Chapter 6 Computerized Layout Procedures - …homes.ieu.edu.tr/~aornek/ISE470_Ch6.pdfConstruction...
Transcript of Chapter 6 Computerized Layout Procedures - …homes.ieu.edu.tr/~aornek/ISE470_Ch6.pdfConstruction...
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Chapter 6 Computerized LayoutProcedures:
Alberto Garcia-Diaz & J. MacGregor Smith
[email protected], [email protected]
Department of Mechanical and Industrial Engineering
University of Massachusetts, Amherst, MA 01003 (USA)
August 8, 2008
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.1/37
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Overview
IntroductionCoating Dock
Finished Dock
Finished Goods
Storage
Printing Dock
Printing Bottle Storage Molding Molding Dock
Warehouse Warehouse Dock
8 Bays @ 25' ≈ 200' 7 B
ays @ 25' ≈ 175'
������������������������������������Coating Dock
Finished Dock
Finished Goods Storage
Printing Dock
Printing Bottle Storage Molding Molding Dock
Warehouse Warehouse Dock
8 Bays @ 25' ≈ 200'
7 Bays @
25' ≈ 175'
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.2/37
![Page 3: Chapter 6 Computerized Layout Procedures - …homes.ieu.edu.tr/~aornek/ISE470_Ch6.pdfConstruction Procedures PLANET BLOCPLAN STEP Graph Theoretic Layout & Network (GTLN) Exact Foulds](https://reader036.fdocuments.in/reader036/viewer/2022081802/5aa10a2f7f8b9a1f6d8b4e7c/html5/thumbnails/3.jpg)
Overview
Introduction
Planning Issues
Coating Dock
Finished Dock
Finished Goods
Storage
Printing Dock
Printing Bottle Storage Molding Molding Dock
Warehouse Warehouse Dock
8 Bays @ 25' ≈ 200' 7 B
ays @ 25' ≈ 175'
������������������������������������Coating Dock
Finished Dock
Finished Goods Storage
Printing Dock
Printing Bottle Storage Molding Molding Dock
Warehouse Warehouse Dock
8 Bays @ 25' ≈ 200'
7 Bays @
25' ≈ 175'
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.2/37
![Page 4: Chapter 6 Computerized Layout Procedures - …homes.ieu.edu.tr/~aornek/ISE470_Ch6.pdfConstruction Procedures PLANET BLOCPLAN STEP Graph Theoretic Layout & Network (GTLN) Exact Foulds](https://reader036.fdocuments.in/reader036/viewer/2022081802/5aa10a2f7f8b9a1f6d8b4e7c/html5/thumbnails/4.jpg)
Overview
Introduction
Planning Issues
Layout algorithms
Coating Dock
Finished Dock
Finished Goods
Storage
Printing Dock
Printing Bottle Storage Molding Molding Dock
Warehouse Warehouse Dock
8 Bays @ 25' ≈ 200' 7 B
ays @ 25' ≈ 175'
������������������������������������Coating Dock
Finished Dock
Finished Goods Storage
Printing Dock
Printing Bottle Storage Molding Molding Dock
Warehouse Warehouse Dock
8 Bays @ 25' ≈ 200'
7 Bays @
25' ≈ 175'
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.2/37
![Page 5: Chapter 6 Computerized Layout Procedures - …homes.ieu.edu.tr/~aornek/ISE470_Ch6.pdfConstruction Procedures PLANET BLOCPLAN STEP Graph Theoretic Layout & Network (GTLN) Exact Foulds](https://reader036.fdocuments.in/reader036/viewer/2022081802/5aa10a2f7f8b9a1f6d8b4e7c/html5/thumbnails/5.jpg)
Overview
Introduction
Planning Issues
Layout algorithms
Exact
Coating Dock
Finished Dock
Finished Goods
Storage
Printing Dock
Printing Bottle Storage Molding Molding Dock
Warehouse Warehouse Dock
8 Bays @ 25' ≈ 200' 7 B
ays @ 25' ≈ 175'
������������������������������������Coating Dock
Finished Dock
Finished Goods Storage
Printing Dock
Printing Bottle Storage Molding Molding Dock
Warehouse Warehouse Dock
8 Bays @ 25' ≈ 200'
7 Bays @
25' ≈ 175'
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.2/37
![Page 6: Chapter 6 Computerized Layout Procedures - …homes.ieu.edu.tr/~aornek/ISE470_Ch6.pdfConstruction Procedures PLANET BLOCPLAN STEP Graph Theoretic Layout & Network (GTLN) Exact Foulds](https://reader036.fdocuments.in/reader036/viewer/2022081802/5aa10a2f7f8b9a1f6d8b4e7c/html5/thumbnails/6.jpg)
Overview
Introduction
Planning Issues
Layout algorithms
Exact
Heuristics
Coating Dock
Finished Dock
Finished Goods
Storage
Printing Dock
Printing Bottle Storage Molding Molding Dock
Warehouse Warehouse Dock
8 Bays @ 25' ≈ 200' 7 B
ays @ 25' ≈ 175'
������������������������������������Coating Dock
Finished Dock
Finished Goods Storage
Printing Dock
Printing Bottle Storage Molding Molding Dock
Warehouse Warehouse Dock
8 Bays @ 25' ≈ 200'
7 Bays @
25' ≈ 175'
