Geoscience Reference
In-Depth Information
Fig. 20.1
An example of solution to the concentrator location problem
directly connected to the concentrators, and the backbone network connecting
the concentrators is also a star—concentrators are directly connected to a central
node. Figure
20.1
illustrates such a topology. The concentrators are represented by
diamonds, round nodes represent end-user, dashed edges are connections between
end-users and concentrators while plain edges form the backbone network.
Let I
Df
1;:::;i;:::;m
g
be the set of potential concentrator locations and
J
Df
1;:::;j;:::;n
g
the set of end-users. The objective is to minimize the sum
of the costs c
ij
incurred by establishing a link between node j and a concentrator at
node i, and the sum of costs f
i
for installing a concentrator at node i,linkedtothe
central node. Furthermore, we denote by d
j
the demand of end-user j and by q
i
the
capacity of concentrator i.
Using binary variables y
i
to indicate if concentrator i is open, and binary
variables x
ij
to indicate if end-user j is assigned to concentrator i, the basic version
of the Concentrator Location Problem can be formulated as
Minimize
X
i2I
f
i
y
i
C
X
i2I
X
c
ij
x
ij
(20.1)
j2J
subject to
X
i2I
x
ij
D
1
j
2
J;
(20.2)