Optimization Analysis for an Uncovered Wagon Transportation with an
Interactive Animated Simulation-Based Platform for Multidisciplinary
Learning
Moritz Hauke Wohlstein, Evgeniya Zakharova, Brit-Maren Block
a
and Paolo Mercorelli
b
Institute for Production Technology and Systems (IPTS), Leuphana University of Lueneburg,
Universitaetsallee 1, 21335 Lueneburg, Germany
Keywords:
Interactive Simulation-Based Learning, Engineering and Non Engineering Education, Computer Supported
Education, Virtual Tools and Augmented Learning Environments.
Abstract:
At an earlier stage of European funding for projects on technology-enhanced learning, the main thrust was to
develop e-learning technologies and on projects that sought to promote the take-up of platforms and services.
This contribution is prepared by students after attending lectures of a multidisciplinary course in the context
of a complementary studies frame. The students of this course summarized, through a case study, concepts
and methods in a straightforward, but structured way. Thanks to the help of a software tool based on Python,
an original and open learning platform is realized for students and lecturers and it represents a part of this
contribution. Concerning the specific lecture, cargo loads and transportation are important logistical topics in
many industries. They dictate the profit of the final product, expenditure, time consumption and labor force
utilization. The optimal transportation of any type of cargo is crucial for businesses. More in general, it is
possible to say that the proposed problem can be generalized and applied in other main economic problems in
which optimization problems are involved. In this work we focused on the optimization of fluid transportation
under specified conditions, or constraints, in other words. The aim of the project is to determine the optimal
parameters of the system to control the transportation in an optimal way. This material which includes an open
software to test the developed concepts through the lecture can be used by students and lecturers. An open
link is accessible to the users.
1 INTRODUCTION
At an earlier stage of European funding for projects
on technology-enhanced learning, the main thrust was
to develop e-learning technologies and on projects
that sought to promote the take-up of platforms and
services. At the initial stage, the need-based use of
web for knowledge acquisition was seldom consid-
ered as ‘e-learning’. At a later phase, major European
projects were funded to support the development of
knowledge process methodologies with web tools and
specific software solutions (such as the EU-funded
Mature project inside the FP7 European Project). The
aim there was to analyse the knowledge-intensive
work processes and practices of ’knowledge work-
ers’. Using the platform will allow participating com-
panies to integrate and transfer knowledge in a more
natural and direct way. In this sense, the crucial con-
cept of the transferability is automatically guaranteed
a
https://orcid.org/0000-0002-2112-5406
b
https://orcid.org/0000-0003-3288-5280
via knowledge integration of industry and academic
world platform. In the past, without upcoming In-
ternet of Things, several “remote laboratories” have
been set up for teaching and research purposes in the
field of automatic control and robotics. In a remote
laboratory, physical systems settled at specific loca-
tions in the world are made available through the in-
ternet to remote users for performing experiments and
validation tests in location where plant models are not
available or are difficult to be reproduced (Gomes and
Bogosyan, 2009), (Casini and Garulli, 2016), (Casini
et al., 2004), (Leva and Donida, 2008), (Balestrino
et al., 2009), (Tzafestas, 2009). All these structures,
although having permitted tangible progresses in the
field to be achieved, have the drawback of requir-
ing complex hardware and demanding communica-
tion equipment. Instead, fully virtual laboratories
have been recently developed by several companies,
also in the framework of collaborations among higher
education institutions or under the patronage of gov-
ernmental institutions – see, e.g., Labster and Virtual
Labs. These solutions are generally oriented to sci-
Wohlstein, M., Zakharova, E., Block, B. and Mercorelli, P.
Optimization Analysis for an Uncovered Wagon Transportation with an Interactive Animated Simulation-Based Platform for Multidisciplinary Learning.
DOI: 10.5220/0012047000003470
In Proceedings of the 15th International Conference on Computer Supported Education (CSEDU 2023) - Volume 2, pages 451-457
ISBN: 978-989-758-641-5; ISSN: 2184-5026
Copyright
c
 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)
451

