DESIGN OF THE LAYOUT OF A MANUFACTURING FACILITY WITH A CLOSED LOOP CONVEYOR

7/23/2019 DESIGN OF THE LAYOUT OF A MANUFACTURING FACILITY WITH A CLOSED LOOP CONVEYOR

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DESIGN OF THE LAYOUT OF A MANUFACTURING FACILITY WITH A

CLOSED LOOP CONVEYOR WITH SHORTCUTS USING QUEUEING

THEORY AND GENETIC ALGORITHMS

by

VERNET MI CHAEL LASRADO

B. Sc. Geor gi a I nst i t ut e of Technol ogy, 2004M. Sc. Uni ver si t y of Cent r al Fl or i da, 2008

A di sser t at i on submi t t ed i n par t i al f ul f i l l ment of t he r equi r e-ment s f or t he degr ee of Doctor of Phi l osophy

i n t he Depar t ment of I ndust r i al Engi neer i ng & Management Syst ems

i n t he Col l ege of Engi neer i ng & Comput er Sci enceat t he Uni ver si t y of Cent r al Fl or i daOr l ando, Fl or i da

Fal l Ter m2011

Maj or Prof essor : Di ma Nazzal


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2011 Vernet Mi chael Lasr ado


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ABSTRACT

Wi t h t he ongoi ng t echnol ogy bat t l es and pr i ce war s i n t oday' s

compet i t i ve economy, every company i s l ooki ng f or an advant age

over i t s peer s. A par t i cul ar choi ce of f aci l i t y l ayout can have

a si gni f i cant i mpact on t he abi l i t y of a company t o mai nt ai n

l ower oper at i onal expenses under uncer t ai n economi c condi t i ons.

I t i s known t hat syst ems wi t h l ess congest i on have l ower oper a-

t i onal cost s. Tr adi t i onal l y, manuf actur i ng f aci l i t y l ayout pr ob-

l em met hods ai m at mi ni mi zi ng t he t ot al di st ance t r avel ed, t he

mat er i al handl i ng cost , or t he t i me i n t he syst em ( based on di s-

t ance t r avel ed at a speci f i c speed) .

The proposed met hodol ogy sol ves t he l ooped l ayout desi gn prob-

l em f or a l ooped l ayout manuf act ur i ng f aci l i t y wi t h a l ooped

conveyor mat er i al handl i ng syst em wi t h shor t cut s usi ng a syst em

per f or mance met r i c, i . e. t he wor k i n pr ocess ( WI P) on t he con-

veyor and at t he i nput st at i ons t o t he conveyor , as a f act or i n

t he mi ni mi zi ng f unct i on f or t he f aci l i t y l ayout opt i mi zat i on

pr obl em whi ch i s sol ved heur i st i cal l y usi ng a per mut at i on genet -

i c al gor i t hm. The pr oposed met hodol ogy al so pr esent s t he case

f or det er mi ni ng t he shor t cut l ocat i ons acr oss t he conveyor si m-

ul t aneousl y (whi l e det er mi ni ng t he l ayout of t he st at i ons around

t he l oop) ver sus t he t r adi t i onal met hod whi ch det er mi nes t he

shor t cut s sequent i al l y ( af t er t he l ayout of t he st at i ons has


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been det ermi ned) . The pr oposed met hodol ogy al so present s an ana-

l yt i cal est i mat e f or t he wor k i n pr ocess at t he i nput st at i ons

t o t he cl osed l ooped conveyor .

I t i s cont ended that t he pr oposed met hodol ogy ( usi ng t he WI P

as a f act or i n t he mi ni mi zi ng f unct i on f or t he f aci l i t y l ayout

whi l e si mul t aneousl y sol vi ng f or t he shor t cut s) wi l l yi el d a f a-

ci l i t y l ayout whi ch i s l ess congest ed t han a f aci l i t y l ayout

gener at ed by t he t r adi t i onal met hods ( usi ng t he t ot al di st ance

t r avel ed as a f act or of t he mi ni mi zi ng f unct i on f or t he f aci l i t y

l ayout whi l e sequent i al l y sol vi ng f or t he shor t cut s) . The pr o-

posed met hodol ogy i s t est ed on a vi r t ual 300mm Semi conduct or Wa-

f er Fabr i cat i on Faci l i t y wi t h a l ooped conveyor mat er i al han-

dl i ng syst em wi t h shor t cut s. The r esul t s show t hat t he f aci l i t y

l ayout s gener ated by t he pr oposed met hodol ogy have si gni f i cant l y

l ess congest i on t han f aci l i t y l ayout s gener at ed by t r adi t i onal

met hods. The val i dat i on of t he devel oped anal yt i cal est i mat e of

t he wor k i n pr ocess at t he i nput st at i ons r eveal s t hat t he pr o-

posed methodol ogy works ext r emel y wel l f or syst ems wi t h Markovi -

an Ar r i val Pr ocesses.


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Thi s wor k i s dedi cat ed t o Capt . Val er i an Lasr ado, Mer l yn

Lasr ado, Mor gan Lasr ado, Fel i x Pi nt o, Hel en Pi nt o, Mont hi e

Lasr ado, Raymond Lasr ado, and t he r est of my f ami l y.

Wi t hout your const ant suppor t and encour agement none of t hi s

woul d be possi bl e.


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ACKNOWLEDGMENTS

I woul d l i ke t o acknowl edge t he var i ous i nst i t ut i ons I have at -

t ended ( i n order of at t endance) : Don Bosco Hi gh School , St .

St ani sl aus Hi gh School , R. D. Nat i onal Col l ege, Geor gi a I nst i t ut e

of Technol ogy, and Uni ver si t y of Cent r al Fl or i da. I am gr at ef ul

f or t he knowl edge, val ues, pr of essi onal i sm, and et hi cs t hat wer e

i mpar t ed ont o me by t hese i nst i t ut i ons.

Much of what I have accompl i shed i n l i f e i s bui l t on t he sup-

por t of ot her s. I am gr at ef ul f or t he mor al suppor t I have r e-

cei ved f r om my f ami l y, t eacher s, and f r i ends t hat has enabl ed me

t o compl et e t hi s wor k. Fur t her mor e, I am gr at ef ul f or t he f i nan-

ci al suppor t I have r ecei ved wi t hout whi ch t hi s wor k woul d not

be possi bl e. I woul d l i ke t o acknowl edge ( i n or der or r ecei pt of

f unds / gr ant s) Capt . Val er i an and Mer l yn Lasr ado, Paul Lasr ado,

and Uni ver si t y of Cent r al Fl or i da ( I EMS Depar t ment , Gr aduat e

St udi es, Dr . Yang Wang, Dr . Di ma Nazzal , and Dr . Thomas O Neal )

f or t hei r gener ous suppor t t hr ough t he year s.

Fi nal l y, I am gr at ef ul f or t he i mmense suppor t and di r ect i on

provi ded t o me by my PhD commi t t ee: Dr . Di ma Nazzal , Dr . Rober t

Ar macost , Dr . I van Gar i bay, Dr . Mansoor eh Mol l aghasemi , Dr .

Char l es Rei l l y, and Dr . St ephen Si vo. Thank you so much f or your

t i me, pat i ence, and gui dance whi ch enabl ed an i dea t o met amor -

phose i nt o t he wor k t hat i s pr esent ed hencef or t h.


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TABLE OF CONTENTS

ACKNOWLEDGMENTS ................................................................................................................................................. VI

TABLE OF CONTENTS ........................................................................................................................................... VII

LI ST OF FI GURES ................................................................................................................................................ XIII

LI ST OF TABLES .................................................................................................................................................. XIV

LI ST OF ACRONYMS / ABBREVI ATI ONS ....................................................................................................... XVI

1 I NTRODUCTI ON ................................................................................................................................................. 1

1. 1 DESCRI PTI ON OF THE LLMF .......................................................................................................................... 6

1. 2 RESEARCH STATEMENT ..................................................................................................................................... 9

2 LI TERATURE REVI EW................................................................................................................................... 12

2. 1 REVI EWPAPERS ON RESEARCHTOPI C .......................................................................................................... 13

2. 2 MANUFACTURI NG FACI LI TY LAYOUT PROBLEM.............................................................................................. 20

2. 2. 1 Looped Layout Desi gn Probl em ( LLDP) .......................................................................... 22

2. 2. 2 For mul at i ons wi t h Mi ni mum WI P desi gn obj ect i ve ................................................ 28

2. 3 SOLUTI ON METHODS ....................................................................................................................................... 30

2. 3. 1 Exact Al gor i t hms ....................................................................................................................... 32

2. 3. 2 Heur i st i cs Al gor i t hms ........................................................................................................... 33

2. 3. 3 Meta- Heur i st i c Al gori t hms .................................................................................................. 34

2. 3. 3. 1 Genet i c Al gor i t hms........................................................................................................................ 35

2. 3. 3. 2 Par t i cl e Swar m Opt i mi zat i on ................................................................................................... 42

2. 3. 3. 3 Si mul ated Anneal i ng ...................................................................................................................... 42

2. 3. 3. 4 Tabu Search Al gor i t hm................................................................................................................. 43

2. 4 CONVEYOR ANALYSI S ..................................................................................................................................... 44


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3 RESEARCH DESI GN ........................................................................................................................................ 50

3. 1 CONVEYOR ANALYSI S ..................................................................................................................................... 50

3. 1. 1 Phase I : The Tr avel i ng WI P on t he Conveyor ......................................................... 52

3. 1. 2 Phase I I : WI P at t he Tur nt abl es ................................................................................... 54

3. 1. 3 Phase I I I : WI P on t he Shor t cut s ................................................................................... 56

3. 1. 3. 1 Est i mati ng t he mean arr i val r ates of l oads................................................................ 58

3. 1. 3. 2 Est i mati ng the aver age WI P at i nput t ur nt abl e of a cel l ................................. 60

3. 1. 3. 3 Est i mati ng t he aver age del ays at t he exi t t ur nt abl e of a cel l................... 61

3. 1. 4 WI P on t he Conveyor ................................................................................................................ 63

3. 1. 5 St abi l i t y Condi t i on f or LLMF .......................................................................................... 63

3. 2 I NPUT STATI ON ANALYSI S ........................................................................................................................... 64

3. 2. 1 Previ ous Model s of WI P at t he I nput ( Loadi ng) St at i ons ............................. 64

3. 2. 1. 1 Met hod of Atmaca ( 1994) ............................................................................................................. 64

3. 2. 1. 2 Met hod of Bozer and Hsi eh ( 2004) ....................................................................................... 64

3. 2. 2 Proposed Methodol ogy f or WI P at I nput St at i ons ................................................ 65

