7/27/2019 Kouvelis Panagiotis - Design and Planning Problems in Flexible Manufacturing Systems, A Critical Review

1/25

J o u r n a l o f I n t e l l i g e n t M a n u f a c t u r i n g

( 1 9 9 2 ) 3 , 7 5 - 9 9

D es ign and p lan ning problems in f lex ib le

m an ufa ctur ing systems a crit ica l review

P A N A G I O T I S K O U V E L I S

Managem ent Department GraduateSchool of Business The University of Texas at Austin

USA

Rec eived Novem ber 1990 and accepted April 1991

This review pape r describes the state-of-the-art research on flexible manufacturing systems

(FMS) design and planning issues. The emphasis is on presenting research results coming ou t

of the curre nt FM S literature that help the FMS manager in setting up a hig hly efficient

man ufacturing system. In addition to that, it discusses relevant research contributions afte r

1986, that we re not pa rt of any of the previous survey papers on operations research models for

FMSs. Also, applications of combinatorial optimization approaches to FMS planning

problems are adequately exposed in the paper.

Keywords: Flexible manufacturing, design, planning, modeling

1 I n t r o d u c t i o n a n d p r o b l e m c l a s si f ic a t io n

1 1

ntroduction

Flex ib le manufac tur ing i s an e f f i c i en t a l t e rna t ive to

c o n v e n t i o n a l b a t c h m a n u f a c t u r i n g . H i g h w o r k - i n - p r o c e s s

( W I P ) l e v e l s a n d l o w m a c h i n e u t i l i z a t i o n w e r e a l w a y s

ind ica t ive of ine f f i c i ency in ba t ch m anufac tur in g . Ev en in

t h e U n i t e d S t a t e s , t h e w o r l d ' s l ar g e s t c e n t e r o f m a ss

p r o d u c t i o n , 7 5 o f t h e p a r t s p r o d u c e d b y m e t a l p r o c e s s i n g

a re in lo ts o f l e ss t han 50 p i eces (Merc han t , 1983) . The n eed

f o r a h i g h ly p r o d u c t i v e a l t e r n a t i v e t o b a t c h m a n u f a c t u r i n g

h a s a l w a y s b e e n t h e m a j o r d r i vi n g f o r c e b e h i n d t h e f l e x ib l e

m a n u f a c t u ri n g s y s t e m ( F M S ) d e v e l o p m e n t . H a r d a u t o m a -

t ion , t ha t co u ld e f f i c ien t ly tu rn tho usan ds an d mi l l ions of

iden t i ca l pa r t s , was no t t he answer to e f f i c i en t ba t ch

m a n u f a c t u r i n g . W h a t w a s n e e d e d w a s f le x i b le a u t o m a t i o n

t h a t c o u l d h a n d l e a l a r g e a n d c o n s t a n t l y c h a n g in g v a r i e t y o f

p r o d u c e d i t e m s . T h e t e c h n o l o g i c a l a d v a n c e m e n t s o f t h e

1970s such a s on- l ine ava i l ab i l i t y o f compute rs and

n u m e r i c a l c o n t r o l t e c h n i q u e s m a d e f l e x i b l e a u t o m a t i o n

p o s s i b l e , a n d t h e d e v e l o p m e n t o f t h e f ir s t F M S s t o o k p l a c e .

F M S s h a v e b e c o m e w i d e l y u se d i n a d i v e r se s e t o f

i n d u s t r ie s . A p p l i c a t i o n o f F M S s c a n b e f o u n d i n t h e

a e r o sp a c e , a g r i c u l t u r a l , a p p l i a n c e , a u t o m o b i l e , d e f e n se ,

e l e c t r o n i c , m a c h i n e t o o l , m o t o r a n d e n g i n e c o m p o n e n t s ,

a n d o t h e r i n d u s t r i e s t h r o u g h o u t t h e U n i t e d S t a t e s , J a p a n

0956-5515 ~ 1992 Chapm an & Hall

a n d E u r o p e . T e c h n i c a l d e sc r ip t i o n s o f F M S s c a n b e f o u n d

i n D u p o n t - G a t e l m a n d ( 19 8 2) a n d H a t v a n y ( 19 8 3) a m o n g

othe rs .

A w i d e l y a c c e p t e d d e f i n it i o n o f a F M S i s t h e f o l l o w i n g

( B r o w n e

e t aL

1984):

' A F l e x i b l e M a n u f a c t u r i n g S y s t e m i s a n i n t e g r a t e d ,

c o m p u t e r - c o n t r o ll e d c o m p l e x o f a u t o m a t e d m a t e r ia l

h a n d l i n g d e v i c e s a n d n u m e r i c a l l y c o n t r o ll e d ( N C )

m a c h i n e t o o l s t h a t c a n s i m u l t a n e o u s l y p r o c e s s m e d i u m -

s i z e d v o l u m e s o f a v a r i e t y o f p a r t t y p e s . T h i s n e w

p r o d u c t i o n t e c h n o l o g y h a s b e e n d e s i g n e d t o a t t a i n t h e

e f f ic i e n c y o f w e l l - b a l a n c e d m a c h i n e p a c e d t r a n s f e r l i n e s ,

whi l e u t i l iz ing the f l ex ib i l it y t ha t j o b shop s have to

s i m u l t a n e o u s l y m a c h i n e m u l t i p l e p a r t t y p e s . '

S o u n d a n a l y s is u se d t o su p p o r t t h e F M S d e s i g n p r o c e s s is

t h e k e y t o a c h i ev i n g a g o o d a n d c o s t - e f f e c ti v e d e s i g n.

T y p i c a l l y , s i m u l a t i o n m o d e l s a r e u se d f o r t h e a n a l y s i s

p e r f o r m e d d u r i n g t h e F M S d e s i g n . S i m u l a t io n m o d e l l in g i s

a power fu l and f l ex ib l e ana lys i s t echnique , bu t i t i s no t

adequa te in address ing des ign i ssues . S ince s imula t ion

m o d e l d e v e l o p m e n t , d e b u g g i n g a n d a n a l y s i s a r e t i m e -

c o n su m i n g p r o c e s se s , a n d c o n se q u e n t l y e x t r e m e l y e x p e n -

s ive ac tiv i t ie s , on ly a limi t ed nu m be r of a l te rna t ives a re

e x p l o r e d f o r t h e d e s i g n i s su e s t h a t a r e a d d r e s se d . T h i s

p o i n t w a s e m p h a s i z e d b y S o l b e r g ( 1 9 7 7) :

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76 K o u v e l i s

' Lo n g b e fo re t h e o p e ra t i n g p o l ic i e s o f a m a n u fa c t u r i n g

s y s t e m a r e c o n s i d e re d m a n y d e s i g n d e c i s i o n s a r e m a d e

w h i c h a f f e c t t h e u l t i m a t e a b i l it y o f p ro d u c t i o n m a n a g e r s

t o c o n t r o l t h e p e r f o r m a n c e o f t h e s y s t e m . A l t h o u g h

s o m e o f t h e m o r e a d v a n c e d c o m p a n i e s e m p l o y s i m u la -

t i o n m e t h o d s t o f i n e t u n e t h e i r s y s t e m d e s i g n , f e w

m a k e u s e o f a n y fo rm a l m e t h o d o l o g i e s a t a l l i n t h e

cr i t i ca l ear ly s tages . Fu nda m en ta l des ign i s sues , such as

h o w l a rg e t h e s y s t e m w i l l b e o r t h e s e l e c t i o n o f

p ro c e s s in g a n d m a t e r i a l h a n d l i n g e q u i p m e n t , a r e u s u a l ly

d e a l t b y a rb i t r a ry c h o i c e o r b a c k o f t h e e n v e l o p e

ca lcu la t ions . I t i s i ron ic tha t the mos t impor tan t

d e c i s io n s , t h o s e h a v i n g t h e g r e a t e s t l o n g - t e rm i m p a c t o n

s y s t e m p ro d u c t i v i t y a r e h a n d l e d i n t h e l e a s t c a r e fu l

m a n n e r . '

A s o n e w o u l d e x p e c t , i n m a n y c a s e s F M S m a n a g e r s

s t ru g g l e w i t h s c h e d u l i n g p ro b l e m s u n d e r u n re a l i s t i c a l l y

t igh t capac i ty cons t ra in t s d ue to inef f i c ien t des igns and

l o n g - t e rm p l a n s .

A f i rs t n e e d e d t o o l f o r a F M S d e s i g n e r is a n a c c u ra t e

p e r f o r m a n c e m o d e l o f t h e m a n u f a c t u r i n g s y s te m . T h o u g h

q u e u e i n g n e t w o rk m o d e l s w e re i n t ro d u c e d in t h e c l a ss i ca l

papers by Jackson (1957 and 1963) a long t ime ago , the i r

e x t e n s i v e u s e a s a d e q u a t e p e r fo rm a n c e m o d e l s f o r a u t o -

m a t e d m a n u fa c t u r i n g s y s t e m s (i n p a r ti c u l a r F M S s )

a p p e a r e d m u c h l a t e r ( S o l be r g , 1 9 7 7 ; B u z a c o t t a n d

S h a n t h i k u m a r , 1 9 8 0 ; S t e c k e a n d S o l b er g , 1 9 8 5 ; Y a o

a n d B u z a c o t t , 1 9 8 6 a n d 1 98 7 ). M o s t o f t h e p r e v i o u s s u rv e y

p a p e r s o n o p e ra t i o n s r e s e a r c h a p p ro a c h e s t o F M S s

(B u z a c o t t a n d Y a o , 1 9 86 ; K a l k u n t e e t a l . 1986 and K us iak ,

1 98 5 a n d 1 9 8 6) e m p h a s i z e t h e m o d e l l i n g a s pe c t s t o F M S

o p e ra t i o n . A l s o , t h e y d e v o t e a s i g n i fi c a n t e f fo r t in p o i n t i n g

o u t a n d c l a s s ify i ng n e w a n d c h a l l e n g in g p ro b l e m s i n F M S

p ro d u c t i o n p l a n n i n g a n d c o n t ro l . Th i s r e v i e w p a p e r

d e s c r i b e s t h e s t a t e -o f - t h e - a r t r e s e a r c h o n F M S d e s i g n a n d

p lann in g i s sues . Th oug h in cer ta in cases it is necessary fo r

c l a r it y o f e x p o s it i o n o f t h e r e s e a r c h r e s u l t s to r e m i n d t h e

r e a d e r o f r e l e v a n t m o d e l l i n g i s s u e s , t h e e m p h a s i s o f o u r

s u rv e y p a p e r i s in e x p o s i n g i m p o r t a n t a p p ro a c h e s a n d

re s e a r c h r e s u l t s c o m i n g o u t o f t h e c u r r e n t F M S l i t e r a t u r e

t h a t h e l p t h e F M S d e s i g n e r a n d m a n a g e r i n s e t t i n g u p a

h i g h l y e ff i c i e n t m a n u fa c t u r i n g s y s t e m . In a d d i t i o n t o t h a t ,

i t d i s cu s s e s r e l e v a n t r e s e a r c h c o n t r i b u t i o n s a f t e r 1 9 8 6 t h a t

w e re n o t p a r t o f a n y o f t h e p r e v i o u s r e v i e w s . Th e p e r i o d

1 98 6 -9 1 i s m a rk e d b y t h e w i d e a c c e p t a n c e o f a p p ro x i m a t e

q u e u e i n g n e t w o r k m o d e l s a s a d e q u a t e p e r f o r m a n c e m o d -

e ls f o r a u t o m a t e d m a n u f a c t u r i n g s ys te m s ( r e s e a r c h w o r k

i n i t ia t e d b y W h i t t ( 19 83 a a n d b ) , f o l l o w e d b y B i t r a n a n d

T i ru p a t i ( 1 9 88 ) , B o x m a e t a l . (1990 and 1991) and o the rs ) .

