CN108229830A - Consider the dynamic hybrid flow operation minimization total complete time problem lower bound algorithm of study efficacy - Google Patents
Consider the dynamic hybrid flow operation minimization total complete time problem lower bound algorithm of study efficacy Download PDFInfo
- Publication number
- CN108229830A CN108229830A CN201810016071.9A CN201810016071A CN108229830A CN 108229830 A CN108229830 A CN 108229830A CN 201810016071 A CN201810016071 A CN 201810016071A CN 108229830 A CN108229830 A CN 108229830A
- Authority
- CN
- China
- Prior art keywords
- stage
- workpiece
- time
- lower bound
- study efficacy
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Classifications
-
- G—PHYSICS
- 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
- G06Q10/00—Administration; Management
- G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
- G06Q10/063—Operations research, analysis or management
- G06Q10/0631—Resource planning, allocation, distributing or scheduling for enterprises or organisations
- G06Q10/06316—Sequencing of tasks or work
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
-
- G—PHYSICS
- 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
- G06Q50/00—Systems or methods specially adapted for specific business sectors, e.g. utilities or tourism
- G06Q50/04—Manufacturing
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
- Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
- Y02P90/30—Computing systems specially adapted for manufacturing
Abstract
The present invention relates to production scheduling field, specifically a kind of algorithm for seeking the dynamic hybrid flow operation minimization total complete time problem lower bound for considering study efficacy.Lower bound is the obtained solution of sequence that some constraints are fallen in relaxation, and algorithm sequence solves to obtain the upper bound, and the optimal solution of sequence is then between the upper bound and lower bound, therefore lower bound can solve the important means of performance as a kind of evaluation algorithms.Lower bound designed by the present invention is acquired a lower bound in each stage, is finally taken big using the method based on hybrid flowshop problem.And using averaging and interruptable mode and it is turned into unit problem solving come loose constraint condition in each stage.The present invention is solved for the dynamic continuous productive process minimization total complete time for considering the problems of study efficacy, can be as the method for the interruptable lower bound for assessment algorithm performance.
Description
Technical field
It is specifically a kind of to ask the dynamic hybrid flow operation pole for considering study efficacy the present invention relates to production scheduling field
The algorithm of smallization total complete time problem lower bound.
Background technology
In the assembly environment of real world, the passage of the component of product at any time successively reaches factory (when discharging
Between).By following identical processing route, component is assembled into final products.When a worker is anti-a specific stage
Similar task is handled again, and obtains knowledge more efficiently to perform task, and the processing time of later stage task can be obviously shortened.
This assembling process can be described as considering the dynamic Flow Shop Scheduling of study efficacy, and wherein learning effect depends on work
The Working position of part.
The problem of existing research is mostly about classical Flow Shop, but in practical factory, each processing rank
Section can't only have a same type machine.Therefore, it is necessary to consider that there is the hybrid flowshop problem of more machines in each stage, with
More tally with the actual situation.
Invention content
It is solved for the dynamic continuous productive process minimization total complete time for considering the problems of study efficacy, the object of the invention exists
In provide it is a kind of consider study efficacy dynamic hybrid flow operation minimization total complete time problem lower bound algorithm, as
The method of the interruptable lower bound of assessment algorithm performance.