3. 2. 2. 1 Type 1 Servi ce Di st r i but i on ................................................................................................... 65

3. 2. 2. 2 Type 2 Servi ce Di st r i but i on ................................................................................................... 66

3. 2. 2. 3 Expect ed WI P at i nput st ati ons ............................................................................................ 67

3. 2. 2. 4 A note on t he adj ust ed pr obabi l i t y................................................................................... 68

3. 2. 3Tot al WI P at t he I nput st at i ons ................................................................................... 69

3. 3 OPTI MI ZATI ON MODEL ................................................................................................................................... 69

3. 3. 1The case f or t he use of genet i c al gor i t hms ......................................................... 70

4 SOLUTI ON ALGORI THM FOR THE LLDP .................................................................................................. 72

4. 1 ENCODI NG THE CHROMOSOMES ........................................................................................................................ 73

4. 1. 1 Encodi ng t he Cel l s: cel l chr omosomes ....................................................................... 73

4. 1. 2 Encodi ng t he Shor t cut s: short cut chromosomes .................................................... 76


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4. 1. 3 Encoding a Layout or permutation ............................................................................ 77

4. 2 HI GH LEVEL SOLUTI ON ALGORI THM.............................................................................................................. 77

4. 2. 1 I ni t i al i z i ng t he GA ................................................................................................................ 79

4. 2. 1. 1 A not e on I ni t i al Par amet er sel ect i on........................................................................... 80

4. 2. 2 Generat e I ni t i al Popul at i on and Cel l Chr omosome ............................................. 83

4. 2. 3 Evaluate Permutation ......................................................................................................... 83

4. 2. 3. 1 GA appl i ed t o sol ve onl y t he l ayout pr obl em............................................................. 84

4. 2. 3. 2 Generat i ng t he shor t cut chr omosome................................................................................... 84

4. 2. 4 Sel ect Cel l Chr omosomes f or Mat i ng ............................................................................ 85

4. 2. 5 Mat e / Cr ossover Cel l Chromosomes............................................................................... 85

4. 2. 6 Mut at e Cel l Chromosomes ...................................................................................................... 88

4. 2. 7Ter mi nat i ng Condi t i on ........................................................................................................... 88

4. 2. 8 Col l ect I t erat i on Stat i s t i cs .......................................................................................... 89

5 TESTI NG PROCEDURE ................................................................................................................................... 90

5. 1TESTI NG THE EXPECTED VALUE OF WI P AT THE I NPUT STATI ONS ........................................................... 90

5. 1. 1 Pr obl em Descr i pt i on ................................................................................................................ 91

5. 1. 2 Par amet ers t o be var i ed ...................................................................................................... 92

5. 1. 3 Summary of Test i ng Procedur e f or WI P at I nput St at i ons ............................. 97

5. 1. 4 Method f or Anal ysi s of Test Data ................................................................................. 97

5. 1. 5 Hypothesi s ................................................................................................................................... 102

5. 1. 5. 1 Hypothesi s Test 1 ......................................................................................................................... 103

5. 1. 5. 2 Hypothesi s Test 2 ......................................................................................................................... 103

5. 1. 5. 3 Hypothesi s Test 3 ......................................................................................................................... 104

5. 1. 5. 4 Hypothesi s Test 4 ......................................................................................................................... 105

5. 1. 5. 5 Hypothesi s Test 5 ......................................................................................................................... 106

5. 2TESTI NG THE LLDP .................................................................................................................................... 107


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5. 2. 1Test Pr obl em Descr i pt i on .................................................................................................. 107

5. 2. 2 LLDP Test Scenar i os .............................................................................................................. 108

5. 2. 2. 1 LLDP Test Scenar i o E.................................................................................................................. 111

5. 2. 2. 2 LLDP Test Scenar i o F .................................................................................................................. 112

5. 2. 2. 3 LLDP Test Scenar i o G.................................................................................................................. 113

5. 2. 2. 4 LLDP Test Scenar i o H.................................................................................................................. 114

5. 2. 3 Par amet ers t o be var i ed .................................................................................................... 115

5. 2. 4 Equi val ent l y var yi ng t he cost s f or al l scenar i os ......................................... 117

5. 2. 5 Summary of t he Test i ng Procedure f or t he LLDP ................................................ 121

5. 2. 6

Method f or Anal ysi s of Test Data f or t he LLDP................................................ 122

5. 2. 8 Hypot heses ................................................................................................................................... 125

5. 2. 8. 1 Hypothesi s Test 1 ......................................................................................................................... 125

5. 2. 8. 2 Hypothesi s Test 2 ......................................................................................................................... 126

5. 2. 8. 3 Hypothesi s Test 3 ......................................................................................................................... 128

5. 2. 8. 4 Hypothesi s Test 4 ......................................................................................................................... 129

5. 2. 8. 5 Hypothesi s Test 5 ......................................................................................................................... 131

5. 2. 9 Fi ne Tuni ng t he Genet i c Al gori t hm Sol ut i on Pr ocedur e ............................... 132

5. 2. 9. 1 Outcomes of Par ameter Sweep f or t he GA sol ut i on Al gor i t hm.......................... 134

6 ANALYSI S OF RESULTS ............................................................................................................................ 135

6. 1 RESULTS FOR THE EXPECTED VALUE OF WI P AT THE I NPUT STATI ON TESTI NG................................... 135

6. 2 GLM ANALYSI S FOR THE EXPECTED VALUE OF WI P AT THE I NPUT STATI ON ....................................... 140

6. 2. 1 Anal ysi s of Var i ance............................................................................................................ 141

6. 2. 1. 1 ANOVA f or Layout X...................................................................................................................... 142

6. 2. 1. 2 ANOVA f or Layout Y...................................................................................................................... 143

6. 2. 1. 3 ANOVA f or Layout Z...................................................................................................................... 144

6. 2. 2 Compar i son of Means .............................................................................................................. 145

6. 2. 2. 1 Vari abl e: Ut i l i zat i on of Conveyor ( LCMHS) .................................................................. 145


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6. 2. 2. 2 Vari abl e: Squar ed Coef f i ci ent of var i at i on of Ar r i val s ( ca2) ..................... 147

6. 2. 2. 3 Vari abl e: WI P Data Sour ce - Si mul ati on or Anal yti cal Est i mate ( M) ....... 149

6. 2. 2. 4 Vari abl e: I nt eract i on between M and ca2 ( SCVM) ....................................................... 150

6. 2. 2. 5 Vari abl e: I nt eract i on between M and LCMHS ( RHOM) .................................................. 153

6. 2. 3 Eval uat i on of Hypot heses .................................................................................................. 155

6. 3 RESULTS FOR THE LOOPED LAYOUT DESI GN PROBLEM TESTI NG ............................................................... 158

6. 4 GLM ANALYSI S FOR THE LOOPED LAYOUT DESI GN PROBLEM.................................................................... 162

6. 4. 1 Anal ysi s of Var i ance ( ANOVA) ........................................................................................ 163

6. 4. 2 Compar i son of Means .............................................................................................................. 164

6. 4. 2. 1 Vari abl e: Shor t cut Cost / WI P Cost ( )....................................................................... 165

6. 4. 2. 2 Vari abl e: Ut i l i zat i on of Conveyor ( LCMHS) .................................................................. 166

6. 4. 2. 3 Vari abl e: Tur nt abl e Tur n Ti me ( t ) ................................................................................... 167

6. 4. 2. 4 Vari abl e: Opt i mi zat i on Cr i t er i a ( ).............................................................................. 168

6. 4. 2. 5 Vari abl e: Shor t cut Sel ecti on Cr i t er i a ( S) ................................................................ 169

6. 4. 2. 6 Var i abl e: Scenar i o ( S) ........................................................................................................... 170

6. 4. 3 Eval uat i on of Hypot heses .................................................................................................. 171

7 DI SCUSSI ON .................................................................................................................................................. 173

7. 1 EXPECTED WI P AT THE I NPUT STATI ONS OF THE CONVEYOR .................................................................. 173

7. 2 LOOPED LAYOUT DESI GN PROBLEM............................................................................................................. 175

8 CONCLUDI NG REMARKS ............................................................................................................................... 179

8. 1 SUMMARY OF PROPOSED METHODOLOGY ........................................................................................................ 179

8. 2

SUMMARY OF FI NDI NGS................................................................................................................................ 180

8. 3 SUMMARY OF CONTRI BUTI ONS ...................................................................................................................... 182

8. 4 I MPLI CATI ONS TO PRACTI TI ONERS ............................................................................................................ 184

8. 5 FUTURE WORK ............................................................................................................................................... 186

8. 6 CONCLUSI ON ................................................................................................................................................. 188


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APPENDI X A: FROM- TO MATRI X FOR LAYOUT X ...................................................................................... 190

APPENDI X B: FROM- TO MATRI X FOR LAYOUT Y ...................................................................................... 192

APPENDI X C: RESULTS FROM WI P AT I NPUT STATI ONS TESTI NG.................................................. 194

APPENDI X D: ABSOLUTE RELATI VE ERROR FOR WI P AT I NPUT STATI ONS TESTI NG............... 198

APPENDI X E: AVERAGE ERROR FOR WI P AT I NPUT STATI ONS TESTI NG...................................... 202

APPENDI X F: GLM PROCEDURE SAS OUTPUT FOR WI P AT I NPUT STATI ONS - LAYOUT X..... 204

APPENDI X G: GLM PROCEDURE SAS OUTPUT FOR WI P AT I NPUT STATI ONS - LAYOUT Y..... 213

APPENDI X H: GLM PROCEDURE SAS OUTPUT FOR WI P AT I NPUT STATI ONS - LAYOUT Z..... 222

APPENDI X I : WI P FROM THE LLDP TESTI NG........................................................................................... 231

APPENDI X J : SOLUTI ONS # SHORTCUTS FROM THE LLDP TESTI NG................................................ 237

APPENDI X K: SOLUTI ONS # I TERATI ONS FROM THE LLDP TESTI NG.............................................. 243

APPENDI X L: SOLUTI ON TI MES (MI NUTES) FROM THE LLDP TESTI NG......................................... 249

APPENDI X M: GLM PROCEDURE SAS OUTPUT FOR THE LLDP .............................................................. 255

LI ST OF REFERENCES ........................................................................................................................................ 263


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LIST OF FIGURES

FI GURE 1. 1: TYPES OF FACI LI TY LAYOUTS W. R. T. MATERI AL HANDLI NG DESI GN ........................................... 2

FI GURE 1. 2: LAYOUT OF THE FACI LI TY ................................................................................................................... 8

FI GURE 1. 3: SHORTCUT DI AGRAM............................................................................................................................... 9

FI GURE 2. 1: MANUFACTURI NG FACI LI TY LAYOUT PROBLEM OUTLI NE .................................................................... 14

