Geography Reference
In-Depth Information
output shipment is made the firm incurs fixed costs associated with switch-
ing or re-tooling the production line or reloading the delivery vehicles, and
these costs are known as set-up costs
S
. The total set-up costs incurred per
time period can be written as
S
1
f
1
5
S
1
m
1
/
Q
1
,
S
2
f
2
5
S
2
m
2
/
Q
2
and
S
3
f
3
5
S
3
m
3
/
Q
3
, respectively.
Broadly, the logistics-costs model demonstrates that the more frequently
[
f
1
,
f
2
,
f
3
. . .] input or output goods are shipped, the smaller is the individual
shipment size [
Q
1
,
Q
2
,
Q
3
. . .] and the lower are the inventory holding costs
[
IQ
1
(
p
1
1
t
1
d
1
)/2;
IQ
2
(
p
1
1
t
1
d
1
)/2;
IQ
3
(
p
3
- t
3
d
3
)/2. . .]. At the same time, the
more frequently [
f
1
,
f
2
,
f
3
. . .] input or output goods are shipped, the higher
are both the total transport costs [
m
1
t
1
d
1
; m
2
t
2
d
2
; m
3
t
3
d
3
. . .] and also the
total set-up costs [
S
1
m
1
/
Q
1
;
S
2
m
2
/
Q
2
;
S
3
m
3
/
Q
3
,]. As such, firms must balance
these opposing trends and for each of the input and output linkages the
firm must optimize its shipments so as to minimize the total {transport 1
inventory holding 1 set-up} costs incurred.
What becomes apparent from these logistics-costs models is that the
combined logistics costs of distance are all square root functions of geo-
graphical distance; in other words they are concave with distance even
for linear transport costs, and this is true for both input and output ship-
ments. In other words, when time costs are incorporated into the true
monetary calculation of distance costs, we see that total distance costs
rise less than proportionately with geographical distance, with the dis-
tance cost function becoming shallower as distance increases. Moreover,
these logistics costs model naturally incorporate the observed structure of
transport costs (McCann 2001), without recourse to artificial and unreal-
istic transport specifications such as the 'iceberg' costs assumed in NEG
models (McCann 2005).
The detailed mathematics of these models are beyond the scope of this
topic (McCann 1998), but in analytical terms the total input and output
inventory holding costs can be treated as additive and separable; in other
words the individual inventory costs components can be analysed indi-
vidually. This is important because it allows us to consider the locational
impacts of differences in the source prices of the inputs, the market prices
of the outputs, the value-added at the plant, and the changes in value-bulk
ratios of the products as the production process proceeds.
Importantly for our purposes, the logistics-costs model recasts the
Weber optimization problem in terms of finding the location which mini-
mizes the sum of the total logistics-costs of inputs and output shipments,
whereby logistics costs equal the sum of the total transport 1 inventory
holding 1 set-up costs incurred by the firm (McCann 1993, 1998). Apart
from an additional layer of sophistication, empirically the justification for
using the logistics costs model as an analytical tool is that for many facto-