A s e x p e c t e d , t h a t m o t i v a t e d t h e d e v e l o p m e n t o f n e w

a p p ro a c h e s t o d e s i g n a n d p l a n n i n g p ro b l e m s i n m a n u fa c -

t u r i n g (S c h w e i t z e r a n d S e i d m a n n , 1 98 8 a a n d b ; B i t r a n a n d

T i ru p a t i , 1 9 89 a; D a l l e ry a n d S t e c k e , 1 9 9 0 a n d B o x m a e t

a l . 1 9 9 0 a n d 1 9 9 1 ) t h a t a r e p r e s e n t e d , a n d a p p ro p r i a t e l y

i n t e rp r e t e d i n a F M S c o n t e x t f o r t h e f i r s t t i m e , t o g e t h e r

w i t h o t h e r r e c e n t o p t i m i z a t i o n a p p ro a c h e s i n q u e u e i n g

n e t w o r k m o d e l li n g f r a m e w o r k s ( S h a n t h i k u m a r a n d Y a o ,

1987 and 1988 and K ouvel i s and Ti rupa t i , 1991) . Also , the

a p p l i c a t i o n o f c o m b i n a t o r i a l a p p ro a c h e s (m o s t l y g r a p h

t h e o re t i c a n d i n t e g e r p ro g ra m m i n g ) t o F M S p l a n n i n g

p ro b l e m s h a s n o t b e e n d e a l t w i t h in d e t a il i n t h e p r e v i o u s

s u rv e y s (w i t h t h e e x c e p t i o n o f a n e x p o s i t io n o f r e s u lt s i n

l o a d i n g a n d g ro u p i n g p ro b l e m s (K a l k u n t e e t a l . 1986;

Stec ke , 1986 and S teck e and Sur i , 1989) , and i s d i scussed

e x t e n s i v e l y i n t hi s r e v i e w p a p e r . A s e p a ra t e s e c t i o n o f t h e

p a p e r i s d e v o t e d t o d i s c u s s i n g r e s e a r c h d i r e c t i o n s o f

p o t e n t i a l i n t e r e s t t o F M S r e s e a r c h e r s . A l t h o u g h t h e p a p e r

d i s cu s s e s a l a rg e s e t o f r e s e a r c h p a p e r s , i t is n o t i n t e n d e d t o

b e a n e x h a u s t i v e r e v i e w o f p a p e r s o n t h e s u b j e c t .

1.2. P r o b l e m c l a s s i f i c a t i o n

FMS i s a l a rge-sca le sys tem and , as such , i t canno t be

a d d re s s e d i n i t s e n t i r e t y w i t h o u t d e v i s i n g a p p ro p r i a t e

d e c i s i o n h i e r a r c h i e s . D i f f e r e n t h i e r a r c h i c a l s t r u c t u r e s

p ro p o s e d i n t h e F M S l i t e r a t u r e a r e b r i e f ly p r e s e n t e d b e l o w .

S u r i a n d W h i t n e y (1 9 8 4 ) p ro p o s e a d e c i s i o n h i e r a r c h y

cons i s t ing o f th ree dec i s ion l eve l s :

F i rs t dec i s ion l eve l : s t ra teg ic dec i s ions ( i . e . par t

f a m i l ie s s e l e c t i o n , s y s t e m

c a p a c i t y ) ;

S e c o n d d e c i s i o n l e v el : b a t c h i n g a n d r e s o u rc e

a l loca t ion dec i s ions ;

Th i rd dec i s ion l eve l : schedu l ing , d i spa tch ing ,

t o o l m a n a g e m e n t , a n d

s y s t e m m o n i t o r i n g

dec i s ions .

S tecke (1984) c las s i f i es FMS prob lems in to fou r

ca tego r ies : (1 ) des ign ; (2 ) p la f in ing ; (3 ) schedu l ing and (4 )

c o n t ro l . I n t h e s a m e p a p e r t h e t e rm ' s y s t e m s e t -u p

p ro b l e m ' i s i n t ro d u c e d fo r a s e t o f F M S s h o r t - t e rm

p l a n n i n g p ro b l e m s t h a t n e e d t o b e s i m u l t a n e o u s l y a d d re s -

s e d (p a r t t y p e s e l e c t i o n , m a c h i n e g ro u p i n g , p ro d u c t i o n

ra t io s , resource a l loca t ion , load ing) . A s imi la r dec i s ion

h i e r a r c h y t o t h e o n e p ro p o s e d b y S t e c k e i s a ls o s u g g e s t e d

by Ki ran and Tanse l (1985b) .

A n i n t e r e s t i n g s t ru c t u r e o f h i e r a r c h i c a l p ro d u c t i o n

p l a n n i n g fo r F M S s f ro m a c o n t ro l t h e o r i s t ' s p e r s p e c ti v e c a n

b e fo u n d i n G e r s h w i n e t a l . (1984 and 1986). Their

h i e r a r c h y p a r t i ti o n s t h e p ro d u c t i o n p l a n n i n g p ro b l e m i n t o

s u b -p ro b l e m s w i t h s u c c e s si v e ly s h o r t e r t i m e s c a l e s , w h e r e

t h e s o l u t i o n o f e a c h s u b -p ro b l e m i m p o s e s c o n s t r a i n t s o n

l o w e r - l e v e l s u b -p ro b l e m s . Th e i r p ro p o s e d h i e r a r c h y i s:

Lo n g t e rm : i n v e s t m e n t a n d i n it ia l d e s i gn

dec i s ions ;

M e d i u m t e rm : d e s i g n a n d p l a n n i n g d e c i s io n s ;

S h o r t t e rm : r e a l t i m e c o n t ro l .

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D e s i g n a n d p l a n n i n g p r o b l e m s i n f l e x i b le m a n u f a c t u r i n g s y s t e m s : a c r it ic a l r e v i e w 7 7

F o r p u rp o s e s o f e x p o s it i o n o f o u r r e s u l ts w e a d o p t e d a

p ro b le m c lass i fi ca t ion sch em e tha t has th e sam e c lassi fi ca-

t i o n c r i t e r i o n a s t h a t o f G e r s h w i n et al. (1986) ( i .e . t ime

s c a l e ) . W e t r e a t i n i ti a l d e s ig n i s su e s a s p a r t o f o u r m o re

g e n e ra l c a t e g o ry o f d e s ig n p ro b l e m s . Th e h i g h e r l e v el o f

t h e u s e d h i e r a r c h y i n t h e p a p e r a d d re s s e s t h e d e s i g n

p ro b l e m s ( s t r a t e g ic d e c i s i o n s fo r S u r i a n d W h i t n e y (19 84 ),

f i rs t le v e l o f S t e c k e s ( 1 9 84 ) h i e r a r c h y ) , a n d t h e n e x t l e v e l

d e a l s w i t h p l a n n i n g p ro b l e m s ( s e c o n d l e v e l d e c i s io n s fo r a l l

p r e v i o u s l y d i s c u s s e d h i e r a r c h i e s ) . W e a r e d e a l i n g m o s t l y

w i t h s h o r t - t e rm p l a n n i n g p ro b l e m s . Th e t h i rd d e c i s i o n

l e v e l f o r m o s t h i e r a r c h i e s d e a l s w i t h r e a l t i m e c o n t ro l a n d

s c h e d u l i n g p ro b l e m s o f F M S s , a n d w e a r e n o t r e v i e w i n g

re s e a r c h w o rk fo r t h a t d e c i s i o n le v e l . F o r a r e v i e w o f r e a l

t i m e c o n t r o l a n d s c h e d u l i n g p r o b l e m s o f F M S s r e f e r t o

K a l k u n t e et al. (1 9 8 6 ) a n d R a c h a m a d u g u a n d S t e c k e

(1987).

O u r p ro p o s e d p ro b l e m c l a ss i fi c a ti o n i s o u t l i n e d b e l o w :

q u e s t i o n s: ( 1 ) H o w m a n y i d e n t i c a l s e rv e r s (m a c h i n e s ) a r e

a c t u a l l y r e q u i r e d a t e a c h w o rk s t a t i o n ? (2 ) W h a t s h o u l d b e

t h e l e v e l o f t h e w o rk i n p ro c e s s in v e n t o ry ?

A s a f i r s t s t e p t o t a c k l e t h e p ro b l e m , a c e n t r a l s e rv e r

c l o s e d q u e u e i n g n e t w o rk i s u s u a l l y u s e d a s a p e r fo rm a n c e

m o d e l o f a F M S t o e v a l u a t e a n d p r e d i c t t h e s t o c h a s t i c

b e h a v i o r o f w o rk f i o w i n t h e s y s te m . T h e m o s t w i d e l y u s e d

p e r f o r m a n c e m o d e l is th e C A N - Q m o d e l d e v e lo p e d by

S o l b e rg (1 97 7) . Th e s e c o n d s t e p i n v o lv e s t h e d e v e l o p m e n t

o f a n o p t i m i z a t i o n p ro c e d u re , e i t h e r i m p l i c i t e n u m e ra t i o n

o r o f a h e u r i s t i c n a t u r e , t h a t e x p l o i t s s o m e o f t h e

m o n o t o n i c i t y p r o p e r t i e s o f t h e p e r f o r m a n c e m e a s u r e s o f a

c l o s e d q u e u e i n g n e t w o r k ( C Q N ) , t o a d d r e s s t h e a b o v e

p ro b l e m s .

V i n o d a n d S o l b e rg (1 98 5) d e v e l o p e d a n o p t i m i z a t i o n

a l g o r it h m u s in g C A N - Q t o d e t e r m i n e t h e o p ti m a l s y s te m

c o n f i g u ra t i o n . Th e b a s i c f o rm u l a t i o n o f t h e p ro b l e m i s a s

fo l lows

F M S d e s ig n p r o b l e ms

(1) O p t i m a l s y s te m c o n f ig u ra t i o n ( i .e . d e t e rm i n a t i o n o f

n u m b e r a n d t y p e s o f m a c h i n e s, l e ve l o f W I P i n th e s y s t e m ) ;

(2 ) S p e c i f ic a t io n o f t h e F M S l a y o u t ;

(3 ) S e l e c t i o n o f a s t o r a g e s y s t e m ( s i ze o f l o c a l b u f f e r s

a n d / o r c e n t r a l s t o r a g e ) ;

(4 ) S p e c i f i ca t i o n o f t h e t y p e a n d c a p a c i t y o f t h e

m a t e r i a l -h a n d l i n g s y s t e m (M H S ) ;

( 5) D e t e r m i n a t i o n o f o t h e r i m p o r t a n t s ys t em r e s o u r c e s

( i .e . n u m b e r o f p a l l e ts , n u m b e r a n d t y p e s o f f i x tu r e s ,

n u m b e r a n d t y p e s o f to o l s ) .

F M S p la n n i n g p r o b l e ms

(1 ) P a r t t y p e s e l e c t io n p ro b l e m ;

( 2) M a c h i n e g r o u p i n g p r o b l e m ;

(3 ) Lo a d i n g p ro b l e m ( i .e . a l l o c a t i o n o f o p e ra t i o n s a n d

a s s o c i a t e d c u t t i n g t o o l s o f t h e s e l e c t e d p a r t t y p e s a m o n g

t h e m a c h i n e g r o u p s ) ;

(4 ) R o u t i n g m i x p ro b l e m ( i .e . r o u t e s e l e c t i o n fo r e a c h

p a r t t y p e ) ;

(5 ) O t h e r p l a n n i n g p ro b l e m s (p a l l e t / f i x t u r e a l l o c a t i o n

a m o n g s e l e c t e d p a r t t y p e s , p ro c e s s p l a n n i n g , s p a r e t o o l

a l l o c a t io n , t o o l s t o r a g e , m a c h i n e p ro c e s s i n g r a t e o p t i m i z a -

t ion ) .

