CN108107848B - Assembly line workshop scheduling method based on minimum idle time - Google Patents

Assembly line workshop scheduling method based on minimum idle time Download PDF

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CN108107848B
CN108107848B CN201611042524.2A CN201611042524A CN108107848B CN 108107848 B CN108107848 B CN 108107848B CN 201611042524 A CN201611042524 A CN 201611042524A CN 108107848 B CN108107848 B CN 108107848B
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idle time
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戴佐俊
张月霞
杨瑞琪
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Beijing Information Science and Technology University
Jiangsu Chuangyuan Electron Co Ltd
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    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/418—Total factory control, i.e. centrally controlling a plurality of machines, e.g. direct or distributed numerical control [DNC], flexible manufacturing systems [FMS], integrated manufacturing systems [IMS] or computer integrated manufacturing [CIM]
    • G05B19/41865—Total factory control, i.e. centrally controlling a plurality of machines, e.g. direct or distributed numerical control [DNC], flexible manufacturing systems [FMS], integrated manufacturing systems [IMS] or computer integrated manufacturing [CIM] characterised by job scheduling, process planning, material flow
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    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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Abstract

The invention provides a pipeline workshop scheduling method based on minimum idle time, which comprises the following steps: (1) establishing a mathematical model of a flow line workshop scheduling problem; (2) establishing constraint conditions of different procedures of the same workpiece; (3) establishing process constraint conditions of different workpieces of the same machine; (4) calculating the idle time of each procedure of each workpiece; (5) and establishing a mathematical model of the assembly line workshop scheduling method based on the minimum idle time. The minimum idle time-based assembly line workshop scheduling method provided by the invention takes the minimum idle time of each process of all workpieces as an optimization target, combines the characteristics of the assembly line workshop, constructs a mathematical model with the minimum idle time, does not need repeated iteration, has short calculation time and high solving efficiency, can effectively solve the problem of scheduling of a job workshop, and can be used for scheduling management and optimization of a workshop production process.

Description

Assembly line workshop scheduling method based on minimum idle time
Technical Field
The invention relates to the technical field of scheduling optimization of a production line workshop, in particular to a production line workshop scheduling method based on minimum idle time.
Background
Pipeline shop scheduling is an important production scheduling problem. The aim of the flow line workshop scheduling is to arrange the processing sequence of the workpieces so as to minimize the time for finishing all the workpieces. The scheduling problem of the assembly line workshop is characterized in that a plurality of workpieces of a plurality of machines need to be processed, the processing sequence of all the workpieces on each machine is the same, each machine is only responsible for one procedure, and the processing sequence of the procedure of each workpiece on the plurality of machines is solved. This type of problem has proven to be an NP-hard (so-called non-deterministic) problem. Aiming at the problem of scheduling the assembly line workshop, the production process is difficult to depend on manual work to carry out effective scheduling, so that the method has important practical significance for the research of the assembly line workshop scheduling problem.
At present, algorithms for solving the pipeline workshop scheduling problem mainly focus on intelligent algorithms and heuristic algorithms, the algorithms can obtain high-quality solutions in a short time, but repeated iteration is needed, the calculation complexity is high, and the algorithms are not easy to realize.
Disclosure of Invention
The invention aims to provide a pipeline workshop scheduling method based on minimum idle time to solve the technical problem.
In order to solve the technical problems, the technical scheme of the invention is as follows: a minimum idle time pipeline workshop scheduling method comprises the following steps:
(1) establishing a mathematical model of a flow line workshop scheduling problem;
(2) establishing constraint conditions of different procedures of the same workpiece;
(3) establishing process constraint conditions of different workpieces of the same machine;
(4) calculating the idle time of each procedure of each workpiece;
(5) and establishing a mathematical model of the assembly line workshop scheduling method based on the minimum idle time.