ence and engineering. Also, it is noticeable that EU-
funded projects have been conceived to devise vir-
tual laboratories. This is the case, for instance, of
the projects Next-Lab and ELLIOT. All these projects
are milestones either as general purpose tools in sci-
ence education (like the H2020 project Next-Lab) or
in their own fields of interest (IOT like in the FP7
project ELLIOTT or physical systems). The proposed
problem is modelled and solved using a python envi-
ronment which fits the recommendation of the 2013
EU Communication on Opening Up Education. To
sum up, in this context, the main features that show-
case the novelty and innovative aspects of this con-
tribution, with the direct participation of the students,
can be stated as follows:
• introducing new and paradigmatic topics in the
teaching and learning contents, which reflect the
latest EU research funding programms in the
broad field of control engineering;
• providing a technical and cultural resource among
different universities and companies to share
available expertise and knowledge promoting in
this sense a knowledge platform which struc-
turally guarantees a direct transferability;
• providing a flexible learning and teaching struc-
ture in which the user can actively interact to test
the proposed solution and to modify the virtual
models.
This work can be seen as a paradigmatic example
of a framework for an integrated transnational ap-
proach to academic teaching and learning, that con-
tributes to the development of the engineering, and
non-engineering, communities, meeting their needs
through an innovative cloud-based virtual platform
shared by external organizations in the first instance
and spread among stakeholders in the long-term.
1.1 Starting with a Virtual Lecture
This contribution proposes a structure of the lecture in
the context of a complementary course which should
be open for Master’s students also with no back-
ground. This material is prepared by students after at-
tending some lectures in this multidisciplinary course
which is in this case dedicated to optimization tech-
niques in the context of a complementary study frame.
In this study frame, engineers and non-engineers can
be admitted. The students of these courses summa-
rized, through a case study, concepts and methods in
a straightforward but structured form. Thanks to the
help of a software tool, an original and open-learning
platform is realized for students and lecturers. This
learning platform can be used both by students and
lecturers. Students can interactively test the effect of
physical variables directly on the developed platform.
Teachers can use this material for their lectures and
they can be inspired by this material for further de-
velopments. The animated structure of the simula-
tion realizes a friendly platform to be used intuitively.
This lecture connects various disciplines. This al-
lows the students to set additional priorities in par-
allel to their special studies and it gives the oppor-
tunity to sharpen their individual competence profile
- subject-related, non-specialist or interdisciplinary.
The shipment loading problem is not only an engi-
neering one. In fact, the problem formulated in the
context of an optimization problem can be seen as an
economical one in which possible cost functions can
be defined together with possible constraints. The
shipment loading problem is highly overspread and
has variations (Aksentijevic et al., 2020). The cargo
can be relocated by different means of transport be-
tween cities or countries, or can be carried from one
department of the plant to another one, depending on
the industrial targets. This project elaborates on the
issue of fluid transportation in the uncovered carriage.
1.2 Structure of the Paper
This paper contains the problem description, see Sec-
tion 2. In this section possible issues and the main
aim are explored together with the system explana-
tion, which helps to understand its parameters, ob-
jects, conditions and states. This part is a fundamen-
tal one and includes knowledge related to the back-
ground. In Section 3, methods, which have been
used to solve the problem formulated in Section 2, are
shown. In Section 4, constraints are explicitly consid-
ered and the Karush-Kuhn-Tucker criteria are used to
find the optima. Section 5 explains the obtained re-
sults in order to give the possibility to the readers to
have access to the interpretation of the visualized re-
sults. Conclusion and future work session closes the
paper. The access to the virtual lecture can be found
via the following link: link.
2 PROBLEM DESCRIPTION
The project assumes a wagon that transports some
amount of fluid. The wagon has a mass M
W
and an
interior of cuboid shape, open at the top. The interior
has height r, length d and depth b. The wagon can
be filled with the fluid. Therefore, the volume of the
fluid is:
V = h · d · b, (1)
CSEDU 2023 - 15th International Conference on Computer Supported Education
452

