple machines simultaneously, which optimizes a production control process thereof by a problem control manner of multiple parallel processors and based on an improved discrete artificial bee colony method, thereby solving the above technical problems of insufficient generation control accuracy and low production efficiency.
To achieve the above object, according to the present invention, there is provided a generating process control method for simultaneously processing single workpieces by multiple machines, comprising the steps of:
(1) the method for establishing the production process control model for simultaneously processing the single workpieces by the multiple machines comprises the following steps:
(1.1) setting optimization targets of the production process control model, namely, taking the minimized maximum completion time and the minimized machine input cost as targets, respectively:
minf1＝maxTi,j(1)
Figure BDA0000999751990000021
wherein, Ti,jThe finishing time of the workpiece j in the working procedure i; p is a radical ofi,jIs the processing time of a workpiece j in a procedure i, M is a procedure set and M is {1,2, …, M }, wherein M is a natural number, i is a procedure number and i ∈ M, N is a workpiece set and N is {1,2, …, N }, wherein N is a natural number, j is a workpiece number and j ∈ N, M is the processing time of a workpiece j in a procedure i, M is a procedure set and M is {1,2, …, M }, wherein M is a natural number, i is a procedure numberiIs a machine set in the ith process, r is a machine serial number and r ∈ MiIf the workpiece j is machined on the machine r in the step i, y i,j,r1, otherwise yi,j,r＝0，μi,jThe number of machines used for the workpiece j in the process i,
Figure BDA0000999751990000022
c is a penalty factor for adding additional machines, C ∈ [0,1]；
(1.2) according to the actual situation of the workshop, setting the following constraints:
Figure BDA0000999751990000023
Figure BDA0000999751990000024
Figure BDA0000999751990000025
Figure BDA0000999751990000026
Figure BDA0000999751990000027
wherein, the constraint (3) determines the first workpiece of each stage, the constraint (4) indicates that the workpieces have a determined sequence precedence relationship, the constraint (5) is the constraint of the total number of parallel processing machines which are put into use in each process at any moment, wherein L is the total number of the parallel processing machines which can be used for processing, is a constant, phii，tThe number of machines put into use in the t minute of processing in the step i, and the constraint (6) and the constraint (7) are variable constraints of 0-1;
(2) solving the model by using an artificial bee colony algorithm to obtain a solving result, which specifically comprises the following steps:
(2.1) setting a population size P, a machine number limit L m, a derotation limit L a and a local search probability Ps, generating a processing sequence permu of an initialized population and a machine allocation matrix mu of each workpiece in each process, and calculating a fitness value pi of each individual indindWherein ind represents the ind-th individual, each individual comprising a processing sequence permu with a length of n workpieces, a machine allocation matrix μ with a size of m × n, and a corresponding fitness value piindThe fitness value is the inverse of the maximum completion time;
(2.2) hiring bee stage, repeating the following process for individuals in the population ind ═ 1, …, P:
(2.2.1) randomly selecting tau 1 insertion/interchange operation to generate a neighborhood, wherein tau 1 ∈ {1,2 };
(2.2.2) generating a random number rand1, if rand1 is less than Ps, carrying out local search to generate a new individual and calculating the fitness value of the new individual;
(2.2.3) comparing the fitness value of the new individual with that of the original individual, and keeping the individual with a larger fitness value;
(2.3) following the bee stage, generating a random number rand2, if
Figure BDA0000999751990000031
Wherein piq(q ═ 1, …, ind) is the fitness value of the qth individual, the ind th hired bee is chosen as the follower bee and the following process is repeated:
(2.3.1) randomly selecting tau 2 insertion/interchange operations to generate a neighborhood, wherein tau 2 ∈ {1,2,3 };
(2.3.2) carrying out local search to generate a new individual and calculating the fitness value of the new individual, wherein the local search is to generate a new individual after carrying out random operation on the individual and solve the new individual into the individual, and the local search is an algorithm mature in the industry.
