Geoscience Reference
In-Depth Information
determined throughout the period. A review on relocation models can be found in
Brotcorne et al. (
2003
).
Relocation approaches proposed so far are based on Markov chain models
(Alanis et al.
2013
) or on approximate dynamic programming (Maxwell et al.
2009
,
2013
;Schmid
2012
). Gendreau et al. (
2001
) use a parallel tabu search heuristic
for solving the dynamic relocation problem. Further approaches were presented by
Rajagopalan et al. (
2008
) and Schmid and Doerner (
2010
).
Because of real-time requirements encountered in practical settings, literature
on ambulance relocation focuses mainly on heuristic solution methods. One such
heuristic was proposed by Andersson and Värbrand (
2007
).Themainideawasto
include a so-called preparedness of ambulances. For this purpose, the area to serve
is divided into a number of zones. Denote by I the set of ambulances and by J
the set of zones which have a demand for ambulances. A weight d
j
is assigned
to each zone j which states the demand for ambulances in the zone. p
j
is the
(exogenous) number of ambulances that contribute to the preparedness in zone j
and
ij
represents the driving time from ambulance location i to zone j. Moreover,
let t
j
denote the travel time of the lth closest ambulance to zone j and let x be
the vector form of the decision variables x
ij
which are equal to 1 if ambulance i is
relocated to zone j and 0 otherwise. Clearly, t
j
.x/ is a function of the x-variables
since the travel time depends on where the ambulances are located currently as
decided by the values in x. In addition, let
l
be the (user-defined) contribution
factor of the lth closest ambulance and let the following two properties be fulfilled:
t
j
t
j
:::
t
p
j
;
(21.51)
1
>
2
>:::>
p
j
:
(21.52)
The preparedness in zone j is then defined as
p
j
X
l
t
j
q
j
D
1
d
j
:
(21.53)
lD1
Andersson and Värbrand (
2007
) proposed a tree search algorithm that tackles the
following relocation model in order to minimize the maximum travel time for the
ambulances (
21.54
) while restricting possible relocations:
minimize
z
(21.54)
z
X
j2J
i
subject to
ij
x
ij
8
i
2
I
(21.55)
p
j
X
l
t
j
.x/
q
min
8
j
2
J
1
c
j
(21.56)
lD1
