Chapter 6 Computerized Layout Procedures - …homes.ieu.edu.tr/~aornek/ISE470_Ch6.pdfConstruction Procedures PLANET BLOCPLAN STEP Graph Theoretic Layout & Network (GTLN) Exact Foulds

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

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



8 Bays @ 25' ≈ 200'

7 Bays @

25' ≈ 175'


Overview

Introduction

Planning Issues

Coating Dock

Finished Dock

Finished Goods

Storage

Printing Dock



8 Bays @ 25' ≈ 200' 7 B

ays @ 25' ≈ 175'

��Coating Dock

Finished Dock


Printing Dock



8 Bays @ 25' ≈ 200'

7 Bays @

25' ≈ 175'


Overview

Introduction

Planning Issues

Layout algorithms

Coating Dock

Finished Dock

Finished Goods

Storage

Printing Dock



8 Bays @ 25' ≈ 200' 7 B

ays @ 25' ≈ 175'

��Coating Dock

Finished Dock


Printing Dock



8 Bays @ 25' ≈ 200'

7 Bays @

25' ≈ 175'


Overview

Introduction

Planning Issues

Layout algorithms

Exact

Coating Dock

Finished Dock

Finished Goods

Storage

Printing Dock



8 Bays @ 25' ≈ 200' 7 B

ays @ 25' ≈ 175'

��Coating Dock

Finished Dock


Printing Dock



8 Bays @ 25' ≈ 200'

7 Bays @

25' ≈ 175'


Overview

Introduction

Planning Issues

Layout algorithms

Exact

Heuristics

Coating Dock

Finished Dock

Finished Goods

Storage

Printing Dock



8 Bays @ 25' ≈ 200' 7 B

ays @ 25' ≈ 175'

��Coating Dock

Finished Dock


Printing Dock



8 Bays @ 25' ≈ 200'

7 Bays @

25' ≈ 175'


Overview

Introduction

Planning Issues

Layout algorithms

Exact

Heuristics

Typical procedures

Coating Dock

Finished Dock

Finished Goods

Storage

Printing Dock



8 Bays @ 25' ≈ 200' 7 B

ays @ 25' ≈ 175'

��Coating Dock

Finished Dock


Printing Dock



8 Bays @ 25' ≈ 200'

7 Bays @

25' ≈ 175'


Overview

Introduction

Planning Issues

Layout algorithms

Exact

Heuristics

Typical procedures

MAFLAD/GMAFLAD

Coating Dock

Finished Dock

Finished Goods

Storage

Printing Dock



8 Bays @ 25' ≈ 200' 7 B

ays @ 25' ≈ 175'

��Coating Dock

Finished Dock


Printing Dock



8 Bays @ 25' ≈ 200'

7 Bays @

25' ≈ 175'


Overview

Introduction

Planning Issues

Layout algorithms

Exact

Heuristics

Typical procedures

MAFLAD/GMAFLAD

STEP

Coating Dock

Finished Dock

Finished Goods

Storage

Printing Dock



8 Bays @ 25' ≈ 200' 7 B

ays @ 25' ≈ 175'

��Coating Dock

Finished Dock


Printing Dock



8 Bays @ 25' ≈ 200'

7 Bays @

25' ≈ 175'


Overview

Introduction

Planning Issues

Layout algorithms

Exact

Heuristics

Typical procedures

MAFLAD/GMAFLAD

STEP∑

& Conclusions

Coating Dock

Finished Dock

Finished Goods

Storage

Printing Dock



8 Bays @ 25' ≈ 200' 7 B

ays @ 25' ≈ 175'

��Coating Dock

Finished Dock


Printing Dock



8 Bays @ 25' ≈ 200'

7 Bays @

25' ≈ 175'


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


Final Manufacturing Floor layout


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).


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


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

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)


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}


Graph Theoretic Layout Solution

8

5

4

4 7

1 3

6 2

5

1

2

8

3

6

7


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


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


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


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


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


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


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


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


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


Optimal Layout Solution, Z = 757.29

A6

A5

A12

A4

A9

A7

A1

A10 A11

A2

A3

A8


Second Best Solution,Z = 727.25

A1

A2

A3

A4

A5A6 A7

A8

A9

A10 A11

A12


Modified 2nd Best,Z = 743.11

A1

A2

A3

A4

A5A6

A7

A8

A9

A10 A11

A12


GMAFLAD output


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.



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




Factory Project Final Layout


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.


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


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.


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).


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


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


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

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


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


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:


Documents

Chapter 6 Computerized Layout Procedures - …homes.ieu.edu.tr/~aornek/ISE470_Ch6.pdfConstruction Procedures PLANET BLOCPLAN STEP Graph Theoretic Layout & Network (GTLN) Exact Foulds