Robust Emergency System Design using Reengineering Approach
Marek Kvet and Jaroslav Janáček
Faculty of Management Science and Informatics, University of Žilina,
Univerzitná 8215/1, 010 26 Žilina, Slovakia
Keywords: Robust Emergency System Design, Detrimental Scenarios, Reengineering Approach.
Abstract: A robust emergency service system is usually designed so that the deployment of given number of service
centers minimizes the maximal value of objective functions corresponding with the specified detrimental
scenarios. If the problem is solved by any solving technique based on the branch-and-bound method, the min-
max link-up constraints cause bad convergence of the associated computational process. Within this paper,
we try to overcome the drawback following from the link-up constraints by usage of an iterative process
applied to a series of surrogate problems. The surrogate problems represent a simple emergency system
reengineering under a given scenario and chosen values of reengineering parameters. The results of the
surrogate problems are used for considerable reduction of the initial set of possible service center locations.
The robust emergency service system is obtained as the optimal solution of the reduced problem. We provide
the reader with a comparison of the original min-max problem solution to the suggested approach.
1 INTRODUCTION
The emergency system design problem is a
challenging task for system designer focusing on
satisfaction of future demands of the system users in
case of emergency. Emergency service system
performance is considerably influenced by
deployment of the service centers, which send
emergency vehicles to satisfy demands on service at
the system users’ locations. The number of service
providing centers is usually limited. As the quality
characteristic of the design corresponds to an average
response time of the system on a demand raised by
a user, then the emergency service system design can
be tackled as the weighted p-median problem, which
was studied in (Current et al., 2002, Ingolfsson et al.,
2008, Jánošíková, 2007, Snyder and Daskin, 2005).
As far as the usage of a general IP-solver is
concerned, the size of the solved integer
programming problem must be taken into account. In
the real problems, the number of serviced users takes
the value of several thousands, and the number of
possible service center locations can take this value
as well (Avella et al., 2007). The number of possible
service center locations seriously impacts the
computational time and the memory demands due to
used branch-and-bound method, which stores the
unfathomed nodes of the inspected searching tree for
the further processing. That is why the direct attempt
at solving the problem described by a location-
allocation model often fails, when larger instances are
solved by a commercial IP-solver. Mentioned
weakness has led to the development of so-called
radial approach, successfulness of which is based on
the fact that there is only finite set of radii, which must
be taken into account (Elloumi et al., 2004, García et
al., 2011, Janáček, 2008). Simultaneously, several
heuristic and approximate approaches have been
developed to get a good solution of the problem in a
short time (Doerner, K.F., et al. 2005, Gendreau, M.
and Potvin, J., 2010).
When the emergency service system is designed,
the designer must take into account that the response
time might be impacted by various random events
caused by partial disruptions of the road network.
That is why; the system resistance to such critical
events is demanded. Host of approaches to increasing
the emergency system resistance (Correia and
Saldanha da Gama, 2015, Kvet and Janáček, 2017b,
Pan et al., 2014, Scaparra and Church, 2015) are
based on incorporating possible failure scenarios into
model of the robust service system design problem.
Focusing on the objective function value of the robust
system design, the most frequently used objective
function consists in minimizing the maximal
objective function of the individual instances
172
Kvet, M. and Janá
ˇ
cek, J.
Robust Emergency System Design using Reengineering Approach.
DOI: 10.5220/0008946401720178
In Proceedings of the 9th International Conference on Operations Research and Enterprise Systems (ICORES 2020), pages 172-178
ISBN: 978-989-758-396-4; ISSN: 2184-4372
Copyright
c
2022 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
corresponding with particular scenarios. It follows
that the min-sum objective function used in the
classical weighted p-median problem is replaced by
the min-max criterion. The associated min-max
model uses link-up constraints to limit from above the
individual scenario min-sum objectives by their upper
bound corresponding to the objective function of the
min-max model. In addition, incorporating
the scenarios into the mathematical programming
model causes that the model magnifies its size
proportionally to the cardinality of the scenario set.
Both the model structure and its magnified size
represent an undesirable burden of the computational
process of most available IP-solvers. Thus,
complementary approximate approaches to the
robustness constitute a big challenge to operational
researchers and professionals in applied informatics
(Janáček and Kvet, 2017, Kvet and Janáček, 2017a,
Kvet and Jaček, 2017b). In this paper, we present
an attempt to the robust emergency system design.