2 FM S design problems

2.1. Optimal system configuration

A f r e q u e n t l y e n c o u n t e r e d d e s i g n p ro b l e m fo r a f l e x i b l e

m a n u fa c t u r i n g s y s t e m is t h e d e t e rm i n a t i o n o f t h e o p t i m a l

s y s t e m c o n f i g u ra t i o n i n o rd e r t o m i n i m i z e t h e c o s t o f

o p e ra t i o n , s u b j e c t t o t h e c o n s t r a i n t o f a c h i e v i n g a

m i n i m u m r e q u i r e d s y s t e m t h r o u g h p u t. T h e o p t im a l s y s t e m

c o n f i g u ra t i o n p ro b l e m u s u a l l y a d d re s s e s t h e fo l lo w i n g t w o

M

min z = E

k i c i

k s N

i=

s . t . TH M-> P0

(1)

w h e r e :

z = t o t a l o p e ra t i n g a n d c a p i ta l in v e s t m e n t c o s t o f th e

F M S ;

k i = o p e ra t i n g a n d c a p i t a l i n v e s t m e n t c o s t o f a

m a c h i n e i n w o rk s t a t i o n i p e r u n i t t i m e ( i = 1 ,

. . . . M ) ;

ci = n u m b e r o f m a c h i n e s ( s e rv e r s ) a t w o rk s t a t i o n i

( i = 1 . . . , M ) ;

kN = i n v e n t o r y h o l d i n g c o st p e r j o b i n t h e s y s te m ;

N = j o b p o p u l a t i o n i n t h e s y s t e m p e r u n i t ti m e ;

TM M = a c t u a l s y s t e m t h ro u g h p u t , w h i c h d e p e n d s o n c i ,

i = 1 , . . . , M ;

P 0 = d e s i r e d s y s t e m t h ro u g h p u t ;

M = t o t a l n u m b e r o f w o rk s t a t i o n s .

Th e a b o v e i n t e g e r p ro g r a m i s v e ry d i f fi c u lt t o s o l v e s i n ce

t h e s y s t e m t h ro u g h p u t c a n n o t b e e x p l i c it l y r e p re s e n t e d i n

t e r m s o f t h e d e c i si o n v ar i ab l e s, N a n d c i i = 1 . . . M . T o

o b v i a t e t h e p r o b l e m t h e a u t h o r s p r o p o se a n a p p r o a c h t h a t

e x p l o i ts t h e fu n c t i o n a l p ro p e r t i e s o f t h e t h ro u g h p u t f u n c -

t i o n o f t h e c l o s e d n e t w o rk . Th e p ro p o s e d i m p l i c i t

e n u m e ra t i o n a l g o r i t h m r e q u i r e s a g o o d s t a r t in g s o l u t io n i n

o r d e r t o b e e f f ic i e n t. E f f i c i e n c y i s a l so i m p ro v e d b y u s e o f

a p p r o p r i a t e b o u n d s o n t h e s y s t e m t h r o u g h p u t , w h i c h

r e d u c e s t h e n u m b e r o f e v a l u a t i o n s o f t h e t h r o u g h p u t

f u n ct io n t h ro u g h C A N - Q .

D a l l e ry a n d F re i n (19 8 6 a n d 1 9 8 8) a d d re s s t h e s a m e

o p t i m i z a t i o n p ro b l e m w i t h a m o r e g e n e ra l o b j e c t i v e fu n c -

t i o n. Th e i r o n l y r e q u i r e m e n t o f t h e o b j e c t i v e fu n c t i o n is

tha t i t is mono ton ic a l ly increas in g in the d ec i s ion var iab les .

A g a i n , t h e F M S i s m o d e l l e d a s a C O N . T h e p r o p o s e d

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7 8

K o u v e l i s

so l u t i o n p r o c e d u r e g o e s t h r o u g h t h e f o l l o w in g t h r e e s t e p s .

F i r s t, b o u n d s o n t h e sy s t e m t h r o u g h p u t a r e u se d i n o r d e r t o

d e t e r m i n e a g o o d i n it ia l c o n f ig u r a t io n . T h e a b o v e b o u n d s

a r e b a se d o n a sy m p t o t i c b o u n d a n a l y s is r e f e r t o K l ei n -

r o c k , 1 9 75 ). S e c o n d , t h e m a r g i n a l a l l o c a t io n s c h e m e o f F o x

1 9 6 6 ) is u se d a s a h e u r is t i c p r o c e d u r e t o i m p r o v e u p o n t h e

s t a r t i ng conf igura t ion pro vide d by the f i rs t s t ep . Thi rd , an

impl i c i t enumera t ion a lgor i thm wi th s t a r t i ng so lu t ion g iven

b y t h e m a r g i n a l a l l o c a t i o n s c h e m e i s u se d t o f i n d t h e

o p t i m a l so l u t i o n . T h e b a s i c d i f f e r e n c e b e t w e e n t h i s m e t h o d

a n d t h a t o f V i n o d a n d S o l b e r g 1 9 8 5 ) i s t h e m o r e so p h i s t i-

c a t e d w a y o f d e t e r m i n i n g t h e i n i ti a l so l u t io n t h a t i s u se d t o

s t a r t t h e i m p l i c i t e n u m e r a t i o n a l g o r i t h m . T h e m e t h o d

sh o w s c o m p u t a t i o n a l e f f ic i e n cy su p e r i o r t o t h a t o f V i n o d

a n d S o l b e r g .

I n K o u v e l i s a n d L e e 1 9 9 0 a ) , a v e r y c o m p u t a t i o n a l l y

e f f i c i e n t a l g o r i t h m f o r t h e o p t i m a l sy s t e m c o n f i g u r a t i o n

p r o b l e m i s p r e se n t e d . T h e a l g o r it h m e x p l o it s t h e c o n c a v i t y

p r o p e r t i e s o f t h e th r o u g h p u t f u n c t i o n , a n d a m o n o t o n i c i t y

p r o p e r t y c h a r a c t e r i z i n g t h e o p t i m a l s e r v e r v e c t o r f o r

spec ia l cases o f t he cos t vec tor .

S h a n t h i k u m a r a n d Y a o 1 9 8 7 ) c o n s i d e r e d t h e s a m e

p r o b l e m w h e r e t h e t o t a l j o b p o p u l a t i o n , w h i c h c o u l d a l so

b e c o n s i d e r e d a s t h e t o t a l b u f f e r c a p a c i t y o f t h e sy s t e m , i s

g i v e n . T h e i r f o r m u l a t i o n o f th e o p t i m i z a t i o n p r o b l e m i s a s

f o l l o w s

M

m a x ~

f i T H i c i ) ) - g i c i )

i =

M

s t ~ ] ~ C m a x

i =

w h e r e :

T H i c i ) =

f i T H i c i ) ) =

g i c i ) =

max

n u m b e r o f s e r v e r s a t s t a t io n i ;

t h ro ugh put o f s t a t ion i , g iven tha t c ; se rve rs

h a v e b e e n a l l o c a t e d t o i t;

p rof i t a t s t a t ion i a s a func t ion of i t s

t h r o u g h p u t ;

c o s t a t s t a ti o n i a s a fu n c t i o n o f n u m b e r o f

se rve rs a l loca t ed ;

m a x i m u m t o t a l n u m b e r o f s e r v e r s t o b e

a l loca ted .

T h e y m a d e t h e f o l l o w i n g a s su m p t i o n s w i t h r e sp e c t t o t h e

func t ions : f i THi ) i s i nc reas ing concave in THi and

g i c i )

is

c o n v e x i n c i .

T h e m a j o r r e su l t o f t h ei r p a p e r i s t h a t T H i c i ) i s p r o v e d

to be an inc reas ing con cave fun c t ion in c ,-. Using th i s re su l t ,

t h e o p t i m i z a t i o n p r o b l e m c a n b e so l v e d b y t h e m a r g i n a l

a l loca t ion proc edu re of Fox 1966) . The d i f fi cu l ty in

a p p l y i n g t h e p r e v i o u s f o r m u l a t i o n i s r e l a t e d t o t h e

m e a n i n g f u l d e f in i t io n o f p r o f it a n d c o s t f u n c ti o n s o f e a c h

i n d i v i d u a l w o r k s t a t i o n i n a c o m p l i c a t e d m a n u f a c t u r i n g

e n v i r o n m e n t su c h a s a F M S .

I n a r e c e n t p a p e r , D a U e r y a n d S t e c k e 1 9 9 0 ) d i s c u s sed a

m o r e r e s t r i c ti v e v e r s i o n o f t h e o p t i m a l c o n f i g u ra t io n p r o b -

l e m . T h e y c o n s i d e r t h e C Q N , w h i c h m o d e l s t h e F M S ,

d i v i d e d i n to a s e t o f su b - n e t w o r k s . E a c h s u b - n e t w o r k i s

a l l o c a t e d a p a r t i c u la r w o r k l o a d . T h i s w o r k l o a d i s f ix e d a n d

g i v e n . T h e p r o b l e m t h e a u t h o r s c o n s i d e r i s t o d e t e r m i n e

t h e b e s t c o n f i g u r a ti o n o f e a c h su b - n e t w o r k t h a t y i e l d s th e

h i g h e s t t h r o u g h p u t f o r t h e o v e r - a ll o r i gi n a l C Q N , w h e r e

t h e n u m b e r o f s ta t i o n s , t h e n u m b e r o f s e r v e rs , a n d t h e

w o r k l o a d a l l o c a t e d t o e a c h s t a t i o n d e f i n e s a p o s s i b l e

c o n f i g u r a t io n f o r e a c h su b - n e t w o r k . S o m e p r o p e r t i e s o f t h e

o p t i m a l so l u t i o n o f t h e a b o v e c o n f i g u r a ti o n p r o b l e m f o r

s i n g le c l as s m u l t i s e r v e r C Q N s a r e d i s c u s se d b y D a l l e r y a n d

S t e c k e 1 9 9 0 ). T h e s i m u l t a n e o u s so l u t i o n o f t h e m i n i m u m

c o s t co n f i g u r a t io n a n d t h e w o r k l o a d a l l o c a t i o n a m o n g t h e

m a c h i n e g r o u p s o f a F M S i s c o n s i d e r e d a l so i n L e e e t a l .

1 9 8 9 ). F o r t h e c a se t h a t t h e F M S c o n s i s ts o f m a c h i n e s o f a

s ing le machine type the au thors p resen t an impl i c i t

e n u m e r a t i o n p r o c e d u r e f o r t h e p r o b le m .

F o r F M S s , t h a t c o u l d b e a d e q u a t e l y m o d e l le d a s o p e n

q u e u e i n g n e t w o r k s O Q N ) B u z a c o t t a n d S h a n t h ik u m a r ,

1980 and Bu zaco t t and Yao , 1986a) , the op t ima l conf igura -

t i o n p r o b l e m c o u l d b e a l so a d d r e s se d a l o n g t h e l in e s o f t h e

B i t r a n a n d T i r u p a t i 1 9 8 9 b ) m o d e l . T h e a u t h o r s c o n s id e r

o p e n n e t w o r k o f si n g le s e r v e r q u e u e s w i t h m u l t i p le c l a s se s,

a n d p e r m i t g e n e r a l d i s t r i b u ti o n s t o d e sc r i b e t h e a r ri v a l a n d

se rv ice t imes . The on ly re s t r i c t ion i s t ha t i n t e r -a r r iva l t imes

wi th in each c l a ss , and the se rv i ce t imes fo r a ll c la sses , have

i n d e p e n d e n t a n d i d e n t ic a l d i s tr i b u t io n s . F o r m e a su r i n g t h e

p e r f o r m a n c e o f su c h sy s t em s a d e c o m p o s i t i o n a p p r o a c h i s

u se d W h i t t 1 9 8 3 a a n d b ) ) , w i t h a n a p p r o p r i a t e m o d i f i ca -

t i o n in t r o d u c e d b y B i t r a n a n d T i r u p a t i 1 9 8 8 ) , t h a t in -

c o r p o r a t e s sp e c i f i c p r o p e r t i e s o f t h e a u t o m a t e d m a n u f a c -

tur ing sys t ems i . e . squ a red coe f f i c i en t o f va r i a t ion of

in t e r -a r r iva l and se rv ice t imes le ss t han o ne , p rod uc t

i n t e r f e r e n c e i n m u l t i - p r o d u c t m a n u f a c t u r i n g e n v i r o n -

m e n t s ) . F o r o p t i m i z a t i o n p u r p o se s t h e d e c o m p o s i t i o n

a p p r o x i m a t i o n e q u a t i o n s c a n b e a d e q u a t e l y d e sc r i b e d w i th

a sys t em o f equ a t ions th ) t, / z , ca , c s ) = 0 , where :

)t

= ) t i ) =

a r r iv a l r a t e v e c t o r , i = 1 , . . . , M ;

= / zi ) = s e r v i c e r a t e v e c t o r , i = 1 , . . . , M ;

ca = ca / ) = v ec tor o f squ a red coe f f i c i en t s o f va r i a t ion

o f i n t e r- a r r iv a l t i m e s , i = 1 , . . . , M ;

cs = c s i) - - vec tor o f squ a red coe f f i c i en t s o f va r i a t ion

o f s e r vi c e t im e s , i = 1 , . . . , M .