𝜶
F=m∙a
V
d
h
r
r
b
e
Figure 1: Wagon: when accelerated, the fluid moves and
the excess e gets bigger. The angle α can be defined as:
tan(α) = 2e/d.
𝑭
𝑵
𝑭
𝒈
𝑭
𝒂
𝜶
𝑭
𝑵
𝜶
𝑭
𝒂
|𝑭
𝒂
|
= 𝒎 ∙ 𝒂
|𝑭
𝑵
|
𝑭
𝒈
= 𝒎 ∙ 𝒈
⇒
Figure 2: Forces: The different forces acting on the fluid
result in a tilted surface with angle α, where tan(α) = g/a
with the acceleration of the cart a and the gravitational ac-
celeration g. Since the wagon accelerates in the forward
direction, a fluid particle of mass m in the reference system
of the wagon feels a force F
a
= a ∗ m in the opposite direc-
tion of the same magnitude, as well as a normal force F
N
and the gravitational force F
g
= mg.
where h is the height up to which the wagon is filled.
The total Mass of the wagon filled by a fluid with den-
sity ρ is:
M = M
W
+ ρ ·V. (2)
The wagon can be accelerated (and decelerated) with
a maximal force of F
max
. Figure 1 shows the level
change of the fluid in the wagon, caused by the move-
ment with acceleration. Since the wagon gets accel-
erated, the fluid moves. The forces that result from
the acceleration can be seen at Fig. 2. The position
x(t) of the wagon after some time with initial values
of velocity and acceleration follows the next relation:
x(t) = x
0
+ v
0
·t +
1
2
a
0
·t
2
+
1
6
j ·t
3
. (3)
The goal of our work is to determine optimal values
for the parameters in (3), as well as an optimal height
h of the fluid, such that the volume V that is moved
over a distance L = x(T ) per time T is maximised.
The boundary conditions under which the optimiza-
tion takes place are those that the maximal achieved
acceleration times the wagons mass is below the max-
imal force the wagon can produce and that the fluid
does not swap over, which puts a constraint on the
maximal angle of α (see Figs. 1 and 2). To sum up
the observations mentioned above, we will determine
the problem with objective function, constraints and
optimization method in Section 3.
3 CONSTRAINED OBJECTIVE
FUNCTION
This part considers the calculations which lead to
the specification of objective function and constraints.
The initial position and velocity of the system are
zero:
x(t = 0) = 0 ⇒ x
0
= 0, (4)
˙x(t = 0) = 0 ⇒ v
0
= 0, (5)
⇒ x(t) =
1
2
a
0
·t
2
+
1
6
j ·t
3
, (6)
=
1
2
t
2
· (a
0
+
1
3
j ·t). (7)
The distance, travelled by the wagon with the fluid for
the defined time, submits to the following constraint:
x(t = T ) = L, (8)
⇒ L = x(T ) =
1
2
T
2
· (a
0
+
1
3
j · T ). (9)
The velocity of the wagon at its destination should be
zero:
˙x(t = T ) = 0, (10)
⇒ 0 = ˙x(T ) = a
0
· T +
1
2
j · T
2
. (11)
This leads to the following equation for the jerk coef-
ficient j which determines the acceleration‘s change
over time:
⇒ j = −2
a
0
T
. (12)
We substitute the found parameters into the distance
defined by (9) and express the time variable:
⇒ L =
1
6
T
2
· a
0
, (13)
⇒ T =
r
6L
a
0
. (14)
The objective function can therefore be written as:
⇒
V
T
= h · d · b ·
r
a
0
6L
. (15)
Now, we can rewrite the kinematic equations of the
system in the following way:
x(t) = a
0
t
2

1
2
−
1
3
t
T

, (16)
v(t) = ˙x(t) = a
0
t

1 −
t
T

, (17)
a(t) = ¨x(t) = a
0

1 − 2
t
T

. (18)
Optimization Analysis for an Uncovered Wagon Transportation with an Interactive Animated Simulation-Based Platform for
Multidisciplinary Learning
453

The force F(t) that has to act on the wagon at the time
t to guarantee the desired dynamics has the following
form:
F(t) = M · a(t) = (M
W
+ ρ ·V ) · (a
0
+t · j), (19)
|F(t)| ≤ F
max
, (20)
and is constrained by the maximal force F
max
that the
wagon can generate. Since the distance L that is trav-
elled by the cart has to be greater than zero, as well as
the time that it took to travel it, we know that:
6L
T
2
> 0, (21)
⇒ a
0
> 0, (22)
⇒ max
t
a(t) = max
t
a
0

