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Efficient Task Prioritisation for Autonomous Transport Systems

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The efficient distribution of scarce resources has been a challenge in many different fields of research. This paper focuses on the area of operations research, more specifically, Automated Guided Vehicles intended for pickup and delivery tasks. In time delivery in general and flexibility in particular are important KPIs for such systems. In order to meet in time requirements and maximising flexibility, three prioritisation methods embedded in a task allocation system for autonomous transport vehicles are introduced. A case study within the BMW Group aims to evaluate all three methods by means of simulation. The simulation results have revealed differences between the three methods regarding the quality of their solutions as well as their calculation performance. Here, the Flexible Prioritisation Window was found to be superior.
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EFFICIENT TASK PRIORITISATION
FOR AUTONOMOUS TRANSPORT
SYSTEMS
Maximilian Selmair
Vincent Pankratz
BMW Group
80788 Munich, Germany
Email: maximilian.selmair@bmw.de
Klaus-J¨urgen Meier
University of Applied Sciences Munich
80335 Munich, Germany
KEYWORDS
Automated Guided Vehicle; autonomous Automated
Guided Vehicle, Self-Driving Vehicle; Task Allocation;
Pick-up and Delivery; Prioritisation
ABSTRACT
The efficient distribution of scarce resources has been
a challenge in many different fields of research. This
paper focuses on the area of operations research, more
specifically, Automated Guided Vehicles intended for
pick-up and delivery tasks. In time delivery in gen-
eral and flexibility in particular are important KPIs for
such systems. In order to meet in time requirements
and maximising flexibility, three prioritisation methods
embedded in a task allocation system for autonomous
transport vehicles are introduced. A case study within
the BMW Group aims to evaluate all three methods by
means of simulation. The simulation results have re-
vealed differences between the three methods regarding
the quality of their solutions as well as their calculation
performance. Here, the Flexible Prioritisation Window
was found to be superior.
LIST OF ABBREVIATIONS
AGV Automated Guided Vehicle
FMS Flexible Manufacturing System
GAP Generalised Assignment Problem
HM Hungarian Method
ILP Integer Linear Programming
KPI Key Performance Indicator
NVA-share non-value-adding share
POI Point of Interest
SDV Self-driving Vehicle
STR Smart Transport Robot
VAM Vogel’s Approximation Method
VAM-nq Vogel’s Approximation Method for
non-quadratic Matrices
aAGV Autonomous Automated Guided Vehicle
INTRODUCTION
Constantly changing external conditions associated
with global competition, individualised customer de-
mands and more complex production structures force
companies to reorganise their production systems to
become more flexible (Braunisch 2015). Amongst
others, Flexible Manufacturing Systems (FMSs) rely
on so-called Autonomous Automated Guided Vehicles
(aAGVs), which are able to find the fastest way from a
source to a sink by themselves and drive around obsta-
cles, something that Automated Guided Vehicle (AGV)
are unable to achieve. The function of the superordi-
nate fleet management system is to allocate the trans-
portation tasks to agents in form of vehicles (Wagner
2018). According to Le-Anh and Koster (2006), there
are three different main criteria that ought to be con-
sidered when allocating tasks: time, utilisation and dis-
tance. The dispatching can be either static or dynamic.
When operating with static dispatching, a task alloca-
tion decision is made and carried out without consider-
ing system changes that occur during the execution of
said task (Gudehus 2012). These system changes (for
instance task urgency, deadline changes, machine mal-
functions) can make the planned sequence inoperative
(Ouelhadj and Petrovic 2009). Dynamic dispatching,
in contrast, adapts the planned sequence of the trans-
portation tasks to changes either in certain time inter-
vals or when a certain event happens. This increases
the flexibility of the task allocation process (Gudehus
2012). After a task is allocated to a vehicle, the ve-
hicle drives to the source of the task and collects the
material. Subsequently, it moves to the source and de-
livers the container at the designated place (sink). Dur-
ing this process, delays can occur due to pedestrians,
other vehicles or obstacles that have to be circumvented
(Clausen et al. 2013).
RELATED LITERATURE
The issue of transportation is an extensively studied
topic in operational research (D´ıaz-Parra et al. 2014).