The technical scheme is that：
A kind of dynamic hybrid flow operation minimization total complete time problem lower bound algorithm for considering study efficacy, seeks lower bound
It is as follows：
Step 1：First, each work is calculated according to the release time of each workpiece and in the process time in each stage
Part is as follows in the average processing time and earliest release time, calculation formula in each stage：
job_aves,j=jobs,j/Ms
And start0,j=rtimej
Step 2：Since second stage, the earliest start time in each stage is calculated, calculation formula is as follows：
Second stage：
stage2=min { job1,j}*g(1)
S-th of stage：
Step 3：It is as follows to calculate each workpiece time, calculation formula in the early start in each stage：
starts,j=max { stages,rs,j, j=1,2 ..., N, s=1,2 ..., S
Step 4：Total complete time of each stage by the sequence of unit problem is calculated by phase sequence；The workpiece first reached
First process；
If a, b workpiece reach simultaneously, smaller workpiece of preferential processing remaining process time；If the workpiece of long processing time
There is process time smaller workpiece to reach when not finishing, then when stopping the processing of the workpiece of long processing time, then processing processing
Between smaller workpiece；So repeatedly, until this stage all workpiece sequencings are completed；
Step 5：Polishing approaches the solution that sequence acquires according to the truncation for obtaining each workpiece in sequence under unit problem
In complete hybrid flowshop solution to model, the computational methods of workpiece truncation are as follows：
And tailS,j=0
Wherein, h represents workpiece j in the position in stage, and position is related with the number of machines in stage, if there are 3 machines in the stage, then
For workpiece per triplets, it is 2 that the 1st, 2,3 location of workpiece, which is the 1, the 4th, 5,6 location of workpiece, and so on；
Step 6：The lower bound in each stage is sought, calculation formula is as follows：
Step 7：It is maximized in the lower bound in each stage acquired as the final lower bound of model；
The symbolic indication being directed to is as follows：
N：The quantity of workpiece
rtimej：The initial release time of workpiece j；
rs,j：Workpiece j is in the earliest release time of stage s；
starts,j：Workpiece j is in the earliest start time of stage s；
stages：The earliest start time of stage s；
jobs,j：Workpiece j is in the process time of stage s；
job_aves,j：Workpiece j is in the average processing time of stage s；
tails,j：Workpiece j is in the truncation of stage s；
Ms：The number of machines of stage s；
completions,j：Workpiece j is in the completion date of stage s；
LBs：The lower bound of stage s；
g(n)：Study efficacy function, n represent the position of workpiece, g (n)=1-0.2*n/N, n=0,1 ..., N-1.
The considerations of described study efficacy dynamic hybrid flow operation minimization total complete time problem lower bound algorithm, step
Five when solving, because with study efficacy, actual processing time of workpiece is equipped with its machining position in this stage
It closes, the more forward workpiece of Working position, study efficacy coefficient is higher.
The considerations of described study efficacy dynamic hybrid flow operation minimization total complete time problem lower bound algorithm, if
Operation 1 is processed first position, and study efficacy coefficient is 1, needs to process 5 unit interval；If place it in the 2nd position
Put processing, then since proficiency improves, study efficacy coefficient becomes 0.98, process time 5*0.98=4.9.
It advantages of the present invention and has the beneficial effect that：
1st, the method for the present invention, which is directed to, considers the problems of that the dynamic continuous productive process minimization total complete time of study efficacy solves,
Using the lower bound design method for being averaging and interrupting.It can be obtained by simulation result, lower bound is convergent, i.e., when workpiece number tends to be infinite
When big, lower bound converges on optimal solution, and unrelated with the sequence of workpiece.In the case that on a large scale, this seeks evaluation algorithms
Solving performance has great significance.
2nd, there are two benefits for the method for the present invention：1. all can be as the substitution value of optimal solution, many algorithm Solve problems
NP hardly possiblies, be difficult to acquire optimal solution, therefore a kind of lower bound computational methods can be used to replace optimal solution in polynomial time.2. to divide
Branch key-machine constructs lower bound, and a good lower bound algorithm can make branch-bound algorithm cut branch as much as possible.
Description of the drawings
Fig. 1 is complete hybrid flowshop sequence Gantt chart.
Fig. 2 is lower bound sequence Gantt chart.
Fig. 3 is the solution flow chart of lower bound algorithm of the present invention.
Specific embodiment
In specific implementation process, lower bound is the obtained solution of sequence that some constraints are fallen in relaxation, and algorithm sequence solves
The upper bound is obtained, the optimal solution of sequence is then between the upper bound and lower bound, therefore lower bound can be used as a kind of evaluation algorithms to solve performance
Important means.Lower bound designed by the present invention is asked using the method based on hybrid flowshop problem in each stage
A lower bound is obtained, is finally taken big.And averaging and interruptable mode are used in each stage and is turned into unit problem and is asked
Solution carrys out loose constraint condition.
It is as follows in the symbolic indication arrived involved in this algorithm：
rtimej：The initial release time of workpiece j；
rs,j：Workpiece j is in the earliest release time of stage s；
starts,j：Workpiece j is in the earliest start time of stage s；
stages：The earliest start time of stage s；
jobs,j：Workpiece j is in the process time of stage s；
job_aves,j：Workpiece j is in the average processing time of stage s；
tails,j：Workpiece j is in the truncation of stage s；
completions,j：Workpiece j is in the completion date of stage s；
LBs：The lower bound of stage s；
(unit of above 9 expression formulas is all a unit interval)
Ms：The number of machines of stage s, unit：It is a；
g(n)：Study efficacy function, n represent the position of workpiece, g (n)=1-0.2*n/N, n=0,1 ..., N-1.
In the following, the specific implementation of the present invention is described in detail.