Preferably, in the step (1), the method for establishing the mathematical model of the pipeline workshop scheduling problem is as follows:
workshop existing M machines, denoted [ A ]1,A2,…,Am,…,AM]，AmDenotes the mth machine, M ═ 1,2, …, M](ii) a Each machine can only complete one process, and the processes on each machine are different; the completion time of different processes of the same workpiece is independent, and the completion time of the same process of different workpieces is independent;
let the existing N workpieces need to be machined, denoted as [ W ]1,W2,…,Wn,…,WN]Wherein W isnDenotes the nth workpiece, N ═ 1,2, …, N]The N workpieces are independent of each other, and each workpiece needs to complete all M working procedures, wherein the sequence of the working procedures is [1,2, …, M, … and M ]]The completion time of each process of each workpiece is independent;
let the completion time of the mth process of the nth workpiece be CnmThe time length of the process completion is Lnm。
Preferably, in step 2, the constraint conditions of different steps for the same workpiece are as follows:
Cnm-Lnm≥Cn(m-1)。
preferably, in the step (3), the process constraints for different workpieces in the same machine are as follows:
Cnm-C(n-1)m≥Lnm。
preferably, in the step (4), the method for calculating the idle time of each workpiece in each process comprises:
setting the idle time before the nth workpiece is subjected to the mth procedure as SnmThen S isnmIs defined as:
Snm＝Cnm-Cn(m-1)-Lnm
Snmthe calculation formula of (2) is as follows:
Figure GDA0002383405420000031
in the above formula, anmRepresents a coefficient whennmWhen the value is 1, the idle time is represented; when a isnmWhen 0, it means no idle time, anmThe calculation formula of (2) is as follows:
Figure GDA0002383405420000032
preferably, in the step (5), the method for establishing the mathematical model of the pipeline workshop scheduling method based on the minimum idle time is as follows:
according to the idle time S of the workpiecenmThe calculation formula for calculating the total idle time of all the workpieces is as follows:
Figure GDA0002383405420000033
assembly line workshop scheduling method based on minimum idle time enables the above-mentioned idle time SnmThe value is minimum, and the time for completing all workpieces is minimum;
the objective function is established as follows:
Figure GDA0002383405420000034
the mathematical model for establishing the assembly line workshop scheduling method based on the minimum idle time is as follows:
Figure GDA0002383405420000035
the minimum idle time-based assembly line workshop scheduling method provided by the invention takes the minimum idle time of each process of all workpieces as an optimization target, combines the characteristics of the assembly line workshop, constructs a mathematical model with the minimum idle time, does not need repeated iteration, has short calculation time and high solving efficiency, can effectively solve the problem of scheduling of a job workshop, and can be used for scheduling management and optimization of a workshop production process.
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FIG. 1 is a schematic diagram illustrating an operation flow of a pipeline workshop scheduling method based on minimum idle time according to the present invention;
FIG. 2 is a simulation result of the relationship between the number of processes and the calculation time under the condition that the number of workpieces is the same according to the minimum idle time-based pipeline workshop scheduling method provided by the invention;
fig. 3 is a simulation result of the relationship between the number of workpieces and the calculation time in the case that the number of processes is the same according to the minimum idle time-based pipeline workshop scheduling method provided by the invention.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below.
A minimum idle time pipeline workshop scheduling method comprises the following steps:
(1) establishing a mathematical model of a flow line workshop scheduling problem;
(2) establishing constraint conditions of different procedures of the same workpiece;
(3) establishing process constraint conditions of different workpieces of the same machine;
(4) calculating the idle time of each procedure of each workpiece;
(5) and establishing a mathematical model of the assembly line workshop scheduling method based on the minimum idle time.