Communications of the ECMS, Volume 34, Issue 1,
Proceedings, ©ECMS Mike Steglich, Christian Mueller,
Gaby Neumann, Mathias Walther (Editors)
ISBN: 978-3-937436-68-5/978-3-937436-69-2(CD) ISSN 2522-2414
The methods for solving the assignment problem aim
to minimise the total transportation costs while bring-
ing goods from several supply points (e. g. warehouses)
to demand locations (e. g. customers). In general, each
point of departure features a prearranged amount of
goods that can be distributed. Correspondingly, every
destination requires a certain amount of units (Shore
1970). The underlying use case, where tasks have to
be assigned to Self-driving Vehicles (SDVs), differs in
some regards from the classical transportation problem.
In our case, each vehicle has a capacity restriction of
one, i. e. a maximum of one load carrier can be trans-
ported at a time. Furthermore, each task corresponds
to a demand of one. This means that every task can
only be allocated to one single vehicle. In the research
domain, the just mentioned case is known as the Gener-
alised Assignment Problem (GAP). In an effort to min-
imise it, researchers aim for minimal costs Zbetween
ntasks and magents while each task is assigned to one
agent (Kundakcioglu and Alizamir 2009). According
to Srinivasan and Thompson (1973) the formulation of
the GAP is:
minimize Z =X
iI
X
jJ
cij xij (1)
In subject to the constraints:
X
jJ
rij xij bi, for iI(2)
X
iI
xij = 1, for jJ(3)
xij ∈ {0,1}, for iIand jJ(4)
A set of agents I={1,2, . . . , i, . . . }has to be as-
signed to a set of tasks J={1,2, . . . , j, . . . }. Variable c
is representing the costs accrued when the task jis allo-
cated to the agent i.rij represents the capacity which
is needed when the task jis allocated to the agent i.
Variable brepresents the available capacity of agent i
in total. The binary variable xij equals 1 if task jis
assigned to agent i, otherwise it remains 0.
There are several methods that solve the GAP. Be-
side optimisation methods like Integer Linear Program-
ming (ILP), there are, for example, algorithms like the
Hungarian Method (HM) proposed by Kuhn (1955),
Vogel’s Approximation Method (VAM) proposed by
Reinfeld and Vogel (1958) or Vogel’s Approximation
Method for non-quadratic Matrices (VAM-nq) pro-
posed by Selmair et al. (2019). The last method was
used in the simulation study of this paper due to its su-
perior calculation performance and satisfactory results
in terms of non-quadratic matrices.
DEVELOPED
PRIORITISATION METHODS
Solving the GAP minimises the transport costs, in
this case operationalised as meters driven, between
tasks and agents. For the presented use case, trans-
port costs can be equated to the transport distances or
– for prioritised orders – the transportation duration.
Minimising transport distances is an important goal as
it leads to faster task processing and less traffic on the
routes. As the transport route between source and sink
is the same for every vehicle, in this scenario only the
empty drive distance from the current location of each
vehicle to the source of a task is minimised.
If there are consistently more tasks than free vehi-
cles in a system, waiting times can occur for tasks that
could not be allocated in former allocation cycles due to
high transport costs or long pick-up distances. These
waiting times can cause the performance of the over-
all system. In automotive intralogistics, which oversees
the supply of parts to assembly lines, delays can cause
high costs and must be reduced as much as possible.
Consequently, the following prioritisation methods were
developed to unite efficiency and in time delivery in the
task allocation of autonomous transport systems.
Fix Prioritisation Window
The first prioritisation method presented here is the
Fix Prioritisation Window. This method was inspired
by the backwards calculation in dynamic task dispatch-
ing, which can be found in the article contributed by
Gudehus (2012). The idea behind this method is to
force the allocation of tasks that are at risk of becom-
ing delayed. When a task exceeds the point of time
where a in time delivery is critical, it is marked “priori-
tised” and is thus allocated in the next allocation cycle.
In this manner, any delays should be avoided. The pri-
oritisation window is the period between the deadline
of a task and time of prioritisation. During this time
the task must be allocated to a vehicle, the vehicle must
drive to the source and collect the material, drive to the
sink and deposit the material. This method requires
that the prioritisation window has the same length for
each task and is determined by analysing the data of
prior simulations.
