facility layout 4 computerized block layout algorithms: aldep, craft, mcraft
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Facility Layout 4
Computerized Block Layout Algorithms:
ALDEP, CRAFT, MCRAFT
Tarea:
• Para la próxima clase, por favor resuelvan en parejas los siguientes problemas:– 6.13– 6.18– 6.28
• Para entregar.
Computer-Aided Layout Methods
Advantages:
• Rapid What-if Analysis
• Evaluate large number of alternatives
Disadvantages:
• Lack human judgment
• Lack qualitative aspects of Layout
Automated Layout Design Program (ALDEP)
Purpose: Generate many layouts
Separate Multiple Floor Capability
Derived from CORELAP
Dummy departments
ALDEP data requirements
REL Chart with A,E,I,O,U,X rankings
Area of Departments
Sweep width
Minimum Closeness Rating (MCR)
Ranking values:
A = 64 O = 1
E = 16 U= 0
I = 4 X = -1024
REL 2 3 4 5 6 Area1 A U O E U 32 - I U U O 43 - - U E O 24 - - - O U 55 - - - - E 46 - - - - - 2
REL Area1 32 43 24 55 46 2
Total 20
Facility LengthFa
cilit
y W
idth
ALDEP Facility Representation
Facility Length
Fac
ility
Wid
thDiscreteRepresentation
Sweep Method
Facility Length
Fac
ility
Wid
th
ALDEP Facility Representation
AAAAA AA A
Facility Length
Fac
ility
Wid
th Dept. size = 8 squares
Facility width = 6 squares
Sweep width = 1 square
C CC CC CC CC CC C C C
Facility Length
Fac
ility
Wid
th
Dept. size = 14 squares
Facility width = 6 squares
Sweep width = 2 squares
ALDEP Facility Representation
Dept. size = 8 squares
Facility width = 6 squares
Sweep width = 3 squares
E E EE E EE E
Facility Length
Fac
ility
Wid
th
ALDEP Procedure
1. Set MCR and sweep width.
2. Choose first department randomly, add it to the first position of the Department Entry Order (DEO).
3. Choose next department:a) Choose department that has A REL with the last
department in DEO.
b) If none, choose department that has E REL with last department in DEO.
c) Continue until MCR REL.
d) If none, choose department randomly
4. Repeat Step 3 until all depts. are in the DEO.
5. Place departments in layout with DEO and sweep method, do not split if possible.
6. Score layout with A-based objective.
ALDEP Example
REL 2 3 4 5 6 Area1 A U O E U 32 - I U U O 43 - - U E O 24 - - - O U 55 - - - - E 46 - - - - - 2
Step 1:• MCR = ‘E’• Sweep Width = 2
Step 2: Select first department• Randomly choose 5
Step 3: Select 2nd Department• No A’s with 5• 1,3, and 6 have E with 5: randomly choose 1
DEO:
5, 1
ALDEP Example
REL 2 3 4 5 6 Area1 A U O E U 32 - I U U O 43 - - U E O 24 - - - O U 55 - - - - E 46 - - - - - 2
Step 3b: Select 3rd dept.• 2 has A with 1, select 2
Step 3c: Select 4th dept• No A’s or E’s with 2• Randomly choose 3
DEO:
5, 1, 2, 3, 4,
Step 3d: Select 5th dept• No A’s or E’s with 3• Randomly choose 4
Step 3e: Select 6th dept• Last dept, choose 6
6
ALDEP Example DEO:
5, 1, 2, 3, 4, 6
REL Area1 32 43 24 55 46 2
Total 20Sweep Width = 2
15 55 5
Length = 4
Wid
th =
5
25 55 51 11
Wid
th =
5
Length = 4
35 55 51 11 22 2 2
Length = 4
Wid
th =
5
45 55 51 11 2 32 2 2 3W
idth
= 5
Length = 4
55 55 5 4 41 1 4 41 2 3 42 2 2 3
Length = 4
Wid
th =
5
65 5 6 65 5 4 41 1 4 41 2 3 42 2 2 3
Length = 4
Wid
th =
5
Dept.
ALDEP Analysis
Random selection does not produce the “best” layouts
Developed for Layout generation on mainframes and has become the basis for future algorithms.