FI GURE 2. 2: MANUFACTURI NG FACI LI TY LAYOUT PROBLEM RESEARCH FOCUS ...................................................... 15

FI GURE 2. 3: FLOWCHART OF A GA .......................................................................................................................... 37

FI GURE 3. 1: THE LLMF WI TH SHORTCUTS.............................................................................................................. 51

FI GURE 3. 2: TYPES OF TURNTABLES....................................................................................................................... 54

FI GURE 3. 3: CELL P ................................................................................................................................................ 56

FI GURE 3. 4: CELLS I N THE LLMHS....................................................................................................................... 56

FI GURE 4. 1: I LLUSTRATI VE FACI LI TY ................................................................................................................... 73

FI GURE 4. 2: ALTERNATE I LLUSTRATI VE FACI LI TY ................................................................................................ 74



FI GURE 4. 5: I LLUSTRATI VE FACI LI TY WI TH SHORTCUTS ...................................................................................... 76

FI GURE 4. 6: FLOWCHART OF SOLUTI ON ALGORI THM............................................................................................... 78

FI GURE 4. 7: FLOWCHART OF THE I NI TI ALI ZE SUB- PROCESS................................................................................ 79

FI GURE 5. 1: 300MM WAFER FABRI CATI ON FACI LI TY ............................................................................................ 92

FI GURE 5. 2: SUMMARY OFTESTI NG PROCEDURE ..................................................................................................... 97

FI GURE 5. 3: LLMF FOR THE LLDP TESTI NG ...................................................................................................... 108

FI GURE 5. 4: SUMMARY OFTESTI NG PROCEDURE FOR LLDP ................................................................................ 121

FI GURE 6. 1: AVERAGE ERROR FOR LAYOUT X ...................................................................................................... 139

FI GURE 6. 2: AVERAGE ERROR FOR LAYOUT Y ...................................................................................................... 139


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LIST OF TABLES

TABLE 4. 1: NUMBER OF BI TS REQUI RED FOR DI FFERENT N S 75

TABLE 5. 1: PARAMETERS TO VARY FOR TESTI NG THE EXPECTED TOTAL WI P AT THE I NPUT STATI ONS 92

TABLE 5. 2: FLOW RATE MULTI PLI ERS AT DI FFERENT CONVEYOR UTI LI ZATI ONS 94

TABLE 5. 3: PARAMETERS FOR WEI BULL DI STRI BUTI ON 96

TABLE 5. 4: DESCRI PTI ON OF RHOM 99

TABLE 5. 5: DESCRI PTI ON OF SCVM 101

TABLE 5. 6: DESCRI PTI ON OF I NDEPENDENT VARI ABLES FOR GLM 101

TABLE 5. 7: EXAMPLE OF SUBSET OF TOTAL WI P AT I NPUT STATI ONS DATA TABLE FOR GLM 102

TABLE 5. 8: TYPE OF TEST SCENARI O 108

TABLE 5. 9: PARAMETERS TO VARY FOR LLDP 116

TABLE 5. 10: DESCRI PTI ON OF S 123

TABLE 5. 11: DESCRI PTI ON OF I NDEPENDENT VARI ABLES FOR GLM 123

TABLE 5. 12: EXAMPLE OF SUBSET OF I NPUT DATA TABLE FOR GLM 124

TABLE 5. 13: PARAMETERS TO VARY TO FI NE-TUNE SOLUTI ON ALGORI THM 132

TABLE 5. 14: FI NAL PARAMETERS FOR GA SOLUTI ON ALGORI THM 134

TABLE 6. 1: AVERAGE ABSOLUTE RELATI VE ERROR FOR EACH LAYOUT AT DI FFERENT LEVELS OF LCMHS 137

TABLE 6. 2: AVERAGE ABSOLUTE RELATI VE ERROR FOR EACH LAYOUT AT DI FFERENT LEVELS OF CA2 138

TABLE 6. 3: ANOVA OF THE WI P AT THE I NPUT STATI ONS FOR LAYOUT X 142

TABLE 6. 4: ANOVA OF THE WI P AT THE I NPUT STATI ONS FOR LAYOUTY 143

TABLE 6. 5: ANOVA OF THE WI P AT THE I NPUT STATI ONS FOR LAYOUT Z 144

TABLE 6. 6: REGWQ ANDTUKEYS MULTI PLE COMPARI SON TEST FOR LCMHS FOR LAYOUT X 146

TABLE 6. 7: REGWQ ANDTUKEYS MULTI PLE COMPARI SON TEST FOR LCMHS FOR LAYOUTY 146

TABLE 6. 8: REGWQ ANDTUKEYS MULTI PLE COMPARI SON TEST FOR LCMHS FOR LAYOUT Z 146

TABLE 6. 9: REGWQ ANDTUKEYS MULTI PLE COMPARI SON TEST FOR CA2 FOR LAYOUT X 147


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TABLE 6. 10: REGWQ ANDTUKEYS MULTI PLE COMPARI SON TEST FOR CA2 FOR LAYOUTY 148

TABLE 6. 11: REGWQ ANDTUKEYS MULTI PLE COMPARI SON TEST FOR CA2 FOR LAYOUT Z 148

TABLE 6. 12: REGWQ ANDTUKEYS MULTI PLE COMPARI SON TEST FOR M FOR LAYOUT X 149

TABLE 6. 13: REGWQ ANDTUKEYS MULTI PLE COMPARI SON TEST FOR M FOR LAYOUTY 149

TABLE 6. 14: REGWQ ANDTUKEYS MULTI PLE COMPARI SON TEST FOR M FOR LAYOUT Z 150

TABLE 6. 15: REGWQ ANDTUKEYS MULTI PLE COMPARI SON TEST FOR SCVM FOR LAYOUT X 151

TABLE 6. 16: REGWQ ANDTUKEYS MULTI PLE COMPARI SON TEST FOR SCVM FOR LAYOUTY 152

TABLE 6. 17: REGWQ ANDTUKEYS MULTI PLE COMPARI SON TEST FOR SCVMFOR LAYOUT Z 152

TABLE 6. 18: REGWQ ANDTUKEYS MULTI PLE COMPARI SON TEST FOR RHOM FOR LAYOUT X 154

TABLE 6. 19: REGWQ ANDTUKEYS MULTI PLE COMPARI SON TEST FOR RHOM FOR LAYOUTY 154

TABLE 6. 20: REGWQ ANDTUKEYS MULTI PLE COMPARI SON TEST FOR RHOMFOR LAYOUT Z 155

TABLE 6. 21: LLDP RESULTS SUMMARY WI TH REGARDS TO SCENARI O 159

TABLE 6. 22: LLDP RESULTS SUMMARY WI TH REGARDS TO LCMHS 160

TABLE 6. 23: LLDP RESULTS SUMMARY WI TH REGARDS TO T 160

TABLE 6. 24: LLDP RESULTS SUMMARY WI TH REGARDS TO 161

TABLE 6. 25: LLDP RESULTS SUMMARY WI TH REGARDS TO 161

TABLE 6. 26: LLDP RESULTS SUMMARY WI TH REGARDS TO S 162

TABLE 6. 27: ANOVA OF THE WI P FOR THE LLDP 163

TABLE 6. 28: REGWQ ANDTUKEYS MULTI PLE COMPARI SON TEST FOR FOR THE LLDP 165

TABLE 6. 29: REGWQ ANDTUKEYS MULTI PLE COMPARI SON TEST FOR LCMHSFOR THE LLDP 166

TABLE 6. 30: REGWQ ANDTUKEYS MULTI PLE COMPARI SON TEST FOR T FOR THE LLDP 167

TABLE 6. 31: REGWQ ANDTUKEYS MULTI PLE COMPARI SON TEST FOR FOR THE LLDP 168

TABLE 6. 32: REGWQ ANDTUKEYS MULTI PLE COMPARI SON TEST FOR S FOR THE LLDP 169

TABLE 6. 33: REGWQ ANDTUKEYS MULTI PLE COMPARI SON TEST FOR S FOR THE LLDP 170

TABLE 7. 1: NUMBER OF DESI GN WI TH AVERAGE MI MI NUM WI P FOR EACH TEST PROBLEM 176


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LIST OF ACRONYMS / ABBREVIATIONS

Abbr evi at i on Meani ngANOVA Anal ysi s of Var i ance

CLC Cl osed l ooped conveyorFLP f aci l i t y l ayout pr obl emGA Genet i c al gor i t hmGLM Gener al i zed Li near ModelLCMHS Looped conveyor mat er i al handl i ng syst emLLDP Looped l ayout desi gn probl emLLMF Looped l ayout manuf act ur i ng f aci l i t yMF Manuf act ur i ng f aci l i t yMFLP Manuf act ur i ng f aci l i t y l ayout pr obl emMHS Mater i al handl i ng syst em

PS Product i on Syst emQAP Quadr at i c assi gnment probl emQNA Queuei ng net wor k anal yzerSA Si mul at ed anneal i ngSCV Squar ed coef f i ci ent of var i at i on


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1 INTRODUCTION

Wi t h t he ongoi ng t echnol ogy bat t l es and pr i ce war s i n t oday s

compet i t i ve economy, every company i s l ooki ng f or an advant age

over i t s peer s; an i mpor t ant pr act i cal quest i on i s, how do com-

pani es cr eat e t hi s compet i t i ve advant age i n t er ms of cr eat i ng

val ue (Hi t t , I r el and, Camp, & Sext on, 2001, 2002; Meyer , 1991) ?

A sust ai nabl e compet i t i ve advant age coul d be pr ovi ded f or by be-

i ng an ef f i ci ent busi ness ( Pet er af , 1993) . As per Tompki ns,

Whi t e, and Bozer ( 2010) , compani es i n t he US spend around 8% of

t he gr oss nat i onal pr oduct annual l y on new f aci l i t i es. The au-

t hor s poi nt out t hat ef f ect i ve f aci l i t y pl anni ng can r educe op-

er at i onal expenses by 10% t o 30% annual l y. Appl e ( 1977) i ndi -

cat es t hat a good f aci l i t y l ayout desi gn i ncor por at es t he

mater i al handl i ng deci si ons at t he devel opment st age. Tompki ns

et al . ( 2010) i ndi cat e t hat mat er i al handl i ng and f aci l i t y pl an-

ni ng cost can at t r i but e ar ound 20% t o 50% of a f aci l i t y s oper -

at i ng expense. Hence, a par t i cul ar choi ce of f aci l i t y Layout can

have a si gni f i cant i mpact on t he abi l i t y of a company t o mai n-

t ai n l ower oper at i onal expenses under uncer t ai n economi c condi -

t i ons. Fur t her mor e, a poor Layout can r esul t i n hi gh mat er i alhandl i ng cost s, excessi ve wor k- i n- pr ocess ( WI P) , and l ow or un-

bal anced equi pment ut i l i zat i on ( Her agu, 2006) .


