Layout design III.
Chapter 6 Layout generation
MCRAFT BLOCPLAN LOGIC
Review of 2 problems
Relationship diagram CRAFT
Algorithm classification
Construction algorithm Improvement algorithm
Graph-based method ALDEP CORELAP PLANET
Pairwise exchange method CRAFT MCCRAFT MULTIPLE
BLOCPLAN LOGIC Mixed integer programming
MCRAFT Micro CRAFT
An algorithm evolved from CRAFT allowing
non-adjacent exchanges Shifts automatically other departments when unequal or non-adjacent departments are being exchanged Horizontal sweep patterns are used to
place departments move departments while two departments are being exchanged
3
MCRAFT Sweep pattern
Layout is specified by a sequence of departments In each iteration, cells are formed starting from the topleft corner.
First department in the sequence is placed in the top-left corner. If there is a space on the immediate right of the first department, next department in the sequence is placed. Otherwise the next row in the building is used to locate the rest of the department (the remaining cells) or the next department in the sequence.
MCRAFT - procedure
1.
2.
3.
4.
5.
MCRAFT requires the user to specify Facility dimensions (rectangular, width x length) Number of bands After the band width is set, MCRAFT requires a vector (the sequence) of the departments in the initial layout. Based on this vector, it locates the departments following the serpentine flow directions A swap/exchange selection procedure similar to that of CRAFT is implemented. Not necessarily limited to adjacent or equal-size departments!! If any improving exchange is selected, then the two departments are swapped using a shifting procedure of the other departments. REPEAT 3 and 4 until no improvement can be made.
5
MCRAFT - Example
Same problem data as in the CRAFT example Facility dimensions:
360ft X 200ft Number of Bands: 3
Initial Layout Vector: 1-7-5-3-2-4-8-6 (A-G-E-C-B-D-H-F)
MCRAFT - Example
Initial layout
Layout Vector: 1-7-5-3-2-4-8-6
Final layout
(after 4 iterations)
Shapes better than CRAFT Try alternative layouts!
MCRAFT - Example
Initial layout
Layout Vector: 1-7-5-3-2-4-8-6
Final layout
(after 4 iterations)
Shapes better than CRAFT Try alternative layouts!
MCRAFT - Example
Initial layout
Layout Vector: 1-7-5-3-2-4-8-6
Final layout
(after 4 iterations)
Shapes better than CRAFT Try alternative layouts!
MCRAFT - Example
A facility with the layout below has 5 departments. Their sizes are given below. An engineering team wants to use MCRAFT method in order to improve the existing layout. The building dimensions are 20m x 9m. Determine the layout vector and create an input layout for MCRAFT using 3 bands.
C A D
A B C D E
Department size (m^2) 30 45 51 39 15
Layout vector is 1-3-4-2-5 (A-C-D-B-E)
D1 D2 D3 D4 D5
Department size (m^2) 30 45 51 39 15
Layout vector is 1-3-4-2-5
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
D1 D2 D3 D4 D5
Department size (m^2) 30 45 51 39 15
Layout vector is 1-3-4-2-5
1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3
D1 D2 D3 D4 D5
Department size (m^2) 30 45 51 39 15
Layout vector is 1-3-4-2-5
1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 3 3
3 3 3 3 3 3
3 3 3 3 3 3
3 3 3 3 3 3
D1 D2 D3 D4 D5
Department size (m^2) 30 45 51 39 15
Layout vector is 1-3-4-2-5
1 1 1 4 4 4
1 1 1 4 4 4
1 1 1 4 4 4
1 1 1 4 4 4
1 1 1 4 4 4
1 1 1 4 4 4
1 1 1 4 4 4
1 1 1 4 4 4
1 1 1 4 4 4
1 1 1 4 4 4
3 3 3 4 4 4
3 3 3 4 4 4
3 3 3 4 4 4
3 3 3 3 3 3
3 3 3 3 3 3
3 3 3 3 3 3
3 3 3 3 3 3
3 3 3 3 3 3
3 3 3 3 3 3
3 3 3 3 3 3
D1 D2 D3 D4 D5
Department size (m^2) 30 45 51 39 15
