Geoscience Reference
In-Depth Information
X
x
ij
1
8
i
2
I
(21.57)
j2J
i
X
X
x
ij
p
(21.58)
i2I
j2J
x
ij
2f
0;1
g
8
i
2
I;j
2
J:
(21.59)
In this formulation, J
i
is the set of zones that can be reached by ambulance
i within a given time frame. The objective function (
21.54
) in conjunction with
constraints (
21.55
) (which ensure that
z
must not be smaller than any of the driving
times
ij
) represents the minimum time it will take so that the preparedness in each
zone is at least q
min
as prescribed in constraints (
21.56
). Hence, the left side of these
constraints can be interpreted as the preparedness for zone j that must be greater
or equal to a minimum value q
min
. Constraints (
21.57
) assure that each ambulance
can only be relocated to at most one zone in J
i
. Constraints (
21.58
) guarantee that at
most p ambulances are relocated in total. Finally, constraints (
21.59
) are the variable
domain constraints.
21.4
Hospital Layout Planning
A special class of location problems are layout planning problems which aim
at minimizing in-house travel distances or costs associated with the positions
of organizational units (OUs) inside a building. This class of problems mainly
originates from industrial applications for layout planning of public buildings.
Layout planning problems in healthcare were first introduced by Elshafei (
1977
).
He modeled a hospital layout problem as a quadratic assignment problem (QAP) and
developed heuristics to solve it. In the framework for hospital planning and control,
the hospital layout planning problem is classified as a resource capacity planning
problem on a strategic level (Hans et al.
2011
). Although it is a long term decision,
the spatial organization within hospitals directly influences the quality and efficiency
of healthcare and secondary services of the daily routine (Choudhary et al.
2010
;
Hignett and Lu
2010
) as well as patient satisfaction (Chaudhury et al.
2005
). The
challenge lies in developing a holistic approach in order to combine the architectural
and legal aspects with logistics, i.e., patient, personnel, and material flows inside the
future hospital building.
In the next section, the quadratic assignment problem (QAP) is presented.
Section
21.4.2
details a mixed-integer programming (MIP) formulation. Thereafter,
in Sect.
21.4.3
, suggestions for further reading are provided in order to show some
extensions of the presented QAP and MIP models with respect to the underlying
assumptions.
