OPTIMAL LOCATION OF CONSUMER FACILITIES WITHIN A CITY
by Kurt E. K l e i n (Regensburg)
1. SOME INTRODUCTORY REMARKS
The a l t e r a t i o n o f innerurban r e t a i l i n g and s e r v i c e can be d i v i d e d i n t o two phases: u n t i l the mid 1970Ts the a r e a l p a t t e r n o f the i n t r a u r b a n commercial c e n t r e s undergoes some s t r u c t u r a l a l t e r a t i o n . Supermarkets i n t r u d e i n t o w e l l e s t a b l i s h e d suburban centres o r c r e a t e - as w e l l as hypermarkets - new l o - c a t i o n s on p r i n c i p a l r a d i a l routes half-way c i t y - c e n t r e . As a r u l e new planned housing areas are provided w i t h concentrations o f establishments a t one o r two l o c a t i o n s w i t h the advantage o f multipurpose shopping t r i p s i n - c l u d i n g r e l a t e d a c t i v i t i e s l i k e r e c r e a t i o n o r education and f a c i l i t i e s o f p u b l i c t r a n s p o r t .
Since the mid 1970!s energy and economic c r i s i s reverse the development.
Urban planning p o l i c y r e s t r i c t s the allowances f o r e s t a b l i s h i n g supermarkets and n e a r l y stops hypermarkets. Instead o f developing new l o c a t i o n s the r e - o r g a n i z a t i o n o f the c i t y centre as w e l l as high-order subcentres gains p r i - o r i t y .
The problem under c o n s i d e r a t i o n w i l l be t o look f o r optimal l o c a t i o n s f o r i n t r a u r b a n commercial centres under r e t a i l o p e r a t i n g c o n s t r a i n t s , demand requirements and general w e l l f a r e aspects. C r i t e r i a f o r optimal l o c a t i o n s w i l l be developed i n m o d i f i c a t i o n o f the theory o f c e n t r a l places w i t h i n the c i t y (Warnes/Daniels) and s t r e s s the o v e r a l l a c c e s s i b i l i t y . Each d i f f e r e n t h i e r a r c h y - l e v e l has i t s s p e c i f i c route-choice assumption which a l s o l i n k s the h i e r a r c h y l e v e l s .
R e t a i l centres c o n s i s t o f s e v e r a l shops, a r e a l l y c l u s t e r e d and w i t h the p o s s i b i l i t y o f multi-purpose shopping. Distances w i t h i n the centre are neg- l i g i b l e a g a i n s t the average d i s t a n c e t o reach the c e n t r e .
The u n d e r l y i n g graph f o r s o l v i n g the nested p-median-problems has been chosen so that the nodes correspond to the d i s t i n c t l o c a t i o n s o f s t i l l e x i s t i n g food-stores and the edges are weighted w i t h the r e a l d i s t a n c e s between the nodes.
2. DEFINITION OF THE HIERARCHY
Suppose a f t e r c a t e g o r i z i n g the demand regarding to frequency and s p e c i a l i - z a t i o n one can d e f i n e standard p r o v i s i o n s i t u a t i o n s (sps) f o r an average household. Then these sps cause t h a t the greater p a r t o f establishments w i t h i n an agglomeration o f shops could be standardized to meet the c o r r e s - pondent demand. The s t a n d a r d i z a t i o n could be used to e s t a b l i s h a catalogue f o r d e s c r i b i n g h i e r a r c h y - l e v e l s of centres (Borcherdt).
The l e f t column o f Table 1 provides an example f o r a f o u r - l e v e l - h i e r a r c h y . I t must be s t r e s s e d that each h i e r a r c h y - l e v e l has a s t r u c t u r a l component w i t h necessary f a c i l i t i e s and an a d d i t i v e component. The s t r u c t u r a l component cumulates w i t h r i s i n g h i e r a r c h y - l e v e l , to some extent a l s o the a d d i t i v e component.
3. THEORETICAL LOCATION CONSIDERATIONS
Top o f the middle column deals w i t h the key v a r i a b l e s f o r determining the l o c a t i o n o f consumer f a c i l i t i e s . They are used to support the l o c a t i o n con- s i d e r a t i o n s on the r i g h t h a l f o f t h i s column. L a t t e r bear some r e l a t i o n s h i p to the t h e o r e t i c a l l o c a t i o n p r i n c i p l e s o f Warnes/Daniels s t a t e t on the l e f t h a l f , but there i s no 1-1 correspondence.
