cont Computerized Layout Planning By Anastasia L Maukar 2 CRAFT Computerized Relative Allocation of Facilities Technique Created in 1964 by Buffa and Armour Process layout approach ID: 745090
Download Presentation The PPT/PDF document "1 Facility Design-Week 10 (" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
1
Facility Design-Week 10 (cont) Computerized Layout Planning
By Anastasia L. MaukarSlide2
2
CRAFT- Computerized Relative Allocation of Facilities Technique
Created in 1964 by Buffa and ArmourProcess layout approachA heuristic computer programCompares process departments
CRAFT requires an initial layout, which is improved by CRAFT.Slide3
3
From-To Chart
Determines which of the two departments has a better from-to matrix, we can calculate the moment of the matrix as follows: Slide4
4
CRAFT
Input for CRAFT:initial spatial array/layoutflow datacost data
Number and location of fixed department
Secara umum, dapat ditambahkan
dummy
yg berfungsi untuk:
Fill building irregularities.
Represent obstacles or unusable areas in facility
Represent extra space in the facility
Aid in evaluating aisle locations in the final layout.Slide5
5
CRAFT
Following are some examples of questions addressed by CRAFT:Is this a good layout?If not, can it be improved?Slide6
6
CRAFT
The possible interchange:only pairwise interchageonly three-way interchangepairwise interchage followed by three-way interchangethree-way interchage followed by pairwise interchange
best of two-way and three-way interchageSlide7
7
Consider the problem of finding the distance between two adjacent departments, separated by a line only.
People needs walking to move from one department to another, even when the departments are adjacent. An estimate of average walking required is obtained from the distance between centroids of two departments. The distance between two departments is taken from the distance between their centroids.
People walks along some rectilinear paths. An Euclidean distance between two centroids is not a true representative of the walking required. The rectilinear distance is a better approximation.
So, Distance (A,B) = rectilinear distance between centroids of departments A and B
CRAFT: Distance Between Two DepartmentsSlide8
8
Let Centroid of Department A =
Centroid of Department B = Then, the distance between departments A and B, Dist(A,B)
Ex: the distance between departments A and C is the rectilinear distance between their centroids (30,75) and (80,35). Distance (A,C)
CRAFT: Distance Between Two DepartmentsSlide9
9
Centroid of A= (30,75)
Centroid of C= (80,35)
Distance (A,C)
= 90
10
20
30
40
50
60
70
80
90
100
10
20
30
40
50
60
70
80
90
100
A
B
C
D
(80,85)
(30,25)
CRAFT: Distance Between Two DepartmentsSlide10
10
If the number of trips between two departments are very high, then such departments should be placed near to each other in order to minimize the total distance traveled.
Distance traveled from department A to B = Distance (A,B)
Number of trips from
department A to B
Total distance traveled is obtained by computing distance traveled between every pair of departments, and then summing up the results.
Given a layout, CRAFT first finds the total distance traveled.
CRAFT: Total Distance TraveledSlide11
11
Material handling trips(given)
(b)
(b) Distances (given)
CRAFT: Total Distance TraveledSlide12
12
Material handling trips (given)
(b) Distances (given)
(a)
(b)
(c)
Total distance traveled
= 100+630+240+….
=
4640
(c) Sample computation:
distance traveled (A,B)
= trips (A,B)
dist (A,B)
=………..
CRAFT: Total Distance TraveledSlide13
13
CRAFT then attempts to improve the layout by pair-wise interchanges.
If some interchange results some savings in the total distance traveled, the interchange that saves the most (total distance traveled) is selected.While searching for the most savings, exact savings are not computed. At the search stage, savings are computed assuming when departments are interchanged, centroids are interchanged too. This assumption does not give the exact savings, but approximate savings only.
Exact centroids are computed later.
CRAFT: SavingsSlide14
14
Savings are computed for all feasible pairwise interchanges. Savings are not computed for the infeasible interchanges.
An interchange between two departments is feasible only if the departments have the same area or they share a common boundary.