We based our approximate approach on replacing the
computational process of the huge original problem
solution with a series of solving processes of the
much simpler problems. Each of the simpler
problems represents the problem of reengineering
(Brotcorne, L. et al., 2003, Guerriero, F. et al., 2016,
Schneeberger, K. et al. 2016) of some original service
center deployment under a given scenario (Kvet and
Janáček, 2018). This approach enables us to identify
the most important changes in the service center
deployment to react on the individual scenarios.
Having inspected all considered scenarios, we can
reduce the set of possible center locations and then
solve much smaller min-max problem with the
original set of scenarios.
The remainder of this paper is organized as
follows: Section 2 is devoted to the description of
original min-max robust design of emergency system,
in which all scenarios and possible center locations
are taken into account either as fixed for center
location or either free or forbidden for locating
a service center. The approach based on system
reengineering process used for identification of
the important locations is explained in Section 3. The
next section contains a description of the complete
iterative approach. The fifth Section contains the
overview of performed numerical experiments and
yields brief comparative analysis of designed service
center deployments. The results and findings are
summarized in Section 6.
2 ROBUST EMERGENCY
SYSTEM DESIGN PROBLEM
The robust emergency system design problem can be
modelled using the following data structures and
decision variables. Symbols J and I will denote the set
of users’ locations and the set of possible service
center locations respectively. The set I will be
partitioned into three subsets F1, F0 and V, where set
F1 contains the locations, in which a service center
must be located. Set F0 consists of center locations,
where no center can be temporarily located, and V is
the set of possible locations, from which p service
centers must be chosen. Symbol b
j
denotes the
number of users sharing the location j. Symbol U
denotes the set of considered failure scenarios.
The response time following from the distance
between locations i and j under a specific scenario
uU is denoted as d
iju
. In this paper, we consider that
each value of d
iju
is integer and less than or equal to
the maximal value D
max
. As we want to make the
system resistant to the individual detrimental
scenarios, the objective function of the robust system
design turns into minimizing the maximal objective
function of the individual scenarios.
Complexity of location problems with limited
number of facilities to be deployed and the necessity
to solve large instances of the problem led the radial
formulation of the problem, which could considerably
accelerate the associated solving process (Kvet and
Janáček, 2017b). As this concept proved to be a
suitable tool, we decided to use the radial formulation
also for the robust emergency system design.
To complete the associated mathematical model,
we introduce the following decision variables. The
variable y
i
{0,1} models the decision on service
center location at the location iV. The variable takes
the value of 1 if a service center is located at i and it
takes the value of 0 otherwise. In the robust problem
formulation, the variable h denotes the upper bound
of the objective functions over the set U of scenarios.
Let us define v= D
max
-1. Next, auxiliary zero-one
variables x
jsu
for s = 0 … v and uU are introduced
to complete the radial model. The variable x
jsu
takes
the value of 1, if the response time of the nearest
service center to the user at j J under the scenario
uU is greater than s and it takes the value of 0
otherwise. Then the expression x
j0u
+ x
j1u
+ … + x
jvu
constitutes the value of response time d
ju*
under the
scenario uU. We introduce a zero-one constant a
iju
s
under the scenario uU for each triple [i, j, s], where
iV
F1, jJ, s[0..v]. The constant a
iju
s
is equal to
1, if the response time d
iju
of a center located at i on a
Robust Emergency System Design using Reengineering Approach
173
user located at j is less than or equal to s, otherwise
a
iju
s
is equal to 0. Then the model, in which the
maximum of the objective function values over
the set U is minimized, follows.
M
inimize h
(1)
1
:1
,0,1 ,
ss
jsu iju i iju
iV iF
Subject to x a y a
for j J s , ,v u U




(2)
i
iV
yp
(3)
0
v
jjsu
jJ s
bx hforuU


(4)
{0, 1}
i
y
for i V
(5)
0,0,1,
jsu
x
for j J s , ,v u U
(6)
0h
(7)
The objective function (1) represents the upper
bound of all objective function values over the
individual scenarios. The constraints (2) ensure that
the variables x
jsu
are allowed to take the value of 0, if
at least one center is located in radius s from the user
location j. The constraint (3) limits the number of
service centers located in V by p. The link-up
constraints (4) ensure that each perceived disutility is
less than or equal to the upper bound h. As the
obligatory constraints (6) are concerned, only values
zero and one are expected in any feasible solution.