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I n gener al , t he manuf act ur i ng f aci l i t y ( MF) consi st s of a pr o-

duct i on syst em ( PS) and a mat er i al handl i ng syst em ( MHS) . The PS

consi st s of numer ous oper at i onal cel l s hencef or t h r ef er r ed t o as

a cel l or cel l s . I n t he l i t er at ur e, a cel l i n t he PS i s ref er r ed

t o as a machi ne, a f aci l i t y, a st at i on, a col l ecti on of st a-

t i ons, a depar t ment , a bay, et c. The manuf act ur ed uni t s, hence-

f or t h r ef er r ed t o as l oads or j obs, ar e t r ansf er r ed f r om one

cel l t o anot her by t he MHS. As seen i n Fi gur e 1. 1, t her e ar e

var i ous t ypes of MF l ayout s wi t h r espect t o mat er i al handl i ng

syst ems desi gn: si ngl e r ow, mul t i r ow, cl osed l oop l ayout ( Kusi -

ak & Her agu, 1987) , and open f i el d l ayout ( Loi ol a, de Abr eu,

Boavent ur a- Net t o, Hahn, & Quer i do, 2007) .

(a) Single Row (b) Multiple Row (c) Closed Loop (d) Open Field

Fi gur e 1. 1: Types of f aci l i t y l ayout s w. r . t . mat er i al handl i ngdesi gn

Thi s r esear ch wi l l f ocus on t he l ayout of a MF, i . e. , t he man-

uf act ur i ng f aci l i t y l ayout pr obl em ( MFLP) f or a cl osed l oop l ay-

out . Thi s speci al case of t he MF wi l l hencef or t h be r ef er r ed t o

as t he l ooped l ayout MF ( LLMF) . Thi s speci al case of MFLP wi l l

hencef or t h be r ef er r ed t o as t he l ooped l ayout desi gn pr obl em

( LLDP) , usi ng t he nomencl atur e i nt r oduced i n Nearchou ( 2006) .


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The subsequent di scussi on wi l l f i r st i nt r oduce t he MFLP, t he

LLMF and LLDP wi l l be di scussed i n gr eat det ai l i n 2. 2. 1.

The MFLP can be def i ned as an opt i mi zat i on pr obl em whose sol u-

t i on det er mi nes t he most ef f i ci ent physi cal or gani zat i on of t he

cel l s i n a PS wi t h r egards t o an obj ect i ve. The most common ob-

j ect i ves ai m t o mi ni mi ze t he mat er i al handl i ng cost ( MHC) , t he

t r avel ed di st ance t r avel ed, or t he t ot al t i me i n syst em ( Ben-

j aaf ar , Her agu, & I r ani , 2002) . Pr evi ous MFLP f or mul at i ons t end

t o i gnor e t he i mpact of t he f aci l i t y l ayout on t he oper at i onal

per f or mance of t he MF i . e. t he wor k- i n- pr ocess ( WI P) , t he

t hr oughput , or t he cycl e t i me. Benj aaf ar ( 2002) shows t hat t r a-

di t i onal MF desi gn cr i t er i a can be a poor i ndi cat or of t he oper -

at i onal per f ormance of t he MF. Bozer and Hsi eh (2005) t oo sup-

por t t hi s ar gument . Kouvel i s, Kur awar wal a, and Gut i er r ez ( 1992)

st at e, t he use of opt i mal i t y wi t h r espect t o a desi gn obj ec-

t i ve, such as t he mi ni mi zat i on of t he mat er i al handl i ng cost , i s

di scr i mi nat i ng. Benj aaf ar ( 2002) ar gues t hat t he oper at i onal

per f ormance of t he MF i s cont i ngent on t he congest i on i n t he MF.

The congest i on i n t he MF i s a f unct i on of i t s capaci t y and var i -

abi l i t y. Hence, i t i s i mper at i ve t hat t he obj ect i ve of t he MFLP

capt ur es t he i mpact of t he f aci l i t y l ayout on t he oper at i onal

per f ormance of t he MF. Thi s can be achi eved, f or exampl e, by

set t i ng t he obj ect i ve of t he MFLP t o mi ni mi ze the WI P i n t he MF


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( Benj aaf ar , 2002; Fu & Kaku, 1997; Kouvel i s & Ki r an, 1991; Ra-

man, Nagal i ngam, & Gur d, 2008) . However , despi t e t he pr esence of

conveyor syst ems i n hi gh vol ume manuf act ur i ng f aci l i t i es, t her e

are no methods t hat generat e t he Layout by mi ni mi zi ng the WI P i n

a LLMF wi t h a cl osed l oop conveyor ( CLC) as t he MHS.

Thi s r esear ch proposes a sol ut i on met hodol ogy t hat addr esses

t he devel opment of a f aci l i t y l ayout f or a LLMF wi t h a l ooped

conveyor mat er i al handl i ng syst em ( LCMHS) t hat can have

shor t cut s across i t usi ng a syst em per f or mance met r i c, i . e. t he

wor k i n pr ocess ( WI P) on t he conveyor and at t he i nput st at i ons

t o t he conveyor , as a f act or i n t he mi ni mi zi ng f unct i on f or t he

f aci l i t y l ayout opt i mi zat i on pr obl em whi ch i s sol ved heur i st i -

cal l y usi ng a per mut at i on genet i c al gor i t hm. I t can be ar gued

t hat t her e i s no di f f er ence i n t he opt i mal l ayout as gener at ed

by mi ni mi zi ng the WI P ver sus t he di st ance or cost , Fu and Kaku

( 1997) suppor t t hi s cl ai m. Benj aaf ar ( 2002) pr oposes t hat t her e

i s a di f f erence and adds t hat Fu and Kaku ( 1997) di d not capt ur e

t hi s as a r esul t of t he si mpl i st i c queuei ng model used t o model

t he MF. Benj aaf ar ( 2002) pr oposes that under cer t ai n condi t i ons

bot h appr oaches wi l l yi el d t he same f aci l i t y l ayout , t hese r e-

str i ct i ng condi t i ons ar e:

1. The f l ow r at es between t he cel l s, machi nes, st at i ons, de-

par t ment s, f aci l i t i es, or bays ar e bal anced


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2. The cel l s, machi nes, st at i ons, depar t ment s, f aci l i t i es, or

bays ar e equi di st ance

3. The demand and process t i me var i abi l i t y ar e l ow

The f i r st condi t i on i s pract i cal l y unr eal i st i c and appl i es i f

and onl y i f al l t he l oads vi si t al l t he machi nes t he same number

of t i mes. Al so, moder n MFs manuf act ur e a mul t i t ude of pr oduct s

and t hi s si t uat i on i s r ar el y encount er ed. As ment i oned, t hi s r e-

search wi l l f ocus on MF t hat have a LCMHS, t heref ore t he second

condi t i on i n i nher ent l y i mpossi bl e gi ven t he MHS i s a l oop. The

t hi r d condi t i on i s pl ausi bl e but t her e ar e many si t uat i ons i n

pr act i ce t hat have hi gh demand var i abi l i t y, hi gh pr ocess var i a-

bi l i t y, or both.

Tr adi t i onal l y f or t he MFLP, t he opt i mal l ayout of a f aci l i t y

i s f i r st det er mi ned. Af t er some t i me of oper at i on, usual l y i f

needed, t he best set of shor t cut s i s det er mi ned t o al l evi at e

congest i on i n t he LLMF as descr i bed by Hong, J ohnson, Car l o,

Nazzal , and J i menez ( 2011) . I t i s t he cont ent i on of t he pr oposed

r esear ch that t he af or ement i oned two- st ep pr ocess yi el ds a sub-

opt i mal sol ut i on. The pr oposed r esear ch ai ms at det er mi ni ng t he

best set of shor t cut s whi l e si mul t aneousl y det er mi ni ng t he f a-

ci l i t y l ayout , t her eby ensur i ng at wor st an equi val ent sol ut i on

t o t he t wo- st ep pr ocess.


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The comput at i onal compl exi t y of t he al gor i t hms r equi r ed t o

sol ve t he pr oposed f or mul at i on of t he MFLP i s t o be consi der ed.

The proposed f or mul at i on i s a NP- Har d probl em as pr oved by Leung

( 1992) . I t has been shown t hat t he comput at i on t i me r equi r ed t o

r each an opt i mal sol ut i on i ncr eases exponent i al l y as t he number

of machi nes t o be ar r anged i ncr eases when usi ng exact sol ut i on

met hods ( Foul ds, 1983) . J ames, Rego, and Gl over ( 2008) and Loi o-

l a, de Abr eu, Boavent ur a- Net t o, Hahn, and Quer i do ( 2007) suppl e-

ment t hi s cl ai m wi t h det ai l ed di scussi ons on t he comput at i onal

compl exi t y and t he requi r ed comput at i on t i me t o r each an opt i mal

sol ut i on usi ng exact sol ut i on met hods. Thi s r esear ch pr oposes

t he use of genet i c al gor i t hms ( GA) t o sol ve t he f or mul at i on as

f ur t her di scussed i n 3. 3. 1 and 4.

The r est of t hi s chapt er i s or gani zed as f ol l ows: 1. 1 wi l l

pr ovi de a descr i pt i on of t he LLMF; and 1. 2 wi l l pr esent t he

r esear ch st at ement .

1.1 Description of the LLMF

A br i ef descr i pt i on of t he LLMF i s gi ven bel ow. Thi s descr i pt i on

ent ai l s t he assumpt i ons, def i ni t i ons and char act er i st i cs of t he

LLMF.

I t i s assumed t hat t he number of machi nes r equi r ed and thei r

groupi ngs ar e predet ermi ned. The machi nes may be used i ndi vi du-


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al l y or as a gr oup; i n ei t her case, t hey wi l l be r ef er r ed t o as

cel l s. Ther e wi l l be M cel l s ( i=1,2,3,..,M) assi gned t o N l oca-

t i ons ( j=1,2,3,..,N) wher e M N. I f M < N dummy cel l s

( M+1,M+2,..,N) are i nt r oduced as r ecommended by Hi l l i er and Con-

nor s ( 1966) . Ther e i s one ent r y poi nt ( l oadi ng cel l ) and one ex-

i t poi nt ( shi ppi ng cel l ) t o t he LLMF. At t he ent r y poi nt ( i=0)

pr oduct s ar e del i ver ed/ l oaded i nt o t he pl ant and at t he exi t

poi nt ( i=N+1) pr oduct s are shi pped/ unl oaded out of t he pl ant .

