Geoscience Reference
In-Depth Information
Note that whereas any of the deterministic utility function could be followed by
any of the allocation functions, the allocation function AP2 is a direct consequence
of the utility function UP1.
Finally, in the third stage in the decision-making process, customers determine
the quantity that they are going to purchase from the chosen facility/facilities. Most
authors opt for the quantity choice rule
Q1:fixed,
in which the quantity customers purchase is fixed. This is typically justified by
asserting that the good in question is essential. While such an assumption is
convenient, there are, actually, relatively few essential goods in real life: butter can
be replaced by margarine, private transportation can—at least within reason—be
replaced by public transportation; potatoes could be replaced by pasta, and so forth.
Yet, true essential goods exist, such as electric power (which cannot be replaced in
the short run), or medical care. Typical examples for the use of this rule include
almost all contributions in the literature, starting with Hotelling (
1929
), Eaton and
Lipsey (
1975
), and d'Aspremont et al. (
1979
) to Drezner and Drezner (
1997
),
Fernández et al. (
2007
), Braid (
2013
), and others.
A very general alternative rule is
Q2:
q
ij
D
f
(
p
j
C
td
ij
,
u
ij
),
where
q
ij
denotes the quantity customer
i
purchases at facility
j
. This rule states that
the quantity that customer
i
purchases from facility
j
is a function of the full price
to be paid for purchases at that facility and of the utility customer
i
achieves from
purchases at facility
j
. While a customer's utility is likely to include the full price
as one of its components, the quantity purchased by a customer is often assumed
to depend on the (full) price of the product, rather than on a customer's utility.
The early contribution by Rothschild (
1979
) uses a negative exponential distribution
to relate a customer's demand and the customer-facility distance, while Aboolian
et al.'s (
2008
) work includes not only distance, but also price, in their negative
exponential relation. The contributions by Penn and Kariv (
1989
) and Matsumura
and Shimizu (
2006
) assume that the demand at a point is the difference between a
constant and the travel distance, and the difference between a constant and the price
paid for the product. Both cases are designed so as to express the amount of money
a customer has left over after this purchase.
Once customers have gone through the three stages of their decision-making
process, they have decided how much to purchase and whom to purchase it from.
This can then be used as input by the competing planners of the facilities. Drezner
et al. (
1996
) analyzed an anomaly in the decision making process that occurs if
customers reevaluate their purchasing decision along the way to the chosen facility.
The authors also delineated areas in which this phenomenon occurs.