4. OPERATIONALIZATION
The o p e r a t i o n a l i z a t i o n i s based upon the r e p r e s e n t a t i o n of the urban road- network as a graph. I t s nodes are weighted w i t h demand v a l u e s , i t s edges w i t h t r a v e l costs ( c f . r i g h t column o f Table 1). The o b j e c t i v e f u n c t i o n of the nested p-median problem has components which are dependent on each other (e.g.Hj).
5. OBJECTIVE FUNCTION
The general form o f the o b j e c t i v e f u n c t i o n w i l l be
K *fi ( W d r , s ^ r , s = m i n w i t h ~ 4: t
q . > 0 , ^ q,=1 f ( ) demand f u n c t i o n g( ) t r a v e l cost f u n c t i o n
£r = j 0 i f r does not belong to the catchment area of s ' ' 1 otherwise
T a b l e 1 H i e r a r c h y , L o c a t i o n a l C o n s i d e r a t i o n s a n d 0 p e r a t i o n a l i 7 . a t d . o n T a b l e 2 : J n n e r u r b a n c e n t r e - h i e r a r c h y T h e o r e t i c a l a n d e m p i r c n l f i g u r e s H i e r a r c h y
C a t a l o g u e o f f a c i l i t i e s a c c o r d i n g t o B o r c h e r d t
g o o d / s e r v i c e demand AO I f r e q u e n t / n o n - d u r a b l e AG I I i n f r e q u e n t / d u r a b l e SD s e l d o m / s p e c i a l i s e d
g r o c e r y s h o p a n d 2 o f ( b a k e r , b u t c h e r , b a n k , d r u g g i s t ) t o t a l o f 3 - 7 s h o p s
H Community AG I I I
w h o l e r a n g e o f 3 o f ( b a r b e r , c l e a n e r , s t a t i o n e r , f l o r i s t / f r u i t s , p o s t - o f f i c e )
t o t a l o f 8 - 30 s h o p s
R e g i o n a l AG I , I I , SD w h o l e r a n g e o f II
i n c l u d i n g a d d i t i o n a l b r a n - c h e s o f AG I I ( c l o t h e s , s h o e s , d o c t o r , d e n t i s t e t c )
and SD
t o t a l o f 31 - 75 s h o p s
C e n t r a l A r e a AG I , I I , SD w h o l e r a n g e o f H^
a n d f u l l r a n g e o f SD
L o c a t i o n a l C o n s i d e r a t i o n s
d e p e n d e n t on - s h o p p i n g b e h a v i o u r - o p e r a t i n g r e q u i r e m e n t
c o n s t r a i n t s
- p u b l i c t r a n s p o r t a t i o n s y s t e m
( W a r n e s / D a n i e l s )
m a r k e t m i n i m i z e t h e m a x i m a l p r i n c i p l e d i s t a n c e o f p o p u l a t i o n
- f r e q u e n t s h o p p i n g - by f o o t
- l o w r a n g e g o o d s
t r a n s p o r t c l o s e t o a s t o p o f t h e p r i n c i p l e p u b l i c t r a n s p o r t a t i o n
s y s t e m
m a x i m i z e t h e p o p u l a t i o n c o v e r e d w i t h i n a s e r v i c e d i s t a n c e S, w h i l e m a i n - t a i n i n g m a n d a t o r y c o v e - r a g e w i t h i n a d i s t a n c e o f T (T>S)
- o p e r a t i n g r e q u i r e m e n t c o n s t r a i n t s o f s u p e r - m a r k e t s
a d m i n i s t r a t i v e p r i n c i p l e
m i n i m i z e t h e a v e r a g e d i s t a n c e o f p o p u l a t i o n a g g r e g a t e d a t n o d e s o f
- i n f r e q u e n t s h o p p i n g - m e c h a n i c a l l y - a s s i s t e d
t r a v e l
c f . II,
O p e r a t i o n a l i z a t i o n
N : s e t o f n o d e s N ^ H ^ H ^ H ^ H j ,
Id, A itj * N : t r a v e l c o s t
^ i t fsj: demand a t node i
p - M e d i a n p r o b l e m on l e v e l ( H / N )
MCLP w i t h m a n d a t o r y c l o s e n e s s on l e v e l
( H2/ N )
p - M e d i a n p r o b l e m on l e v e l
( H5/ H2)
• P*
c f .
