Published in: Proc. of 38th CIRP International Seminar on Manufacturing Systems.
Florianopolis, Brazil, 2005, CD-ROM.
Modelling and Analysis of Autonomous Shop Floor Control
B. Scholz-Reiter (2), M. Freitag, Ch. de Beer, Th. Jagalski
Department of Planning and Control of Production Systems,
University of Bremen, Germany
Abstract
To manage the increasing dynamics inside and outside a production system, a decentralised and
autonomous control of shop floor logistics is a promising approach. For developing and benchmarking such
autonomous control methods, dynamic models are essential. The paper introduces the idea of autonomous
logistic processes and presents a dynamic simulation model of a shop floor with both a conventionally
planned and an autonomously controlled scenario. The decentralised and autonomous control strategy bases
on autonomous elements that are able to make decisions by themselves using distributed local information.
The simulation model is used for analysing the system’s dynamics at varying workloads. The logistic
performance is analysed by comparing throughput times for the different logistics situations and during
expected and unexpected disturbances.
Keywords:
Production, Control, Autonomy
1 INTRODUCTION
Due to increasing market dynamics, Production Planning
and Control (PPC) has become more challenging for
manufacturing companies. Today, production plans have
to adapt quickly to changing market demands while
conventional PPC methods cannot handle unpredictable
events and disturbances in a satisfactory manner [1].
One reason is that in practice the complexity of
centralised architectures tends to grow rapidly with size,
resulting in rapid deterioration of fault tolerance,
adaptability and flexibility [2].
To solve this dilemma and to manage the dynamics inside
and outside the production system the development of
decentralised and autonomous control strategies is a
promising research field [3]. Here autonomous control
means a decentralised coordination of intelligent logistic
objects (parts, machines etc.) and the routing through a
logistic system by the intelligent parts themselves.
Those intelligent items follow autonomously decision rules
that are based on local information. The dynamics of such
a system depends on the decision-making processes and
produces a global behaviour of the system that has new
emerging characteristics. Thereby the interactions and
interdependencies between local and global behaviour
are not trivial. Remember a colony of ants where a single
ant has no idea about the whole colony. It only acts by a
few simple rules but the entire colony consisting of
thousands of ants is able to build gigantic nests, to find
shortest paths between food and nest etc. This selforganisation is a so-called emergent behaviour of a
complex dynamic system and not derivable from single
characteristics [4].
2 AUTONOMY IN PRODUCTION LOGISTICS
The concept of autonomous control requires on one hand
logistic objects that are able to receive local information,
process this information, and make a decision about their
next action. On the other hand, the logistic structure has
to provide distributed information about local states and
different alternatives to enable decisions generally. These
features will be made possible through the development
of Ubiquitous Computing technologies [5].
The application of autonomous control in production and
logistics can be realised by recent information and
communication technologies such as radio frequency
identification (RFID), wireless communication networks
etc. These technologies facilitate intelligent and
autonomous parts and products which are able to
communicate with each other and with their resources
such as machines and transport systems and to process
the acquired information. This leads to a coalescence of
material flow and information flow and enables every item
or product to manage and control its manufacturing
process autonomously [3]. The coordination of these
intelligent objects requires advanced PPC concepts and
strategies to realise autonomous control of logistic
processes. To develop and analyze such autonomous
control strategies dynamic models are required. In the
following a shop floor scenario introduced by ScholzReiter et al. [6] is modified and used to model
autonomous processes in a flexible production scenario.
3 SHOP FLOOR SCENARIO
The considered shop floor scenario is a dynamic flow-line
manufacturing system. It consists of n parallel production
lines each with m machines Mij and an input buffer Bij in
front of each machine (see Figure 1). Every line
processes a certain kind of product A, B, … X by m job
steps. The raw materials for each product enter the
system via sources; the final products leave the system
via drains.
In this shop floor, two different logistic situations will be
compared. In the first case, each line processes its
associated product independently from the other lines.
Here, the way of the single parts through the machines is
pre-determined by a hierarchical planning process. This
case will be called conventional planning in the following.