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.2/37
![Page 7: Chapter 6 Computerized Layout Procedures - …homes.ieu.edu.tr/~aornek/ISE470_Ch6.pdfConstruction Procedures PLANET BLOCPLAN STEP Graph Theoretic Layout & Network (GTLN) Exact Foulds](https://reader036.fdocuments.in/reader036/viewer/2022081802/5aa10a2f7f8b9a1f6d8b4e7c/html5/thumbnails/7.jpg)
Overview
Introduction
Planning Issues
Layout algorithms
Exact
Heuristics
Typical procedures
Coating Dock
Finished Dock
Finished Goods
Storage
Printing Dock
Printing Bottle Storage Molding Molding Dock
Warehouse Warehouse Dock
8 Bays @ 25' ≈ 200' 7 B
ays @ 25' ≈ 175'
������������������������������������Coating Dock
Finished Dock
Finished Goods Storage
Printing Dock
Printing Bottle Storage Molding Molding Dock
Warehouse Warehouse Dock
8 Bays @ 25' ≈ 200'
7 Bays @
25' ≈ 175'
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.2/37
![Page 8: Chapter 6 Computerized Layout Procedures - …homes.ieu.edu.tr/~aornek/ISE470_Ch6.pdfConstruction Procedures PLANET BLOCPLAN STEP Graph Theoretic Layout & Network (GTLN) Exact Foulds](https://reader036.fdocuments.in/reader036/viewer/2022081802/5aa10a2f7f8b9a1f6d8b4e7c/html5/thumbnails/8.jpg)
Overview
Introduction
Planning Issues
Layout algorithms
Exact
Heuristics
Typical procedures
MAFLAD/GMAFLAD
Coating Dock
Finished Dock
Finished Goods
Storage
Printing Dock
Printing Bottle Storage Molding Molding Dock
Warehouse Warehouse Dock
8 Bays @ 25' ≈ 200' 7 B
ays @ 25' ≈ 175'
������������������������������������Coating Dock
Finished Dock
Finished Goods Storage
Printing Dock
Printing Bottle Storage Molding Molding Dock
Warehouse Warehouse Dock
8 Bays @ 25' ≈ 200'
7 Bays @
25' ≈ 175'
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.2/37
![Page 9: Chapter 6 Computerized Layout Procedures - …homes.ieu.edu.tr/~aornek/ISE470_Ch6.pdfConstruction Procedures PLANET BLOCPLAN STEP Graph Theoretic Layout & Network (GTLN) Exact Foulds](https://reader036.fdocuments.in/reader036/viewer/2022081802/5aa10a2f7f8b9a1f6d8b4e7c/html5/thumbnails/9.jpg)
Overview
Introduction
Planning Issues
Layout algorithms
Exact
Heuristics
Typical procedures
MAFLAD/GMAFLAD
STEP
Coating Dock
Finished Dock
Finished Goods
Storage
Printing Dock
Printing Bottle Storage Molding Molding Dock
Warehouse Warehouse Dock
8 Bays @ 25' ≈ 200' 7 B
ays @ 25' ≈ 175'
������������������������������������Coating Dock
Finished Dock
Finished Goods Storage
Printing Dock
Printing Bottle Storage Molding Molding Dock
Warehouse Warehouse Dock
8 Bays @ 25' ≈ 200'
7 Bays @
25' ≈ 175'
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.2/37
![Page 10: Chapter 6 Computerized Layout Procedures - …homes.ieu.edu.tr/~aornek/ISE470_Ch6.pdfConstruction Procedures PLANET BLOCPLAN STEP Graph Theoretic Layout & Network (GTLN) Exact Foulds](https://reader036.fdocuments.in/reader036/viewer/2022081802/5aa10a2f7f8b9a1f6d8b4e7c/html5/thumbnails/10.jpg)
Overview
Introduction
Planning Issues
Layout algorithms
Exact
Heuristics
Typical procedures
MAFLAD/GMAFLAD
STEP∑
& Conclusions
Coating Dock
Finished Dock
Finished Goods
Storage
Printing Dock
Printing Bottle Storage Molding Molding Dock
Warehouse Warehouse Dock
8 Bays @ 25' ≈ 200' 7 B
ays @ 25' ≈ 175'
������������������������������������Coating Dock
Finished Dock
Finished Goods Storage
Printing Dock
Printing Bottle Storage Molding Molding Dock
Warehouse Warehouse Dock
8 Bays @ 25' ≈ 200'
7 Bays @
25' ≈ 175'
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.2/37
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Network Design Problem
0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
Manufacturing
Assembly
Rec./Shipping
Offices
Reception
0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
M
A
S
O
R
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.3/37
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Final Manufacturing Floor layout
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.4/37
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Scope and Definitions
The problem can be viewed as a task in topologicalnetwork design comprised of two fundamental problems:
Generation or selection of the topological configurationof the finite set of nodes V and set of arcs A whichdefine the planar graph G(V,A).