Layout vector is 1-3-4-2-5
1 1 1 4 4 4 2 2 2
1 1 1 4 4 4 2 2 2
1 1 1 4 4 4 2 2 2
1 1 1 4 4 4 2 2 2
1 1 1 4 4 4 2 2 2
1 1 1 4 4 4 2 2 2
1 1 1 4 4 4 2 2 2
1 1 1 4 4 4 2 2 2
1 1 1 4 4 4 2 2 2
1 1 1 4 4 4 2 2 2
3 3 3 4 4 4 2 2 2
3 3 3 4 4 4 2 2 2
3 3 3 4 4 4 2 2 2
3 3 3 3 3 3 2 2 2
3 3 3 3 3 3 2 2 2
3 3 3 3 3 3 5 5 5
3 3 3 3 3 3 5 5 5
3 3 3 3 3 3 5 5 5
3 3 3 3 3 3 5 5 5
3 3 3 3 3 3 5 5 5
D1 D2 D3 D4 D5
Department size (m^2) 30 45 51 39 15
Layout vector is 1-3-4-2-5
C A D
Real layout
Input used for MCRAFT
MCRAFT - Comments
Strengths:
Unlike the CRAFT algorithm, it does not restrict the exchange to the adjacent cells Smoother shapes compared to CRAFT (in most cases rectangular cells can be formed) More exchange alternatives. The number of alternatives increases exponentially with the number of departments Allows multi-floor layout planning
Weaknesses:
Facility shape is a restriction
The initial layout cannot be captured accurately unless the departments are already arranged in bands Band width is assumed to be the same for all the bands
MCRAFT is not as effective in treating fixed departments and obstacles (they can get shifted)
Input data
Qualitative data
Graph-based CORELAP ALDEP
Adjacency-based objective Input: Relationship chart Algorithms:
Quantitative data
Distance-based objective Input: From-to chart Algorithms:
Pairwise exchange CRAFT MCRAFT MULTIPLE
Both
Algorithms:
BLOCPLAN
BLOCPLAN
Construction and improvement algorithm Distance-based and adjacency-based objective Departments are in bands (2 or 3 bands), but the band width may vary All departments are rectangular Continuous representation Input
From-To Chart Relationship chart
BLOCPLAN converts:
From-to chart to Relationship chart through Flow-between chart Relationship chart to numerical relationship chart based on closeness ratings
From-To and Flow-Between Charts
Given M activities, a From-To Chart represents M(M-1) asymmetric quantitative relationships. Example:
D1 D1 D2 D3 f21 f31 D2 f12 f32 D3 f13 f23
A Flow-Between Chart represents M(M-1)/2 symmetric quantitative relationships.
D1 D1 D2 D3 D2 g12 D3 g13 g23
where fij = material flow from activity i to activity j.
gij = fij + fji, for all i > j, where gij = material flow between activities i and j.
D1 D1 D2 D3 D2 f12 + f21 D3 f13 + f31 f23 + f32
BLOCPLAN (quantitative qualitative)
From-to-chart Relationship diagram Procedure:
BLOCPLAN creates Flow Between Chart The highest value in the matrix is divided by 5 The flow values in Flow Between Chart are divided by the resulting value and 5 intervals are created Five intervals correspond to five relationships A, E, I, O and U Relationship Chart is created This is a BLOCPLAN-specific procedure
BLOCPLAN (qualitative quantitative)
Relationship diagram Numerical relationship chart
Procedure:
Based on the selected closeness ratings transform the alphabetical values in Relationship diagram to numerical values For example: A=10, E=5, I=2, O=1, U=0 and X=-10
D1
D1 D2 D3 D4 D5 D6
D2 A
D3 I
D4
E
D5 I E A
D6
O X O D1 D2 D3 D4 D5 D6
D1
D2 10
D3 2
D4
5
D5 2 5 10
D6
1 -10 1
Relationship chart
Numerical relationship chart
BLOCPLAN
Example 1
BLOCPLAN has proposed an improved layout for your existing facility. Given the Flow-to chart below calculate the adjacency and normalized adjacency scores for both and determine whether the proposed layout is more suitable. Use these closeness ratings: A=10, E=5, I=2, O=1, U=0 and X=-10
BLOCPLAN
Example 1
Initial layout of the facility
Final layout of the facility created by BLOCPLAN
BLOCPLAN