The prioritisation window must allow enough time
for the transport vehicles to fulfil tasks with long dis-
tances between the source and the sink as well as in-
clude a buffer for unexpected delays. However, a too
generously planned prioritisation window will reduce
the system’s flexibility and thus impact negatively on
its efficiency. Furthermore, if too many tasks were to
become prioritised and had to compete for vehicles, de-
lays might become inevitable.
Flexible Prioritisation Window
The Flexible Prioritisation Window is quite similar
to the Fix Prioritisation Window, yet they differ in
that the Flexible Prioritisation Window assigns an in-
dividual time window for each task, depending on the
distance between source and sink and the time required
to cover this distance. In order to determine the du-
ration of this time window, an analysis of statistical
data is performed. In this case, the time between the
allocation of the task and the delivery is measured,
Parameter Characteristics
Prioritisation No Fix Prioritisation Flexible Prioritisation Bidding
Methods Prioritisation Window Window Approach
Number of Vehicles 10 25 50
Ratio Vehicles / Tasks 1 / 0.5 1 / 1 1 / 1.5 1 / 2
TABLE I:Experimental Plan illustrated as Morphological Box
Combination Fix Time Flexible Time
(vehicles / mission pool) Window Window
10 / 5 468 s 309 s
10 / 10 468 s 305 s
10 / 15 519 s 407 s
10 / 20 475 s 298 s
25 / 13 485 s 309 s
25 / 25 437 s 279 s
25 / 38 437 s 346 s
25 / 50 485 s 344 s
50 / 25 452 s 280 s
50 / 50 439 s 244 s
50 / 75 442 s 279 s
50 / 100 444 s 291 s
TABLE II:Fix and Flex Time Window Values for the Scenarios
of the Simulation-Study
but without the theoretical travel time between source
and sink (distance divided by the average speed of the
vehicle). This theoretical travel time is different for
each task and is added to the determined time window
value. This total duration represents the Flexible Pri-
oritisation Window, which is calculated individually by
backward-scheduling from the deadline of each task.
This approach can be considered an extension of the
Fix Prioritisation Window method. It is expected that
by means of the Flexible Prioritisation Window, fewer
tasks are going to be prioritised, which will result in
advantages in terms of efficiency and in time delivery.
Bidding Approach
The bidding approach adds a further strategy for
prioritising tasks increased in complexity. Its oper-
ation method is different from the former presented
approaches. The main difference being that this ap-
proach does not allocate prioritised tasks ahead of non-
prioritised tasks, but adjusts the transportation costs
when tasks become critical, ensuring these tasks are
allocated and are dispatched on time. This approach
was inspired by multi-attribute dispatching rules like
Lampe and Clausen (2006) or Klein and Kim (1996)
which take into account multiple criteria to determine
the priority / costs of a task. These multi-attribute
costs are processed by the GAP method which is solved
Vehicle delivers in time? Bidding Factor
Yes and more than two others 1
Yes and two others 0.7
Yes and one other 0.2
Yes – the only one 0.1
No 3
TABLE III:Bidding Factors for different Situations
by the VAM-nq heuristic developed by Selmair et al.
(2019).
The bidding factors that lower or raise the costs are
calculated by including the distance of pick-up and
transport from source to sink in a formula, to estab-
lish whether a vehicle is able to carry out the task in
time. The prioritisation window wis compared with
the period between the deadline of the task and the
current time. If wis smaller than the period between
the deadline and current time the task can be executed
on time.
w=dP+dS
v(1 + u) + tP+tD(5)
Where dPis the distance from the current location
of the vehicle to the source, dSis the distance between
the source and sink of the task, vis the average speed
of the vehicle, uis the uncertainty factor that increases
the travel time to compensate for unforeseen events, tP
is the time for collecting the material at the source, tD
is the time to deposit the material at the sink.
After ascertaining if the vehicle is able to fulfil the
task in time, the vehicle checks if it is the only one to do
so and recalculates the costs for the task with the bid-
ding factor in Table III. These factors were determined
by means of a parameter simulation.