Optimal assignment of activities to the nodes of G(V,A).
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.5/37
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Facility Layout Software Issues
Optimal vs. sub-optimal solutions
Equal vs. unequal areas
Existing vs. new facilities
Deterministic vs. stochastic flows
Quantitative vs. qualitative REL-data
Grid decomposition vs. continuous space
Explicit shape vs. rectangular activity shape
Layout and material handling integration
Multi-story layouts
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.6/37
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Morphology of Layout Programs
FacilityLayoutProblems
QuadraticAssignment
(QAP)
Exact
QAPGQAP
B& B
Quadratic Set
Packing (QSP)
Bazarra
MAFLAD
Heuristics
ImprovementProcedures
CRAFT
COFAD
ConstructionProcedures
PLANET
BLOCPLAN
STEP
Graph TheoreticLayout & Network
(GTLN)
ExactFoulds and Robinson,
Christofides et. al.
Heuristics
CORELAP
ALDEP
RUGR
DELTAHEDRON
SPIRAL GJ. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.7/37
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Exact QAP
Minimizen∑
i=1
n∑
k=1
cikxik +n∑
i=1
n∑
j=1
n∑
k=1
n∑
h=1
fijdkhxikxjh
s.t.
n∑
i=1
xik = 1, (k = 1, 2, ...n)
n∑
k=1
xik = 1, (i = 1, 2, ...n)
xik = 0, 1 (i, k = 1, ..., n)
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.8/37
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Exact GTL
Maximize∑
(i,j)∈E′
wijxij
s.t.
G(V,E) = is a planar subgraph of G′ = (V,E ′) with
E = {(i, j) ∈ E ′|xij = 1}
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.9/37
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Graph Theoretic Layout Solution
8
5
4
4 7
1 3
6 2
5
1
2
8
3
6
7
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.10/37
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Improvement Procedures
Improvement Procedures: These procedures require afeasible layout as input and continue to modify the layoutby swapping areas and scoring the revised layouts until nofurther improvement can be found. The scores are basedupon a from-to chart, which is part of the input. Twowell-known improvement-type procedures are:• CRAFT: Computerized Relative Allocation of FacilitiesTechnique
• COFAD: Computerized Facilities Design
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.11/37
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Construction Procedures
Construction Procedures: These procedures start withan open floor space and construct a single floor layoutlogically, based upon input data, a relationship chart, andspace allocations. A partial list of these proceduresincludes:• PLANET: Plant Layout Analysis and Evaluation Technique• CORELAP: Computerized Relationship Layout Planning• ALDEP: Automated layout design Program
• BLOCPLAN: Block Plan
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.12/37
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Exact Algorithm
The program MAFLAD (Multi-attribute Layout and Design)is a Quadratic Set Packing (QSP) branch and boundalgorithm for solving an exact solution.
Maximize Z =X
k
X
t
uktxkt +X
k
X
j
ukj
„
X
mnǫA
1
dmn
xkmxjn
«
s.t.