1 − 2
t
T

, (23)
= a(0) = a
0
, (24)
similarly we can show, that for t < T the minimal ac-
celeration is: min a(t) = a(T ) = −a
0
. Now, we can
reformulate the constraint (19):
a
0
≤
F
max
M
. (25)
The second constraint deals with the problem of con-
taining the fluid inside the wagon. The maximal rising
of the fluid‘s level e should be smaller than the differ-
ence between the fluid‘s height without acceleration
and the height of the carts rim:
e ≤ r − h. (26)
The maximal excess e is in relation to the width of the
cart d and the angle α by which the fluid‘s surface is
tilted according to the following equation:
e = tan(α)
d
2
, (27)
(see Fig. 1). According to the force diagram at Fig. 2,
we can define the angle α by the forces acting on the
fluid. At the maximal acceleration a
0
, at which the
maximal rising of the fluid happens, the forces are the
following:
⃗
F
g
= M
f
l · g, (28)
⃗
F
a
= M
f
l · a
0
, (29)
⇒ tan(α) =
|
⃗
F
a
|
|
⃗
F
g
|
=
a
0
g
. (30)
Now, we can rewrite the constraint 26:
d
2
a
0
g
≤ r − h. (31)
We will keep the minimization of the objective func-
tion:
Loss = −
V
T
= −h · d · b ·
r
a
0
6L
. (32)
4 Karush-Kuhn-Tucker
We can use the Karush-Kuhn-Tucker (KKT) crite-
ria (Brezhneva et al., 2009) to do the optimisation
with constraints. We want to minimise the function
f (h,a
0
) under the constraints g
i
(h,a
0
) ≤ 0:
f (h,a
0
) = −dhb
r
a
0
6L
, (33)
g
1
(h,a
0
) =
da
0
2g
+ h − r ≤ 0, (34)
g
2
(h,a
0
) = a
0
(M
W
+ dhbρ) − F
max
≤ 0. (35)
From this result, the following KKT conditions are
derived:
∇ f (h
∗
,a
∗
0
) +
2
∑
i=1
µ
∗
i
∇g
i
(x
∗
) = 0, (36)
g
1
(h
∗
,a
∗
o
) ≤ 0, g
2
(h
∗
,a
∗
o
) ≤ 0, (37)
µ
∗
1
≥ 0,µ
∗
2
≥ 0, (38)
µ
∗
1
g
1
(h
∗
,a
∗
o
) = µ
∗
2
g
2
(h
∗
,a
∗
o
) = 0, (39)
from equation (36), we get two separate equations:
−db
r
a
0
6L
+ µ
1
+ µ
2
a
0
dbρ = 0
(40)
−
1
2
dhb
r
1
a
0
· 6L
+ µ
1
d
2g
+ µ
2
(M
W
+ dhbρ) = 0.
(41)
Equation (39) also leads to two equations:
µ
1

da
0
2g
+ h − r

= 0, (42)
µ
2
(a
0
[M
W
+ dhbρ] − F
max
) = 0. (43)
Now, we can solve these equations to get the optimal
a
0
, h and µ
1
and µ
2
. First, we will do a distinction of
different cases.
4.1 Case1: µ
2
= 0
If µ
2
is 0, the four equations above are reduced to the
following three equations:
−db
r
a
0
6L
+ µ
1
= 0, (44)
−
1
2
dhb
r
1
a
0
· 6L
+ µ
1
d
2g
= 0, (45)
µ
1

da
0
2g
+ h − r

= 0. (46)
From (44) we get
µ
1
= db
r
a
0
6L
, (47)
CSEDU 2023 - 15th International Conference on Computer Supported Education
454

which can be set into (45) to get a relation between
the optimal h and a
0
:
h =
da
0
g
. (48)
Using these two equations in (46), we get:
db
r
a
0
6L

3da
0
2g
− r

= 0. (49)
Since d, b, a
0
and L are all unequal 0, we get the
optimal solutions in this case as:
a
0
=
2rg
3d
, (50)
h =
2r
3
. (51)
4.2 Case2: µ
2
> 0
4.2.1 Case 2.1: µ
1
= 0
From µ
1
= 0 follows for (44):
db
r
a
0
6L
= 0. (52)
Since d,b, and a
0
cannot be equal to zero, this case
cannot be optimal.
4.2.2 Case 2.2: µ
1
> 0
If µ
1
> 0 and µ
2
> 0, (42) and (43) are simplified in
the following way:
h = r −
da
0
2g
, (53)
a
0
(M
W
+ dhbρ) − F
max
= 0. (54)
Now, we can solve these two equations to get the two
unknowns h and a
0
:
a
0