SIMULATION STUDY
The following study built in the software AnyLogic
aims to examine whether the presented methods of pri-
oritisation achieve results that are similar in terms of ef-
ficiency to those obtained when solving the GAP with-
out prioritisation. The main KPI used to proof the
efficiency of the system will be the non-value-adding
share of vehicles. Vehicles are not adding value when
driving without any load – accordingly they are adding
value when delivering a load from a source to its sink.
The non-value-adding share of movement per task will
be referred simply to NVA-share in the further course.
Additionally, it is proposed that, by means of these
measures, better results in terms of deliveries in time
will be yielded. Therefore, the different methods were
tested in a simulation study with different scenarios
(see Table I).
The scenarios are simulated in a homogeneous grid-
structured production environment with a total length
of 4,072 meters in which a number of 5,000 tasks are
processed for each scenario. The ratio between vehi-
cles and tasks remains constant during every simula-
tion run. That is, every time a task is completed, a new
one appears – until the limit of 5,000 tasks is reached.
The vehicles move with a maximum speed of 1.5 m
s.
Their acceleration is parametrised to 1 m
s2, the deceler-
ation is set to 5 m
s2. The tasks must be performed at
an randomly selected point in time that lies between
9 to 15 minutes after a task has been generated. Ad-
ditionally, tasks are more likely to be allocated at the
beginning of said time interval. A solution is calcu-
lated in a cycle-time of 20 seconds to react to changes
in the system, such as the appearance of new tasks or
changes of the vehicles’ status. While picking up or de-
positing material, the vehicles lower their speed so that
the corresponding path is blocked for 25 seconds. In
actual industrial applications, during this time period,
the vehicles calculate the exact angle in which to drive
to the Point of Interest (POI), by means of information
gathered by 3D cameras.
The parameters of the Fix and Flexible Prioritisa-
tion Windows are determined by analysing the times
between allocation and delivery of a task in a simu-
lation run performed without prioritisation by using
the GAP for allocating the tasks. The final parame-
ter was set to the longest time that was measured for
each vehicle/ utilisation (v/u) combination (equals the
100 %-percentile) plus a 20-second-cycle time. Table II
shows the parameters for the Fix and Flexible Priori-
tisation Windows.
For the uncertainty variable uof the bidding ap-
proach, a value of 30% was used. This was based on the
average travel uncertainty of the combinations, which
lies between 20 % and 25 %. The set value includes a
small buffer for accidental uncertainties.
RESULTS
The following section provides a summary of the re-
sults with particular focus on the two main Key Per-
formance Indicators (KPIs): in time delivery and NVA-
share of the vehicles. Moreover, it was decided to only
include the results of simulation runs with 50 vehicles,
as all other scenarios yielded very similar behaviour.
In order to explore the lower range of values associ-
ated with the NVA-share of vehicles, a scenario free of
any prioritisation rules was utilised. This means that
for the task allocation determined by the GAP, all tasks
were assigned by following the fewest possible NVA-
share (from the overall system perspective) – without
imposing any deadlines and thus time pressure. In Fig-
ure 1, this value is represented by the first bar, from
25 50 75 100
0
50
100
size of task pool
meter
none FIFO FIX FLEX BIDDING
Fig. 1:Mean NVA-share per task for a scenario with
50 vehicles (5,000 Tasks)
25 50 75 100
0
1,000
2,000
size of task pool
lately delivered tasks
FIFO FIX FLEX BIDDING
Fig. 2:Late Tasks of the original FIFO method and the three
developed prioritisation approaches (5,000 Tasks)
25 50 75 100
0
5,000
10,000
size of task pool
prio allocations
FIX FLEX
Fig. 3:Total Allocations with Priority for the fix and flex
approach (5,000 Tasks) – Each task can be assigned more than
once if decisions are frequently changed
left to right, of every group, where each group repre-
sents one scenario of utilisation. The different levels
of utilisation are achieved by keeping the simultaneous
task pool sizes constant (25, 50, 75 and 100 tasks).
The second bar in Figure 1 represents the origi-
nally applied task allocation strategy: first-in-first-out
in combination with the nearest-agent-first policy. For
the first scenario with a pool of 25 tasks, the system can
freely select the closest of two vehicles, as the task to ve-
hicle ratio is favourable at 1: 2. As the number of tasks
exceeds 50, substantially changing the allocation ratio,
the system’s choice is restricted to only one idle vehi-
cle, which may not be the closest. It follows that the
pick-up distances, measured in meters, are thus more
likely to exceed 120 m.
