Simulation and Optimisation of Trailer Floors Assembly Marc-Andr - - PowerPoint PPT Presentation

Simulation and Optimisation of Trailer Floors Assembly

Marc-André Carle Jacques Renaud Angel Ruiz Université Laval May 12th, 2004

Presentation outline

• Problem definition
• Methodology
• Heuristics
• Results
• Conclusion

• 1. Problem
• Manually-assembled Trailer floors
• Batten lengths ranges from 8 to 70 inches
• Once assembled, battens are fixed with glue
• Assembly chain fed by conveyor

(4 battens / second)

Operators have only 1,5 second to choose the right batten and to position it.

Performance criterion

• Industry quality standard: At least 3 inches

between two joints on adjacent battens

• Shortest euclidian distances are used.

joint joint distances

Performance criterion

• What we call an « error percentage » is:

100 joints

• f

Nb error in pairs joint

• f

Nb ×

• 2. Hypothesis
• Battens arrive one by one in the assembly

process;

• It is impossible to move a batten once it is

fixed to the floor;

• Batten lengths are random, but the random

distribution of batten lengths is known;

• Batten lengths follows a stationary

stochastic process;

Research objectives:

• Reproduce the assembly process
• Develop assembly rules to mechanize trailer

floor assembly process

• Evaluate the resulting floor quality

• 3. Methodology
• Simulation-based approach

– Generation of a population of battens; – Assembling the floor(s) using a specific rule;

• Assembly rules are in fact constructive

heuristics;

• All « assembly rules » refer to processes

that can be mechanized;

• 3. Heuristics
• A very simple rule:

– Put the incoming batten at the first available space, i.e., without reference to performance criterias.

• Two heuristics:

– Assembly « line by line » – « Parallel Assembly »

Assembly heuristics

• « Line-by-line » Assembly

• « Line-by-line » Assembly

Assembly heuristics

• « Line-by-line » Assembly

Assembly heuristics

Etc…

• « Line-by-line » Assembly

Assembly heuristics

• Parallel Assembly

Assembly heuristics

• Parallel Assembly

Assembly heuristics

• Parallel Assembly

Assembly heuristics

• Parallel Assembly

Assembly heuristics

Etc…

Assembly heuristics

• Parallel Assembly

What else can we do within 0,25 second?

• Three heuristics:

– SWAP – Rejection – Temporary storage

• « SWAP » heuristic

Assembly heuristics

• Rejection heuristic

Assembly heuristics

Assembly heuristics

• Rejection heuristic

Assembly heuristics

• Rejection heuristic

• Temporary storage

Assembly heuristics

Assembly heuristics

• Temporary storage

Assembly heuristics

• Temporary storage

Assembly heuristics

• Temporary storage

Assembly heuristics

• Temporary storage

• 4. Simulation results

Results for the two « basic » heuristics

14,43% 14,59% Error % 750 750 Nb of floors Parallel Line-by-line Statistics

SWAP heuristic:

80 0,704 14,24 SWAP 750 1,051 14,59 Line-by-line Nb of Floors Variance Error % Heuristic

• 4. Results

Rejection heuristic:

• 4,74%

16,3% 0,26% 80 Rejection (max=5)

• 4,63%

16% 0,37% 80 Rejection (max=3)

• 4,25%

15,5% 0,75 % 80 Rejection (max=2)

• 2,12%

13,4% 2,88 % 80 Rejection (max=1) 9,6%

• 14,59 %

750 Line-by-line

Difference with manual process Rejection % Error % Nb floors Heuristic

• 4. Results

Rejection heuristic

Performance vs Number of battens rejected

2 4 6 8 10 12 14 16 1 2 3 4 5 6 Max consecutive rejected battens Error %

• 4. Results

Temporary storage heuristic

• 4,48 %

0,52 % 80 Storage (2)

• 4,85 %

0,15 % 80 Storage (3)

• 4,98 %

0,02 % 80 Storage (5)

• 2,81 %

2,19 % 80 Storage (1) 9,61 % 14,59 % 750 Line-by-line Difference with manual process Error % Nb of Floors Heuristic

• 4. Results

• 5. Conclusions
• We developed simple yet powerful heuristics for

this problem.

• Parallel, line-by-line and SWAP heuristics

produce solutions of poor quality. (about 14% of errors)

• Both Rejection and Temporary storage heuristics

produce solutions of good quality. (Less than 2% of errors)

• These heuristics can be easily mechanized

Questions?