In the step (1), the method for establishing the mathematical model of the assembly line workshop scheduling problem comprises the following steps:
workshop existing M machines, denoted [ A ]1,A2,…,Am,…,AM]，AmDenotes the mth machine, M ═ 1,2, …, M](ii) a Each machine can only complete one process, and the processes on each machine are different; the completion time of different processes of the same workpiece is independent, and the completion time of the same process of different workpieces is independent;
let the existing N workpieces need to be machined, denoted as [ W ]1,W2,…,Wn,…,WN]Wherein W isnDenotes the nth workpiece, N ═ 1,2, …, N]The N workpieces are independent of each other, and each workpiece needs to complete all M working procedures, wherein the sequence of the working procedures is [1,2, …, M, … and M ]]The completion time of each process of each workpiece is independent;
let the completion time of the mth process of the nth workpiece be CnmThe time length of the process completion is Lnm。
In the step 2, the constraint conditions of different processes of the same workpiece are as follows:
Cnm-Lnm≥Cn(m-1)。
preferably, in the step (3), the process constraints for different workpieces in the same machine are as follows:
Cnm-C(n-1)m≥Lnm。
in the step (4), the method for calculating the idle time of each workpiece in each process of each workpiece comprises the following steps:
setting the idle time before the nth workpiece is subjected to the mth procedure as SnmThen S isnmIs defined as:
Snm＝Cnm-Cn(m-1)-Lnm
Snmthe calculation formula of (2) is as follows:
Figure GDA0002383405420000051
in the above formula, anmRepresents a coefficient whennmWhen the value is 1, the idle time is represented; when a isnmWhen 0, it means no idle time, anmThe calculation formula of (2) is as follows:
Figure GDA0002383405420000052
in the step (5), the method for establishing the mathematical model of the pipeline workshop scheduling method based on the minimum idle time is as follows:
according to the idle time S of the workpiecenmThe calculation formula for calculating the total idle time of all the workpieces is as follows:
Figure GDA0002383405420000053
assembly line workshop scheduling method based on minimum idle time enables the above-mentioned idle time SnmThe value is minimum, and the time for completing all workpieces is minimum;
the objective function is established as follows:
Figure GDA0002383405420000061
the mathematical model for establishing the assembly line workshop scheduling method based on the minimum idle time is as follows:
Figure GDA0002383405420000062
referring to fig. 1, the specific steps are as follows:
firstly, generating a scheme group by using the known number of workpieces;
then, selecting a scheme in the scheme group, and calculating the idle time of the workpiece to be processed in the scheme by using the known completion time length of the workpiece procedure;
calculating all idle time of each workpiece according to the number of working procedures, and summing the idle time of all the workpieces to obtain the total idle time of the scheme;
and (4) carrying out the steps on the schemes in the scheme group, and selecting the scheme with the minimum total idle time, namely the scheme with the minimum time for finishing the processing of the workpiece.
1. Generating a set of recipes
The method for generating the scheme group by using the known number n of the workpieces comprises the following steps:
since the sequence in which each machine processes the workpieces is the same, each scenario is an ordered sequence of workpieces, n workpieces { J }1,J2,…,JnN | can be generated by full permutation! And (6) a processing scheme is adopted.
2. Calculating the idle time of each workpiece
Assuming that the idle time before the nth workpiece is subjected to the m processes is SnmThen S isnmCan be defined as:
Snm＝Cnm-Cn(m-1)-Lnm
Snmthe calculation formula of (2) is as follows:
Figure GDA0002383405420000071
in the formula (4), anmRepresents a coefficient, a represents an idle time when 1, and represents no idle time when 0, anmThe calculation formula of (2) is as follows:
Figure GDA0002383405420000072
the idle time for the nth workpiece is therefore:
Figure GDA0002383405420000073
3. calculating the idle time of all workpieces
The formula for calculating the idle time of all workpieces is as follows:
Figure GDA0002383405420000074
4. selecting the scheme with the minimum total idle time
After the idle time calculation of all the schemes in the scheme group is completed, selecting the scheme with the minimum idle time, and even if the calculation result of the step 3 is minimum, the time for completing all the workpieces is minimum, and the corresponding objective function is as follows:
Figure GDA0002383405420000075
and finally, verifying the performance of the algorithm through experimental simulation.
The present algorithm uses the computation time spent in the computation process to evaluate the performance of the algorithm.