T h e i m p o r t a n t p e r f o r m a n c e m e a su r e f o r su c h sy s t e m s i s

t h e m e a n n u m b e r o f j o b s a t e a c h s t a t io n , t h a t c a n b e

r e p r e s e n t e d a s

N i

= t~ )ti , P~i, ca/, csi), i = 1, . . . , M

a c c o r d i n g t o t h e d e c o m p o s i t i o n p r i n c i p l e . I f

v i

i s the

a v e r a g e W I P v a l u e a s so c i a t e d w i t h e a c h j o b a t s t a t i o n i ,

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D e s i g n a n d p l a n n i n g p r o b l e m s i n f l e x i b l e m a n u f a c t u r i n g s y s te m s : a c r it ic a l re v i e w 7 9

t h e n t h e f o r m u l a t i o n o f t h e o p t i m a l c o n f ig u r a ti o n p ro b l e m

is

M

M i n Z

F i ( / ~ i )

i = 1

s . t . ~ b A , ~, ca , cs ) = 0

N i

= q~(Ai,/zi, cai,

C S i , i = 1 . . . . ,

M

M

Z vi i ~ WO

i = 1

/.~i->/x~ i = 1 . . . . , M

w h e re : W 0 i s a n u p p e r b o u n d o n W IP i n v e s t m e n t . I n t h e

o b j e c t i v e fu n c t i o n o f t h e fo rm u l a t i o n , t h e c o s t f u n c t i o n s ,

F i, r e p re s e n t c o s t o f c a p a c i t y a d d i t i o n s t o a c h i e v e a d e s i r e d

W l P v a l u e ,

Wo

a n d a r e a s s u m e d m o n o t o n i c a l l y i n c re a s in g

in the se rv ice ra te ~g a t s t a t ion i . Th e serv ice ra te a t each

s t a t io n i s b o u n d e d b e l o w b y t h e q u a n t i t y / ~ o . I n t h e a b o v e

fo rm u l a t i o n t h e d e c i s i o n v a r i a b l e s a r e t h e c o n t i n u o u s

v a r i a b l e s / z i s . F o r s i n g l e s e rv e r n e t w o rk s a s s i g n m e n t o f

c a p a c i t y c a n b e e a s i ly t r a n s l a t e d i n t o a l l o c a t io n o f s e rv i c e

r a t e s . T re a t i n g c a p a c i t y a s a c o n t i n u o u s v a r ia b l e p r e c l u d e s

c e r t a i n t y p e s o f c a p a c i t y c h a n g e s ( i . e . a d d i t i o n o f

m a c h i n e s ) a n d t h u s i s n o t a p p ro p r i a t e f o r t h e i n i ti a l d e s ig n

p h a s e o f t h e m a n u fa c t u r i n g sy s t e m , b u t c o u l d b e h e l p fu l f o r

l o n g - t e rm c a p a c i t y e x p a n s i o n i s s u e s ( i . e . l a b o r r e a l l o c a -

t i o n , t o o l a c q u i s it i o n s o r m a c h i n e m o d i f i c a t io n s ) f o r a n

e x i s ti n g F M S . In t h e B i t r a n a n d T i ru p a t i ( 1 98 9 a) p a p e r t h e

fo l lo w i n g t w o s i m p l i fy in g a ss u m p t i o n s a r e m a d e : ( 1 ) t h e

fu n c t i o n s F i a r e c o n v e x , a n d (2 ) t h e c a a n d c s a r e

i n d e p e n d e n t o f c a p a c i t y c h a n g e s . Th e s e c o n d a s s u m p t i o n i s

j u s t if i e d b y o b s e rv a t i o n s i n B i t r a n a n d T i ru p a t i ( 19 89 b ). A s

t h e n u m b e r o f p r o d u c ts i n c r e a s e s t h e i n t e r - d e p a r t u r e

p r o c e ss o f a q u e u e b e c o m e s i n d e p e n d e n t o f t h e q u e u e a n d

t h e s e rv i c e p ro c e s s , a n d r e s e m b l e s t h e i n t e r - a r ri v a l p ro c e s s

( fo r a mor e r igo rous ju s t i f ica t ion re fe r to Wh i t t (1987)) . As

a r e s u l t o f t h e t w o s i m p l i fy in g a s s u m p t i o n s, t h e p r e v i o u s

fo rm u l a t i o n is a c o n v e x p ro g ra m . B i t r a n a n d T i ru p a t i

( 19 88 ) p ro p o s e a g r e e d y h e u r i st i c so l u t io n a p p ro a c h t o t h e

p ro b l e m , i n s t e a d o f u s i n g c o n v e n t i o n a l c o n v e x p ro -

g ra m m i n g m e t h o d s , i n o rd e r t o f a c i li t a te p a r a m e t r i c a n a l y -

s i s o f t h e p ro b l e m . Th e p a ra m e t r i c a n a l y s i s l e a d s t o

i n t e r e s t i n g tr a d e -o f f c u rv e s b e t w e e n c a p a c i t y , W IP a n d

m a n u fa c t u r i n g l e a d t i m e s . Th e r e s u l t i n g c u rv e s a r e a c c u -

r a t e e n o u g h fo r a ll p r a c t ic a l p u rp o s e s , d u e t o t h e c l o s e - t o -

o p t i m a l i t y p e r fo rm a n c e o f t h e h e u r i s t i c . S u g g e s t i o n s fo r

a p p ro p r i a t e u s e o f t h e s e c u rv e s fo r s tr a t e g i c m a n u fa c t u r i n g

d e c i s i o n s ( i. e . t e c h n o l o g y c h o i c e , c a p it a l i n v e s t m e n t , p ro -

d u c t m i x ) a r e r e p o r t e d i n B i t r a n et al. (1987).

A n e x t e n s i o n o f t h e B i t r a n a n d T i ru p a t i (1 98 8 ) fo rm u l a -

t i o n i s p r e s e n t e d i n B o x m a

et al.

(1990) fo r a mul t i se rver

O Q N w i t h e x p o n e n t i a l i n t e r - a r r i v a l a n d s e rv i c e t i m e

p ro c e s s e s . U n d e r t h e s a m e s i m p l ify i n g a s s u m p t i o n s (1 ) a n d

(2 ) , t h e a u t h o r s p ro v e t h a t a m a rg i n a l a l l o c a t i o n p ro c e -

d u re , t h a t a d d s a s e rv e r ( i . e . c o n s i d e r s d i s c r e t e o p t i o n s ) a t

t h e w o r k s t a t i o n w h e r e t h e q u o t i e n t o f t h e i n c re a s e o f t h e

o b j e c t iv e f u n c t i o n to t h e d e c r e a s e o f W I P i s t h e s m a l l es t,

g e n e ra t e s n o n d o m i n a t e d s o l u t i o n s i n t h e s e n s e t h a t y o u

c a n n o t d e c re a s e t h e i n v e s t m e n t c o s t w i t h o u t i n c r e a s i n g

W l P . Th e d e v i a t i o n f ro m o p t i m a l i t y o f t h e h e u r i s t i c i s

r e p o r t e d a s s a t i s f a c t o ry . B o x m a et al. (1991) ex tend the i r

fo rm u l a t i o n a n d t h e c o r r e s p o n d i n g r e s u l t s f o r g e n e ra l

O Q N s , w i t h n o d e s m o d e l l e d as GI/G/ci q u e u e s . D e c o m -

p o s i t io n a p p ro x i m a t i o n s a r e u s e d fo r p e r fo rm a n c e e v a l u a -

t i o n o f t h e O Q N . B i t r a n a n d T i ru p a t i ( 1 9 8 9a ) a d d re s s

o p t i m a l s y s t e m c o n f i g u ra t i o n p ro b l e m s w i t h d i s c r e t e o p -

t i o n s fo r g e n e ra l O Q N s . A n o p t i o n fo r a w o rk s t a t i o n

( m o d e l l e d a s a

GI/G/ci

q u e u e ) i n c lu d e s t h e t y p e o f m a c h i n e

t o b e u s e d , w h i c h a f f e c ts th e m a c h i n e s e rv i c e r a t e s , c o u p l e d

w i t h t h e n u m b e r o f s u ch m a c h i n e s . T h e y p r e s e n t a h e u r i s ti c

s o l u t i o n b a s e d o n a l i n e a r r e l a x a t i o n o f t h e p ro p o s e d

i n t e g e r p r o g r a m m i n g f o r m u l a t i o n f o r t h e p r o b l e m . T h e

h e u r i s t ic r e p o r t e d l y p e r fo rm s w e l l .

2 .2 . FM S lay-out problem

Th e d e s i g n o f t h e p h y s i c a l l a y -o u t o f a F M S i s o f

t r e m e n d o u s i m p o r t a n c e fo r t h e e f f e c t i v e u t i li z a t io n o f t h e

s y s t e m . To m p k i n s a n d W h i t e (1 9 8 4 ) e m p h a s i z e d t h e

i m p o r t a n c e o f l a y -o u t d e c i s i o n s fo r e f f e c t i v e m a t e r i a l

h a n d l i n g b y p o i n t i n g o u t t h a t 20 t o 5 0 O f t h e t o ta l

o p e ra t i n g e x p e n s e s i n m a n u fa c t u r i n g a r e a t t r i b u t e d t o

m a t e r i a l -h a n d l i n g a n d l a y -o u t - r e l a t e d c o s t s . Th e l a y -o u t

d e c i s i o n s d e a l w i t h t h e a r r a n g e m e n t o f t h e w o rk s t a t i o n s

( u s u al ly r e f e r r e d a s t h e m a c h i n e l a y - o u t p r o b l e m i n F M S ,

H e ra g u a n d K u s i a k (1 98 8 )) a n d t h e w a y t h e w o rk s t a t i o n s

a r e c o n n e c t e d t h r o u g h t h e t r a n s p o r t a t i o n l i n e s o f t h e

m a t e r i a l -h a n d l i n g s y s t e m (M H S ) (u s u a l l y r e f e r r e d t o a s t h e

M H S l a y -o u t p ro b l e m , K o u v e l i s a n d Le e (1 9 9 0 b )) . Th e

o b j e c t i v e fu n c t i o n u s u a l l y c o n s i d e re d i n t h e l i t e r a t u r e i s

t h a t o f m a t e r i a l -h a n d l i n g c o s t m i n i m i z a t i o n .

In g e n e ra l , t h e p l a n t l a y -o u t p ro b l e m i s f o rm u l a t e d a s a

q u a d r a t i c a ss i g n m e n t p r o b l e m ( Q A P ) ( F r a nc i s a n d W h i t e ,

1974) . Gi lm ore (1963) and Law ler (1963) deve lope d op t im-

a l p ro c e d u re s t o m i n i m i z e t h e t o t a l m a t e r i a l h a n d l i n g c o s ts .

Th e s e o p t i m a l p ro c e d u r e s a r e e f f i c ie n t f o r s m a l l -s i z e d

p r o b l e m s , b e c a u s e o f t h e c o m p u t a t i o n a l c o m p l e x i ty o f t h e

Q A P . S a h n i a n d G o n z a l e z (1 97 6) s h o w e d t h a t t h e Q A P i s

N P - c o m p l e t e . T h i s l e d r e s e a r c h e r s to c o n c e n t r a t e o n

h e u r i s t i c a l g o r i t h m d e v e l o p m e n t fo r s o l v i n g t h e p ro b l e m

( A r m o u r a n d B u f f a , 1 9 6 3 ; H i U i er , 1 9 6 3 ; H i l li e r a n d

C o n n o r s , 1 9 6 6; D r e z n e r , 1 9 8 0 a n d P i c o n e a n d W i l h e l m ,

1984).