For low utilisation scenarios (25 and 50 tasks), the
fix and the flex approaches yield results close to those
of the bidding approach with a maximum difference of
18 %. For a high utilisation (100 tasks), the NVA-share
per task is 40 % higher than for the bidding approach.
This will be elucidated further in the discussion.
The next three bars in the same Figure, bars 3 to
5, represent the pick-up meters for the three developed
prioritisation methods in combination with the assign-
ment by means of the GAP. For low utilisation levels,
e. g. 25 and 50 tasks in the pool, all three prioritisa-
tion methods are quite similar to the “optimal” first
bar which is not involving any prioritisation. The dif-
ferences are only between 1 % and 8 %.
To evaluate all three methods, a closer look at the
respective late tasks is deemed essential. Figure 2 il-
lustrates the number of late orders for each scenario of
utilisation. For the first scenarios with task pools of 25
and 50, all methods resulted in late orders below 0.3 %.
However, the initially applied FIFO method resulted in
6 % late orders for the scenario with 75 tasks, that is,
as soon as the content of the task pool exceeded the
number of available vehicles. The high-pressure sce-
nario with a task pool of 100, yielded late orders for
every applied method. 55 % were on time when apply-
ing the FIFO rule, the fix approach delivered 93% of
all orders on time, while the flex approach resulted in
97 % of tasks being delivered on schedule. The results
of the bidding approach in combination with the high
utilisation scenario showed that only 86% of all orders
were able to be delivered on time.
DISCUSSION
The previously presented simulation results support
the notion that the three methods, developed within
this scope of research, are quite similar in terms of effi-
ciency (see Figure 1). Furthermore, in high utilisation
scenarios (75 and 100 tasks), all three methods yielded
superior results in comparison to the currently applied
FIFO method (see also Figure 1). Based on the concept
that the fix and flex approach will prioritise more tasks
in a high utilisation than in a low utilisation scenario
(see Figure 3), it was expected that for high utilisation
scenarios, the pick-up meters would exceed those of the
scenarios without prioritisation. That is, all three ap-
proaches reduce flexibility and force the system to allo-
cate urgent tasks immediately and these priority-tasks
are delivered as fast as possible instead of way-efficient.
That means, that the bidding approach is able to
prioritise each scenario with only little impact on NVA-
share of vehicles in terms of meters. Nonetheless, it is
presumed that the late tasks contribute to this out-
Fig. 4:The Smart Transport Robot (STR) of the BMW Group
in its natural habitat
come: starting with the scenario of 75 tasks, the bid-
ding approach begins to deliver undesirable results. In
order to ascertain the reason behind this, a close look
at the calculation method of the bidding approach was
necessary. In this approach, the calculation effort for
urgent tasks is scaled down to support an urgent allo-
cation. When handling more tasks with fewer available
vehicles, the calculation efforts are scaled down in the
calculation matrix for formulating the GAP. This leads
to a reduction in the relative differences between the
already scaled down efforts. Subsequently, tasks which
are located peripherally are more likely to be processed
than others. Especially these tasks contribute to the
large number of delayed deliveries. Furthermore, the
bidding approach is the approach with the highest cal-
culation effort of all three introduced methods due to
its complexity.
The fix and the flex approach yielded comparatively
good results, both in terms of the distance of NVA-
share as well as number of late tasks. The disadvantage
of the fix and flex approach is associated with their
independence regarding their possible vehicle choice.
This independence is assessed through a time buffer
that leads to lower flexibility, which in turn ensures
that tasks are processed in time. The advantage of
both methods is the low calculation effort: only one
statistical value has to be determined in advance and
applied continuously to each task. As described in the
Section Simulation Study, this value is determined by
using the 100 %-percentile. Due to this fact, most of the
values are ascertained with a long buffer (see Table II).
Nevertheless, this technique is necessary to ensure a
minimal number of delayed tasks.