(2.3.3) selecting an individual with a larger fitness value as a hiring bee by comparing the fitness values of the new individual and the original individual;
(2.4) a scout bee stage, if max (Bas) > L a, where Bas is the cumulative number of times the fitness value of an individual ind has not improved, selecting the hiring bee as the scout bee and repeating the following process:
(2.4.1) applying a Destrconstr algorithm to generate a new individual as a scout bee; wherein, the process of the DestrConstr algorithm is as follows: taking out the processing sequence permu and the machine distribution matrix mu of the individual ind, randomly removing three numbers from the permu to obtain a residual sequence permu0, sequentially inserting the three removed numbers into a sequence permu0, and reserving the sequence with the maximum fitness value to obtain a new sequence and a machine distribution matrix;
(2.4.2) generating a new machine allocation matrix μ 1 when N μ > L m, where N μ is the total number of machines;
(2.4.3) calculating the fitness value of the new individual and replacing mu with mu 1 if the fitness value of the new individual is larger by comparing the fitness value of the new individual with the fitness value of the original individual;
(2.5) recording the currently found optimal individuals and parameters such as corresponding workpiece sequencing and machine allocation matrix;
and (2.6) stopping if the termination condition is met, otherwise, turning to the step (2.2).
Generally, compared with the prior art, the above technical solution conceived by the present invention has the following beneficial effects:
(1) in the method, the problem of control over the production process of simultaneously processing a single workpiece processing scene by a plurality of machines can be solved; the processing sequence of the workpieces and the machine resource allocation are comprehensively considered, and the obtained production task control scheme is more reasonable;
(2) in the method, the production process is controlled more accurately by considering the preparation time and optimizing the machine resource allocation, so that the resource utilization rate is improved, and the workshop production cost is reduced;
(3) in the method, the problem solving efficiency is improved by improving the DABC algorithm, and the productivity is greatly improved by optimizing the production control scheme.
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FIG. 1 is a block diagram of an embodiment of a method for controlling a manufacturing process for processing a single workpiece by multiple machines simultaneously;
FIG. 2 is a flow chart of a method of controlling a manufacturing process for multiple machines simultaneously processing a single workpiece according to one embodiment of the present invention;
FIG. 3 is a diagram illustrating the results of a method for controlling a manufacturing process for processing single workpieces simultaneously by multiple machines according to one embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
A production process control method for simultaneously processing single workpieces by multiple machines according to an embodiment of the present invention is described in detail below with reference to fig. 1 to 2, which includes the steps of constructing a production process control model and solving the model:
1) construction of a production Process control model
As shown in the implementation block diagram of the technical scheme shown in FIG. 1, customer order information, process characteristic information, available equipment information and material information are collected according to the specific situation of a workshop. The customer order information determines the type of the production control model, and the sales department generally provides order demand information; the process characteristic information is provided by a process department and determines the number of workstations, the characteristics and the constraint of a processing machine and the like in the production control model; available equipment information is provided by an equipment department, and the total machine number, machine distribution constraint and the like of the production control problem can be known from the equipment information; the material information is provided by a material department, and the preparation and starting processing states of the workpiece can be known by the material information. The model construction process is as follows:
(1.1) defining variables
M ═ {1,2, …, M }: the process set includes that all the workpieces flow through the process sets in the designated sequence in sequence, and m is a natural number
MiSet of machines of the ith process, i ∈ M
Φi,t: number of parallel processors in the t minute process i
L total number of processing machines
N ═ {1,2, …, N }: a workpiece set, n is a natural number
pi,j: the processing time of the workpiece j in the step i.
si,j: preparation time of workpiece j independent of the sequence of processing in step i
Ti,j: finishing time of workpiece j in process i
Adding penalty factor for additional machines, C ∈ [0,1]
xi,j,kIf a workpiece j is processed immediately before a workpiece k in a process i, xi,j,k1, otherwise xi,j,k＝0
yi,j,rIf the workpiece j is machined on the machine r in the step i, y i,j,r1, otherwise yi,j,r＝0
μi,jThe number of machines used on the workpiece j in the step i,
Figure BDA0000999751990000051
(1.2) setting optimization objectives of the model
The optimization objectives are (1) minimizing the maximum completion time and (2) minimizing the machine investment cost:
minf1＝maxTi,j(1)
Figure BDA0000999751990000052
wherein, Ti,jThe finishing time of the workpiece j in the working procedure i is determined by the formula (8); the target (2) represents an increased cost after the input of the machine is increased, and is determined by the processing time of each step and the number of machines to be allocated to the machine.