Ther e ar e K pr oduct s ( k=1,2,3,..,K) f l owi ng t hr ough t he LLMF

each char act er i zed by an i ndependent l y di st r i but ed random var i a-

bl e wi t h an aver age demand ( Dk) and a squar ed coef f i ci ent of var -

i at i on ( ck2) .

The r out i ng f or each product t hrough t he LLMF i s known and i s

det er mi ni st i c. Product s may vi si t each cel l mor e t han once. The

decomposi t i on method as pr esent ed i n Whi t t ( 1983) i s used t o de-

t er mi ne t he i nt er nal f l ows bet ween t he cel l s. The i nt er nal f l ow

bet ween cel l s f or each pr oduct wi l l be r epr esent ed by ij, where

t he pr oduct t r avel s f r om cel l i ( i=1,2,3,..,N) t o cel l j

( j=1,2,3,..,N) usi ng a LCMHS and ii=0.

The LLMF i s a j ob shop wi t h i nt er connect ed bays/ cel l s t hat

each consi st s of a gr oup of machi nes or i ndi vi dual machi nes, an

aut omat ed mat er i al handl i ng syst em ( AMHS) whi ch i s a LCMHS wi t h

no l oad r eci r cul at i on i . e. i nf i ni t e buf f er at unl oadi ng st at i on


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f r om t he conveyor , an i nput st at i on ( wher e new j obs ar e i nt r o-

duced t o t he LLMF) and an out put st at i on ( where compl et ed j obs

are moved away f r om t he LLMF) , and shor t cuts as shown i n Fi gur e

1. 2.

The MF has a var i abl e demand, a r egul ar shape wi t h f i xed di -

mensi ons. The l oads can backt r ack t o cel l s, i . e. r evi si t f aci l i -

t i es, and bypass cel l s i n t he MF. Each cel l has a l oadi ng / un-

l oadi ng st at i on wher e l oads are l oaded t o / unl oaded f r om t he

conveyor .

1 2 3 4

N N-1 N-2

B-1 B

B+2 B+1

Output

Input

Turntables

Cell

N-3

Shortcuts

Fi gur e 1. 2: Layout of t he Faci l i t y

The ar r i val process t o cel l i i s char act er i zed by an i nde-

pendent l y di st r i but ed r andom var i abl e wi t h an aver age i nt er ar r i -

val t i me ( 1/i) and a squar ed coef f i ci ent of var i at i on ( cai2) ,

whi l e t he ser vi ce pr ocess at each cel l i s char act er i zed by an

i ndependent l y di st r i but ed r andom var i abl e wi t h a mean ser vi ce

t i me (i) and a squar ed coef f i ci ent of var i at i on ( csi2) .

I n t he LLMF, a shor t cut can be pl aced af t er each cel l i i n t he

di r ect i on of f l ow such t hat i t i s bef or e t he next cel l i +1 and


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bef or e t he cor r espondi ng shor t cut f r om t he opposi t e si de of t he

conveyor .

As i l l ust r at ed by Fi gur e 1. 3, t wo si des of t he conveyor ar e

shown. Cel l p and cel l q ar e on one si de of t he conveyor , whi l e

cel l r and cel l s ar e on t he ot her ( opposi t e) si de of t he con-

veyor . The shor t cut p ( ar c eh ) af t er cel l p i s pl aced i n t he

di r ect i on of f l ow bef or e cel l q and bef or e t he cor r espondi ng

shor t cut r ( ar c gf ) f r om cel l r opposi t e si de of t he conveyor .

s rh g

p qe f

Fi gur e 1. 3: Shor t cut di agr am

I f a cel l i s t he l ast cel l on i t s si de of t he conveyor i n t he

di r ect i on of f l ow, t hen a shor t cut i s al ways pl aced af t er t hat

cel l ( t he shor t wal l of t he conveyor t hat connect s t he t wo

si des. )

1.2 Research Statement

For a LLMF, t he pr oposed met hodol ogy wi l l ai m t o sol ve t he LLDP

f or a LCMHS wi t h shor t cut s, usi ng a syst em per f or mance met r i c,

i . e. t he wor k i n pr ocess ( WI P) on t he conveyor and at t he i nput


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st at i ons t o t he conveyor , as a f act or i n t he mi ni mi zi ng f unct i on

f or t he f aci l i t y l ayout opt i mi zat i on pr obl em whi ch i s sol ved

heur i st i cal l y usi ng a per mut at i on genet i c al gor i t hm. usi ng an op-

er at i onal per f or mance met r i c, i . e. t he wor k i n pr ocess on t he

conveyor and t he i nput st at i ons i n a MF, as t he mi ni mi zi ng f unc-

t i on of t he desi gn cr i t er i a. Bozer & Hsi eh ( 2005) suggest s t hat

f or a LLMF, t he most appr opr i at e desi gn cr i t er i on f or t he LLDP

woul d be t o mi ni mi ze t he tot al WI P on t he conveyor and t he i nput

st at i ons f or al l t he cel l s i n t he LLMF. Benj aaf ar ( 2002) shows

t hat usi ng t he t ot al WI P i n t he syst em ( WI P i n t he pr oduct i on

syst em, t he unl oadi ng and unl oadi ng st at i ons, and t he MHS) as a

desi gn cr i t er i on f or a MF wi t h aut omat ed vehi cl es as t he MHS can

have a si gni f i cant i mpact on t he l ayout of t he MF.

As descr i bed ear l i er , most t r adi t i onal MFLP met hods ai m at

mi ni mi zi ng t he tot al di st ance t r avel ed, t he mat er i al handl i ng

cost , or t he t i me i n t he syst em ( based on di st ance t r avel ed at a

speci f i c speed) . However , Bozer & Hsi eh ( 2005) suggest t hat one

or more l oadi ng st at i ons i n t he LLMF mi ght become unst abl e as a

r esul t of t he t r adi t i onal l ayout s cr eat i ng t oo much f l ow over

cer t ai n segment s of t he conveyor . Al so, one of t he out comes of

t he pr oposed r esear ch i s t hat t he t r adi t i onal opt i mal l ayout ,

i . e. , t he l ayout wi t h t he mi ni mum di st ance may not have t he mi n-

i mum WI P f or t he LLMF.


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Fur t her , as descri bed ear l i er , t he t wo st ep pr ocess of f i r st

det er mi ni ng t he opt i mal Layout and t hen det er mi ni ng t he best set

of shor t cut s wi l l yi el d a sub opt i mal sol ut i on. The pr oposed r e-

sear ch addr esses t hi s i ssue by det er mi ni ng t he set of shor t cut s

and t he l ayout si mul t aneousl y and i t er at i vel y, t her eby ensur i ng

at wor st an equi val ent sol ut i on t o t he t wo- st ep pr ocess.

The r emai nder of t he document i s or gani zed as f ol l ows: 2

wi l l pr esent t he l i t er at ur e r evi ew wi t h r egar ds t o t he pr oposed

methodol ogy; 3 wi l l pr esent t he r esear ch desi gn; 4 wi l l pr e-

sent t he pr oposed i mpl ement at i on; and 5. 2. 9 wi l l di scuss t he

concl udi ng st atement s and f ut ur e work.


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2 LITERATURE REVIEW

The amount of r esearch done on t he manuf act ur i ng f aci l i t y l ayout

pr obl em ( MFLP) i s ver y vast . Due t o i t s br oad appl i cabi l i t y and

sol ut i on compl exi t y i t has been t he subj ect of act i ve r esear ch

over t he l ast 50 year s. Koopmans and Beckmann ( 1957) are t he

f i r st t o di scuss t he FLP. They def i ne t he FLP as a quadr at i c as-

si gnment pr obl em ( QAP) t hat det er mi nes t he l ayout of f aci l i t i es

so t hat t he mat er i al handl i ng cost bet ween t he f aci l i t i es i s

mi ni mi zed. Sahni and Gonzal ez ( 1976) pr ove t he comput at i onal

compl exi t y and t he di f f i cul t y i nvol ved i n sol vi ng QAP pr obl ems

by showi ng t he QAP i s NP- Compl et e.

Fi gur e 2. 1 on page 14 as pr esent ed i n ( Dr i r a, Pi er r eval , &

Haj r i - Gabouj , 2007) i l l ust r at es t he br oad nat ur e of t he MFLP.

Thi s l i t er at ure r evi ew wi l l f ocus on t he f aci l i t y l ayout pr oce-

dur es f or a st at i c MF wi t h ( r ef er t o

Fi gur e 2. 2 on page 15) : avai l abl e dat a, a var i abl e ( st ochast i c?)

demand, a r egul ar shape wi t h f i xed di mensi ons, a l ooped conveyor

based MHS wi t h no l oad r eci r cul at i on i . e. i nf i ni t e buf f er at un-

l oadi ng st at i on f r om t he conveyor , wi t h backt r acki ng and bypass-

i ng enabl ed, f ormul ated as a QAP t hat mi ni mi zes mater i al han-dl i ng cost by mi ni mi zi ng t he congest i on i n t he syst em i . e. t he

WI P i n t he manuf act ur i ng f aci l i t y.


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The r est of t hi s chapt er i s or gani zed as f ol l ows: 2. 1 wi l l

pr esent a l i st of r evi ew paper s r el at ed t o t he pr oposed met hod-

ol ogy; 2. 2 wi l l pr esent a r evi ew of t he MFLP; 2. 3 wi l l pr e-

sent a revi ew of t he sol ut i on met hods f or t he MLFP; 2. 4 wi l l

pr esent a revi ew of conveyor syst ems and met hods of anal ysi s f or

such syst ems.

2.1 Review Papers on Research Topic

Ther e have been numer ous r evi ew and sur vey paper s t hat have

t r acked t he resear ch on FLP and ot her r esear ch subj ect s r el at ed

t o t he FLP over t i me per t ai ni ng t o t he cur r ent r esear ch t opi c of

a LLDP wi t h a LCMHS.