M
W
+ dbρ

r −
da
0
2g

− F
max
= 0, (55)
⇒a
2
0
− a
0
· 2g
M
W
+ dbρr
d
2
bρ
+
2gF
max
d
2
bρ
= 0, (56)
⇒ a
0
= g
M
W
+ dbρr
d
2
bρ
±
s
g
2

M
W
+ dbρr
d
2
bρ

2
−
2gF
max
d
2
bρ
. (57)
Using this solution for a
0
, we get the optimal h using
(53).
5 RESULTS
In this work the team accomplished the project via
programming language Python. It has necessary
modules and libraries for optimization problems
solving, (see scipy), tools for the results visualization
and graphs’ construction. The Sequential Least
Squares Programming (SLSQP) method has been
applied. This method it suitable for this issue,
because it is non-linearly constrained gradient-based
optimization for a scalar function of one or more
variables (Fu et al., 2019). As it was noticed at the
Section KKT we minimize the objective function
(33) under constraints (34)-(35). Using the constant
variables:
d = 20.0 # wagon length
b = 2.5 # wagon width
r = 3.0 # wagon height
g = 9.8 # free fall acceleration
L = 120 # distance of transportation
ρ = 1 # fluid density
M
w
= 50 # wagon mass
F
max
= 200 # maximal pulling force,
the optimal values of the height and acceleration
have been found automatically:
Optimal height: 2.0
Optimal acceleration: 0.98.
We implied the received values into the movement
law in order to see the alterations of position, velocity
and acceleration due time. The graphs are presented
in Figs. 3-5, accordingly.
Figure 3: Optimal position of the cart over time.
Optimization Analysis for an Uncovered Wagon Transportation with an Interactive Animated Simulation-Based Platform for
Multidisciplinary Learning
455

Figure 4: Optimal velocity of the cart over time.
Figure 5: Optimal acceleration over time of the cart.
We replicated the level of the fluid in the wagon
as a blue line at a rectangle in a 2D space. Figure 6
shows the changes of fluid‘s level at three moments
of time during the movement.
Figure 6: Wagon with fluid over time.
The project provides the solution for the technical
side of the fluid transportation problem in the uncov-
ered wagon. After the issue‘s exploration the parame-
ters of the system, which include the characteristics of
the cart and fluid, have been defined. The analysis led
the team to the optimization of the fluid transporta-
tion via the determination of optimal values for the
fluid height and the acceleration of the wagon. The
received results could be applied to real world situ-
ation, for example to achieve the maximal profit for
a specific transportation task. The output affects the
volume of the fluid and the time of the wagon reloca-
tion. This may decrease shipment or energy costs and
increase the utility of the transportation.
6 CONCLUSION AND FUTURE
WORK
This contribution deals with an interactive software
platform dedicated to realization of lectures in the
context of optimization problems. The platform, to-
gether with the lecture structure were realized by stu-
dents after attending lectures of a multidisciplinary
course in the context of a complementary study. The
proposed lecture considers an optimization problem
in the context of transportation. The contribution is
addressed to students and lecturers who can find in-
spiration and idea for further development or they
can directly use this material. This contribution is on
track with EU-funded projects which have been con-
ceived to devise virtual laboratories, as, for instance,
the projects Next-Lab and ELLIOT. As the contribu-
tion is on track with the main guideline and research
directions of EU in the field of didactic, future work
can include also building a set of different examples
with even more possibilities to change parameters and
conditions in the initialization phase of the simula-
tions. The platform is fully accessible and the soft-
ware in use is Python. An open link is accessible to
the users.
ACKNOWLEDGEMENTS
This work was inspired by the lecture ”Optimiza-
tion Techniques” held by Paolo Mercorelli within the
scope of the Complementary Studies Programme at
Leuphana University of Lueneburg during the sum-
mer semester 2022. In this framework, students
can explore different disciplinary and methodologi-
cal approaches from the second semester onwards,
focussing on additional aspects in parallel with their
subjects and giving them the opportunity to sharpen
skills across disciplines.
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Multidisciplinary Learning
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