Nevertheless, it can be seen that the model has
integrality property concerning the variables x
jsu
. It
follows that the relevant values of x
jsu
in the optimal
solution will be equal to one or zero without imposing
binary constraints upon these variables.
For purpose of conciseness, we introduce the
denotation of the set of resulting (optimal) service
center locations as IR(U,F1,F0). The set includes
service centers from both F1 and V.
3 EMERGENCY SERVICE
SYSTEM REENGINEERING
PROBLEM
The emergency system reengineering was originally
studied in (Kvet and Janáček, 2018), where the radial
model of the problem was also employed. The basic
idea follows from the analysis of current service
center deployment, which may not be optimal due to
changing demands and development of the
underlying transportation network.
To describe the problem of the system average
response time minimization by changing the
deployment of centers belonging to a given sub-set of
the located centers. Let I be a finite set of all possible
center locations. As above, the response time
following from the distance between locations i and j
under a specific scenario uU is denoted as d
iju
. The
current emergency service center deployment is
described by union of two disjoint sets of located
centers L and F1, where I
L
contains p centers under
reconstruction and F1 is the set of fixed centers.
The center locations from I
L
can be relocated within
the set I- F1-F0, where F0 is the set of temporarily
forbidden locations.
When reengineering of an emergency service
system is performed, the administrator of the system
sets up parameters of rules to prevent a designer of
new center deployment from changes, which can be
perceived by system users as obnoxious. We consider
two formal rules within this study. The first rule limits
the total number w of the centers, which locations can
be changed. The second rule limits the time distance
between current and newly suggested location of
a service center by the given value D. To be able to
formulate the rules in a concise way, we derive
several auxiliary structures.
Let N
t
={i I- F1-F0: d
ti
D} denote the set of all
possible center locations, to which the center tL can
be moved subject to limited length of the move.
Additionally, symbol S
i
={tL: iN
t
} denotes a set of
all centers of L, which can be moved to i I- F1-F0
subject to the mentioned limitation. Now, we
introduce series of decision reallocation variables,
which model the decisions on moving centers from
their original positions to new ones. The variable
u
ti
{0, 1} for tL and iN
t
takes the value of one, if
the service center at t is to be moved to i and it takes
the value of zero otherwise.
For the given scenario uU the problem can be
formulated as follows.
1
0
m
j
js
jJ s
inimize b x


(8)
10 1
:1
,0,1
ss
js iju i iju
iIF F iF
Subject to x a y a
for j J s , ,v



(9)
ICORES 2020 - 9th International Conference on Operations Research and Enterprise Systems
174
10
i
iIF F
yp

(10)
i
iL
ypw

(11)
1
t
ti
iN
ufortL

(12)
10
i
ti i
tS
uy foriIFF

(13)
{0, 1} ,
ti t
ufortLiN
(14)
{0, 1} 1 0
i
yforiIFF
(15)
0,0,1
js
x
for j J s , ,v
(16)
As the constraints (9), (10) and formulae together
with used decision variables were explained in the
previous section, we restrict explanation only on
remainder of the above model. Constraint (11) limits
the number of changed center locations by
the constant w. Constraints (12) allow moving the
center from the current location t to at most one other
possible location in the radius D. Constraints (13)
enable to bring at most one center to a location i
subject to condition that the original location of the
brought center lies in the radius D. These constraints
also assure consistency among the decisions on move
and decisions on center location.
To be concise in the next explanation, we
introduce the denotation of the set of resulting
(optimal) service center locations for given scenario
u as I(u,F1,F0,L,w,D). The set also includes the
service centers from F1.
4 APPROXIMATE APPROACH
TO THE ROBUST SERVICE
SYSTEM DESIGN
To formulate the suggested approximate algorithm
for solving of the robust service system design, we
employ the procedures IR(U,F1,F0) and
I(u,F1,F0,L,w,D) introduced in Section 2 and Section
3 respectively. We assume that the data structures J,
{b
j
}, I, U, {d
iju
} introduced in Section 2 are given and
the number p of centers to be located is also known.
