Geoscience Reference
In-Depth Information
service for all patients in a location. However, in case of capacity constrained
systems, this may not be a reasonable assumption since the capacity of a facility may
not be sufficient to serve large population centers. In that case, multiple assignment
can be modeled by redefining the variable x
ijs
as the number of patients from district
j assignedtolocationi for service s, and by changing the assignment constraint
(
21.12
) as follows:
X
x
ijs
D
d
j
8
j
2
J;s
2
S:
(21.13)
i2I
Notice that these models do not account for preferences of patients in different
locations, while healthcare facilities are utilized by consumers who may have
discretion on which one to patronize. A common approach to incorporate these
preferences is to use
closest assignment constraints
in order to ensure that each
population will patronize its assigned facility, assuming that the closest facility is the
most preferred one (cf. Verter and Lapierre
2002
). The following set of constraints
can be added to model (
21.3
)-(
21.8
) (see, e.g., Canovas et al.
2007
; Güne¸setal.
2014
):
X
x
kj
C
y
i
1
8
i
2
I;j
2
J:
(21.14)
k2IWc
kj
>c
ij
These constraints ensure that for a given zone j
2
J, if a facility at location
i
2
I is open, then j is not assigned to any facility whose distance to j is more than
the distance between j and i. For other examples of closest assignment constraints
in a healthcare context see Verter and Lapierre (
2002
), Smith et al. (
2009
,
2013
).
21.2.2.3
Assumptions on Demand and Patient Choice
The problem of locating healthcare facilities is characterized by various complexi-
ties due to the central presence of the human element in the system. Consequently,
the demand for health services is uncertain and its estimation is not trivial since there
are various relevant factors influencing it, such as disease prevalence, insurance
coverage, demographics, and accessibility of the facilities. Therefore, there is a
need for a better understanding of the patient behavior and preferences, and for
incorporating them in location models.
Parker and Srinivasan (
1976
) were the first authors incorporating consumer
preferences. Their model was built for expanding a rural primary care facility
network. They estimated the benefit of a patient when getting service from a facility
as a function of several attributes, such as distance, waiting time, time to get an
appointment, and the type of facility. In that paper, the total benefit was maximized
using an iterative procedure which finds the equilibrium allocation. Some recent
papers investigate models that include demand estimation. For example, Griffin et al.
(
2008
) embedded statistical estimation of demand for community health clinics.