In the second case, the production lines are coupled at
every stage. Furthermore, every line is able to process
every kind of product within a certain stage. The
processing times for each product are higher on foreign
lines than on their own. This structure allows the parts to
Published in: Proc. of 38th CIRP International Seminar on Manufacturing Systems.
Florianopolis, Brazil, 2005, CD-ROM.
switch lines at every stage. The decision about changing
the line is made by the part itself on the basis of local
information about buffer levels and expected waiting times
until processing. Thereby, the parts take into account that
the processing times are higher on foreign lines than on
their own. This logistic strategy will be called autonomous
control because the parts are autonomous in their
decision and there is no superior controller who decides in
which way the parts will be processed [7].
Processing times [h:min] and
processing rates [1/h]
at production line n
1
2
3
Stage m
1
2:00 / 0.5
2:00 / 0.5
2:00 / 0.5
2
2:00 / 0.5
2:00 / 0.5
2:00 / 0.5
3
2:00 / 0.5
2:00 / 0.5
2:00 / 0.5
Product
Type A
Product
Type B
Product
Type X
B11
B12
B1n
M11
M12
M1n
The mean arrival rate 8m has to be equal or lower than the
total processing rate : to guarantee stable system
behaviour with finite buffer levels:
B21
B22
B2n
λm ≤ µ .
M21
M22
M2n
For the described 3x3 machine model, the mean arrival
rate has to be chosen to:
Table 1: Processing times and resulting processing rates
of the 3x3 machine model.
Here, 8m is the mean arrival rate, " is the amplitude of the
sine function, and ϕ indicates a phase shift.
…
Bm1
Mm1
Bm2
Mm2
λm ≤ 0.5
(2)
1
.
h
(3)
Bmn
Due to a usual workload of about 80 % in real production
systems, a mean arrival rate 8m = 0.4 1/h and amplitude
of " = 0.15 1/h are chosen:
Mmn
λ (t ) = 0.4 + 0.15 ⋅ sin(t + ϕ ) .
Figure 1: mxn machines shop floor scenario.
In the following the dynamics and performance of both the
conventionally planned and the autonomously controlled
shop floor will be analysed using a dynamic simulation
model.
(4)
The arrival functions for the three product types A, B and
C are identical except for the phase shift ϕ = 1/3 period.
This phase shift is chosen to simulate a seasonal varying
demand for the three different products. Figure 2 shows
the three arrival functions. Here, the arrival rate is plotted
against the simulation time for one simulation period.
0,6
0,5
Arrival Rate [1/h]
4 DISCRETE-EVENT SIMULATION MODEL
To handle the complexity of the shop floor the described
scenario is reduced to 3x3 machines, i.e. three production
lines each with three stages. Every line processes a
certain product A, B, and C by three job steps. This shop
floor structure is modelled using a discrete-event
simulation software tool.
0,4
0,3
0,2
Arrival Rate Type A
Arrival Rate Type B
Arrival Rate Type C
0,1
4.1 Conventional Planning
The first case to be investigated is the conventional
situation where the lines work independent from each
other and a plan determines which job step will be done at
which machine. Each line is balanced i.e. every machine
within a line has the same processing rate of 0.5 parts per
hour. From these processing rates result processing
times of 2 hours for processing one part at one machine.
The processing times and the resulting processing rates
are shown in Table 1.
To analyse the system’s behaviour at varying demand
and workload fluctuations, an arrival function 8(t) is
defined and set as a sine function:
λ (t ) = λm + α ⋅ sin(t + ϕ )
(1)
0
0
5
10
15
20
25
30
Simulation Time [d]
Figure 2: Arrival rate for the three part types.
To analyse the system’s performance, the throughput
times (TPT) for the three different part types are
examined. Figure 3 shows these throughput times.
Because of the identical arrival functions for each part
type, the time series of the throughput times have the
same shape with a phase shift of 1/3 period.
Published in: Proc. of 38th CIRP International Seminar on Manufacturing Systems.
Florianopolis, Brazil, 2005, CD-ROM.