X
k
X
t
αiktxkt ≤ 1 i = 1, . . . , I subareas
X
t
xkt = 1 k = 1, . . . , K activity
xkt = 0, 1 k = 1, . . . , K t = 1, . . . , T
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.13/37
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Hierarchical Planning Levels
Regional planning level
residential neighborhoods shopping centers community-college districts highway corridors airports cemeteries industrial parks
Urban-design planning level
single-family housing units duplex units townhouses street patterns neighborhood parks schools convenience stores day-care centers
Architectural planning level
AIS
UIS
GIS
living rooms hallways bedrooms kitchens studies garages
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.14/37
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Branch and Bound Algorithm
Step 1.0: Pre-Processing
Step 2.0: Activity Node Set Generation
Step 3.0: Critical Communicating Pairs Generation
Step 4.0: Branching Process
Step 5.0: Bounding Process
Step 6.0: Backtracking
Step 7.0: Solution Output
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.15/37
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Facility Planning Grid
0 1 2 3 4 5 6 7 8 9 100
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8 9 1011 12 13 · · · 18 19 20
28
·
·
·
·
7382
91 92 93 · · · 98 99100
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.16/37
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Example Layout
0 1 2 3 4 5 6 7 8 9 100
1
2
3
4
5
6
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
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Activity 1 + alternatives
Act 1 6 alts.1,2,3,11,12,13,21,22,23
24,25,26,34,35,36,44,45,4628,29,30,38,39,40,48,49,5031,32,33,41,42,43,51,52,534,5,6,14,15,16,24,25,26
27,28,29,37,38,39,47,48,49
0 1 2 30
1
2
3
A1
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.18/37
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Flow Matrix
F =
2
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
4
activities A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12
A1 − 288 180 54 72 180 27 72 36 0 0 9
A2 − 240 54 72 24 48 160 16 64 8 16
A3 − 120 80 0 60 120 60 0 0 30
A4 − 72 18 18 48 24 48 12 0
A5 − 12 12 64 16 16 4 8
A6 − 18 24 6 12 3 3
A7 − 0 6 6 3 6
A8 − 16 16 16 4
A9 − 4 4 2
A10 − 2 2
A11 − 2
A12 −
3
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
5
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.19/37
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Optimal Layout Solution, Z = 757.29
A6
A5
A12
A4
A9
A7
A1
A10 A11
A2
A3
A8
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.20/37
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Second Best Solution,Z = 727.25
A1
A2
A3
A4
A5A6 A7
A8
A9
A10 A11
A12
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.21/37
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Modified 2nd Best,Z = 743.11
A1
A2
A3
A4
A5A6
A7
A8
A9
A10 A11
A12
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.22/37
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GMAFLAD output
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Factory Project Example
1. Manufacturing (15,753.5 sf)
2. Warehouse (Shipping and Re-ceiving)(13,378 sf)
3. Assembly (Main and Sub-assembly) (7,722 sf)
4. Offices (5447.5 sf)
5. Net Square Footage 43,512.5 sf
6. Non-assignable (30%) 13,053.75sf
7. Grand Total 56,566.25 sf≈ (300′x200′)
Activity List with (s.f.)
0 1 2 3 4 50
1
2
3
4
Factory Footprint (6x4 grid)(50’ units) ≈ 60, 000s.f.
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.24/37
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Factory Project Example
2
6
6
6
6
6
6
6
6
6
6
6
6
6
4
activities A1 A2 A3 A4 A5 A6 A7
A1(RE) − A U 0 U U I
A2(MA) − E O U U I
A3(SA) − E U U I
A4(AS) − A U I
A5(P K) − A I
A6(SH) − I
A7(OF ) −
3
7
7
7
7
7
7
7
7
7
7
7
7
7
5
OF MA SA
ASRE
PKSH
I
EI
I A
O
E
I
I
I
A
O
A
Graph Decomposition
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.25/37
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Factory Project Example
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Factory Project Final Layout
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STEP Algorithm
The Sampling Test and Pairwise Exchange Procedure(STEP) is an algorithm for constructing an heuristicsolution where stochastic or deterministic flows can bemodeled.It assumes that the material handling system is captured ina network as depicted on the next slide.
The Steiner node is termed a circulation passage.
In this node, the dynamic flow of people, parts, orvehicles is represented.
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.28/37
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STEP Assumptions
1
2
3
4
5
6
1
2
3
4
5
6
1
2
3
4
5
6
1
2
3
4
5
6
S
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.29/37
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STEP Assumptions
1. At time (t, t + ∆t), the number of customers arriving to a circulation passage is
independent and stationary, and the probability of one customer arrival is equal
to λ∆t that is
P (N(∆t) = 1) = λ∆t + 0∆t
and
P (N(∆t) > 1) = 0∆t
Here, batch arrivals are not considered. Hence, it is assumed that customers
arrive in accordance with a Poisson process having rate λ.