Wi l son ( 1964) pr esent s a r evi ew of var i ous FLP s wi t h r e-

gards t o f i xed desi gns, mater i al f l ow net works, and commu-

ni cat i on net wor ks

El - Rayah and Hol l i er ( 1970) pr esent a r evi ew of var i ous FLP

whi l e al so r evi ewi ng opt i mal and subopt i mal al gor i t hms f or

sol vi ng a QAP

Pi erce and Cr owst on ( 1971) pr esent a r evi ew of al gor i t hms

f or sol vi ng t he QAP usi ng t r ee- sear ch al gor i t hms


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Fi gur e 2. 1: Manuf act ur i ng Faci l i t y Layout Pr obl em Out l i ne


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Fi gur e 2. 2: Manuf act ur i ng Faci l i t y Layout Pr obl em Resear ch Focus


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Hanan and Kur t zber g ( 1972) pr esent a sur vey of al gor i t hms

f or sol vi ng appl i cat i ons of t he QAP t o a var i et y of i ndus-

t r i es

Moor e ( 1974) pr esent s a r evi ew of t he, t hen, cur r ent st at e

of FLP r esearch i n Europe and Nor t h Amer i ca based on r e-

sponses t o a sur vey sent t o aut hor s of var i ous FLP al go-

r i t hms

Franci s and Gol dst ei n ( 1974) pr esent a l i st of paper s pub-

l i shed i n bet ween 1960 t o 1973 on l ocat i on t heory, however ,

many of t hese ref er ences al l ude t o the FLP and al gor i t hms

used t o sol ve t he QAP

Burkard and St r at mann ( 1978) pr esent a revi ew t hat ext ends

t he wor k per f ormed by Pi erce and Cr owst on (1971) by compar -

i ng t he ef f i cacy of var i ous subopt i mal al gor i t hms

Mut h and Whi t e ( 1979) di scuss det er mi ni st i c, pr obabi l i st i c,

descr i pt i ve and normat i ve appr oaches used t o model conveyor

syst ems

Foul ds ( 1983) pr esent s a r evi ew of opt i mal and sub opt i mal

al gor i t hms f or t he QAP hi ghl i ght i ng t he appl i cat i on of

gr aph theor y t o sol ve t he FLP

Levar y and Kal chi k ( 1985) pr esent a r evi ew t hat compares

and cont r ast s sever al sub opt i mal al gor i t hms used t o sol ve

t he QAP


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Buzacot t and Yao ( 1986) present a revi ew t hat compar es and

cont r ast s sever al anal yt i cal model s of f l exi bl e manuf act ur -

i ng syst ems by eval uat i ng t he st r engt hs and weaknesses of

each model

Fi nke, Bur kar d, and Rendl ( 1987) pr esent a sur vey of t he

t heor y and sol ut i on pr ocedur es ( exact and appr oxi mat e) f or

t he QAP wi t h speci al i nt er est devot es t o i nt eger pr ogr am-

mi ng equi val ent s t o t he QAP

Hassan and Hogg ( 1987) present a r evi ew and eval uat i on of

al gor i t hms t hat appl y gr aph t heor y t o sol ve t he FLP

Kusi ak and Her agu ( 1987) pr esent a r evi ew t hat eval uates

t he, t hen, cur r ent st at e of opt i mal and subopt i mal al go-

r i t hms t o sol ve t he FLP

Bi t r an and Dasu ( 1992) pr esent a r evi ew of manuf act ur i ng

syst ems model ed as open queuei ng networ ks

Par dal os, Rendl , and Wol kowi cz ( 1994) pr esent a survey of

t he, t hen, cur r ent st at e of QAP r esear ch cover i ng QAP f or -

mul at i ons, sol ut i on met hods and appl i cat i ons

Mel l er and Gau ( 1996) present a survey t hat compar es and

cont r ast s t he, t hen, cur r ent FLP sof t war e t o t he FLP r e-

search


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Mavr i dou and Pardal os ( 1997) pr esent a sur vey of si mul ated

anneal i ng al gor i t hms and genet i c al gor i t hms used f or gener -

at i ng appr oxi mat e sol ut i ons f or t he FLP

Bal akr i shnan and Cheng ( 1998) pr esent a r evi ew of t he al go-

r i t hms t o sol ve t he FLP based on mul t i pl e per i ods pl anni ng

hor i zons ( Dynami c FLP1) as opposed t o st at i c unchangi ng l ay-

out s

Govi l and Fu ( 1999) pr esent a sur vey of queuei ng network

model s f or t he anal ysi s of var i ous manuf actur i ng syst ems by

i dent i f yi ng t he mai n f act or s af f ect i ng t he model s as wel l

as var i at i ons of t he model s

Pi er r eval et al . ( 2003) pr esent a r evi ew of manuf act ur i ng

f aci l i t y l ayout wher e evol ut i onar y pr i nci pl es have been ap-

pl i ed t o opt i mi ze t he MFLP

Haupt and Haupt ( 2004) pr esent a detai l ed r evi ew and anal y-

si s of GAs and t he pr act i cal appl i cat i on of GAs wi t h exam-

pl es of execut abl e Mat l ab and For t r an code.

1 The cur r ent r esear ch wi l l f ocus on st at i c f aci l i t y l ayout s al t -

hough f ut ur e wor k wi l l ext end t he st at i c f aci l i t y l ayout model

t o a dynami c f aci l i t y l ayout model


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Asef - Vazi r i and Lapor t e (2005) pr esent a revi ew of l oop

based f aci l i t y pl anni ng met hodol ogi es f or MF wi t h t r i p

based MHS i . e. aut omat ed gui ded vehi cl es ( AGV)

Agrawal and Heragu ( 2006) present a r evi ew of aut omat ed ma-

t er i al handl i ng syst ems ( AMHS) used i n Semi conduct or Fabs

Si ngh and Sharma ( 2006) pr esent an exhaust i ve sur vey of

var i ous al gor i t hms as wel l as comput er i zed f aci l i t y l ayout

sof t ware devel oped si nce 1980 f or t he FLP

Dr i r a, Pi er r eval , and Haj r i - Gabouj ( 2007) pr esent a revi ew

of al gor i t hms f or t he FLP al ong wi t h a gener al i zed f r ame-

wor k f or t he anal ysi s of l i t er at ur e wi t h r egar ds t o FLP as

shown i n Fi gur e 2. 1 on page 14

Loi ol a et al . ( 2007) pr esent a sur vey of QAP and associ at ed

pr ocedur es by di scussi ng t he most i nf l uent i al QAP f or mul a-

t i ons and QAP sol ut i ons pr ocedur es

Nazzal and El - Nashar ( 2007) pr esent a sur vey of model s of

conveyor syst ems i n semi conduct or f abs and an over vi ew of

t he corr espondi ng si mul at i on based model s.

Shant hi kumar , Di ng, & Zhang ( 2007) pr esent a sur vey of t he

appl i cat i on of queuei ng t heor y l i t er at ur e t o semi conduct or

manuf act ur i ng syst ems


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2.2Manufacturing Facility Layout Problem

Thi s sect i on f i r st present s a r evi ew of t he gener al MFLP f or mu-

l at i ons wher e M f aci l i t i es / cel l s ar e assi gned t o N l ocat i ons

wi t h r egards t o a cert ai n obj ect i ve. The most common obj ect i ves

ai m t o mi ni mi ze t he mat er i al handl i ng cost ( MHC) , t he di st ance

t r avel ed, or t he t ot al t i me i n syst em ( Benj aaf ar , Her agu, & I r a-

ni , 2002) . The pr oposed r esear ch wi l l f or mul at e t he LLDP as a

QAP t o generat e an opt i mal l ayout f or a LLMF. Second, a revi ew

of t he LLDP i s pr esent ed i n 2. 2. 1 on page 22. Thi r d, a r evi ew

of MFLP f ormul at i ons wi t h t hat mi ni mi ze t he WI P i n t he MF i s

pr esent ed i n 2. 2. 2 on page 28.

The MFLP i s f or mul at ed as a QAP by Koopmans and Beckmann

( 1957) . Sahni and Gonzal ez ( 1976) show t hat t he QAP i s NP-

Compl et e. Gi ven t hat t her e ar e M cel l s and N l ocat i ons, i f M < N

dummy cel l s ( M+1,M+2,..,N) ar e i nt r oduced as st at ed i n Hi l l i er

and Connors ( 1966) . The f ol l owi ng notat i on i s used wher e xij i s

t he deci si on var i abl e:

ik - f l ow of l oads f r om cel l i t o cel l k

cji - cost of t r anspor t i ng l oad f r om l ocat i on j t o l ocat i on l

xij - 1 i f c e l l i i s at l ocat i on j; 0 ot her wi se

Mi n1 1 1 1

N N N N

ik jl ij kl

i j k l

c x x= = = =

(1)


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s . t .1

1N

ij

i

x=

=

, 1j j N ( 2)

1

1N

ij

j

x=

= , 1i i N (3)

{ }0,1ijx 1 ,i j N (4)

The f or mul at i on as present ed i n ( 1) - ( 4) mi ni mi zes t he t r anspor -

t at i on cost of a MF. Gi ven t hat dji i s t he di st ance bet ween l oca-

t i on j and l ocat i on l; ( 1) can be r est at ed as f ol l ows t o gener at e

a l ayout t hat mi ni mi zes t he t ot al di st ance t r avel ed by the l oads

i n a MF.

Mi n1 1 1 1

N N N N

ik jl ij kl

i j k l

d x x= = = =

(5)

s . t . ( 2) - ( 4)

As i ndi cat ed by Loi ol a et al . ( 2007) , t her e ar e var i ous f or mul a-

t i ons of t he FLP; al l of t hese f or mul at i ons can be t r aced back

t o t he QAP. Exampl es of such f or mul at i ons i ncl ude: quadr at i c set

cover i ng pr obl em ( QSP) f or mul at i on ( Bazar aa, 1975) , l i near i nt e-

ger pr ogr ammi ng f ormul at i on ( Lawl er , 1963) , mi xed i nt eger pr o-

grammi ng f ormul at i on ( Bazar aa & Sheral i , 1980; Kauf man &

Br oeckx, 1978) , gr aph t heor et i c f or mul at i on ( Foul ds & Robi nson,


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1976) , f or mul at i ons by per mut at i ons ( Hi l l i er & Connor s, 1966) ,

and t r ace f or mul at i ons ( Edwar ds, 1980) .