(1.3) according to the actual situation of the workshop, setting the following constraints:
Figure BDA0000999751990000053
Figure BDA0000999751990000054
Figure BDA0000999751990000055
Figure BDA0000999751990000061
Figure BDA0000999751990000062
constraints (3) determine the first artifact for each stage.
And (4) representing that the workpieces have a determined sequence precedence relationship.
Constraint (5) is a constraint on the total number of parallel processors to be used in each process at any time, wherein L is the total number of processable machines and is a constant value,. phii，tIs a process ofi number of machines put into use at the t minute of processing.
Constraint (6) and constraint (7) are decision variables xi,j,k、yi,j,r0-1 variable constraints.
And (1.4) determining the finishing time of the workpiece on each process, as shown in a formula (8).
Figure BDA0000999751990000063
2) Solving production control models using an improved DABC algorithm
The DABC algorithm shown in the attached figure 2 is used for solving the model which is constructed in the part 1 and is provided with a plurality of machines and can process a single-workpiece processing scene simultaneously. The detailed steps are as follows:
(2.1) setting a population size P, a machine number limit L m, a derogation limit L a and a local search probability Ps;
(2.2) generating an initialization population, generating a processing sequence permu of the initialization population and a machine allocation matrix mu of each workpiece in each process, and calculating a fitness value pi of each individual indindWherein ind represents the ind-th individual, each individual comprising a processing sequence permu with a length of n workpieces, a machine allocation matrix μ with a size of m × n, and a corresponding fitness value piind；
(2.3) hiring bee stage, repeating for individual ind ═ 1, …, P:
(2.3.1) randomly selecting τ 1(τ 1 ∈ {1,2}) times of insert/swap operation to generate a neighborhood, wherein four insert/swap operation operators are designed:
m1: performing a proximity insertion operation on the current generation
M2: performing a proximity swap operation on the current generation
M3: performing a random insertion operation on the current generation
M4: performing a random interchange operation on the current generation
(2.3.2) generating a random number rand1, if rand1 is less than Ps, carrying out local search to generate a new individual and calculating the fitness value of the new individual;
(2.3.3) comparing the fitness value of the new individual with that of the original individual, and keeping the individual with a larger fitness value;
(2.4) following the bee stage, generating a random number rand2, if
Figure BDA0000999751990000071
Wherein piq(q ═ 1, …, ind) is the fitness value of the qth individual, the ind th hired bee is chosen as the follower bee and the following process is repeated:
(2.4.1) randomly selecting tau 2 (tau 2 ∈ {1,2,3}) times of insertion/interchange operations to generate a neighborhood;
(2.4.2) carrying out local search to generate a new individual and calculating the fitness value of the new individual;
(2.4.3) selecting an individual with a larger fitness value as a hiring bee by comparing the fitness values of the new individual and the original individual;
(2.5) a scout bee stage, if max (Bas) > L a, where Bas is the cumulative number of times the fitness value of an individual ind has not improved, selecting the hiring bee as the scout bee and repeating the following process:
(2.5.1) applying a Destrconstr algorithm to generate a new individual as a scout bee; wherein, the process of the DestrConstr algorithm is as follows: taking out the processing sequence permu and the machine distribution matrix mu of the individual ind, randomly removing three numbers from the permu to obtain a residual sequence permu0, sequentially inserting the three removed numbers into a sequence permu0, and reserving the sequence with the maximum fitness value to obtain a new sequence and a machine distribution matrix;
(2.5.2) generating a new machine allocation matrix μ 1 when N μ > L m, where N μ is the total number of machines;
(2.5.3) calculating the fitness value of the new individual and replacing mu with mu 1 if the fitness value of the new individual is larger by comparing the fitness value of the new individual with the fitness value of the original individual;
(2.6) recording the currently found optimal individuals and parameters such as corresponding workpiece sequencing and machine allocation matrix;
and (2.7) stopping if the termination condition is met, otherwise, turning to the step (2.3).
In the scheme, the constraints (3), (4), (6) and (7) are compulsorily met in population initialization, and the constraint (5) is in a 2.4.1 part, wherein the part is a loop, namely a new machine allocation matrix is generated when N mu is greater than L m until the constraint (5) is met.
