Geoscience Reference
In-Depth Information
the dispatching of ambulances, i.e., the allocation and reallocation to emergencies
and stations. In the next two sections, exemplary models for the planning problems
at the three levels are presented. Section
21.3.1
looks at strategic and tactical models,
while Sect.
21.3.2
concentrates on operational aspects.
21.3.1
The Strategic and Tactical Level: Finding Ambulance
Base Locations and Assigning Ambulances
One possibility for determining ambulance base locations is to use the location set
covering model (LSCM) that has been first introduced by Toregas et al. (
1971
). The
objective is to find the minimum number of ambulance bases needed to cover all
demand points.
For the LSCM, a set J of demand nodes is given, and these nodes are also
the potential locations for the ambulances. Moreover, as usually done in covering
problems in ambulance planning, a maximum response time T is defined. Therefore,
a node i can cover an emergency in node j if and only if the driving time t
ij
between
the two nodes is less than or equal to T . The set of all the nodes i that fulfill
this condition is denoted by J
j
Df
i
2
J
j
t
ij
T
g
;
8
j
2
J. For each node
j
2
J, a binary decision variable x
j
is considered, equal to 1 if an ambulance is
located at site j and 0 otherwise. The objective function represents the number of
ambulances, which is to be minimized. The constraints ensure that each demand
node can be served within the given response time by at least one ambulance. The
LSCM therefore looks as follows:
minimize
X
j2J
x
j
(21.31)
subject to
X
i2J
j
x
i
1
8
j
2
J
(21.32)
x
j
2f
0;1
g8
j
2
J:
(21.33)
21.3.1.1
A Double Coverage Model
The model by Toregas et al. (
1971
) only assures that all demand points can be
reached within a given time interval, but it does not consider the possibility of
covering demands from multiple nodes. Therefore, Gendreau et al. (
1997
)presented
a so-called double standard model (DSM) that includes what is referred to as
double coverage for the demand points. Compared to LSCM, DSM includes several
additional features. First, the number of ambulances to be located is fixed and equal
to p. Second, for demand and potential ambulance locations, two node sets I and
J are considered, which may be distinct. Third, for each node i
2
I,uptop
i