6
1
2 3
45
Computerized Relative Allocation of Facilities Technique (CRAFT)
From-To Matrix
Improvement Algorithm
Discrete Representation
Pairwise Exchange
Distance-Based Objective
4
7
8 5
2
1
6
3
4
7
8 5
2
1
6
3
CRAFT Algorithm
1. Determine the department centroids.
2. Calculate the inter department rectilinear distances.
3. Calculate the initial cost of the layout by multiplying the from-to matrix with the cost matrix.
4. CRAFT then considers all the possible two-way or three-way department exchanges and identifies the best “exchange”.
5. Update the layout and calculate the new department centroids.
6. The above procedure is repeated until no further reduction in the cost can be obtained.
CRAFT Example
1
5
7 8
2
4
6
3
Initial Layout CentroidDept X Y 1 3 3 2 13 2 3 16.5 8 4 9.5 7 5 3 7 6 9.5 11 7 1.5 10 8 4.5 10
Find Centroids
Cost of the initial Layout
dist 1 2 3 4 5 6 7 8
1 0 18.5 8.5
2 0 16.5
3 0 14.5
4 8.5 8 0 11
5 0 4.5
6 14.5 10 4 0
7 0
8 8.5 8 0
FxC 1 2 3 4 5 6 7 8
1 0 20 2
2 0 1
3 0 2
4 1 0 2
5 0 1
6 10 5 0
7 0
8 2 0
Cost = Distance x Reward
20* 18.5 + 2* 8.5 + 1* 16.5 + 2* 14.5 + 1* 8.5 + 2* 11 + 1* 4.5 + 10* 14.5 + 5* 10 + 2* 8 =
= 678.5
Find Distances
Reward Matrix
Only equal areas or adjacent depts. are feasible exchanges
“Exchange 1-2” CentroidDept X Y . 1 13 2 2 3 3 3 16.5 8 4 9.5 7 5 3 7 6 9.5 11 7 1.5 10 8 4.5 10
“Exchange 1-3” CentroidDept X Y . 1 13 2 2 3 3 3 16.5 8 4 9.5 7 5 3 7 6 9.5 11 7 1.5 10 8 4.5 10
Infe
asib
le E
xcha
nge
“Exchange 1-4” CentroidDept X Y . 1 9.5 7 2 13 2 3 16.5 8 4 3 3 5 3 7 6 9.5 11 7 1.5 10 8 4.5 10
… and so on…
1
5
7 8
2
4
6
3
CRAFT exchanges centroids first
Then calculates a new table of distances
And then new layout costs
All possible exchanges are evaluated
The one with the most savings is selected
1
5
8
2
4
6
3
7
4
5
8
2
1
6
3
7
And the centroids, distances and actual layout are updated
Exchange depts. 1 and 4 gives the most savings
Exchange CentroidsDept X Y . 1 9.5 7 2 13 2 3 16.5 8 4 3 3 5 3 7 6 9.5 11 7 1.5 10 8 4.5 10
Updated CentroidsDept X Y . 1 10 7 2 13 2 3 16.5 8 4 3.5 3.57 5 3 7 6 9.5 11 7 1.5 10 8 4.5 10
1
5
8
2
4
6
3
7
4
5
8
2
1
6
3
7
08.58
07
041046
4.505
8.50114
14.503
16.502
11801
87654321dist
08.58
07
041046
4.505
8.50114
14.503
16.502
11801
87654321dist
07.438
07
041046
4.505
8.43011.074
14.503
16.502
11.57.501
87654321dist
07.438
07
041046
4.505
8.43011.074
14.503
16.502
11.57.501
87654321dist
Let’s calculate the cost of the layout after exchanging depts. 1 and 4
028
07
05106
105
2014
203
102
22001
87654321FxC
028
07
05106
105
2014
203
102
22001
87654321FxC
07.438
07
041046
4.505
8.43011.074
14.503
16.502
11.57.501
87654321dist
07.438
07
041046
4.505
8.43011.074
14.503
16.502
11.57.501
87654321dist Cost = Distance x Reward
20* 7.5 + 2* 11.5 + 1* 16.5 + 2* 14.5 + 1* 11.07 + 2* 8.43 + 1* 4.5 + 10* 4 +10* 5 + 2* 7.43 =
= 355.79
678.5 – 355.79Savings = --------------- = 47.56% 678.5
3 iterations take us to the final layout
4
5
8
2
1
6
3
7
4
7
8 5
2
1
6
3
Exchange 1 and 4
Exchange 5 and 7
Exchange 5 and 8
Final cost = 345.29
CRAFT Pros
Initial layout can be captured accurately
CRAFT Allows:• Flexible Department Shapes• Dummy depts.• Fixed Departments• Non-rectangular buildings
Evaluates MANY exchanges very quickly
1
5
8
2
4
6
3
7
Dummy
CRAFT Cons
Limited exchange options
Greedy Algorithm => Local Optima
CRAFT is path dependent: The starting layout makes a difference
Results in Odd Department Shapes
4
MCRAFT (Micro-CRAFT) – PC Implementation
• Similar to CRAFT, except it can exchange two non-adjacent departments
• Layout formation technique that allows easy shifting of departments
• Facility divided into bands
• Layout formed by starting at the upper-left-hand corner of the building and sweeping the bands in serpentine fashion
• Two way exchanges formed until no further improvement is achieved.
MCRAFT Limitations
• May be hard to fit the existing factory layout into bands
• Band width assumed to be same for all bands
• A fixed department may “float” when certain non-equal area departments are exchanged.
1 7
532
4 8 6
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