The method of the present invention may further include a process of issuing a production control scheme and managing data information, which specifically includes:
3) production control result scheme publishing
Fig. 3 shows a gantt chart example of the problem of multiple parallel processors proposed by the present solution. In the figure, white stripes divide a processing time block into several longitudinal blocks, thereby indicating a multi-machine problem. For example, in the 5 th step of the workpiece 3, since 3 machines process the workpiece at the same time, 2 white bars are provided in the gray color block at this stage in the drawing, indicating that the number of machines to be processed at the same time is 3. The gantt chart shows that the maximum completion time is 305 min. It should be noted that although the multiple parallel processor model has a shorter maximum completion time than the conventional model, while also increasing the total machine usage, the machine allocation matrix is:
Figure DEST_PATH_GDA0001063581370000011
the machine allocation matrix is unique to the solution of the multiple parallel processor problem, but it can be considered that the machine allocation matrix in the conventional problem is a 1-matrix. The machine assignment matrix herein reflects the machine requirements of each workpiece at each process step, which is an important reference in discussing the goodness of the outcome of the production control scheme.
Through the production control scheme visualization technique shown in fig. 3, the production manager can clearly obtain the sequence of the planned order to be processed, and the type and number of machines required for processing each workpiece in each process.
4) Database management
Data is the driving force for production control management, and workshop data mainly comprises two contents: on the one hand, data related to the characteristics of the production control model, such as customer order information, process characteristic information, available equipment information and the like, can be used for embodying the model; on the other hand, the data related to the production process, such as preparation time, processing time, etc., are the objects processed by the production process control method provided by the invention, and are also the abstractions of the production process of the workpiece in the workshop, and the processing result is the generation of the production control scheme. Some data need to be collected and stored before the production control model is constructed, and the result data need to be released and stored after the production control scheme is generated.
To further illustrate the practice of the present invention, the following examples of the weld shop manufacturing process are provided.
1) Construction of a welding shop model
In an embodiment, the first step is the construction of a production control problem model based on plant characteristics. The welding production process is a typical application scene that multiple machines simultaneously process a single-workpiece processing scene. In the welding of large structural parts, the welding process is carried out around a workpiece, and a plurality of welding machines can simultaneously weld the same workpiece, namely the problem that a plurality of machines process a single workpiece. Consider a typical welding shop having 5 main processes, or 5 stages, each with a number of machines, tooling fixtures, workers, etc. All the workpieces sequentially pass through these 5 processes in the same order. For a welding workshop of the box-shaped beam, 5 processes are as follows: splicing small parts, splicing large parts, welding inner seams, packaging and welding outer seams.
The production control model of the present embodiment can be directly cited to the aforementioned model.
2) Solving examples with modified DABC Algorithm
Three examples of 10 × 5, 30 × 5 and 60 × 5 are respectively designed for analysis, and in order to embody the effect of the invention, two algorithms of DABC and GA are compared, the population scale is set to be 50, the iteration number of the algorithm is 1000, the number of machines is restricted to be 7, the abandon limit is 3, and the local search probability is 0.2.
Calculation and analysis are carried out according to the algorithm steps, and the obtained results are shown in the following table 1:
TABLE 1 simulation calculation results of DABC and GA algorithms
Figure BDA0000999751990000091
The results in table 1 show that the DABC algorithm used in the present invention has significant advantages over GA for different scale problems, whether compared in terms of production efficiency or machine input.
