facility layout 4 computerized block layout algorithms: aldep, craft, mcraft

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


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


Sweep width = 2 squares


Dept. size = 8 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


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


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

facility layout 4 computerized block layout algorithms: aldep, craft, mcraft

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