As the set U of scenarios contains one special
scenario b corresponding to standard conditions, we
start the process of designing the robust system with
solving the weighted p-median problem for time
distances {d
ijb
}. This problem can be described by the
model (8)-(10), (15), (16).The resulting set of p center
locations will be denoted as L.
Then we set parameters w and D of the algorithm
at chosen values from the ranges [1 .. p] and [1 .. D
max
]
respectively. We set F1=
and F0=
. The
suggested algorithm consists of two following steps.
1. For each u
U-{b} compute the set
One(u)= I(u,F1,F0,L,w,D).
2. Set F1=
()
∈{}
and
F0=−
()
()
and compute
Output= IR(U,F1,F0).
The objective function value of the resulting
center deployment Output can be enumerated
according to (17).

()maxmin: :
j iju
jJ
f
Output b d i Output u U


(17)
5 NUMERICAL EXPERIMENTS
The presented numerical experiments were focused
on comparison of the presented approximate
approach to the exact method of the robust emergency
system design from the points of computational time
and the solution accuracy. We performed the
numerical experiments using the optimization
software FICO Xpress 8.3 (64-bit, release 2017). The
experiments were run on a PC equipped with the
Intel® Core™ i7 5500U processor with the
parameters: 2.4 GHz and 16 GB RAM.
The used benchmarks were derived from the real
emergency health care system, which was originally
implemented in seven regions of Slovak Republic.
For each self-governing region from the following list
of region names followed by their abbreviations, all
cities and villages with corresponding population b
j
were taken into account. The mentioned list contains
Bratislava (BA), Banská Bystrica (BB), Košice (KE),
Nitra (NR), Prešov (PO), Trenčín (TN), Trnava (TT)
and Žilina (ZA). The coefficients b
j
were rounded to
hundreds. In the benchmarks, the set of communities
represents both the set J of users’ locations and the set
I of possible center locations as well. The cardinalities
of these sets are reported in Table 1 together with the
number p of located centers. The network time -
Robust Emergency System Design using Reengineering Approach
175
distances from a user to the nearest located center
were derived from the real transportation network.
Due to the lack of scenario benchmarks for the
experiments, the problem instances used in our
computational study were created in the way used in
(Janáček and Kvet, 2016). There were selected one
quarter of matrix rows so that these rows
corresponded to the biggest cities concerning the
number of system users. Then same of them were
chosen randomly and the associated time distance
values were multiplied by the randomly chosen
constant from the numbers 2, 3 and 4. The rows,
which were not chosen by this random process, stay
unchanged. This way, 10 different scenarios were
generated for each self-governing region.
The first series of experiments was performed so
that the exact model (1) - (7) was used to obtain the
optimal solution of the robust emergency system
design problem. The achieved results of the first
series are reported in Table 1. The computational
times in seconds are given in the column denoted by
CT and the optimal objective function values are
reported in the column denoted by ObjF
robust
.
Table 1: Results of the exact approach for robust service
system designing applied on the self-governing regions of
Slovakia.
Region |I| p CT ObjF
robust
BA 87 9 52.8 25417
BB 515 52 1605.0 18549
KE 460 46 1235.5 21286
NR 350 35 11055.1 24193
PO 664 67 3078.2 21298
TN 276 28 616.6 17535
TT 249 25 563.8 20558
ZA 315 32 1304.7 23004
The next series of experiments was performed
with the goal to find a suitable setting of the
parameters w and D used in the approximate
approach, see model (8) – (16) of the reengineering
process. For this study, the benchmark Žilina (ZA)
was used. In this portion of experiments, the
parameter p was set at the value 32 reported in Table
1. The maximal radius D was fixed at one of the
values 5, 10, 15, 20 and 25 and the maximal number
w of centers allowed to change their locations was set
to p/4, p/2, 3p/4, and p respectively. The results of this
series of experiments are summarized in Table 2.