Feasible pairs are {A,B}, {A,C}, {A,D}, {B,C}, {C,D}
and an infeasible pair is {B,D}
In this example savings are not computed for interchanging B and D. Savings are computed for each of the 5 other pair-wise interchanges and the best one chosen.
After the departments are interchanged, every exact centroid is found. This may require more computation if one or more shape is composed of rectangular pieces.
CRAFT: SavingsSlide15
15
CRAFT: A Sample Computation of Savings from a Feasible Pairwise Interchange
To illustrate the computation of savings, we shall compute the savings from interchanging Departments C and D
New centroids:
A (30,75) Unchanged
B (30,25) Unchanged
C (80,85) Previous centroid of Department D
D (80,35) Previous centroid of Department C
Note: If C and D are interchanged, exact centroids are C(80,65) and D(80,15). So, the centroids C(80,85) and D(80,35) are not exact, but approximate.Slide16
16
CRAFT: A Sample Computation of Savings from a Feasible Pairwise Interchange
The first job in the computation of savings is to reconstruct the distance matrix that would result if the interchange was made.
The purpose of using approximate centroids will be clearer now.
If the exact centroids were used, we would have to recompute distances between every pair of departments that would include one or both of C and D.
However, since we assume that centroids of C and D will be interchanged, the new distance matrix can be obtained just by rearranging some rows and columns of the original distance matrix. Slide17
17
CRAFT: A Sample Computation of Savings from a Feasible Pairwise Interchange
The matrix on the left is the previous matrix, before interchange. The matrix on the right is after.
Dist (A,B) and (C,D) does not change.
New dist (A,C) = Previous dist (A,D)
New dist (A,D) = Previous dist (A,C)
New dist (B,C) = Previous dist (B,D)
New dist (B,D) = Previous dist (A,C)
Interchange
C,DSlide18
18
CRAFT: A Sample Computation of Savings
(a)
(b)
(c)
Material handling trips
(given)
(b) Distances (rearranged)
Total distance traveled
= 100+420+360+…
= 4480
Savings
=
(c) Sample computation:
distance traveled (A,B)
= trips (A,B)
dist (A,B)
=Slide19
19
CRAFT: Improvement Procedure
To complete the exercise
1. Compute savings from all the feasible interchanges. If there is no (positive) savings, stop.
2. If any interchange gives some (positive) savings, choose the interchange that gives the maximum savings
3. If an interchange is chosen, then for every department find an exact centroid after the interchange is implemented
4. Repeat the above 3 steps as longs as Step 1 finds an interchange with some (positive) savings.Slide20
20
CRAFT: Exact Coordinates of Centroids
Sometimes, an interchange may result in a peculiar shape of a department; a shape that is composed of some rectangular pieces
For example, consider the layout (from example) and interchange departments A and D. The resulting picture is shown on the right.
How to compute the exact coordinate of the centroid (of a shape like A)? Slide21
21
CRAFT: Exact Coordinates of Centroids
Find the centroid of A
10
20
30
40
50
60
70
80
90
100
50
60
70
80
90
100
A
A1
A2Slide22
22
X-coordinate Multiply
Rectangle Area of centroid (2) and (3) (1) (2) (3) (4) A1 A2 Total
X
-coordinate of the centroid of A
CRAFT: Exact Coordinates of CentroidsSlide23
23
Y
-coordinate Multiply
Rectangle Area of centroid (2) and (3)
(1) (2) (3) (4)
A1
A2
Total
Y
-coordinate of the centroid of A
CRAFT: Exact Coordinates of CentroidsSlide24
24
CRAFT: Exact Coordinates of Centroids
Exact coordinate of area A is
10
20
30
40
50
60
70
80
90
100
50
60
70
80
90
100
A
A1
A2Slide25
25
CRAFT: Some Comments
An improvement procedure, not a construction procedureAt every stage some pairwise interchanges are considered and the best one is chosenInterchanges are only feasible if departments have the same area; or they share a common boundary
Departments of unequal size that are not adjacent are not considered for interchange
Estimated cost reduction may not be obtained after interchange (because the savings are based on approximate centroids)
Strangely shaped departments may be formedSlide26
26
Computerized Layout Planning
Graphical Representation
“Points and lines” representation is not convenient for analysisSlide27
27
Layout Evaluation
An Algorithm needs to distinguish between “good” layouts and “bad” ones
Develop scoring model,
s
=
g
(
X
)
Adjacency-based scoring (Komsuluk Bazli Skorlama)
Based on the relationship chart and diagram
X
i
is the number of times an adjacency
i
is satisfied, i=A, E, I, O, U, X
Aldep uses (
w
i
values) A=64, E=16, I=4, O=1, U=0, and X=-1024
Scoring model has intuitive appeal; the ranking of layouts is sensitive to the weight values. Layout “B” may be preferred to “C” with certain weights but not with others.
