Geoscience Reference
In-Depth Information
X
y
i
p
(21.48)
i2I
y
i
2f
0;1;:::;p
g
8
i
2
I
(21.49)
x
jk
2f
0;1
g
8
j
2
J;k
2
K:
(21.50)
The objective function (
21.46
) maximizes the expected demand that is covered.
Note that this expression adds the expected coverage over all possible numbers of
ambulances. Constraints (
21.47
) ensure that the number of ambulances used to cover
j is bounded by the number of ambulances located not farther away than time T
from j. Constraints (
21.48
) impose that in total at most p ambulances are located.
Constraints (
21.49
)and(
21.50
) are the variable domain constraints. A heuristic for
the problem has also been devised in Daskin (
1983
).
21.3.1.3
Further Reading
In addition to the models presented in the previous sections, several more can be
found in the literature. Chapman and White (
1974
) proposed the first probabilistic
approach by considering a probabilistic set covering model in which servers are
not always available. Nowadays, different kinds of probabilistic approaches can
be found for ambulance location planning. They use, for example, reliability
constraints and busy fractions for servers. The same probabilistic approach is used
in the maximal cover location problem investigated by ReVelle and Hogan (
1988
).
The maximum availability location problem by ReVelle and Hogan (
1989
)isalso
worth mentioning. Overall, we can identify two main approaches for including
stochasticity into the ambulance location problem, namely hypercube queuing
models and stochastic programming. Larson (
1974
) introduced the first hypercube
queuing model which represents a general planning approach where a set of states
is considered as well as the transition probabilities between them. Based on that,
different variations can be found, such as in Geroliminis et al. (
2009
), Iannoni and
Morabito (
2007
), Iannoni et al. (
2011
), Silva and Serra (
2008
), and Takeda et al.
(
2007
). Stochastic programming approaches have also been proposed as it is the
case with the works by Beraldi et al. (
2004
), Beraldi and Bruni (
2009
), and Noyan
(
2010
).
21.3.2
The Operational Level: Ambulance Relocation
At an operational decision level, decisions usually concern the allocation of
ambulances to emergencies and the reassignment of ambulances to bases after
having finished a service. In addition, relocations of ambulances during some time
period (e.g., 1 day) are possible, and they can either be predefined or dynamically