H e ra g u a n d K u s i a k (1 98 8) r a i s e q u e s t i o n s r e g a rd i n g t h e

a p p l i c a b i l i t y o f t h e Q A P fo rm u l a t i o n fo r c e r t a i n F M S

i m p l e m e n t a t i o n s . I n F M S s , t h e m a c h i n e s iz e s a r e g e n e ra l l y

n o t e q u a l , a n d a s t h e c l e a r a n c e b e t w e e n m a c h i n e s t e n d s to

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8 0

K o u v e l i s

b e c o n s t a n t , t h e d i s t a n c e b e t w e e n l o c a t i o n s d e p e n d s o n t h e

s e q u e n c e o f t h e m a c h i n e s , t h a t v i o l a te s t h e a s s u m p t i o n o f

t h e Q A P f o r m u l a t i o n f o r c a n d i d a t e l o c a t i o n d i s t a n c e s

b e i n g i n d e p e n d e n t o f m a c h i n e s e q u e n c e . F o r s u c h c a s e s ,

t h e a p p ro p r i a t e f o rm u l a t i o n o f t h e F M S l a y -o u t d e si g n is a s

a q u a d ra t i c s e t - c o v e r i n g p ro b l e m (Q S P ) . Th e Q S P p ro b -

l e m i s d i s c u s se d i n B a z a ra a (19 75 ), a n d a b r a n c h a n d b o u n d

a p p ro a c h fo r i ts s o l u t i o n is p r e s e n t e d .

T h e Q A P a n d Q S P f o r m u l a t i o n s i g n o r e i n t er a c t io n s

b e t w e e n t h e l a y - o ut d e c is io n s a n d t h e q u e u e i n g p e r f o r m -

a n c e m e a s u re s o f a F M S . Th e s i g ni f ic a n c e o f s u c h i n te r a c -

t i o n s h a s b e e n d e m o n s t r a t e d i n S o l b e rg a n d N o f (1 9 8 0 ) ,

w h e r e t h e C A N - Q m o d e l i s u s e d t o e x p l o r e i m p o r t a n t

f a c t o r s a f f e c t i n g l a y -o u t c o n f i g u ra t i o n d e c i s i o n s . F o u r

d i f f e r e n t l a y -o u t c o n f i g u ra t i o n s a r e c o n s i d e re d : p ro d u c t

l a y -o u t ; c a r t l i n e ; c o n v e y o r lo o p a n d p ro c e s s l a y -o u t . Th e

c o m p u t a t i o n a l r e s u l t s s h o w e d t h a t f l o w c o n t ro l i s s u e s ,

i n c l u d i n g i n t e rp l a y o f p ro c e s s i n g r e q u i r e m e n t s , t r a v e l

t i m e s , p a r t m i x a n d p ro c e s s s e l e c t i o n s c a n y i e l d c i r c u m -

s t a n c e s f a v o r i n g a n y o f t h e f o u r l a y -o u t s c o n s i d e re d .

K o u v e l i s a n d K i r a n (19 90 ) p r e s e n t a m o d e l t h a t i n c o rp o -

r a t e s t h e q u e u e i n g - r e l a t e d a s p e c t s o f l a y -o u t d e c is i o n s. I n a

F M S , p a r t s a r e l o a d e d o n t o p a l l e t - f i x t u r e s fo r a u t o m a t e d

h a n d l in g a n d p r o c es s in g , a n d a r e t r a n s p o r t e d b e t w e e n t h e

s ta t ions

v i a

a n a u t o m a t e d M H S . F M S s a r e u s u al ly d e si g n e d

t o a c c o m m o d a t e a l i m i t e d n u m b e r o f p a l l e t - f i x t u r e s ( i . e .

j o b p o p u l a t i o n i n t h e s y s t e m ) . Th i s l i m i t e d a m o u n t o f

w o rk - i n -p ro c e s s (W IP ) t i g h t l y c o u p l e s t h e w o rk s t a t i o n s ;

h e n c e , t h e t h ro u g h p u t t i m e ( i . e . t h e a v e ra g e t i m e t h a t a

p a r t s p e n d s i n t h e s y s t e m ) b e c o m e s m o re s e n s i t i v e t o

m a t e r i a l -h a n d l i n g d e l a y s a n d t r a n s p o r t a t i o n t i m e s . S i n c e

t h e j o b p o p u l a t i o n i s f i x e d , t h e t h ro u g h p u t r a t e s a r e

d i r e c t l y r e l a t e d t o t h ro u g h p u t t i m e s . Th e re fo r e , t h e e f f e c t s

o f l a y -o u t d e c is i o n s o n t h r o u g h p u t r a t e s v i a t r a n s p o r t a t i o n

t i m e ) m u s t b e c a p t u r e d i n a f o rm u l a t i o n o f t h e F M S l a y -o u t

p r o b l e m . U s i n g a C Q N m o d e l f o r m e a s u r in g th e F M S

t h r o u g h p u t , w i th o n e n o d e o f t h e n e t w o r k ( l e t s c a ll it n o d e

M ) r e p re s e n t i n g t h e M H S , t h is c a n b e c lo n e b y o b s e rv i n g

t h e e f f e c t s o f t h e l a y -o u t d e c i s i o n s o n t h e t h ro u g h p u t

fu n c t i o n o f t h e C Q N . I t i s k n o w n f ro m c l o s e d q u e u e i n g

n e t w o rk t h e o ry ( e . g . G ro s s a n d H a r r i s ( 1 98 5 )) t h a t t h e

t h ro u g h p u t f u n c t i o n o f s u c h a n e t w o rk i s a f u n c t i o n o f t h e

s e rv i c e r a t e a t e a c h s t a ti o n . T h e l a y -o u t d e c is i o n s b y

s p e c i fyi n g t h e r e l a t i v e l o c a t i o n o f w o rk s t a t i o n s a f f e c t t h e

t r a n s i t t i m e s b e t w e e n t h e m , a n d h e n c e d e t e r m i n e t h e

s e r vi c e r a t e o f n o d e M t h a t m o d e l s th e M H S . H e n c e , t h e

t h ro u g h p u t f u n c t i o n i s a f u n c t i o n o f t h e l a y -o u t d e c is i o n s.

K o u v e l i s a n d K i r a n (1 99 0) p ro p o s e a m o d i f i c a t io n o f t h e

r e g u l a r Q A P f o r m u l a t io n b y a d d i n g a l o w e r b o u n d p r o d u c -

t i o n r e q u i r e m e n t c o n s t r a i n t , a w a y t o i n v ol v e th e t h ro u g h -

p u t e f f e c t s o f t h e l a y -o u t d e c i s i o n s i n t h e o p t i m i z a t i o n

f r a m e w o rk , a n d b y i n c l u d i n g a n a d d i t i o n a l t e rm i n t h e

o b j e c t i v e fu n c t i o n , t h a t r e f l e c t s W IP c o n s i d e ra t i o n s . Th e

re s u l t in g fo rm u l a t i o n , r e f e r r e d a s M Q A P , i s s o l v e d b y a n

a p p r o p r i a t e m o d i f i c a t i o n o f t h e L a w l e r - G i l m o r e p r o c e -

dur e (Fra nc i s and W hi te , 1974) , and i s e f f i c ien t fo r rea l i s t i c

F M S s iz e (5 -1 0 w o rk s t a t i o n s ) p ro b l e m s .

R o s e n b l a t t ( 1 98 6) u s e d a d y n a m i c p ro g ra m m i n g

a p p ro a c h t o a d d re s s t h e d y n a m i c a s p e c t s o f t h e p l a n t

l a y -o u t p ro b l e m , s i m i l a r t o t h e a p p ro a c h o f S w e e n e y a n d

Ta t h a m (19 76 ) fo r a d d re s s i n g t h e d y n a m i c n a t u r e o f t h e

w a r e h o u s e l o c a t i on p r o b l e m . T h e a p p r o a c h s o lv e s n u m e r -

o u s s t a t i c p l a n t l a y -o u t p ro b l e m s , w h i c h a r e b a s i c a l l y

q u a d ra t i c a s s i g n m e n t p ro b l e m s . I n t h e p a p e r , i t is r e p o r t e d

t h a t t h e S w e e n e y a n d T a t h a m s t a te s p a c e r e d u c t i o n o f t h e

d y n a m i c p r o g r a m d o e s n o t w o r k e f fi c ie n t ly f o r t h e d y n a m i c

l a y -o u t p ro b l e m . T h e a p p l i c a t i o n o f a h e u r i s ti c p ro c e d u r e

fo r s t a t e s p a c e r e d u c t i o n i s s u g g e s t e d i n t h e p a p e r a n d i t

s e e m s to b e c o m p u t a t i o n a l l y p ro m i s i n g .

Th e l a y -o u t d e s i g n e r o f a F M S f a c e s th e d i ff i c ul t t a s k o f

d e v e l o p i n g a s y s t e m t h a t i s c a p a b l e o f h a n d l i n g a v a r i e t y o f

p ro d u c t s w i t h v a r i a b l e d e m a n d s , a l t e rn a t e a n d p ro b a b i l is -

t i c r o u t i n g s , a t a r e a s o n a b l e o p e ra t i n g c o s t . I n p a r t i c u l a r ,

d u r i n g t h e l a y -o u t d e s i g n p h a s e , t h e o p e ra t i o n a l p ro d u c t

m i x i s h i g h l y u n c e r t a i n . U s u a l l y a t t h e t i m e t h e l a y -o u t

d e c i s i o n s a r e m a d e , t h e p ro d u c t s a n d t h e p ro c e s s p l a n s

h a v e n o t b e e n c o m p l e t e l y d e t e r m i n e d . F u r t h e r m o r e , t h e

p ro d u c t m i x (g i v e n a s p a r t p ro d u c t i o n r a t e s ) i s s u b j e c t t o

c h a n g e s d u e t o fo r e c a s t i n g e r ro r a n d d e m a n d f l u c t u a ti o n s .

K o u v e l i s a n d K i r a n (1 99 1) d e v e l o p e d s i n g le a n d m u l t i p le

p e r i o d l a y -o u t m o d e l s , t h a t i n c o rp o ra t e t h e q u e u e i n g a n d

p ro d u c t m i x u n c e r t a i n t y a s p e c ts o f t h e F M S l a y -o u t d e c i-

s i on s . S i n g l e p e r i o d m o d e l s a r e a p p l i c a b l e fo r F M S i m p l e -

m e n t a t i o n s w i t h v e ry h i g h l a y -o u t c h a n g e o v e r c o s t s a n d

u n c o n t ro l l a b l e c h a n g e o v e r t i m e s . Th e p ro d u c t m i x i s

u n c e r t a i n d u r i n g t h e l a y -o u t d e s i g n p h a s e , b u t o n c e r e a l -

i z e d d u r i n g t h e s y s t e m o p e ra t i o n i s e x p e c t e d t o r e m a i n

s t a b l e o v e r t h e p l a n n i n g h o r i z o n . Th e m u l t i p e r i o d m o d e l s

a r e a p p l i c a b le t o t h e m a j o r i t y o f F M S i m p l e m e n t a t i o n s .