Table 2: Detailed results of numerical experiments for the
self-governing region of Žilina: computational study of the
impact of individual parameters on the results accuracy.
w D CT SCT [%] ObjF
approx
gap [%] HD
8 5 231.6 82.25 23411 1.77 14
8 10 430.9 66.98 23377 1.62 14
8 15 502.8 61.46 23236 1.01 6
8 20 516.8 60.39 23359 1.54 10
8 25 529.5 59.42 23359 1.54 10
16 5 234.8 82.00 23411 1.77 14
16 10 455.1 65.12 23377 1.62 14
16 15 516.0 60.45 23236 1.01 6
16 20 529.9 59.38 23359 1.54 10
16 25 542.6 58.41 23359 1.54 10
24 5 232.5 82.18 23411 1.77 14
24 10 434.6 66.69 23377 1.62 14
24 15 508.5 61.02 23236 1.01 6
24 20 531.3 59.28 23359 1.54 10
24 25 534.6 59.02 23359 1.54 10
32 5 231.6 82.25 23411 1.77 14
32 10 427.8 67.21 23377 1.62 14
32 15 509.2 60.97 23236 1.01 6
32 20 531.4 59.27 23359 1.54 10
32 25 534.8 59.01 23359 1.54 10
Each row of the table corresponds to one setting
of the parameters w and D. In this portion of
experiments, several characteristics were studied.
The computational time in seconds is reported in the
column denoted by CT. Since the approximate
approach proved to be much faster than the exact one,
the percentage save of computational time SCT was
computed. Here, the computational time of the exact
approach was taken as the base. Furthermore, the
objective function associated with the obtained
service center deployment is reported in the column
denoted by ObjF
approx
. To evaluate the accuracy of
suggested approximate method, the value of gap was
also computed. It expresses the difference between
the objective function values of the exact and
approximate models. The objective value of the exact
approach was taken as the base. The value of gap is
reported also in percentage. Finally, the resulting
service center deployments were compared in the
terms of Hamming distance of the vectors of location
variables y. This value is denoted by HD.
It can be seen that the lowest computational time
of the approximate method was reached for the
settings w = p/4 and D = 5. As the associated gap was
acceptable, we used this setting in the third series of
experiments, which was performed for each self-
governing region. The obtained results are reported in
Table 3, where the same denotations as in Tables 1
and 2 were used. The table is divided into two
sections denoted by EXACT and APPROXIMATE.
The first section contains the results from Table 1 for
bigger comfort of the readers. The second section
ICORES 2020 - 9th International Conference on Operations Research and Enterprise Systems
176
contains the results obtained by the approximate
approach for each of considered benchmarks.
Table 3: Comparison of the approximate approach to the
exact approach applied on the self-governing regions of
Slovakia. Parameters of the approximate approach were set
in this way: w = p/4, D = 5.
EXACT APPROXIMATE
CT ObjF
robust
CT ObjF
approx
gap HD
BA 52.8 25417 11.8 26197 3.07 4
BB 1605.0 18549 679.8 18861 1.68 12
KE 1235.5 21286 633.4 21935 3.05 16
NR 11055.1 24193 274.2 24732 2.23 14
PO 3078.2 21298 1601.9 21843 2.56 20
TN 616.6 17535 223.1 17851 1.80 10
TT 563.8 20558 152.4 20980 2.05 10
ZA 1304.7 23004 231.6 23411 1.77 14
6 CONCLUSIONS
This paper was focused on mastering dimensionality
of the robust emergency system design problem using
commercial IP-solver. The robustness follows the
idea of making the system resistant to various
randomly occurring detrimental events. The original
approach with the min-max objective function value
proved to be extremely time consuming due to the
fact, that the min-max link-up constraints cause bad
convergence of the branch-and-bound method. This
obstacle can be overcome by presented approximate
solving method, which is based on reengineering
approach applied on individual scenarios. The
approximate approach enables to obtain the resulting
robust service center deployment in the
computational time, which is much less than half of
the computational time demanded by the exact
approach. As concerns the accuracy of the resulting
solution, it can be observed that the approximate
method is very satisfactory. Thus, we can conclude
that we have presented a very useful tool for robust
service system designing.
The future research in this field could be aimed at
other approximate techniques, which will enable to
reach shorter computational time under the
acceptable solution accuracy. Another future research
goal could be focused on mastering the presented
problem with larger set of detrimental scenarios.
ACKNOWLEDGEMENT
This work was supported by the research grants
VEGA 1/0342/18 "Optimal dimensioning of service
systems", VEGA1/0089/19 “Data analysis methods
and decisions support tools for service systems
supporting electric vehicles” and APVV-15-0179
"Reliability of emergency systems on infrastructure
with uncertain functionality of critical elements".