1st, example calculates as follows：
Table 1
| Workpiece is numbered | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| rtimej(minute) | 10 | 3 | 0 | 5 | 19 | 7 | 13 |
| job1,j(minute) | 8 | 10 | 4 | 4 | 9 | 4 | 3 |
| job2,j(minute) | 8 | 4 | 6 | 7 | 5 | 9 | 4 |
| job3,j(minute) | 8 | 7 | 10 | 4 | 5 | 6 | 1 |
As shown in Figure 1, by complete hybrid flowshop model it can be calculated that the considerations of being solved using the algorithm is learnt
The total complete time ∑ Cmax=190.286 (minute) of effect, i.e., the target function value that the algorithm acquires for 190.286 (point
Clock).
Lower bound calculating is carried out below：
As shown in figure 3, calculating the release time according to each workpiece and the process time in each stage first, calculate each
Average processing time and earliest release time of a workpiece in each stage, it is as a result as follows：
Table 2
| Workpiece is numbered | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| job_ave1,j(minute) | 2.667 | 3.333 | 1.333 | 1.333 | 3 | 1.333 | 1 |
| job_ave2,j(minute) | 4 | 2 | 3 | 3.5 | 2.5 | 4.5 | 2 |
| job_ave3,j(minute) | 4 | 3.5 | 5 | 2 | 2.5 | 3 | 0.5 |
| r2,j(minute) | 16.632 | 11.29 | 3.316 | 8.316 | 26.461 | 10.316 | 15.487 |
| r3,j(minute) | 23.264 | 14.606 | 8.29 | 14.119 | 30.606 | 17.777 | 18.803 |
Calculate the earliest start time of each stage (since second stage)：
stage2=3 (minutes)；stage3=7 (minutes)
Calculating each workpiece, the time (g (n)=0.829) is such as in the early start in each stage (since second stage)
Under：
Table 3
| Workpiece is numbered | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| start2,j(minute) | 16.632 | 11.29 | 3.316 | 8.316 | 26.461 | 10.316 | 15.487 |
| start3,j(minute) | 23.264 | 14.606 | 8.29 | 14.119 | 30.606 | 17.777 | 18.803 |
As shown in Fig. 2, sorting according to unit problem, LB can be obtained by figure1=155.055 (minutes)；LB2=162.606 (point
Clock)；LB3=151.430 (minutes)；LB=MAX { LB1, LB2, LB3}=162.606 (minute), and have GAP=(190.286-
162.606)/162.606*100=17.023%, wherein, GAP=(target function value-floor value)/floor value * 100, for weighing apparatus
One user-defined counter of quantity algorithm performance quality, GAP values are bigger, illustrate that algorithm improvement amount is bigger.
Total complete time of each stage by the sequence of unit problem is calculated by phase sequence；The workpiece first reached is first processed；
If a, b workpiece reach simultaneously, smaller workpiece of preferential processing remaining process time；If the workpiece of long processing time is not finished
There is process time smaller workpiece to reach, then stop the processing of the workpiece of long processing time, then it is smaller to process process time
Workpiece；So repeatedly, until this stage all workpiece sequencings are completed.
After the completion of workpiece sequencing, polishing acquires sequence according to the truncation for obtaining each workpiece in sequence under unit problem
Solution close to complete hybrid flowshop solution to model, the computational methods of workpiece truncation are as follows：
Wherein, h represents workpiece j in the position in stage.Position is related with the number of machines in stage, if there are 3 machines in the stage, then
For workpiece per triplets, it is 2 that the 1st, 2,3 location of workpiece, which is the 1, the 4th, 5,6 location of workpiece, and so on.
Finally, the lower bound in each stage is sought, calculation formula is as follows：
It is maximized in the lower bound in each stage acquired as the final lower bound of model.
2nd, it repeats to test
Experimental size：Number of stages S is respectively 2/5/10, and the generation section of number of machines M is [2,8]；Workpiece number N is respectively
100/200/500/800/1000.
The experiment is emulated using c language, and workpiece is generated at random in the process time in each stage by function, and section is
[1,10]；The initial release time generation section of each workpiece is [1,3*N].Each scale carries out 10 experiments, records GAP
Value, and be averaged.Wherein, GAP=(target function value-floor value)/floor value * 100.
Shown in the experimental data are shown in the following table：
Table 4. emulates data result
As can be seen from the data in the table, in the case where number of stages is constant, with the increase of workpiece number, GAP values are in integrally
Reveal convergent trend, that is, illustrate designed lower bound in convergent tendency.