Th e p l a n n i n g p e r i o d fo r t h e F M S d e s i g n i s d i v i d e d i n t o

s m a l l e r o p e ra t i o n a l p l a n n i n g p e r i o d s . Th e p ro d u c t m i x fo r

e a c h p l a n n i n g p e r i o d , t h o u g h u n c e r t a i n d u r i n g t h e d e s i g n

p h a s e , r e m a i n s s t a b l e o v e r t h a t p e r i o d . M o s t F M S s c o n s is t

o f c e l ls o f p h y s i c a l ly id e n t i c a l m a c h i n e s t h a t c a n p e r fo rm a

v a r i e t y o f o p e ra t i o n s . A t t h e b e g i n n i n g o f e a c h p l a n n i n g

p e r i o d (w e e k , m o n t h ) o p e ra t i o n s a l l o c a t i o n d e c i s i o n s a r e

m a d e . Th e s e d e c i s io n s c a u s e a s i g n if i ca n t c h a n g e i n t h e

o p e ra t i o n a l p ro d u c t m i x o f t h e c e l l in e a c h p e r i o d , a n d i n

m o s t c a s e s i m p l y s u b -o p t i m a l i t y o f a s t a t i c l a y -o u t c o n -

f i g u ra ti o n . K o u v e l i s a n d K i r a n (19 9 1) d e v e l o p e d a d y n a m i c

m o d e l t h a t a l lo w s t h e d e s i g n e r t o s p e c i fy d i f f e r e n t l a y -o u ts ,

o n e fo r e a c h p l a n n i n g p e r i o d b a s e d o n t h e p ro d u c t m i x

c h a ra c t e r i s ti c s ( o r t h e d e m a n d fo r e c a s t s ) f o r e a c h p e r i o d .

A fe n t a k i s ( 1 9 86 ) , u s i ng t h e m o d e l l i n g f r a m e w o rk d e -

v e l o p e d i n C h a t t e r j e e

et a l .

(1984), d eve lope d a g raph

t h e o re t i c f o rm u l a t i o n o f t h e s t a t i c F M S l a y o u t p ro b l e m .

Th e fo l lo w i n g t w o a s s u m p t i o n s a r e m a d e : ( 1 ) t h e M H S i s

u n i d i r e c i i o n a l , w h e re b y p a s s i n g o f c e r t a i n m a c h i n e s i s

p e r m i t t e d ; ( 2 ) A n o p e r a t i o n i c a n b e p e r f o r m e d o n l y o n a

p a r t ic u l a r m a c h i n e . T h e a u t h o r m o d e l s th e M H S u s in g t h e

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D e s i g n a n d p l a n n i n g p r o b l e m s i n f l e x ib l e m a n u f a c t u r i n g s y s t e m s : a cr it ic a l r e v i e w

81

n o t i o n o f a l a y - o u t g r a p h L ( M , T ) , w h e r e t h e s e t o f n o d e s M

d e n o t e s t h e s e t o f w o rk s t a t i o n s , a n d t h e s e t o f a r c s T t h e

m a t e r i a l h a n d l i n g s y s t e m l i n k s . I f t h e p a r t m i x a n d t h e

r o u t i n g p r o b l e m h a d b e e n s o lv e d , a n d o p e r a t i o n s h a d b e e n

a s s i g n e d t o w o rk s t a t i o n s , t h e n o n e c o u l d p ro c e e d t o t h e

d e f i n i t i o n o f a p a r t t r a n s i t i o n g r a p h

G i M , E l ) ,

w h e r e :

E i

= se t o f a rcs , wi th

j , k ) E

E i

i f p a r t i m u s t g o f ro m

w o rk s t a t i o n j t o w o rk s t a t i o n k .

Th e re i s a w e i g h t a s s o c i a t e d w i t h e a c h l i n k ( j , k )E

Ei ,

w h i c h r e p re s e n t s t h e n u m b e r o f p a r t s m o v i n g a l o n g l i n k

j , k ) .

Le t s c a l l

G M , E )

t h e g r a p h o b t a i n e d b y s u p e rp o si -

t i o n o f t h e p a r t t r a n s i t i o n g r a p h s fo r a l l p a r t s , a f t e r

r e m o v i n g fo r e a c h l in k w i t h m o re t h a n o n e a r c al l b u t o n e

a r c . T h e n , t h e g r a p h t h e o r e t i c f o r m u l a ti o n o f t h e F M S

l a y -o u t p ro b l e m i s:

F i n d t h e l a y -o u t g r a p h , L , w i t h t h e fo l l o w i n g p ro p e r t i e s :

( i) G r a p h L h a s t h e s a m e n o d e s a s G ;

(i i ) If

i , j )

E G , t h e n t h e r e i s e x a c t ly o n e p a t h f r o m i t o j

in L.

( i ii ) Th e sum of the weigh ts as soc ia ted wi th l inks ( i , j ) i s

m i n i m i z e d .

A fe n t a k i s ( 1 9 8 6 ) c l a s s i f i e s t h e p ro b l e m a s N P -c o m p l e t e ,

a n d p ro p o s e s h e u r i s t i c a l g o r i t h m s , b a s e d o n s w i t c h -a n d -

c h e c k t e c h n i q u e s , f o r i t s s o l u t i o n . A fe n t a k i s

et al.

(1986)

r e p o r t s i m u l at i on r e s u l ts o n t h e d y n a m i c n a tu r e o f t h e F M S

l a y - o u t p r o b l e m , a n d e x a m i n e t h e i n f lu e n c e o f a n u m b e r o f

s y s t e m p a r a m e t e r s , p a r t ic u l a rl y t h e p r o d u c t m i x , o n

s e v e ra l r e l a y -o u t s t r a te g i e s .

R e c e n t l y , s o m e F M S r e s e a r c h e r s d e v o t e d t h e ir a t t e n t io n

to ana lyz ing , in de ta i l , spec i f i c l ay -o u t types tha t a re

i m p l e m e n t e d in F M S s . A s r e p o r t e d i n H e r a g u a n d K u s i a k

(1988) and A fen tak i s (1989) these a re ( fo r de ta i l ed descr ip -

t i o n r e f e r t o t h e o r i g i n a l r e f e r e n c e s ) :

( 1 ) U n i d i r e c t i o n a l l o o p n e t w o r k ;

(2 ) C i r c u l a r m a c h i n e la y o u t ;

(3 ) L i n e a r si n g l e - ro w m a c h i n e l a y o u t ;

( 4) L i n e a r d o u b l e - r o w m a c h i n e la y o u t ;

(5 ) C l u s t e r m a c h i n e la y o u t .

A n a l y s i s o f e x i s ti n g F M S s s h o w s t h a t t h e m a c h i n e l a y -o u t i s

d e t e rm i n e d b y t h e t y p e o f m a t e r i a l -h a n d l i n g d e v i c e s u s e d .

In F M S s u n i d i r e c t i o n a l l o o p n e t w o rk l a y -o u t s a r e e x t e n -

s i v e l y i m p l e m e n t e d d u e t o t h e w i d e u s e o f e f f i c i e n t

u n i c y c l ic m a t e r i a l -h a n d l i n g n e t w o rk s . S u c h n e t w o rk s c o n -

n e c t a l l w o rk s t a t i o n s b y a p a t h p a s s i n g t h ro u g h e a c h

w o rk s t a t i o n e x a c t l y o n c e . A u n i c y c l ic m a t e r i a l -h a n d l i n g

n e t w o r k m a y r e p r e s e n t a l o o p c o n v e y o r , t o w l i ne , o v e r -

h e a d m o n o ra i l s y s t e m o r w i r e p a t h s o f a u n i d i r e c t i o n a l

a u t o m a t e d g u i d e d v e h i c l e ( A G V ) s y s t e m . A f e n t a k i s

(19 89 ) p o i n t s o u t t h a t s u c h l a y -o u t s a r e p r e f e r r e d t o o t h e r

conf igu ra t ions due to the i r re la t ive ly lower in i t i a l inves t -

m e n t c o s t , s i n c e t h e y c o n t a i n t h e m i n i m u m n u m b e r o f

r e q u i r e d m a t e r i a l -h a n d l i n g l i n k s t o c o n n e c t a l l w o rk s t a -

t i o n s , a n d h i g h e r m a t e r i a l -h a n d l i n g f le x ib i li ty . P a r t o f t h e

f lex ib il i ty aspec t s o f th e abo ve con f igu ra t ion i s it s ab i l i ty to

s a t is fy a l l m a t e r i a l -h a n d l i n g r e q u i r e m e n t s f o r t h e p a r t t y p e s

s c h e d u l e d fo r m a n u fa c t u r i n g i n t h e s y s t e m , a n d e a s i l y

a c c o m m o d a t e a n y f u t u r e i n t r o d u c ti o n o f n e w p a r t t y p e s o r

p ro c e s s c h a n g e s . Th e r e a s o n fo r t h i s i s t h a t t h e m a t e r i a l -

h a n d l i n g r e q u i r e m e n t s o f a n y p a r t t y p e p ro c e s s e d a t a

w o rk s t a t i o n c a n b e a c c o m m o d a t e d , a s t h e r e i s a t l ea s t o n e

d i r e c t e d p a t h c o n n e c t i n g a n y p a i r o f w o rk s t a t i o n s . A f e n t a -

k i s ( 19 8 9) p r e s e n t s a m a t h e m a t i c a l p ro g ra m m i n g fo rm u l a -

t i o n o f t h e l a y -o u t p ro b l e m fo r s u c h c o n f i g u ra ti o n s u n d e r

t h e o b j e c t i v e o f m i n i m i z i n g t h e a v e r a g e n u m b e r o f

m a c h i n e s t h a t p a r t s c ro s s p e r u n i t t i m e , w h i c h i s a n i n d i r e c t

w a y t o r e d u c e c o n g e s t i o n i n t h e s y s t e m b y m i n i m i z i n g

m a t e r i a l -h a n d l i n g d e l a y s . H e p r e s e n t s a s o p h i s t i c a t e d

b l o c k i n t e r c h a n g e h e u r i s t i c f o r i ts s o l u t io n . K o u v e l i s a n d

K i m (1 9 91 ) , u s in g a n a p p ro p r i a t e w o rk s t a t i o n i n t e r c h a n g e

a rg u m e n t , p r e s e n t d o m i n a n c e r e l a t i o n s h i p s fo r e a s il y i d e n -

t i f y in g l o ca l o p t i m a l s o l u t io n s fo r t h e u n i d i r e c t i o n a l l o o p

n e t w o rk l a y -o u t p ro b l e m . S i m p l e c o n s t ru c t i v e h e u r i s t i c s ,

a n o p t im a l b r a n c h a n d b o u n d p r o c e d u r e , a n d a n a p p r o p r i-

a t e d e c o m p o s i t i o n p r i n c ip l e fo r l a rg e s iz e p ro b l e m s a r e a l s o

d i s c u s se d i n t h e p a p e r . K i r a n a n d K a ra b a t i ( 1 99 0) a d d re s s

t h e s a m e p r o b l e m u n d e r a d i f f e re n t o b j e c ti v e , t h a t o f

m i n i m i z i n g t h e t o t a l m a t e r i a l -h a n d l i n g c o s t. A n e x a c t

i m p l i c i t e n u m e r a t i o n p r o c e d u r e , e n h a n c e d w i t h d o m i -

n a n c e r e l a t io n s h i p s fo r i d e n t i fy in g l o ca l o p t i m a l s o l u ti o n s ,

i s d e v e l o p e d .