20
18
0.6
0.5
14
Arrival Rate [1/h]
Throughput Time [h]
16
12
10
8
6
0.4
0.3
0.2
4
TPT Type A
TPT Type B
TPT Type C
2
0.1
0
30
35
40
45
50
55
60
0
0
Simulation Time [d]
5
10
15
20
25
30
Simulation Time [d]
Figure 3: Throughput times for the three different part
types in case of conventional planning.
Figure 4: Varying amplitudes of the arrival function for
part type A
During the periods of overload, the throughput times rise
because the buffer levels at the first stage machines rise
and the parts have a higher waiting time before they are
processed. When the arrival rate drops below 0.5 1/h, the
buffer levels and the waiting times decline until the
minimum throughput time of 6 h is reached.
For all three part types the maximum throughput time in
this case is 19:48 h and the mean throughput time is
9:55 h with a standard deviation of 5:08 h (see Table 3).
To understand the impact of seasonal demand
fluctuations on the system’s behaviour, the amplitude of
the sinusoidal arrival rate is varied like shown in figure 4.
The amplitude rises here from " = 0.0 1/h to " = 0.2 1/h.
The resulting throughput times are shown in figure 5. For
amplitudes lower than 0.1 1/h, the throughput time
remains constantly 6 h which is the total processing time
at all three machines. For amplitudes higher than 0.1 1/h,
the temporary overload results in an increased throughput
time caused by an additional waiting time in the first
buffer. This effect shows the system’s inability to react on
demand fluctuations. Notice the maximum throughput
time of 37:24 h for the amplitude " = 0,2 1/h.
To analyse the robustness of the conventionally planned
system, a machine failure at machine M21 and a downtime
for 12 h is modelled. Due to this single breakdown, the
complete production line is blocked for 12 h. The arriving
parts pile up in the second buffer and no products leave
the line.
Figure 6 shows the effect of this breakdown on the
throughput time for product type A. The abrupt rise can be
interpreted as system’s inability to react to unexpected
disturbances and changing constraints.
40
Throughput Time [h]
35
30
25
20
15
10
5
0
5
10
15
20
25
30
Simulation Time [h]
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Arrival Amplitude [1/h]
Figure 5: Throughput time of product type A for rising amplitudes in the sinusoidal arrival rate.
0.18
0.2
Published in: Proc. of 38th CIRP International Seminar on Manufacturing Systems.
Florianopolis, Brazil, 2005, CD-ROM.
W =
35
Throughput Time [h]
30
λ
.
µ
(4)
where 8 is the arrival rate and : the processing rate. The
workload of the machines at the first stage is defined by:
25
20
15
W11 =
λ1 − ( w12 + w13 ) w21
w
+
+ 31
µ A11
µ B11 µC11
(5)
W12 =
λ2 − ( w21 + w23 ) w12
w
+
+ 32
µ B12
µ A12 µC12
(6)
W13 =
λ3 − ( w31 + w32 ) w13
w
+
+ 23
µC13
µ A13 µ B13
(7)
10
5
TPT Type A
0
30
35
40
45
50
55
60
Simulation Time [d]
4.2 Autonomous Control
The second case to be analysed is the autonomous
control situation. Here, the parts are autonomous in their
decision which machine to choose. They take into
account the fact that the processing times are different for
each product type. The processing times are on foreign
lines higher than on their own line. Table 2 shows the
processing times and the resulting processing rates for
the three different product types on the three production
lines.
Part Type
Processing times [h:min] /
Processing rates [1/h]
at production line n
1
2
3
Type A
2:00 / 0.5
2:30 / 0.4
3:00 / 0.33
Type B
3:00 / 0.33
2:00 / 0.5
2:30 / 0.4
Type C
2:30 / 0.4
3:00 / 0.33
2:00 / 0.5
Table 2: Processing times and resulting processing rates
of the 3x3 machine model.