In conclusion consider the dynamic hybrid flow operation minimization total complete time problem lower bound design side of study efficacy
Method, more can accurately evaluation algorithms solve performance.
Claims (3)
1. a kind of dynamic hybrid flow operation minimization total complete time problem lower bound algorithm for considering study efficacy, feature exist
In lower bound is asked to be as follows：
Step 1：First, each workpiece of process time calculating according to the release time of each workpiece and in each stage exists
The average processing time and earliest release time, calculation formula in each stage are as follows：
job_aves,j=jobs,j/Ms
And start0,j=rtimej
Step 2：Since second stage, the earliest start time in each stage is calculated, calculation formula is as follows：
Second stage：
stage2=min { job1,j}*g(1)
S-th of stage：
Step 3：It is as follows to calculate each workpiece time, calculation formula in the early start in each stage：
starts,j=max { stages,rs,j, j=1,2 ..., N, s=1,2 ..., S
Step 4：Total complete time of each stage by the sequence of unit problem is calculated by phase sequence；The workpiece first reached first adds
Work；If a, b workpiece reach simultaneously, smaller workpiece of preferential processing remaining process time；If the workpiece of long processing time is not done
There is process time smaller workpiece to reach when complete, then stop the processing of the workpiece of long processing time, then process process time more
Small workpiece；So repeatedly, until this stage all workpiece sequencings are completed；
Step 5：Polishing makes the solution that sequence acquires close to complete according to the truncation that each workpiece in sequence is obtained under unit problem
Whole hybrid flowshop solution to model, the computational methods of workpiece truncation are as follows：
And tailS,j=0
Wherein, h represents workpiece j in the position in stage, and position is related with the number of machines in stage, if there are 3 machines in the stage, then workpiece
Per triplets, it is 2 that the 1st, 2,3 location of workpiece, which is the 1, the 4th, 5,6 location of workpiece, and so on；
Step 6：The lower bound in each stage is sought, calculation formula is as follows：
Step 7：It is maximized in the lower bound in each stage acquired as the final lower bound of model；
The symbolic indication being directed to is as follows：
N：The quantity of workpiece
rtimej：The initial release time of workpiece j；
rs,j：Workpiece j is in the earliest release time of stage s；
starts,j：Workpiece j is in the earliest start time of stage s；
stages：The earliest start time of stage s；
jobs,j：Workpiece j is in the process time of stage s；
job_aves,j：Workpiece j is in the average processing time of stage s；
tails,j：Workpiece j is in the truncation of stage s；
Ms：The number of machines of stage s；
completions,j：Workpiece j is in the completion date of stage s；
LBs：The lower bound of stage s；
g(n)：Study efficacy function, n represent the position of workpiece, g (n)=1-0.2*n/N, n=0,1 ..., N-1.
2. under the dynamic hybrid flow operation minimization total complete time problem described in accordance with the claim 1 for considering study efficacy
Boundary's algorithm, which is characterized in that step 5 is when solving because with study efficacy, actual processing time of workpiece be with
It is related in the Working position in this stage, the more forward workpiece of Working position, and study efficacy coefficient is higher.
3. under the dynamic hybrid flow operation minimization total complete time problem described in accordance with the claim 2 for considering study efficacy
Boundary's algorithm, which is characterized in that if operation 1 is processed first position, study efficacy coefficient is 1, when needing to process 5 units
Between；If place it in the 2nd position processing, then since proficiency improves, study efficacy coefficient becomes 0.98, process time
For 5*0.98=4.9.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810016071.9A CN108229830B (en) | 2018-01-08 | 2018-01-08 | Dynamic hybrid line production minimization total completion time lower bound algorithm considering learning effect |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810016071.9A CN108229830B (en) | 2018-01-08 | 2018-01-08 | Dynamic hybrid line production minimization total completion time lower bound algorithm considering learning effect |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN108229830A true CN108229830A (en) | 2018-06-29 |
| CN108229830B CN108229830B (en) | 2021-09-10 |
Family
ID=62640177
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201810016071.9A Expired - Fee Related CN108229830B (en) | 2018-01-08 | 2018-01-08 | Dynamic hybrid line production minimization total completion time lower bound algorithm considering learning effect |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN108229830B (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109325680A (en) * | 2018-09-12 | 2019-02-12 | 山东大学 | Consider the single machine batch sort method of the minimum delay total time of study efficacy |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5715165A (en) * | 1994-12-23 | 1998-02-03 | The University Of Connecticut | Method and system for scheduling using a facet ascending algorithm or a reduced complexity bundle method for solving an integer programming problem |