A n O t h e r l a y -o u t t y p e e x t e n s i v e l y i m p l e m e n t e d i n f l e xi -

b l e m a n u fa c t u r i n g e n v i ro n m e n t s i s t h e l i n e a r s i n g l e - ro w

m a c h i n e l a y -o u t ( L S R M L ) . T h e m a c h i n e s a r e a r r a n g e d

a l o n g a s t r a i g h t t r a c k w i t h a m a t e r i a l -h a n d l i n g d e v i c e

m o v i n g j o b s f r o m o n e m a c h i n e t o a n o t h e r . I n s u c h

e n v i r o n m e n t s , j o bs e n t e r t h e p r o d u c t i o n l in e a t o n e e n d o f

t h e t r a c k , w h i c h i s u su a l l y c l o s e to t h e r a w m a t e r i a l s t o r a g e

p o i n t , a n d l e a v e t h e l in e a t t h e o t h e r e n d o f it t o e n t e r a W IP

o r a f i n i s h e d g o o d s s t o r a g e a r e a . K o u v e l i s a n d C h i a n g

(1 9 9 0 ) a d d re s s t h e LS R M L p ro b l e m h a v i n g a s d e s i g n

o b j e c t i v e t h e m i n i m i z a t i o n o f t h e t o t a l b a c k - t r a c k i n g

d i s t a n c e o f t h e m a t e r i a l -h a n d l i n g d e v i c e ( i. e . t h e t r a v e l i n

r e v e r s e d i r ec t i o n to t h e p a r t f l o w m o v e m e n t ) . T h e y p r o v e d

t h a t t h e p ro b l e m i s N P -c o m p l e t e . S p e c i a l c a s e s o f t h e

p ro b l e m t h a t a r e p o l y n o m i a l l y s o l v a b le a r e p r e s e n t e d . Th e

a u t h o r s u s e s i m p l e l o c a l o p t im a l i t y c o n d i t i o n s to d e v e l o p

e f f e c t i v e h e u r i s ti c s f o r t h e p ro b l e m . K o u v e l i s a n d C h i a n g

(1991) d i scuss the use o f a s imula ted annea l ing (SA)

h e u r is t ic f o r t h e L S R M L p r o b l e m . T h e i r e x t e n si v e co m -

p u t a t i o n a l e x p e r i m e n t a t i o n i n d i c a te s t h a t t h e S A h e u r i s t i c ,

w i t h i ts c o n t ro l p a r a m e t e r s f i n e t u n e d t o t h e b e s t l e v e l f o r

t h e s p e c i f ic a p p l ic a t i o n , p ro v i d e s , i n r e a s o n a b l e c o m p u t a -

t i o n a l t i m e , n e a r -o p t i m a l s o l u t i o n s . Th e h e u r i s t i c s o f

Kouvel i s and Ch iang (1990) a re used to inpu t the in i t i a l

l a y -o u t t o t h e S A a l g o r i t h m . F o r a m o re d e t a i l e d d i s c us s io n

o n a l g o r i t h m i c a p p ro a c h e s t o s p e c i a l l y s t r u c t u r e d F M S

lay-ou t p rob lem s , see Kou vel i s and Ki ran (1989) .

Th e l a y -o u t t y p e s (2 ) - (5 ) a r e u s u a l l y i m p l e m e n t e d w i t h

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8 2

K o u v e l i s

t h e u se o f h a n d l i n g r o b o t s , A G V s , a n d g a n t r y r o b o t s a s

m a t e r i a l - h a n d l i n g d e v i c e s . H e r a g u a n d K u s i a k ( 1 9 8 8 )

p r o p o se t w o h e u r i s t i c p r o c e d u r e s t h a t e x p l o i t t h e sp e c i a l

s t r u c t u r e o f t h e l a y - o u t d e c i s i o n s fo r t h e a b o v e l a y - o u t

t y p e s . M a t h e m a t i c a l p r o g r a m m i n g m o d e l s f o r an a l y si s a n d

d e s i g n o f l a y - o u t s fo r r o b o t i c sy s t e m s a r e p r e se n t e d i n S a r in

a n d W i l h e l m ( 1 9 8 4 ) . K i r a n a n d T a n se l ( 1 9 8 8 ) c o n s i d e r

t h e s t o r a g e l o c a t io n f o r W l P i n f le x i b le m a n u f a c t u r i n g c e ll s

w i t h t h e m a t e r i a l h a n d l in g p e r f o r m e d b y r o b o t s . T h e

opera t ion of such ce l l s i s a s fo l lows: t he robot p i cks up a

p a r t a n d p l a c e s it o n t h e m a c h i n e . A f t e r c o m p l e t i o n o f th e

o p e r a t i o n t h e p a r t m a y b e t a k e n t o a n o t h e r m a c h i n e f o r it s

n e x t o p e r a t i o n . I f t h e n e x t m a c h i n e i s c u r r e n t l y o c c u p i e d ,

t h e p a r t i s t a k e n t o t h e W I P s t o r a g e a r e a , w h e r e i t w a i t s t il l

t h e r e q u i r e d s t a t i o n b e c o m e s av a i la b l e . K i r a n a n d T a n se l

( 1 9 8 8 a ) i n v e s t i g a t e t h e p r o b l e m u n d e r d i s c r e t e a n d c o n -

t i n u o u s sp a c e a s su m p t i o n s . I n t h e d i s c r e t e c a se , t h e

p r o b l e m o f W I P s t o r a g e l o c a t i o n f o r m a t e ri a l -h a n d l i n g c o s t

m i n i m i z a t i o n i s t r a n s f o r m e d t o a g e n e r a l i z e d a s s i g n m e n t

p r o b l e m . T h e c o n t i n u o u s l a y - o u t i s d i s c u s se d u n d e r d i f f -

e r e n t d i s t a n c e m e a su r e s .

T h e M H S l a y - o u t p r o b l e m i n c l u d e s l o c a ti o n o f p i c k - u p

poin t s an d de l iv e ry s t a t ions , spec i f i ca tion of t r ack l ay-o ut s

and choice of un id i rec t iona l o r b id i rec t iona l f l ows ( f low

p a t h d e s i g n ). I t is o f e x t r e m e i n t e r e s t f o r F M S i m p l e m e n t a -

t i o n s w i t h A G V s a s t h e m a t e r i a l- h a n d l i n g d e v i c e s . G a sk i n s

a n d T a n c h o c o ( 1 9 8 7 ) p r o p o se a n i n t e g e r p r o g r a m m i n g

f o r m u l a t i o n f o r d e t e r m i n i n g t h e o p t i m a l f l ow p a t h t h a t

m i n i m i z es t h e t o t a l tr a v e l d i s t a n c e o f l o a d e d A G V s . I t is

a s su m e d t h a t t h e M H S n e t w o r k i s g i v e n , a n d t h e o n l y

d e c i s i o n i s t o c h o o se t h e d i r e c t i o n o f f l o w o n e a c h

mate r i a l -hand l ing l i nk , a ssuming tha t un id i rec t iona l f lows

a r e p r e f e r a b l e . T h e f o r m u l a t i o n b e c o m e s in e f f ic i e n t f o r

l a r g e - s i z e M H S n e t w o r k s . S h a r p a n d L i u ( 1 9 8 7 ) p r o p o se d

a n a n a l y t ic a l m e t h o d f o r c o n f ig u r in g t h e n e t w o r k o f a f i x e d

p a t h , c l o se d l o o p M H S . T h e p u r p o se o f th e m o d e l is t o

m a k e g o o d i n i t i a l d e c i s i o n s w i t h r e sp e c t t o sh o r t c u t s ,

o f f - l i n e sp u r c o n s t r u c t i o n a n d sp u r l e n g t h . K i r a n a n d

T a n se l ( 1 9 8 8 b ) c o n s i d e r t h e o p t i m a l l o c a t i o n o f a p i c k - u p

p o i n t o n a m a t e r i a l - h a n d l i n g n e t w o r k . T h e p i c k - u p p o i n t

m a y c o n n e c t t h e m a t e r i a l - h a n d l i n g n e t w o r k t o a n y o n e o f

the fo l lowing: machin ing s t a t ion , l oad /un load s t a t ion ,

cen t ra l o r l oca l s to rage . I t cou ld even se rve a s j us t a t r ansfe r

p o i n t t o / f r o m a n o t h e r m a t e r i a l - h a n d l i n g n e t w o r k . T h e

a u t h o r s e x t e n d H a k i m i ' s r e su l t f o r n o d e o p t i m a l i t y o f

m e d i a n l o c a t i o n f o r d i r e c t e d n e t w o r k s . S o , t h e p i c k - u p

p o i n t , i f p o s s ib l e , sh o u l d b e l o c a t e d a t a n o d e o f t h e

m a t e r i a l - h a n d l i n g n e t w o r k ( i . e . a j u n c t i o n p o i n t o r a

w o r k s t a t i o n ) . F o r r e a l F M S i m p l e m e n t a t i o n s l o c a t i n g t h e

p i c k - u p p o i n t a t e x i s t in g n o d e s m a y n o t b e p o s s i b l e . C a se s

i n w h i c h t h e p i c k - u p p o i n t m u s t b e l o c a t e d o n a n a r c o f th e

M H N a r e a n a l y z e d , a n d i t i s d e m o n s t r a t e d t h a t t h e

o p t i m u m l o c a t i o n c a n b e f o u n d i n p o l y n o m i a l t i m e .

K o u v e l i s a n d L e e ( 1 9 9 0 b ) p r e se n t a d i f f e r e n t f o r m u l a t i o n

o f t h e M H S l a y - o u t p r o b l e m . A d i s c r e t e d i r e c t e d n e t w o r k

d e s i g n p r o b l e m o n a p l a n e f o r m u l a t i o n i s g i v e n , a n d

s t a n d a r d r e su l ts f r o m t h e g r a p h t h e o r e t i c l i te r a t u r e a s t h e y

a p p l y to F M S i m p l e m e n t a t i o n s a r e d i s c u sse d .

2 .3 . Opt imal s torage capac i t i e s in a FMS

A s m e n t i o n e d e a r l ie r , t h e m o s t w i d e ly u se d m o d e l t o

e v a l u a t e t h e p e r f o r m a n c e o f a F M S i s t h e C A N - Q m o d e l

b y S o l b e r g ( 1 9 7 7 ) . T h e m o d e l m a k e s a n i n f i n i t e b u f f e r

a s su m p t i o n , i .e . e a c h w o r k s t a t i o n c o n t a i n s a d e q u a t e b u f f e r

c a p a c i t y t o a c c o m m o d a t e a l l p a r t s t h a t a r e q u e u e d f o r

p r o c e s s i n g t h e r e . H o w e v e r , i n m o s t F M S i m p l e m e n t a t i o n s

e a c h m a c h i n e h a s a v e r y sm a l l b u f f e r , u su a l l y o f 2 p a r t s p e r

m a c h i n e . N e v e r t h e l e s s , S u r i (1 9 8 3 ) sh o w e d t h a t th i s

a s su m p t i o n i s q u i t e r o b u s t f o r F M S p e r f o r m a n c e e v a l u a -

t i o n . A l so , Y a o a n d B u z a c o t t ( 1 9 8 7) sh o w e d t h a t , f o r F M S

i m p l e m e n t a t i o n s w i t h c e n t r a l i z e d M H S s ( i . e . a l o o p c o n -

v e y o r ) a n d z e r o b u f f e r w o r k s t a t i o n s , t h e p r o d u c t - f o r m

s o l u ti o n o f th e C Q N m o d e l f o r t h e F M S p e r f o r m a n c e

r e m a i n s v a l i d f o r a n y s e r v i c e t i m e d i s t r i b u t i o n a t t h e

w o r k s t a t i o n s . T h e se r o b u s t r e su l t s p r o v i d e i n s ig h t s i n to t h e

g o o d p e r f o r m a n c e o b t a i n e d w h e n J a c k s o n C Q N s a r e

appl i ed to F M Ss wi th sma l l l oca l buf fe r s . S im ula t ion re su l t s

d e m o n s t r a ti n g t h e a b o v e p o i n t ( C A N - Q e s t im a t e d t h e

t h r o u g h p u t o f a n a c t u a l m a n u f a c t u r in g sy s t e m w i th a n

e r r o r o f l e s s t h a n 1 0 ) a r e r e p o r t e d i n H a i d e r et al (1986).

P e r f o r m a n c e m o d e l l i n g o f F M S s w i t h li m i t ed s t o r a g e

c a p a c i t i e s h a s b e e n e x t e n s i v e l y r e se a r c h e d b y B u z a c o t t ,

S h a n t h i k u m a r a n d Y a o . B u z a c o t t a n d S h a n t h i k u m a r

( 1 9 8 0 ) c o n s i d e r v a r i a t i o n s o f a m u l t i c l a s s o p e n q u e u e i n g

n e t w o r k m o d e l o f a F M S w i t h l o c a l s t o r a g e o n l y , w i t h

c e n t r a l s t o r a g e o n l y , a n d w i t h so m e c o m b i n a t i o n o f th e

t w o . T h e y p o i n t o u t t h a t c o m m o n s t o r a g e i s su p e r i o r t o

l o c al s t o r a g e , a n d t h a t f o r a sy s t e m w i t h M w o r k s t a t i o n s

( M > 2 ) , p r o d u c t i o n c a p a c i t y is c o n j e c t u r e d t o i n c r e a se i n

t h e j o b p o p u l a t i o n , N , w h e r e B + 2 < N < B + M , w i th

B = c e n t r a l s t o r a g e c a p a c it y . I n c u r r e n t F M S i m p l e m e n t a -

t ions , cen t ra l s to rage i s augmented wi th loca l s to rage wi th

o n e o r t w o w o r k p i e c e s a t e a c h s t a t i o n . T h e su p p o r t i n g

a r g u m e n t c o m i n g f r o m p r a c t i c a l e x p e r i e n c e i s t h a t su c h a

sc h e m e r e d u c e s m a c h i n e i d l e t i m e w h i l e m a i n t a i n i n g

e f f i c i en t use o f s to rag e fac i li t ie s .