Therefore, the specification of the weights is very important.
The weights
w
i
can also be represented by the flow amounts between the adjacent departments
instead of scores assigned to A, E, I, O, U, X.Slide28
28
1
2
3
4
5
6
7
1
2
3
4
5
6
7
U
U
U
U
I
E
U
I
O
U
A
O
I
U
I
I
E
U
O
U
E
Receiving
Milling
Press
Screw Machine
Assembly
Plating
Shipping
3
Press
7
Shipping
6
Plating
2
Milling
4
Screw Machine
5
Assembly
1
Receiving
A
E
I
E
O
I
O
1
2
3
4
5
6
7
1 2 3 4 5 6 7
I O
E I U
O U
A
E
4+1 =5
16+4+0 =20
1+0 =1
----
64 =64
16 =16
Total Score 106
Example
U
USlide29
29
Exercise: Find the score of the layout shown below. Use
A=8, E=4, I=2, O=1, U=0 and X=-8.
1
2
3
4
5
6
7
1
2
3
4
5
6
7
U
U
U
U
I
E
U
I
O
U
A
O
I
U
I
I
E
U
O
U
E
Receiving
Milling
Press
Screw Machine
Assembly
Plating
Shipping
3
Press
7
Shipping
6
Plating
4
Screw Machine
1
Receiving
2
Milling
5
AssemblySlide30
30
Layout Evaluation (cont’d)
Distance-based scoring (Mesafe Bazli Skorlama)
Approximate the cost of flow between activities
Requires explicit evaluation of the flow volumes and costs
c
ij
covers both the
i
to
j
and the
j to i material flowsDij can be determined with any appropriate distance metric
Often the rectilinear distance between department centroids
Assumes that the material flow system has already been specified (c
ij
=flow required* cost /flow-distance)
Assumes that the variable flow cost is proportional to distance
Distance often depends on the aisle layout and material handling equipmentSlide31
31
CRAFT - Example 2
Initial Layout
Flow Data
Distance Data
Total Cost
MaSlide32
32
CRAFT - Example 2
A & D interchange Total cost = 1.095A (60, 10) dan D (25, 30)A & C
interchange
Total cost = 99
C & D
interchange
Total cost = 1.040B & D interchange Total cost = 945
estimated total cost B & C tidak dapat dipertukarkanSlide33
33
CRAFT - Example 2
Yang dipilih adalah pertukaran B & D menghasilkan layout baru dg department centroid, sesuai dengan luas yang diinginkan pada layout awal (XA, YA) = (25, 30) (XB, YB) = (55, 10)
(XC, YC) = (20, 10)
(XD, YD) = (67.5, 25)Slide34
34
CRAFT - Example 2
To
From
A
B
C
D
A
50
25
47.5
B
50
35
27.5
C
25
35
62.5
D
47.5
27.5
62.5
20’
40’
60’
80’
40’
30’
20’
10’Slide35
35
Layout Evaluation – Distance-Based Scoring
Distance-based scoring
Impact of aisle layout and direction of travelSlide36
36
Benefits and Problems
BenefitA Computer ProgramFlexibiltyProblemsGreedy AlgorithmInefficient
End result may need to be modifiedSlide37
37
Summary
It is beneficial to use CRAFT but you should also realize that the program is not flawless. The user must understand how the program works of the end product is not as efficient as you had hope.