3) Publishing of production control result schema
Taking the problem of 10 × 5 scale as an example, after the production control result scheme is generated, the workpiece processing steps are as follows:
8→10→1→6→5→2→7→3→9→4
the corresponding machine allocation matrix is:
Figure BDA0000999751990000092
according to the result, the corresponding production and control can be carried out.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (1)

1. A generation process control method for simultaneously processing single workpieces by multiple machines comprises the following steps:
(1) establishing a generation process control model for simultaneously processing single workpieces by multiple machines, which specifically comprises the following steps:
setting an optimization target for generating a process control model, namely taking the minimized maximum completion time and the minimized machine input cost as targets, respectively:
min f1＝max Ti,j(1)
Figure FDA0002494110990000011
wherein, Ti,jThe finishing time of the workpiece j in the working procedure i; p is a radical ofi,jThe processing time of a workpiece j in a process i, M is a process set and M is {1,2, ·, M }, wherein M is a natural number, i is a process number and i ∈ M, N is a workpiece set and N is {1,2, ·, N }, wherein N is a natural number, j is a workpiece number and j ∈ N, M is a time sequence of the workpiece j in the process i, M is a process set and M is {1,2, ·, M }, wherein M is a natural number, i is a process number and i ∈ M, N is a workpieceiIs a machine set in the ith process, r is a machine serial number and r ∈ MiIf the workpiece j is machined on the machine r in the step i, yi,j,r1, otherwise yi,j,r＝0，μi,jThe number of machines used for the workpiece j in the process i,
Figure FDA0002494110990000012
c is a penalty factor for adding additional machines, C ∈ [0,1]；
(2) Solving the model by using an artificial bee colony algorithm to obtain a solving result, which specifically comprises the following steps:
(2.1) setting a population size P, a machine number limit L m, a derotation limit L a and a local search probability Ps, generating a processing sequence permu of an initialized population and a machine allocation matrix mu of each workpiece in each process, and calculating a fitness value pi of each individual indindWherein ind represents the ind-th individual, each individual comprising a processing sequence permu with a length of n workpieces, a machine allocation matrix μ with a size of m × n, and a corresponding fitness value piind；
(2.2) employing bee stage, repeating the following process for individuals in the population ind ═ 1, ·, P:
(2.2.1) randomly selecting tau 1 insertion/interchange operation to generate a neighborhood, wherein tau 1 ∈ {1,2 };
(2.2.2) generating a random number rand1, if rand1 is less than Ps, carrying out local search to generate a new individual and calculating the fitness value of the new individual;
(2.2.3) comparing the fitness value of the new individual with that of the original individual, and keeping the individual with a larger fitness value;
(2.3) following the bee stage, generating a random number rand2, if
Figure FDA0002494110990000013
Wherein piq(q 1, ·, ind) is the fitness value of the qth individual, chooses the ind th employed bee as a follower bee and repeats the following process:
(2.3.1) randomly selecting tau 2 insertion/interchange operations to generate a neighborhood, wherein tau 2 ∈ {1,2,3 };
(2.3.2) carrying out local search to generate a new individual and calculating the fitness value of the new individual;
(2.3.3) selecting an individual with a larger fitness value as a hiring bee by comparing the fitness values of the new individual and the original individual;
(2.4) a scout bee stage, if max (Bas) > L a, where Bas is the cumulative number of times the fitness value of an individual ind has not improved, selecting the hiring bee as the scout bee and repeating the following process:
(2.4.1) applying the DestrConstr algorithm to generate a new individual as a scout bee, which specifically comprises the following steps: taking out the processing sequence permu and the machine distribution matrix mu of the individual ind, randomly removing three numbers from the permu to obtain a residual sequence permu0, sequentially inserting the three removed numbers into a sequence permu0, and reserving the sequence with the maximum fitness value to obtain a new sequence and a machine distribution matrix;
(2.4.2) generating a new machine allocation matrix μ 1 when N μ > L m, where N μ is the total number of machines;
(2.4.3) calculating the fitness value of the new individual and replacing mu with mu 1 if the fitness value of the new individual is larger by comparing the fitness value of the new individual with the fitness value of the original individual;
(2.5) recording the currently found optimal individuals and corresponding workpiece sequencing and machine allocation matrix parameters;
(2.6) stopping if the termination condition is met, otherwise, turning to the step (2.2);
the step of establishing a process control model for generating a plurality of machines to process single workpieces simultaneously further comprises the following steps of:
Figure FDA0002494110990000021
Figure FDA0002494110990000022
Figure FDA0002494110990000024
Figure FDA0002494110990000025
wherein, the constraint (3) determines the first workpiece of each stage, the constraint (4) indicates that the workpieces have a determined sequence precedence relationship, the constraint (5) is the constraint of the total number of parallel processing machines which are put into use in each process at any moment, wherein L is the total number of the parallel processing machines which can be used for processing, is a constant, phii,tThe number of machines put into use in the t minute of processing in the step i, and the constraint (6) and the constraint (7) are variable constraints of 0-1;
the method is suitable for processing a single workpiece with multiple machines simultaneously in a discrete manufacturing plant.
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