Geoscience Reference
In-Depth Information
The objective function (
21.64
) minimizes the sum of the rectilinear distances of
all the flows between the centroids of the OUs. Constraints (
21.65
)and(
21.66
)are
needed in order to linearize the model given by Montreuil (
1991
): in order to get a
linear objective function, the auxiliary decision variables Ǜ
jk
;Ǜ
jk
;LJ
jk
and LJ
jk
have
to be introduced such that with (
21.65
)and(
21.66
), we have
LJ
LJ
Ǜ
j
Ǜ
k
LJ
LJ
D
Ǜ
jk
C
Ǜ
jk
and
LJ
LJ
LJ
j
LJ
k
LJ
LJ
D
LJ
jk
C
LJ
jk
. Constraints (
21.67
), (
21.68
)and(
21.69
) control the
lower and upper limits of the length, width and perimeter of the OUs, respectively.
The correct definition of the sides of the OUs as well as their location inside the
building is ensured by constraints (
21.70
)and(
21.71
). The centroid of each OU
is defined by constraints (
21.72
)and(
21.73
). The non-overlapping requirements for
the OUs are formulated by constraints (
21.74
)-(
21.76
). The domains of the decision
variables are given in constraints (
21.77
)-(
21.79
). We finally remark that the model
has been first used by Montreuil (
1991
) in order to devise a comprehensive modeling
framework which aims at integrating layout design and material flow network design
in material handling and logistics systems.
21.4.3
Further Reading
In this section, some possible extensions to the two models discussed in Sects.
21.4.1
and
21.4.2
are presented. Important characteristics which were not considered
above, but which are also of importance for hospital layout planning problems
comprise the consideration of multiple periods, multiple floors, multiple objectives
as well as uncertainty in patient, personnel, and material flows. Overall, there are
very few publications considering the application of layout planning problems in
hospitals from a mathematical perspective. General surveys on layout planning have
been conducted, among others, by Drira et al. (
2007
) and Singh and Sharma (
2006
).
Textbooks on facility layout planning and design are given by Tompkins et al. (
2010
)
and Heragu (
2008
).
A general review on dynamic layout problems which takes into account multiple
periods and, thus, changing process flows, is given by Balakrishnan and Cheng
(
1998
). A very recent approach for a multi-period ward layout planning problem
for hospitals has been presented by Arnolds and Nickel (
2013b
).
Since hospital buildings usually have more than one floor, another extension
comprises multiple floors. In this respect, the planning of elevators such as their
location, number, capacity and control is a quite new and challenging field that has
been addressed for example by Matsuzaki et al. (
1999
), Goetschalckx and Irohara
(
2007a
,
b
), and Krishnan et al. (
2009
). Further modeling and solution approaches
for multi-floor layout problems can be found in Bozer et al. (
1994
), Patsiatzis and
Papageorgiou (
2002
), and Meller and Bozer (
1997
).
In the last years, a number of papers has been published with respect to multiple
objectives (Chen and Sha
1999
,
2005
; Sha and Chen
2001
; Tenfelde-Podehl
2002
;
Aiello et al.
2006
; Chen and Rogers
2009a
,
b
; Bashiri and Dehghan
2010
). This is