Referring to fig. 2, under the condition that the number of workpieces is the same, the simulation result of the relationship between the number of processes and the calculation time shows that the number of processes has little influence on the performance of the algorithm, and the algorithm has short calculation time and high calculation speed.
Referring to fig. 3, in the case of the same number of processes, the simulation result of the relationship between the number of processes and the calculation time shows that: under the condition that the number of the workpieces is not large, the algorithm is short in calculation time and high in speed.
In conclusion, the minimum idle time-based pipeline workshop scheduling method provided by the invention takes the minimum idle time of each process of all workpieces as an optimization target, combines the characteristics of the pipeline workshop, constructs a mathematical model with the minimum idle time, does not need repeated iteration, has short calculation time and high solving efficiency, can effectively solve the problem of scheduling of a job workshop, and can be used for scheduling management and optimization of a workshop production process.
Various modifications and alterations of this invention may be made by those skilled in the art without departing from the spirit and scope of this invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (3)

1. The method for scheduling the pipeline workshop based on the minimum idle time is characterized by comprising the following steps of:
(1) establishing a mathematical model of a flow line workshop scheduling problem;
(2) establishing constraint conditions of different procedures of the same workpiece;
(3) establishing process constraint conditions of different workpieces of the same machine;
(4) calculating the idle time of each procedure of each workpiece;
(5) establishing a mathematical model of a production line workshop scheduling method based on minimum idle time;
in the step (1), the method for establishing the mathematical model of the assembly line workshop scheduling problem comprises the following steps:
workshop existing M machines, denoted [ A ]1,A2,…,Am,…,AM]，AmDenotes the mth machine, M ═ 1,2, …, M](ii) a Each machine can only complete one process, and the processes on each machine are different; the completion time of different processes of the same workpiece is independent, and the completion time of the same process of different workpieces is independent; let the existing N workpieces need to be machined, denoted as [ W ]1,W2,…,Wn,…,WN]Wherein W isnDenotes the nth workpiece, N ═ 1,2, …, N]The N workpieces are independent of each other, and each workpiece needs to complete all M working procedures, wherein the sequence of the working procedures is [1,2, …, M, … and M ]]The completion time of each process of each workpiece is independent; let the completion time of the mth process of the nth workpiece be CnmThe time length of the process completion is Lnm(ii) a In the step (4), the method for calculating the idle time of each workpiece in each process of each workpiece comprises the following steps:
setting the idle time before the nth workpiece is subjected to the mth procedure as SnmThen S isnmIs defined as:
Snm＝Cnm-Cn(m-1)-Lnm
Snmthe calculation formula of (2) is as follows:
Figure FDA0002392164440000011
in the above formula, anmRepresents a coefficient whennmWhen the value is 1, the idle time is represented; when a isnmWhen 0, it means no idle time, anmThe calculation formula of (2) is as follows:
Figure FDA0002392164440000021
in the step (5), the method for establishing the mathematical model of the pipeline workshop scheduling method based on the minimum idle time is as follows:
according to the idle time S of the workpiecenmThe calculation formula for calculating the total idle time of all the workpieces is as follows:
Figure FDA0002392164440000022
assembly line workshop scheduling method based on minimum idle time enables the above-mentioned idle time SnmThe value is minimum, and the time for completing all workpieces is minimum;
the objective function is established as follows:
Figure FDA0002392164440000023
the mathematical model for establishing the assembly line workshop scheduling method based on the minimum idle time is as follows:
Figure FDA0002392164440000024
2. the method for pipeline shop scheduling based on minimum idle time as claimed in claim 1, wherein in the step (2), the constraints of different processes of the same workpiece are as follows:
Cnm-Lnm≥Cn(m-1)。
3. the method for pipeline shop scheduling based on minimum idle time as claimed in claim 1, wherein in the step (3), the process constraints of different workpieces in the same machine are as follows:
Cnm-C(n-1)m≥Lnm。
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