The parts have the lowest processing times on their own
line and have higher processing times if they change the
line. The decision about changing the line is made by the
part itself on the basis of local information about buffer
levels, i.e the expected waiting time until processing and
the processing time itself. Thereby, the parts take into
account that the processing times are higher on foreign
lines than on their own. At each production stage the
parts compare the future processing times of the parts in
the buffers and their own processing time on the
respective machine and choose the machine with the
minimal time for being processed.
Like the conventionally planned system, the mean arrival
rate 8m has to be equal or lower than the total processing
rate : to guarantee stable system behaviour with finite
buffer levels. Unfortunately, the mean arrival rate cannot
be determined trivially by equation (2) because of the line
switching of the parts i.e. the number of parts that switch
the line and the different processing times at different
lines.
For description of the relation between arrival rate and
processing rate, the workload is defined as:
where 8i is the arrival rate at source i, :Xij is the
corresponding processing rate for the different part types
(see Table 2) and wij is the switching rate from line i to
line j.
Because of the interdependencies between the switching
rates wij and the dependencies from the arrival rates 8i,
the workload problem is not analytically solvable.
Therefore the stability condition in this case is not trivial to
define. Nevertheless, the mean arrival rate still has to be
equal or smaller than the processing rate. But due to
reduced processing rates, the maximum mean arrival rate
is not anymore 8m,max = 0.5 1/h.
In high workload situations, the systems total processing
rate :total is a function of the arrival rate because a high
arrival amplitude causes line switching and therefore a
changing total processing rate.
µtotal = f (λ (t ))
(7)
Thus, the stability of the system for different mean arrival
rates and amplitudes is tested by analysing the amount of
work-in-process (WIP) after a simulation run. If the
system reaches the instable area the work-in-process
rises to infinity.
The simulation results for different mean arrival rates and
different amplitudes are shown in figure 7.
1200
Alpha = 0.03 1/h
1000
Alpha = 0.15 1/h
Alpha = 0.19 1/h
Alpha = 0.31 1/h
800
WIP [h]
Figure 6: Throughput time for product type A during a
breakdown of machine M21.
600
400
200
0
0,3
0,35
0,4
0,45
0,5
0,55
Mean Arrival Rate [1/h]
Figure 7: Work-in-process against the mean arrival rate
for different amplitudes.
Each point indicates the total work-in-process (WIP) after
one simulation run for a certain mean arrival rate. The
four different curves denote four different amplitudes. For
each curve, a critical mean arrival rate 8c is observed
beyond which the system becomes instable.
Published in: Proc. of 38th CIRP International Seminar on Manufacturing Systems.
Florianopolis, Brazil, 2005, CD-ROM.
Obviously, this effect occurs because in case of work
overload the parts switch to other lines even if the
processing time is higher there. In this case the maximum
throughput time is reduced by 36 % to 12:17 h and the
mean throughput time is reduced by 30 % to 6:46 h with a
standard deviation of only 1:07 h (see Table 3).
0,6
Critical Mean Arrival Rate [1/h]
0,5
0,4
0,3
0,2
20
0,1
18
0
0
0,05
0,1
0,15
0,2
0,25
0,3
16
0,35
Throughput Time [h]
Amplitude [1/h]
Figure 8: Critical mean arrival rate against the amplitude.
Figure 8 shows these critical arrival rates 8c for different
amplitudes. A linear falling trend between the amplitude
and the critical mean arrival rate is observed. This means
that in case of autonomous control i.e. the admittance of
line switches, the maximum mean arrival rate 8m,max
depends on the demand variance i.e the amplitude " of
the arrival rate.
λm, max = f (α )
12
10
8
6
TPT Type A
TPT Type B
TPT Type C
4
2
0
30
35
40
45
50
55
Figure 9: Throughput times for the three different part
types in case of autonomous control.
From the data points plotted in figure 8 equation (9) for
the maximum mean arrival rate is extrapolated.
To understand the impact of seasonable demand
fluctuations on the system’s behaviour, the amplitude of
the sinusoidal arrival function with a mean arrival rate
8m = 0.4 1/h is varied like shown in figure 4. The resulting
time series of the throughput time are shown in figure 10.