REFERENCES
Avella, P., Sassano, A., Vasil’ev, I., 2007. Computational
study of large scale p-median problems. In
Mathematical Programming, Vol. 109, No 1, pp. 89-
114.
Brotcorne, L., Laporte, G., Semet, F. 2003. Ambulance
location and relocation models. European Journal of
Operational Research 147, pp. 451–463.
Correia, I. and Saldanha da Gama, F. 2015 Facility
locations under uncertainty. In Laporte, G. Nikel, S. and
Saldanha da Gama, F. (Eds). Location Science,
Heidelberg: Springer Verlag, pp. 177-203.
Current, J., Daskin, M., Schilling, D., 2002. Discrete
network location models. In Drezner Z. (ed) et al.
Facility location. Applications and theory, Berlin,
Springer, pp. 81-118.
Doerner, K. F. et al., 2005. Heuristic solution of an
extended double-coverage ambulance location problem
for Austria. In Central European Journal of Operations
Research, Vol. 13, No 4, pp. 325-340.
Elloumi, S., Labbé, M., Pochet, Y., 2004. A new
formulation and resolution method for the p-center
problem. INFORMS Journal on Computing 16, pp. 84-
94.
García, S., Labbé, M., Marín, A., 2011. Solving large p-
median problems with a radius formulation. INFORMS
Journal on Computing, Vol. 23, No 4, pp. 546-556.
Gendreau, M., Potvin, J. 2010. Handbook of
Metaheuristics, Springer Science & Business Media,
648 p.
Guerriero, F., Miglionico, G., Olivito, F. 2016. Location
and reorganization problems: The Calabrian health care
system case. European Journal of Operational
Research 250, pp. 939-954.
Ingolfsson, A., Budge, S., Erkut, E., 2008. Optimal
ambulance location with random delays and travel
times, In Health Care Management Science, Vol. 11,
No 3, pp. 262-274.
Janáček, J., 2008. Approximate Covering Models of
Location Problems. In Lecture Notes in Management
Science: Proceedings of the 1st International
Conference ICAOR, Yerevan, Armenia, pp. 53-61.
Janáček, J. and Kvet, M. 2016. Designing a Robust
Emergency Service System by Lagrangean Relaxation.
In Proceedings of the conference Mathematical
Methods in Economics, September 6th -9th 2016,
Liberec, Czech Republic, pp. 349-353.
Janáček, J. and Kvet, M. 2017. An Approach to Uncertainty
via Scenarios and Fuzzy Values. Croatian Operational
Research Review 8 (1), pp. 237-248.
Robust Emergency System Design using Reengineering Approach
177
Jánošíková, Ľ. 2007. Emergency Medical Service Planning.
Communications Scientific Letters of the University of
Žilina, 9(2), pp. 64-68.
Kvet, M. and Janáček, J. 2017a. Hill-Climbing Algorithm
for Robust Emergency System Design with Return
Preventing Constraints. In 9th International Conference
on Applied Economics: Contemporary Issues in
Economy, 2017, Toruń, Poland, pp. 156-165.
Kvet, M. and Janáček, J. 2017b. Struggle with curse of
dimensionality in robust emergency system design. In
Proceedings of the 35th international conference
Mathematical Methods in Economics MME 2017,
September 13th -15th 2017, Hradec Králové, Czech
Republic, pp. 396-401.
Kvet, M. and Janáček, J. 2018. Reengineering of the
Emergency Service System under Generalized
Disutility. In the7th International Conference on
Operations Research and Enterprise Systems ICORES
2018, Madeira, Portugal, pp. 85-93.
Pan, Y., Du, Y. and Wei, Z. 2014. Reliable facility system
design subject to edge failures. American Journal of
Operations Research 4, pp. 164-172.
Scaparra, M.P., Church, R.L. 2015. Location Problems
under Disaster Events. Location Science, eds. Laporte,
Nikel, Saldanha da Gama, pp. 623-642.
Schneeberger, K. et al. 2016. Ambulance location and
relocation models in a crisis. Central European Journal
of Operations Research, Vol. 24, No. 1, Springer, pp.
1-27.
Snyder, L. V., Daskin, M. S., 2005. Reliability models for
facility location; The expected failure cost case. In
Transport Science, Vol. 39, No 3, pp. 400-416.
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