| US20130024409A1 (en) * | 2011-07-21 | 2013-01-24 | Qualcomm Incorporated | Method and apparatus of robust neural temporal coding, learning and cell recruitments for memory using oscillation |
| CN106228265A (en) * | 2016-07-18 | 2016-12-14 | 中山大学 | Based on Modified particle swarm optimization always drag phase transport project dispatching algorithm |
| CN107392384A (en) * | 2017-07-28 | 2017-11-24 | 东北大学 | A kind of lower bound method for solving based on the dual-proxy problem with release time Flow Shop |
| CN107491863A (en) * | 2017-07-28 | 2017-12-19 | 东北大学 | A kind of branch and bound method that initial lower bound beta pruning is used based on straight-line code mode |
-
2018
- 2018-01-08 CN CN201810016071.9A patent/CN108229830B/en not_active Expired - Fee Related
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5715165A (en) * | 1994-12-23 | 1998-02-03 | The University Of Connecticut | Method and system for scheduling using a facet ascending algorithm or a reduced complexity bundle method for solving an integer programming problem |
| US20130024409A1 (en) * | 2011-07-21 | 2013-01-24 | Qualcomm Incorporated | Method and apparatus of robust neural temporal coding, learning and cell recruitments for memory using oscillation |
| CN106228265A (en) * | 2016-07-18 | 2016-12-14 | 中山大学 | Based on Modified particle swarm optimization always drag phase transport project dispatching algorithm |
| CN107392384A (en) * | 2017-07-28 | 2017-11-24 | 东北大学 | A kind of lower bound method for solving based on the dual-proxy problem with release time Flow Shop |
| CN107491863A (en) * | 2017-07-28 | 2017-12-19 | 东北大学 | A kind of branch and bound method that initial lower bound beta pruning is used based on straight-line code mode |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109325680A (en) * | 2018-09-12 | 2019-02-12 | 山东大学 | Consider the single machine batch sort method of the minimum delay total time of study efficacy |
Also Published As
| Publication number | Publication date |
|---|---|
| CN108229830B (en) | 2021-09-10 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN103765334B (en) | Method and system for simulating a working process on a machine tool | |
| JP6475763B2 (en) | System and method for searching machining knowledge database | |
| CN110955206B (en) | Order scheduling and distribution scheduling method and system | |
| CN110738413A (en) | Multi-constraint scheduling calculation method and device for automatic aviation part machining production line | |
| US20210073695A1 (en) | Production scheduling system and method | |
| Budiono et al. | Method and model development for manufacturing cost estimation during the early design phase related to the complexity of the machining processes | |
| Suhardini et al. | Design and improvement layout of a production floor using automated layout design program (ALDEP) and CRAFT algorithm at CV. Aji Jaya Mandiri | |
| CN108229830A (en) | Consider the dynamic hybrid flow operation minimization total complete time problem lower bound algorithm of study efficacy | |
| CN112435095A (en) | Carton workshop order production management device | |
| Vaghefinezhad et al. | A genetic algorithm approach for solving a flexible job shop scheduling problem | |
| JP7022085B2 (en) | Planning support device, planning support method, and planning support system | |
| CN107392384B (en) | Lower bound solving method based on double-agent problem with release time flow shop | |
| JP7261639B2 (en) | Production control system and production control method | |
| CN106909992B (en) | Split charging production method and device of multi-variety small-batch mixed flow assembly line | |
| CN106873555A (en) | A kind of general assembly production scheduling method and device of multi-varieties and small-batch mixed-model assembly line | |
| Dewa et al. | Managing bottlenecks in manual automobile assembly systems using discrete event simulation: case study | |
| JP2021096563A (en) | Production planning support system and production planning support method | |
| Saleeshya et al. | Productivity improvement through lean initiative in a surgical equipment manufacturing company: a case study | |
| CN110851920A (en) | Automatic generation method for main rib line of die pressing device | |
| JP6939016B2 (en) | Worker decision support device | |
| Singholi | Impact of manufacturing flexibility and pallets on buffer delay in flexible manufacturing systems | |
| Roy et al. | Productivity Improvement of a fan manufacturing company by using DMAIC approach: A Six-Sigma practice | |
| CN108196518A (en) | Dual-proxy dynamic mixed flow operation minimization weights manufacture phase problem lower bound method for solving | |
| Rudnik | Decision-making in a manufacturing system based on MADM methods | |
| Falcone et al. | Study and modelling of very flexible lines through simulation |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20210910 Termination date: 20220108 |