E x a m p l e H i e r a r c h y - 1 e v e l
T h e o r . a 88 6 1
f i g u r e s ( W a r n e s / D a n . )c
120 3? 7
1
a 36 vi h 1
R e g e n s b u r g
c y> 19 5 1
D a r m s t a d t a 17 27 5
c 50 33 6 1
S t o c k p o r t a 19 9 2
( P o t t e r ) c 7.2 31 1? 3 1
a a b s o l u t e
c c u m u l a t e d 04
I t must be mentioned t h a t there has to be taken i n t o account b a r r i e r s whose impact i s decreasing w i t h r i s i n g h i e r a r c h y l e v e l .
6. RESULTS
The p o p u l a t i o n o f Regensburg sums up to 130 000 i n h a b i t a n t s , unevenly d i s - t r i b u t e d on an overbounded area. As i n t e r a c t i o n b a r r i e r s a c t the r i v e r s Danube and Regen, highways, r a i l w a y l i n e s and the r e l i e f (NW, NE).
55 r e t a i l centres have been d e f i n e d and c l a s s i f i e d according to an 4-order- h i e r a r c h y . Table 2 shows c o n s i d e r a b l e d i f f e r e n c e s between t h e o r e t i c a l f i g - ures -which h o l d f o r a 4-order-hierarchy independent o f p o p u l a t i o n s i z e - and e m p i r i c a l ones o f comparable towns. D i f f e r e n c e s between the l a t t e r are due to d i s t i n c t i v e o v e r a l l a c c e s s i b i l i t y , purchasing power o f p o p u l a t i o n and r e g i o n a l dynamics.
Considering Fig.1 the s i t e s o f e x i s t i n g centres seem to be unevenly d i s - t r i b u t e d and there i s no correspondence between l o c a t i o n s o f succeeding h i e r a r c h y l e v e l s as p r e d i c t e d by Warnes/Daniels. On the other hand the pre- d i c t e d connection between l o c a t i o n s o f - and the road net c o u l d be v e r i f i e d .
I t has been t r i e d to r e l o c a t e the 55 r e t a i l centres according to the d e v e l - oped o p t i m i z a t i o n c r i t e r i u m and u s i n g 111 p o t e n t i a l l o c a t i o n s . R e s u l t s are shown i n Fig.1 and can be summed up as f o l l o w s :
- r e l o c a t e d s i t e s show no c l u s t e r s
- urban f r i n g e i s r e v a l o r i z e d , c i t y centre devaluated, planned centres w i l l be confirmed
- ( r e g i o n a l ) centres are r e l o c a t e d outwards, l e a v i n g t h e i r l o c a t i o n a t former n u c l e i o f town development.
Comparison o f e x i s t i n g and r e l o c a t e d s i t e s c o u l d be used to d e r i v e guide- l i n e s f o r r e o r g a n i z i n g the p u b l i c t r a n s p o r t a t i o n system - H ^ - l e v e l - as w e l l as developing r e t a i l centres by l o c a t i n g o f f i c e s and i n s t i t u t i o n s f o r adjacent a c t i v i t i e s ( r e c r e a t i o n , education, p u b l i c a d m i n i s t r a t i o n ) o r c r e - a t i n g p e d e s t r i a n p r e c i n c t s , adjacent p a r k i n g space and bus stops.
7. CONCLUDING REMARKS
Development o f the presented l o c a t i o n a l c o n s i d e r a t i o n s has been based upon very r i g i d assumptions concerning shopping behaviour. I t i s expected t h a t the e v a l u a t i o n o f a household and customer survey both h e l d a t Regensburg should r e v e a l i n s i g h t s about shopping behaviour e s p e c i a l l y the t r a n s i t i o n
f i g u r e 1 : E x i s t i n g and computed l o c a t i o n of r e t a i l c e n t r e s i n Regensburg 1982
M 1 : SO 000
H i e r a r c h i c a l c l a s s i f i c a t i o n o f r e t a i l c e n t r e s
* o Neighbourhood
* A Community
* • R e g i o n a l O C e n t r a l a r e a
computed V—e x i s t i n g
between centres o f d i f f e r e n t h i e r a r c h i c a l l e v e l s . This w i l l l e a d t o an ob- j e c t i v e f u n c t i o n which allows m i n i m i z a t i o n o f t r a v e l l i n g c o s t s as w e l l as maximization o f a l t e r n a t i v e consumer c h o i c e .
To increase the r e l i a b i l i t y o f r e s u l t s i s seems important t o c a l c u l a t e the minimal net o f consumer f a c i l i t i e s . But t h i s r e q u i r e s p l a n n e rfs consensus about h i e r a r c h i c a l s e r v i c e ranges.
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