2. Each customer requires an amount of work, tij , which is further distributed by
G. Here, G is an arbitrary distribution.
3. We assume that the systems to be designed are in steady state.
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Facility Layout with M/G/∞ system
Written in standard QAP type form
Min1
v
nX
i=1
nX
j=1
nX
k=1
nX
h=1
qijdkhxikxjh
s.t.
nX
i=1
xik = 1 (k = 1, 2, ..., n)
nX
k=1
xik = 1 (i = 1, 2, ..., n)
xik = 0, 1 (i, k = 1, 2, ..., n).
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.31/37
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STEP Example
Dkh =
2
6
6
6
6
6
6
6
6
6
6
4
0 1 1 2 2 3
1 0 2 1 3 2
1 2 0 1 1 2
2 1 1 0 2 1
2 3 1 2 0 1
3 2 2 1 2 0
3
7
7
7
7
7
7
7
7
7
7
5
Distance Matrix
Pij =
2
6
6
6
6
6
6
6
6
6
6
4
activity A1 A2 A3 A4 A5 A6
A1 .13 .20 .15 .37 .15
A2 .50 0.0 .10 .40 0.0
A3 .62 0.0 0.18 0.10 0.10
A4 .28 .18 .20 .34 0.0
A5 .76 .10 0.0 .04 .10
A6 .32 0.0 0.0 0.0 .68
Transition Matrix
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.32/37
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STEP Final Solution
Qij =
2
6
6
6
6
6
6
6
6
6
6
4
0 .52 .80 .60 1.48 .60
.50 0 0.0 .10 .40 0.0
.62 0.0 0 .18 .10 .10
.28 .18 .20 0 .34 0.0
2.28 .30 0.0 .12 0 .30
.32 0.0 0.0 0.0 .68 0
3
7
7
7
7
7
7
7
7
7
7
5
qij = λi ∗ pij elements
0 1 2 30
1
2
3
Steiner Circulation Node
4
5
2
6
3
1
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STEP Computational Results
File(N) Optimal Heuristic % Deviation
Nug12 578 578 0.00
Nug14 1014 1022 0.79
Nug15 1150 1162 1.04
Nug16a 1610 1636 1.60
Nug16b 1240 1240 0.00
Nug17 1732 1734 0.12
Nug18 1930 1930 0.00
Nug20 2570 2570 0.00
Nug21 2438 2442 0.16
Nug22 3596 3596 0.00
Nug24 3488 3488 0.00
Nug25 3744 3744 0.00
Nug30 6124 6146 0.36
Average - - 0.31
std.dev - - (.51)J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.34/37
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STEP Factory Example
1. Receiving (RE) (3500)
2. Stamping (ST) (300)
3. Compression Molding (CM)(2000)
4. Injection Molding (IM) (500)
5. Blow Molding (BM) (1500)
6. Die Cast (DC) (700)
7. Lathes (LA) (3000)
8. Painting (PA) (600)
9. Band Saw (BS) (200)
10. Cleaning (CL) (500)
11. Assembly area(AS) (1500)
12. Packaging (PK) (500)
13. Shipping (SH) (2000)
14. Offices (OF) (5000)
15. Net-assignable 21,800
16. Non-assignable 6,540
17. Grand Total 28,340 sf
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.35/37
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REL Flow Matrix
2
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
4
activity A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
A1(RE) − I O O O E O I U U I U U U
A2(ST ) − U U U U U U U U I U U U
A3(CM) − U U U U U U O U U U U
A4(IM) − U U U U U O O U U U
A5(BM) − U U U U U O U U U
A6(DC) − O U U E U U U U
A7(LA) − I E O U U U U
A8(P A) − U U U U U U
A9(BS) − A U A U U
A10(CL) − I U U U
A11(AS) − A U U
A12(P K) − A U
A13(SH) − 0
A14(OF ) −
3
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
5
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.36/37
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Factory Project Step Layout
OFSHBMCLBS
IM RE DC ST CM
PA LA PK AS
RE
ST
DC
SH
PK AS
PACL
CM BM
BS IM
OF
LA
Figure 0:
J. MacGregor Smith, Department of Mech. and Industrial Engineering , University of Massachusetts http://www.ecs.umass.edu/faculty/smith/ – p.37/37