The proposed r esear ch wi l l f ocus on t he f or mul at i on by permu-

t at i ons as i t i s t he most commonl y used f ormul at i on and ext ends

i t sel f wel l t o f or mul at i ons wi t h ver y compl i cat ed obj ect i ve

f unct i ons. Accor di ng t o Hi l l i er and Connor s ( 1966) and Loi ol a et

al . ( 2007) i f SN i s t he set of al l per mut at i ons of N var i abl es,

SN, and C (i ) (j ) i s t he cost of t r anspor t i ng l oad f r om l ocat i on

(i ) t o l ocat i on (j ) . Then, gi ven t hat each per mut at i on ( ) rep-

r esent s a uni que l ayout of t he MF, i . e. a uni que assi gnment M

cel l s to N l ocat i ons, t he MFLP t hat mi ni mi zes t he t r anspor t at i on

cost s i n t he MF reduces t o:

NSMi n ( ) ( )

1 1

N N

ij i j

i j

c

= =

(6)

Loi ol a et al . ( 2007) st at e t hat t he above f or mul at i on i s equi va-

l ent t o ( 1) - ( 4) , as ( 2) and ( 3) def i ne a mat r i x X=[ xij] f or each

r el at ed t o SN as i n ( 6) , wher e f or al l 1 i,j N,

( )

( )

1, ;

0, .ij

if i jx

if i j

==

(7)

2.2.1

Looped Layout Design Problem (LLDP)

The LLDP i s a speci al case of t he MFLP appl i ed t o LLMF. LLMF s

ar e at t r act i ve due t o thei r l ow set up cost s as t he LLMF r equi r es


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mi ni mal mat er i al handl i ng r esour ces t o l i nk t he var i ous cel l s t o

each ot her ( Af ent aki s, 1989) . By desi gn, i n a LLMF al l t he cel l s

ar e easi l y accessi bl e ( Af ent aki s, 1989) . Ther e ar e t wo t ypes of

l ayout pat t er ns: t he cl osed l oop l ayout t hat has a pr edet er mi ned

pat t er n and t he open f i el d t ype l ayout t hat has no pr edet ermi ned

pat t er n. Chae and Pet er s ( 2006) i ndi cat e t hat t he l at t er i s mor e

di f f i cul t t o sol ve and may r esul t i n l ess desi r abl e sol ut i ons as

a r esul t of t he l ack of modul ar i t y and/ or st r uct ur e i n t he pr e-

scr i bed l ayout of t he LLMF.

As i n t he case of t he MFLP, t he LLDP ai ms t o determi ne the

most ef f ect i ve arr angement of M cel l s to N l ocat i ons ( ar ound a

l oop) wi t h regards t o a cer t ai n obj ect i ve. The most common ob-

j ect i ve f or t he LLDP i s t o mi ni mi ze t he mat er i al handl i ng cost

( Asef - Vazi r i & Lapor t e, 2005) . Most of t he cur r ent r esear ch of

t he LLDP i s gear ed t owards LLMF s wi t h AGV s as t he MHS ( Asef -

Vazi r i & Laport e, 2005; Nearchou, 2006) , Bozer and Hsi eh ( 2005)

pr esent a sol ut i on t o the LLDP f or a LLMF wi t h a cl osed l oop

conveyor as t he MHS. Kouvel i s and Ki m ( 1992) and Leung ( 1992)

show t he LLDP i s NP- Compl et e. As i n t he case of MFLP, met a-

heur i st i c sol ut i on appr oaches are most ef f ect i ve t o sol ve LLDP

wi t h gr eat er t han 20 cel l s ( Asef - Vazi r i & Lapor t e, 2005) .

Af ent aki s ( 1989) i s t he f i r st t o pr opose an al gor i t hm t o ex-

pl i ci t l y desi gn t he l ayout of LLMF. Af ent aki s ( 1989) pr oposes t o


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mi ni mi ze t he t r af f i c congest i on, whi ch can be def i ned as t he

number of t i mes a l oad t r aver ses the l oop bef or e i t depar t s f r om

t he syst em. Af ent aki s ( 1989) pr oposes a heur i st i c based on a

gr aph t heor et i c appr oach t o mi ni mi ze t he t r af f i c congest i on of

al l t he l oads ( al so ref er r ed t o as MI N- SUM) . The heur i st i c con-

st r uct s a l ayout f r om t he dual of a l i near pr ogr ammi ng ( LP) r e-

l axat i on of t he pr obl em. Af ent aki s ( 1989) was abl e t o sol ve a

LLDP wi t h up t o 12 cel l s.

Leung (1992) bui l ds on Af ent aki s ( 1989) by pr oposi ng a heur i s-

t i c based on a gr aph theor et i c appr oach t o mi ni mi ze t he maxi mum

t r af f i c congest i on of al l t he l oads ( al so r ef er r ed t o as MI N-

MAX) . Kaku and Rachamadugu ( 1992) model t he LLDP as a QAP and

f i nd opt i mal and near opt i mal sol ut i ons f or smal l er pr obl ems.

Mi l l en, Sol omon, and Af ent aki s ( 1992) anal yze t he i mpact of

t he number of l oadi ng and unl oadi ng st at i ons on t he mat er i al

handl i ng r equi r ement s f or a LLDP usi ng si mul at i on. They poi nt

out t hat havi ng a si ngl e l oadi ng and unl oadi ng st at i on f or t he

LLDP i ncr eases t he mat er i al handl i ng r equi r ement s by as much as

200% ver sus havi ng a l oadi ng and unl oadi ng st at i on at each cel l .

Kouvel i s and Ki m ( 1992) pr opose an al gor i t hm t o sol ve t he

LLDP. By usi ng t he f ormul at i on as descr i bed by ( 6) , t hey devel op

domi nance r el at i onshi ps t o easi l y i dent i f y l ocal opt i mal sol u-

t i ons t hereby reduci ng t he sol ut i on space. They devel op and ap-


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pl y a br anch- and- bound pr ocedur e and heur i st i c methods success-

f ul l y t o a LLDP wi t h 12 cel l s.

Ki r an and Karabat i ( 1993) pr esent a br anch- and- bound pr ocedur e

and heur i st i c met hods f or a LLDP. As i n Kouvel i s and Ki m ( 1992) ,

Ki r an and Karabat i ( 1993) t oo pr esent domi nance r ul es based on a

speci al di st ance met r i c t o i dent i f y l ocal sol ut i ons. They pr e-

sent a speci al case of t he LLDP / QAP that i s sol vabl e i n pol y-

nomi al t i me. When al l t he cel l s i n a LLMF i nt er act wi t h onl y one

cel l , t he LLDP can be sol ve i n O( n2

l ogn) t i me.

Das ( 1993) pr esent s a f our st ep heur i st i c pr ocedur e f or sol v-

i ng t he LLDP t hat combi nes var i abl e par t i t i oni ng and i nt eger

pr ogr ammi ng t o mi ni mi ze t he t otal pr oj ect ed t r avel t i me bet ween

cel l s. Each cel l i s r epr esent ed by i t s speci al coor di nat e, i t s

or i ent at i on wi t h r espect t o t he l ayout ( hor i zont al or ver t i cal ) ,

and t he l ocat i on of i t s l oadi ng or unl oadi ng st at i on. The heu-

r i st i c becomes comput at i onal l y i nef f i ci ent f or pr obl ems wi t h

gr eat er t han 12 cel l s.

Baner j ee and Zhou ( 1995) pr esent a f ormul at i on of t he LLDP as

a speci al i zat i on of t he f l ow network based MFLP pr oposed by Mon-

t r eui l ( 1990) . The met hod as proposed by Mont r eui l ( 1990) i s

mor e compl i cat ed as t he physi cal consi der at i ons of t he cel l s are

t aken i nt o account ( Af ent aki s ( 1989) and rel at ed met hods i gnor e

t he di mensi onal char act er i st i cs of a cel l and i t s r el at i onshi p


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t o the l ocat i ons i t i s assi gned t o. ) The cel l s are assumed t o be

r ect angul ar and t he di mensi ons are the deci si on var i abl es.

Cheng, Gent , and Tosawa ( 1996) and Cheng and Gen ( 1998) ext end

Af ent aki s ( 1989) by appl yi ng a genet i c al gor i t hm wi t h a modi f i ed

mut at i on pr ocess t o sol ve t he LLDP by i nvest i gat i ng i t s per f or -

mance on bot h MI N- SUM and MI N- MAX congest i on measur es. A near est

nei ghbor l ocal sear ch i s used t o det er mi ne t he best genes t o mu-

t at e.

Tansel and Bi l en ( 1998) pr esent a sol ut i on t o t he LLDP by pro-

posi ng a heur i st i c t hat appl i es posi t i onal moves and l ocal i m-

provement al gor i t hms based on k- way i nterchanges or swaps be-

t ween cel l s i n a par t i cul ar l ayout so as t o det er mi ne t he best

l ayout f or t he LLMF.

Bennel l , Pot t s, and Whi t ehead ( 2002) pr esent a l ocal sear ch

and a r andomi zed i nsert i on al gor i t hm f or t he MI N- MAX LLDP. The

proposed met hod i s an ext ensi on of Leung ( 1992) t hat over comes

t he i mpl ement at i on di f f i cul t i es, comput at i onal r equi r ement s, and

gener at es bet t er sol ut i ons wi t h r espect t o Leung ( 1992) .

Bozer and Hsi eh ( 2005) anal yze t he per f ormance of a LCMHS wi t h

f i xed wi ndows. A st abi l i t y f act or ( SF) f or t he LCMHS i s der i ved

by det er mi ni ng t he maxi mum ut i l i zat i on of t he l oadi ng st at i ons

al ong t he LCMHS. The ut i l i zat i on at each l oadi ng st at i on i s

char act er i zed by t he speed of t he LCMHS, t he ar r i val r at e t o t he


43/292


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ncan and Al t I nel ( 2008) pr esent t wo exact sol ut i on appr oaches

f or LLDP: a dynami c progr ammi ng al gor i t hm and a br anch and bound

scheme. They al so pr esent new upper and l ower bound procedur es

f or t he QAP usi ng t he branch and bound scheme.

Ozcel i k and I sl i er ( 2011) pr esent a met hodol ogy f or opt i mi zi ng

t he number of l oadi ng and unl oadi ng st at i ons whi l e det er mi ni ng

t he l ayout t he LLDP. However , t he pr oposed methodol ogy uses t he

t r adi t i onal deci si on cr i t er i on f or t he obj ect i ve f unct i on, i . e.

ai ms t o gener at e a l ayout t hat mi ni mi zes the t ot al di st ance

t r avel l ed.

2.2.2

Formulations with Minimum WIP design objective

Ther e i s ext ensi ve l i t er at ure f or t he MFLP wi t h t he desi gn ob-

j ect i ve of mi ni mi zi ng t he mat er i al handl i ng cost , t he t r avel

t i me i n syst em, or t he t ot al di st ance t r avel ed by t he l oads i n

t he syst em. Ther e ar e numer ous l i t er at ur e revi ew and sur vey pa-

per s as pr esent ed i n 2. 1 on page 16 on t hi s subj ect mat t er .

However , t hese t r adi t i onal cr i t er i a f or desi gn can be poor pr e-

di ct or s of t he oper at i onal per f or mance of a MF. The paper s pre-

sent ed i n t hi s sect i on ar e the f ew appr oaches t hat pr opose t o

sol ve t he MFLP usi ng t he operat i onal per f ormance of a MF as t he

desi gn cr i t er i a, t hi s appr oach wi l l be ut i l i zed by t he pr oposed

r esear ch.


