Geoscience Reference
In-Depth Information
21.2.2
An Overview of Healthcare Facility Location Models
The classical p-median problem seeks for the optimal location of p facilities to
minimize a demand-weighted cost of access (or equivalently distance, or time) for
the population residing at the nodes of the network (see Chap. 2 for a detailed
discussion of this problem). Therefore, the problem that consists of deciding where
to locate a set of primary care facilities, such as community clinics or family centers,
or hospitals, is often casted as a p-median problem. Assuming, as before, that I
denotes the set of potential locations for the facilities and J the set of districts or
populations to serve, the basic formulation is as follows:
minimize
X
i2I
X
d
j
c
ij
x
ij
(21.3)
j2J
subject to
X
i2I
y
i
D
p
(21.4)
X
x
ij
D
1
8
j
2
J
(21.5)
i2I
x
ij
y
i
8
i
2
I;j
2
J
(21.6)
y
i
2f
0;1
g
i
2
I
(21.7)
x
ij
2f
0;1
g
i
2
I;j
2
J;
(21.8)
where d
j
is the population in district j, c
ij
is the distance between location i and
district j, x
ij
is a binary variable equal to 1 if the population in district j is served
from the facility at location i and 0 otherwise, y
i
is a binary variable equal to 1 if a
facility is opened at location i and 0 otherwise, and p is the total number of facilities
to open.
The formulation assumes an unlimited capacity for each facility which is
rarely the case in practice. Therefore, most practical applications use a capacitated
formulation by adding the following constraint:
X
d
j
x
ij
q
i
8
i
2
I;
(21.9)
j2J
where q
i
is the exogenous capacity of the facility at node i. In some situations, facil-
ity capacities can also be decision variables. This can be modeled by incorporating
the cost associated with building capacity in the objective function.