Example 1
From-to chart
Flow-between chart
BLOCPLAN
Example 1
The highest value is 90 => 90/5=18 Intervals:
73 to 90 units ..A 55 to 72 units ..E 37 to 54 units ..I 19 to 36 units ..O 0 to 18 units ....U
Flow-between chart
Relationship chart
BLOCPLAN
Example 1
Adjacency-based score
Initial layout: z=15 Final layout: z=15
z f ij xij
i 1 j i 1
m
Normalized adjacency score (efficiency rating)
Initial layout: z=15/24=0.63 Final layout: z=15/24=0.63
f
i 1 j 1 m m i 1 j 1
ij
xij
ij
Both layouts have the same adjacency-based scores If evaluated based on the total costs (distance-based scores), the results are different: CInitial=61,062,70 CFinal=58,133.34
BLOCPLAN
Example 1
Initial layout of the facility
Final layout of the facility created by BLOCPLAN
BLOCPLAN
Example 1
Adjacency-based score
Initial layout: z=15 Final layout: z=15
z f ij xij
i 1 j i 1
m
Normalized adjacency score (efficiency rating)
Initial layout: z=15/24=0.63 Final layout: z=15/24=0.63
f
i 1 j 1 m m i 1 j 1
ij
xij
ij
Both layouts have the same adjacency-based scores If evaluated based on the total costs (distance-based scores), the results are different: CInitial=61,062,70 CFinal=58,133.34
BLOCPLAN
REL-DIST score BLOCPLAN calculates:
Adjacency-based score (relationship chart) Distance-based score (flow-between chart) REL-DIST score (numerical relationship chart)
Distance-based layout cost that uses numerical closeness ratings rij instead of the flow values
z rij cij d ij
i 1 j i 1
Very useful if From-to chart is not available
BLOCPLAN
REL-DIST score Example 2
Following Relationship chart and layout
are given. Suppose that the following scoring vector is used: A=10, E=5, I=2, O=1, U=0 and X=-10, and compute efficiency rating and REL-DIST score.
D1
D1 D2 D3 D4 D5
D2 A
D3 U U
D4 E I U
D5 U I I A
5
Relationship chart
Proposed layout
BLOCPLAN
A=10, E=5, I=2, O=1, U=0 and X=-10
REL-DIST score Example 2
Efficiency rating
A E I A A E I I I A 10 5 2 10 27 0.87 10 5 2 2 2 10 31
D2 A D3 U U D4 E I U D5 U I I A
5
f
i 1 j 1 m m i 1 j 1
ij
xij
ij
D1
D1 D2 D3 D4 D5
Relationship chart
Proposed layout
BLOCPLAN
A=10, E=5, I=2, O=1, U=0 and X=-10
REL-DIST score Example 2
REL-DIST score
1. Calculate distance matrix
Find centroids Determine the distances between the centroids
Proposed layout
Distance matrix
REL-DIST score
D1
A=10, E=5, I=2, O=1, U=0 and X=-10
D1 D1 D2 D3 D4 D5 D2 10 D3 0 0 D4 5 2 0 D5 0 2 2 10
2. Create numerical relationship chart
D1 D2 D3 D4 D5
D2 A D3 U U D4 E I U D5 U I I A
Relationship chart 3. Calculate the total cost
Numerical relationship chart
D1 D1 D2 D3 D4 D5
D2 30
D3 0 0
D4 25 16 0
D5 0 12 6 40
Distance matrix
m m
Total cost matrix
z rij cij dij 30 25 16 12 40 123
i 1 j i 1
LOGIC Layout Optimization with
Guillotine Induced Cuts A series of horizontal and vertical cuts that slice the area to divide the building into departments Distance-based objective function Continuous representation Both construction and improvement algorithm
LOGIC Construction algorithm
LOGIC Construction algorithm
LOGIC Cut-tree
LOGIC Improvement algorithm
Exchanging the departments (the cut-tree remains the same)
Example: Exchange D and E (not equal area)
LOGIC - Comments
Not effective in tackling:
Fixed departments Prescribed shapes
If the building is rectangular LOGIC generates only rectangular departments Could be applied to non-rectangular buildings Supersedes BLOCPLAN, because all BLOCPLAN layouts are LOGIC layouts (BLOCPLANs solution space is a subset of LOGICs solution space)
Next lecture
Layout generation
MULTIPLE CORELAP ALDEP MIP