(9)
To analyse the performance of the system the time series
of throughput times for the three different product types
for a mean arrival rate 8m = 0.4 1/h with an amplitude " =
0.15 1/h are shown in figure 9. Again identical shaped
time series of the throughput times of each lot type are
observed but the maximum and the mean throughput
times have been significantly reduced in comparison to
the conventionally planned system.
Throughput Time [h]
20
15
10
5
0
5
0.22
10
0.2
15
0.18
0.16
20
0.14
25
0.12
30
Simulation Time [d]
60
Simulation Time [d]
(8)
λm, max = −0,5 ⋅ α + 0,5
14
0.1
Arrival Amplitude [1/h]
Figure 10: Throughput time of product type A for rising amplitudes in the sinusoidal arrival rate.
Published in: Proc. of 38th CIRP International Seminar on Manufacturing Systems.
Florianopolis, Brazil, 2005, CD-ROM.
The autonomous control effects start at amplitude of
0.1 1/h. The time series show the more complex
dynamics, but a significantly reduced throughput time in
maximum, mean, and variance. Notice the maximum
throughput time of 12:00 h for the amplitude of 0.2 1/h
before beginning to destabilise.
In the upper right corner, a beginning destabilisation is
observed. For higher amplitudes, the throughput time
rises to infinity because of the system’s overload (see
also figure 8 and equation 9).
To analyse the robustness of the autonomously controlled
shop floor, a machine failure at machine M21 and a
downtime for 12 h is modelled. Figure 8 shows the
resulting throughput times for autonomously switching
parts.
20
18
Throughput Time [h]
16
14
12
10
8
Table 3 summarises the results for a sinusoidal arrival
function with a mean arrival rate 8m = 0.4 1/h and an
amplitude " = 0.15 1/h. These results underline the
benefits of a autonomous control of shop floor logistics.
Although the highest possible workload for the system is
reduced, the ability to react autonomously to varying
conditions like demand fluctuations or unexpected
disturbances like machine failures is extremely improved.
5 SUMMARY AND OUTLOOK
Summarising one can say that by introduction of
alternative processing capacities and autonomous control
strategies based on local information and local decisionmaking of intelligent parts, the shop floor can adapt itself
to changing work loads and can autonomously react to
unexpected disturbances. This motivates further research
in this area. In particular it will be interesting to analyse
the impact of set up times, dynamic lot sizing and a
dynamic capacity control. This will increase the level of
autonomy in the system. It will be interesting to
investigate which combination of the different autonomous
strategies results in what kind of global behaviour.
Furthermore the higher level of autonomy will produce a
more complex dynamic that could be analysed using tools
from the field of nonlinear dynamics.
6
4
TPT Type A
TPT Type B
TPT Type C
2
0
30
35
40
45
50
55
60
Simulation Time [d]
Figure 11: Throughput times for the three part types
during a breakdown of machine M21.
One can see a sudden rise of the throughput time of part
type A which reaches a maximum of 21:00 h. But this high
throughput time is quickly reduced and again the parts are
distributed between the lines. In this case the mean
throughput time for parts of type A rises to 7:00 h with a
standard deviation of 1:34 h (see Table 3) while the mean
throughput times for type B rises to 6:55 h respectively to
6:52 h for parts of type C.
Min
TPT
[h:min]
Max
TPT
[h:min]
Mean
TPT
[h:min]
SDV
TPT
[h:min]
Conventional
planning
6:00
18:42
9:42
4:42
Autonomous
control
6:00
12:17
6:46
1:07
Conventional
planning and
machine failure
(only type A)
6:00
30:42
11:23
7:35
Autonomous
control and
machine failure
(only type A)
6:00
21:00
7:00
1:34
Table 3: Performance measures of the 3x3 machine
model.
6 ACKNOWLEDGMENTS
This research is founded by the German Research
Foundation (DFG) as part of the Collaborative Research
Centre
637
“Autonomous
Cooperating
Logistic
Processes: A Paradigm Shift and its Limitations” (SFB
637). The authors wish to thank Prof. Neil A. Duffie for
interesting and valuable discussions.
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