6
2
55
43
2
47
0
3
54
46
1
4
58
46
3
5
58
46
5
2
161
112
6
116
0
8
3
145
110
5
4
160
112
4
S
144
109
7
1
392
306
17
315
1
12
2
392
302
11
4
425
295
11
5
373
296
8
1
4030
3128
71
3184
27
30
2
3879
3150
69
43824
3176
65
T a b l e 7 . 2 N u g e n t ’ s p r o b l e m s f o r w h i c h C R A F T produced b e t t e r f i n a l s o l u t i o n s t a r t i n g w i t h a p o o r e r random I n i t i a l s o l u t i o n .chance as p o s s i b l e of allowing a d j a c e n t location of
facilities with high material flow be t w e e n them. In this
sense the p h i l o s o p h y of ILG is similar to that of dynamic layout planning in that it is the overall p e r f o r m a n c e of the syst e m that is important and not o p t i m u m location of a limited number of f acilities or o p t i m u m layout for a limited period of time.
7.2.2 ILG Speed
(a) In almost all c o n s t r u c t i o n t e c h n i q u e s the decision process of se l e c t i n g a facility and a s s i g n i n g it to a
location is made in either 2-dimensional or 3-dimensional
w a y s .[Liggett (1981)]
In 2-dimensional assignment, a faci l i t y is f ixed to a
location at ea c h kth assig n m e n t stage a n d the remaining ( n - k + 1 ) p o s s i b l e a s s i gnments are e v a l u a t e d w h e r e a s in 3- dimensional m e t h o d s all (n-k+1)*2 f a c i l i t y - l o c a t i o n combinations are e v a luated [Heider (1973)]. As me n t i o n e d in chapter four th i s iterative e v a l u a t i o n p r o c e d u r e is not
embedded in the ILG p rocedures r e s u l t i n g in only n
assignments in the a llocation procedure. This results in a
dramatic r e d uction in solution time w h i c h is a necessity if a layout solu t i o n is sought for m a n u f a c t u r i n g s y stems with a relatively large number of facilities.
(b) T h e f a c i l i t y layout p r o b l e m has been f o r m u l a t e d as a q u a d r a t i c a s s i g n m e n t problem. The latter belongs to the set of N P - C o m p l e t e problems. T h e implication of this is that the a m o u n t of c o m p u t a t i o n required to solve large scale problems increases e x p o n e n t i a l l y as the number of f a c i l i t i e s involved in the p r o b l e m increases. Even he u r i s t i c m e t h o d s d e v e l o p e d t o date r e quire e x p e n s i v e c o m p u t e r s y s t e m s i m a i n f r a m e s ) to s o l v e large scale problems. The e f f i c i e n c y of ILG m a k e s it t h e only h e u r i s t i c among the e x i s t i n g m e t h o d s that can h a n d l e large siz e p r o b l e m s in a short time with less cos t l y c o m p u t e r s y s t e m s i.e m i c r o c o m p u t e r s .
7.2.3 ILG A p p l i c a b i l i t y
(a) B e c a u s e of the a l t e r n a t i n g v e r t i c a l / h o r i z o n t a l (or h o r i z o n t a l / v e r t i c a l ) m e t h o d of f a c i l i t i e s a s s i g n m e n t in alloc a t i o n p r o c e d u r e of the I L G and d e p e n d i n g on the s t r u c t u r e of the material flo w matrix, it is s o m etimes p o s s i b l e that the a l l o c a t i o n p r o c e d u r e m a y be cu r t a i l e d before the a s s i g n m e n t of all f a c i l i t i e s is completed. For e x a m p l e c o n s i d e r ILG a p p l i e d to g e n e r a t e a layout solu t i o n for a s y s t e m c o n s i s t i n g of six f a c i l i t i e s with material flow links s hown in T a b l e 7.3. T h e s e f acilities have to be assig n e d to a p p r o p r i a t e l o c ations in a plant
such as shown in F i g . 7.1 in a way that mate r i a l movement co s t is a minimum.
Ac c o r d i n g to ILG procedures, f a cilities 1,4,5 and 6 are
selected and assigned to locations B,A,F and D
respectively in a manner illustrated in F i g . 7.2. As can be
seen f r o m this figure faci l i t y number 6 is assigned to D rather than to location F.
T a b l e 7 . 3 The l i n k t a b l e f o r t h e h y p o t h e t i c a l e x a m p le o f a m a n u f a c t u r i n g s y s t e m w i t h s i x f a c i l i t i e s .