CONCLUSION
This paper has introduced three prioritisation ap-
proaches for a task allocation system of a transport ve-
hicle system. All approaches differ in their complexity
and calculation efforts. To evaluate their suitability for
industrial application, all approaches were compared
by means of simulation. Three different fleet sizes and
four levels of utilisation were combined in order to as-
sess performance under a variety of conditions. For the
evaluation, two KPIs were focused on: the number of
late tasks and the NVA-share in the system, mapped
as average distance per task. While the significance of
the first KPI is presumed to be self-evident, the im-
portance of the second KPI is associated with resource
conservation. That is, by minimising the NVA-share,
fewer traffic conflicts occur, which allows traffic to flow
more smoothly.
On the whole, all three approaches have qualified
for regular utilised transport vehicle systems due to
their ability to ensure that tasks are delivered in time.
For performance and robustness reasons, the fix and
flex approach are suggested to be more economically
attractive within actual industrial use-cases. At the
BMW Group, the flex approach has been implemented
in a self-developed and self-built transport vehicle sys-
tem (see Figure 4). The critical factor for this decision
were the readily comprehensible calculation effort and
the consistently positive results.
Further research might evolve the methods in order
to provide a higher flexibility to the system whenever
possible. Currently, the statistical determined values of
Table II are overstated for the most tasks. This issue
might be tackled in the next level of development.
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MAXIMILIAN SELMAIR is doctoral
student at the University of Plymouth.
Recently employed at the SimPlanAG, he
was in charge of projects in the area of
material flow simulation. Currently, he is
working on his doctoral thesis with a fel-
lowship of the BMW Group. His email
address is: maximilian.selmair@bmw.de
and his website can be found at maxim-
ilian.selmair.de.
VINCENT PANKRATZ contributed
to the paper during his master thesis
which was written in collaboration with
the BMW Group. With this thesis, he
finished his logistics studies at the Re-
gensburg University of Applied Sciences
and works now for a renowned automo-
tive company. His email address is: vin-
cent.pankratz@gmx.de.
KLAUS-J ¨
URGEN MEIER holds the
professorship for production planning and
logistic systems in the Department of
Engineering and Management at the
University of Applied Sciences Munich
and he is the head of the Institute
for Production Management and Logis-
tics (IPL). His email address is: klaus-
juergen.meier@hm.edu.
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The efficient allocation of tasks to vehicles in a fleet of self-driving vehicles (SDV) becomes challenging for large-scale systems (e. g. more than hundred vehicles). Operations research provides different methods that can be applied to solve such assignment problems. Integer Linear Programming (ILP), the Hungarian Method (HM) or Vogel's Approximation Method (VAM) are frequently used in related literature (Paul 2018; Dinagar and Keerthivasan 2018; Nahar et al. 2018; Ahmed et al. 2016; Koruko˘ glu and Ballı 2011; Balakrishnan 1990). The underlying paper proposes an adapted version of VAM which reaches better solutions for non-quadratic matrices, namely Vogel's Approximation Method for non-quadratic Matrices (VAM-nq). Subsequently, VAM-nq is compared with ILP, HM and VAM by solving matrices of different sizes in computational experiments in order to determine the proximity to the optimal solution and the computation time. The experimental results demonstrated that both VAM and VAM-nq are five to ten times faster in computing results than HM and ILP across all tested matrix sizes. However, we proved that VAM is not able to generate optimal solutions in large quadratic matrices constantly (starting at approx. 15 × 15) or small non-quadratic matrices (starting at approx. 5 × 6). In fact, we show that VAM produces insufficient results especially for non-quadratic matrices. The result deviate further from the optimum if the matrix size increases. Our proposed VAM-nq is able to provide similar results as the original VAM for quadratic matrices, but delivers much better results in non-quadratic instances often reaching an optimum solution. This is especially important for practical use cases since quadratic matrices are rather rare.
Chapter
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Introduction Extensions Multiple-Resource Generalized Assignment Problem Multilevel Generalized Assignment Problem Dynamic Generalized Assignment Problem Bottleneck Generalized Assignment Problem Generalized Assignment Problem with Special Ordered Set Stochastic Generalized Assignment Problem Bi-Objective Generalized Assignment Problem Generalized Multi-Assignment Problem Methods Exact Algorithms Heuristics Conclusions References
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