Y a o a n d B u z a c o t t ( 1 9 8 6 ) m o d e l l e d a F M S a s a n o p e n

n e t w o r k o f m u l t i s e r v e r q u e u e s w i t h g e n e r a l s e r v i c e t i m e s

a n d l i m i te d s t o r a g e c a p a c i t y b o t h a t t h e sy s t e m l e v e l a n d

loca l ly a t each works t a t ion . A ra th e r i n t e res t ing v i ew of t he

M H S i s e x p r e s se d i n t h e p a p e r a s t h e y s e e i t d i v i d e d i n to

t w o se c t i o n s : ( 1 ) o n e s e c t i o n , t h e so - c a l l e d M H S ( I ) ,

h a n d l e s t h e i n p u t f l o w t o t h e w o r k s t a t i o n s ; ( 2 ) t h e o t h e r

se c t i o n , t h e so - c a l l e d M H S ( O ) , h a n d l e s t h e o u t p u t f l o w

f r o m t h e w o r k s t a t i o n .

T h e r e a so n f o r t h a t m o d e l l in g p e c u l i a r it y i s t h e i r a t t e m p t

to . j us t i fy the a ssumpt ion tha t machines a re neve r b locked

f r o m f i n ish e d j o b s , s i n c e f i n ish e d j o b s a r e h a n d l e d b y t h e

M H S ( O ) , w h i c h is a s su m e d t o h a v e t h e c a p a c i ty t o p r o v i d e

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D e s i g n a n d p l a n n i n g p r o b l e m s i n f l e x ib l e m a n u f a c t u r i n g s y s t em s : a cr it ic a l r e v i e w 83

such a service level since it is basically a dedicated conveyor

for finished jobs. Such a modelling approach does not agree

with the physical implementat ion of a general FMS, but it is

not restrictive, on the other hand, as one can ignore the

MHS O) and just keep the implied assumption of non-

blocked machines from finished jobs. In the model the

probability tha t input flow into a station is blocked due to

limited local storage is explicitly calculated. The case of

feed-back flow where part of the output flow from the

workstation will be fed back to the central storage is also

considered. In order to derive results for such a general

model, a renewal approximation technique was used.

Yao and Buzacott 1986 and 1987) address the modelling

of limited local buffers within the context of a CQN. In

order to maintain the product form solution for such a

network model, properties stronger than the Jackson

networks are needed. The reversibility of the mean queue

length process Kelly , 1979), which is equivalent to the

reversibillity of the Markov chain of the job routing, is

required. Routings that can be shown to be reversible and

of interest to FMS modelling are:

1) Symmetric routing from station to station;

2) Job routing in a central server network CAN -Q

situation);

3) Probabilistic shortest que ue routing, by which jobs

are ro uted with the highest probability to the station which

has the relatively shortest queue more empty spaces in its

buffer).

For those cases the calculation of the steady-state

probabilities of the CQN is relatively easy and can be

obtained from the product form solution for the Jackson

CQN, with an appropriate adjustment of the normalizing

constant, since the new state space results from truncation

of the Jackson CQN model state space. In the paper,

results are presented for a CQN with single server,

exponential service times at stations with state-dependent

processing rates, and under different operational

strategies. An explanation of the need for specifying an

operational str ategy in the case of limited buffers follows.

One of the maj or attractive feature s of a closed queueing

network model of a FMS like CAN-Q, which assumes

infinite local buffers, is the ease of input specification.

The basic inputs to the CAN-Q model are the visit fre-

quencies of parts to the workstations i.e. the number of

visits of a part to the workstation per visit to the load/

unload station)

e i i = 1 , . . . , M ) .

Those visit frequencies

can be easily determined once the product mix, the

processed plan for the process parts and the operation

assignment decisions are made. Actually, ei = THi/THM

for the CAN -Q model, where THi = throughput of

workstation i. But when we have a model with limited local

buffers then e i 4 T H i / T H M , since it is possible that jobs

attempting to enter the workstations are blocked. Now the

e; can be interpreted as the average proportion of opera-

tions in the central storage that need to be delivered to

station i. So for such a model, a way for specifying the

ei

from available input data is needed. That is achieved by

specifying an operational strategy. The operational

strategies discussed in the paper are:

1) Fixed routing model: jobs are released into the

system in such a way that ei follow a set of fixed values;

2) Fixed loading model: a set of values for THi/THM

are given;

3) Dynamic routing model: the probabilistic shortest

queue PSQ) mechanism is used.

Yao and Buzacott 1986) generalize the results for a PSQ

routing scheme for a multiclass, multiserver CQN with

exponential service rates dependent on the part type

processed at a particular workstation. Alth ough in all of the

above models the routing conditions are quite restrictive,

still they are quite suitable for a FMS. The problem with

them is the difficulty in specifying an appropriate opera-

tional strategy for a FMS.

A modelling idea used by Yao 1986) to develop an

optimal central storage model for a FMS, is the controlled

arrival single-stage queue model CASQ). The model can

be easily transformed to a CQN with the addition of

another station indexed as station 0 with service rate

/~0 n0) = A N- no), where

A = arrival rate to the system

no = numbe r of jobs in the system

N = upper limit on the number of jobs in the system.

In an attempt to add more realistic control features to it,

externally blocked jobs are not lost but queued outside of

the FMS at the central common storage area. It has been

proven by Shanthikumar and Sargent 1981) that the total

number of jobs in a restricted open queueing network

OQN) has the same equilibrium distribution as the

number of jobs in a birth and death queue with a state

dependent birth rate

A n) = A n -< N

A n) = 0 n > N

and a state-dependent death rate equal to the throughput

of a CQN, TH n). Based on that fact, the CASQ model was

developed by Shanthikuma r 1979), where the system is

transformed into a single-stage queue. Yao 1986) uses

CASQ, with the FMS being the single-stage queue, to

develop an inventory model for the system. The FMS is

assumed to be equipped with N pallets and a central

common storage area. Parts to be processed are delivered

in batches from a central warehouse to the storage and then

inserted into the FMS whenever a pallet is available. Since

the product ion rate o f FMS depends on the number of parts

circulating in it, the following costs have to be considered:

fixed ordering material handling and transportation);

inventory holding cost associated with parts in storage)

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8 4 Kouvelis

a n d c o s t s a s so c ia t e d w i t h l o ss o f p r o d u c t i o n i f th e n u m b e r

o f p a r t s w i th i n t h e F M S d r o p s b e l o w N . T h e m o d e l

c o m p u t e s t h e o p t i m a l o r d e r p o i n t a n d o p t i m a l b a t c h s i z e

u n d e r t h e a b o v e c o n s i d e r a t i o n s .

2 4 M ater ia l h and l in g ys tem design

Even though ma te r i a l handl ing i s a c r i t i ca l f ac tor i n FMSs

p e r f o r m a n c e , w i t h s e v e r e c o n se q u e n c e s d u e t o i t s i n -

e f f i c i en t des ign i . e . d i sorganized s to rag e ac t iv i t i e s , exces-

s i ve m a n u a l e f f o r t , i dl e m a c h i n e s , m a t e r ia l s p i l e d u p o n t h e

f l o o r , p o o r i n v e n t o r y c o n t r o l ) , l i tt le b a s i c r e se a r c h h a s b e e n

d e v o t e d t o i s su e s r e la t e d t o t h e d e s i g n o f i n t e g r a te d

m a t e r i a l- h a n d l in g sy s t e m s i n a F M S c o n t e x t . T h i s s e c t i o n

d o e s n o t r e p r e se n t a n e x h a u s t i v e su r v e y o f o p e r a t i o n s

r e s e a r c h a p p r o a c h e s t o t h e M H S d e s i g n p r o b l e m s , b u t

i n t e n d s t o g i v e a b r i e f r e v ie w o f i m p o r t a n t w o r k i n t h e a r e a ,

w i t h p a r ti c u l a r e m p h a s i s o n i n t e g r a t e d M H S d e s i g n a p p li c -

a b l e t o F M S e n v i r o n m e n t s .

A b r i e f d e sc r ip t i o n o f so m e o f t h e g e n e r i c r e se a r c h a r e a s

o f o p e r a t i o n s r e se a r c h t h a t r e l a te t o m a t e r ia l - h a n d l in g i s

g i v e n b y M a x w e l l 1 9 8 1 ). A m o r e d e t a i l e d r e v i e w o f v e h i c l e

r o u t i n g a n d s c h e d u l i n g p r o b l e m s r e l a t e d t o M H S d e s i g n is

t h e p a p e r b y K u s i a k 1 9 8 5 ). A su r v e y o f o p e r a t i o n s

r e se a r c h a p p r o a c h e s t o t e n c a t e g o r i e s o f m a t e ri a l -h a n d l i n g

i s su es e . g . r o b o t i c s , c o n v e y o r t h e o r y , t r a n s f e r l in e s , F M S ,

e q u i p m e n t s e l e c t i o n , s t o r a g e a l t e r n a t i v e s , a u t o m a t e d

s t o r a g e a n d r e t r ie v a l sy s t e m s A S / R S ) , w a r e h o u s e la y - o u t ,

pa l l e t i z ing , o rde r p i ck ing and accumula t ion) i s g iven in

M a t so n a n d W h i t e 1 9 8 2 ) . M o s t o f t h e re se a r c h d e a l in g

w i t h d e s i g n i s su e s o f M H S s c o n c e n t r a t e s o n sp e c i f i c

sy s t e m s , w i t h c o n v e y o r sy s t e m s r e c e i v i n g m o s t o f t h e

a t t e n t i o n M u t h a n d W h i t e , 1 97 9 ). L a t e l y , r e s e a r c h e r s

c o n c e n t r a t e d o n t h e d e s i g n o f a u t o m a t i c g u i d e d v e h i c le

sy s t e m s A G V S ) , a n e f fi c ie n t m a t e r i a l- h a n d l i n g a l t e r n a -

t i v e f o r F M S i m p l e m e n t a t i o n s . A n i n t e r e s t i n g m o d e l

a d d r e s s i n g t h e p r o b l e m o f d e t e r m i n i n g t h e o p t im a l n u m b e r

o f v e h i c l e s i n a n A G V S w a s d e v e l o p e d b y M a x w e l l a n d

M u c k s t a d t 1 9 8 2 ). A n i n g e n io u s f o r m u l a t io n o f t h e p r o b -

l e m i n to a t r a n sp o r t a t i o n p r o b l e m , w i t h t h e o b j e c t i v e to

m i n i m i z e th e n u m b e r o f e m p t y t ri p s b e t w e e n w o r k s t a t i o n s

sub jec t t o flow cons t ra in t s a t each s t a t ion , i s p res en ted .

F o r t h e M H S d e s i g n e n g i n e e r d u r i n g t h e i n i t i a l d e s i g n

p h a se o f a F M S , t h e p r o b l e m f a c e d i s t h a t o f s e le c t in g f r o m

a m u l t i t u d e o f p o s s i b l e c o m b i n a t i o n s o f s ta n d a r d e l e m e n t s

t h a t c a n p e r f o r m t h e r e q u i r e d m a t e r i a l- h a n d l i n g f u n c t i o n s

i .e . r o b o t s , a u t o m a t i c g u i d e d v e h i c l e , c o n v e y o r s , A S / R S )

a se t t ha t w i ll do the j ob m ost e f fe