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Sol ber g and Nof ( 1980) present a mat hemat i cal model based on

queuei ng net wor k t heor y f or t he anal ysi s of var i ous Layout con-

f i gur at i ons f or a MF. The met hod pr esent ed i s not a MFLP but r a-

t her an at t empt t o expl i ci t l y devel op an al t er nat i ve desi gn cr i -

t er i on f or t he MFLP.

Kouvel i s and Ki r an ( 1991a, 1991b) and Kouvel i s et al . ( 1992)

pr esent t he MFLP f ormul ated as a QAP wi t h t he obj ect i ve of mi ni -

mi zi ng t he mat er i al handl i ng cost and t he WI P hol di ng cost f or a

MF wi t h AGV s as t he MHS over si ngl e and mul t i pl e per i ods.

Fu and Kaku ( 1997a, 1997b) pr esent a MFLP wi t h t he obj ect i ve

on mi ni mi zi ng t he aver age WI P f or t he MF. The obj ect i ve f unct i on

i s si mi l ar t o t hat used i n Kouvel i s and Ki r an ( 1991a, 1991b) ,

i . e. , mi ni mi zi ng t he mat er i al handl i ng cost and t he WI P hol di ng

cost f or a MF wi t h AGV s as t he MHS over a si ngl e per i od. They

made numerous si mpl i f yi ng assumpt i ons t o model t he queuei ng net -

wor k as a J ackson net wor k so as t o obt ai n a cl osed f or m expr es-

si on of t he aver age WI P. They show t hat t her e i s no di f f er ence

bet ween t he t r adi t i onal f aci l i t y desi gn obj ect i ve and t he t est ed

obj ect i ve t hat t ake t he oper at i onal per f or mance as t he desi gn

cr i t er i a.

Benj aaf ar ( 2002) ext ends Fu and Kaku ( 1997a, 1997b) by r el ax-

i ng sever al assumpt i ons and usi ng t he queuei ng net work anal yzer

as pr esented by Whi t t ( 1983a) . Benj aaf ar ( 2002) shows t hat when


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some of t he assumpt i ons made by Fu and Kaku ( 1997a, 1997b) ar e

r el axed, t he cl ai m of equi val ent out comes bet ween t he t wo f ormu-

l at i ons i s not al ways val i d. Benj aaf ar ( 2002) shows t hat under

gener al condi t i ons t he l ayout s gener at ed by t he t wo f or mul at i ons

can be ver y di f f er ent . The key di f f er ence bet ween Benj aaf ar

( 2002) and Fu and Kaku ( 1997a, 1997b) i s t hat as a r esul t of us-

i ng t he QNA, Benj aaf ar ( 2002) i s abl e t o capt ur e t he i nt er act i on

bet ween t he var i ous syst ems i n t he MF t hat were absent i n Fu and

Kaku ( 1997a, 1997b) . Raman et al . ( 2008) ext end Benj aaf ar ( 2002)

f or MF s wi t h unequal ar ea cel l s.

J ohnson, Car l o, J i menez, Nazzal , and Lasr ado ( 2009) present a

gr eedy heur i st i c f or det er mi ni ng t he best set of shor t cut s f or a

LLMF wi t h a LCMHS.

Hong et al . ( 2011) ext end J ohnson et al . ( 2009) and pr esent a

met hodol ogy f or det er mi ni ng t he l ocat i on of shor t cut s f or a LLMF

wi t h a LCMHS usi ng WI P as t he deci si on cr i t er i on.

2.3 Solution Methods

The var i ous al gor i t hms used t o r evol ve MFLP f or mul at ed as a QAP

can be cat egor i zed i nt o: exact al gor i t hms, heur i st i c al gor i t hms,

and met a- heur i st i c al gor i t hms. As a r esul t of t he choi ce of de-

si gn obj ect i ve, i . e. gener at e a l ayout t hat mi ni mi zes t he aver -

age WI P i n t he MF/ LLMF, t he exact and heur i st i c sol ut i on met hods


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cannot be used t o sol ve t he pr oposed LLDP as f ur t her di scussed

i n 3. 3. 1 on page 70.

Two r ecent r evi ew paper s ( Dr i r a et al . , 2007; Loi ol a et al . ,

2007) i ndi cate t hat met a- heur i st i c appr oaches ar e t he most popu-

l ar sol ut i on met hods. These met hods are abl e t o cope wi t h l arge

pr obl em si zes and ar e abl e t o ef f ect i vel y sol ve an opt i mal or

near opt i mal sol ut i on. The pr oposed r esear ch wi l l ut i l i ze t he

met a- heur i st i c appr oach t o sol ve t he LLDP f ormul ated as a QAP,

mor e speci f i cal l y, genet i c al gor i t hms ( GA) t o sol ve t he LLDP.

However , f or sake of compl et eness, a br i ef over vi ew of ot her

methods and al gor i t hms used t o sol ve t he MFLP wi l l be pr esent ed

i n t he subsequent sect i ons.

Exact sol ut i on al gor i t hms are l i mi t ed as a resul t of comput a-

t i onal i nef f i ci enci es and comput er memor y i ssues. As di scussed

ear l i er , Foul ds ( 1983) show t hat when usi ng exact sol ut i on met h-

ods t he comput at i on t i me requi r ed t o reach an opt i mal sol ut i on

i ncr eases exponent i al l y as t he number of cel l s t o be ar r anged

i ncr eases. Thi s out come i s r ei t er ated by J ames, Rego, and Gl over

( 2008) and Loi ol a, de Abr eu, Boavent ur a- Net t o, Hahn, and Quer i do

( 2007) who pr esent detai l ed di scussi ons on t he comput at i on com-

pl exi t y and t he r equi r ed comput at i on t i me t o r each an opt i mal

sol ut i on usi ng exact sol ut i on met hods. Thi s shor t comi ng of t he

exact al gor i t hms has l ed t o t he devel opment of many heur i st i c


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appr oaches t o sol ve t he MFLP. Wi t h t he devel opment of sophi st i -

cat ed gener al l y appl i cabl e met a- heur i st i c al gor i t hms, t he ol der

pr obl em speci f i c heur i st i c al gor i t hms have l ost f avor wi t h pr ac-

t i t i oners .

2.3.1

Exact Algorithms

Ther e ar e t wo t ypes of exact sol ut i on al gor i t hms used t o deter -

mi ne t he gl obal opt i mum f or t he MFLP f ormul at ed as a QAP: br anch

and bound al gor i t hms and cut t i ng pl ane al gor i t hms ( Kusi ak &Her agu, 1987) . I n gener al , exact sol ut i on met hods i mpl ement con-

t r ol l ed enumer at i on as a means t o obt ai n t he opt i mal sol ut i on

whi l e not enumer at i ng t hr ough al l t he possi bl e sol ut i ons ( i n-

cl udi ng i nf easi bl e sol ut i ons) i . e. t ot al enumer at i on. The exami -

nat i on of t he l ower bounds f or t he QAP i s cr uci al t o t he devel -

opment of ef f i ci ent and expedi t i ous cont r ol l ed enumer at i on based

exact sol ut i on met hods. A good l ower bound pr ocedur e wi l l yi el d

val ues cl ose t o t he opt i mal val ue f or t he QAP ( Loi ol a et al . ,

2007) .

The branch and bound al gor i t hm i s t he most commonl y i mpl ement -

ed and most r esear ched exact sol ut i on al gor i t hm. Thi s al gor i t hm

i s f i r st pr esent ed i ndependent l y by bot h Gi l mor e ( 1962) and

Lawl er ( 1963) , t he al gor i t hms di f f er i n t he comput at i on of t he

l ower bound used t o el i mi nat e undesi r ed sol ut i ons. The l ower

bound procedures as present ed by Gi l mor e ( 1962) and Lawl er


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( 1963) ar e t he most popul ar pr ocedur es due t o t hei r si mpl i ci t y

and ef f i ci ency i n t er ms of comput at i onal r equi r ement s. These

l ower bound pr ocedur es are l i mi t ed i n t hat f or l ar ger pr obl ems

t hey pr ovi de weak l ower bounds.

Bazaraa and Sher al i ( 1980) pr esent t he cut t i ng pl ane al go-

r i t hm. Thi s al gor i t hm i s comput at i onal l y i nef f i ci ent and r e-

qui r es a l ar ge amount of comput er memor y and works wel l onl y f or

smal l pr obl em si zes.

2.3.2

Heuristics Algorithms

Pr obl em speci f i c heur i st i c al gor i t hms have l ost f avor t o mor e

gener al l y appl i cabl e met a- heur i st i c al gor i t hms. The f ol l owi ng

di scussi on pr ovi des a br i ef over vi ew of heur i st i c al gor i t hms,

mor e det ai l ed descr i pt i on of t he heur i st i c al gor i t hms i s pr ovi d-

ed by Kusi ak and Heragu (1987) . There ar e t wo br oad cat egor i es

of heur i st i c al gor i t hms i n t he l i t er at ur e: Const r uct i on al go-

r i t hms, and i mpr ovement al gor i t hms.

I n const r uct i on al gor i t hms each cel l i s assi gned t o a l ocat i on

i ndi vi dual l y unt i l t he l ayout i s obt ai ned, i . e. t he sol ut i on i s

const r uct ed ab i ni t i o. I mpr ovement al gor i t hms begi n wi t h a ran-

doml y gener at ed i ni t i al sol ut i on and t r y t o i mpr ove i t by sys-

t emat i c assi gni ng cel l s t o l ocat i ons. The assi gnment yi el di ng

t he best sol ut i on i s r et ai ned and t he pr ocess i s r epeat ed unt i l


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no f ur t her i mpr ovement i s possi bl e or a stoppi ng cr i t er i on i s

met .

2.3.3

Meta-Heuristic Algorithms

Met a- heur i st i c al gor i t hms have gai ned much t r act i on si nce 1980

and have been appl i ed t o a wi de var i et y of opt i mi zat i on pr ob-

l ems. I n gener al , met a- heur i st i c al gor i t hms bui l d on t he t heor y

and appl i cat i on of nat ur al pr ocess t o t he r esol ut i on of t he QAP

by i t er at i ng unt i l a st oppi ng cri t er i on i s sat i sf i ed. A ver y i m-por t ant st ep f or al l t hese al gor i t hms i s par amet er sel ect i on at

t he i ni t i al i zat i on of t he al gor i t hm. By ef f ecti vel y var yi ng t he

parameters, conver gence t o poor l ocal mi ni ma can be avoi ded.

Thi s f eat ure makes met a- heur i st i c al gor i t hms ver y at t r act i ve as

t hey usual l y gener at e opt i mal or near opt i mal sol ut i ons f or ver y

compl i cat ed pr obl ems t hat cannot be sol ved by exact and heur i s-

t i c al gor i t hms.

Th

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