
Tentative list of working problems (in no special order):
Modelling
and optimization of production scheduling
Physical
model of MDF boards
Setting
the Reserve Fleet
Surgical
cases packages
Prediction
model to textile parameters
Stock and
production planning
A
short description:
Modelling and optimization of
production scheduling
It is aimed to model and
optimize a company's productive system. The
model to be developed is expected to determine
the optimal planning subject to a set of
production orders and deadlines, and also
allowing the computation of new orders delivery
time. Due to the high number of products and
orders, the complexity of the production
scheduling is expected to be a largescale
optimization problem, which may lead to the use
of heuristics. The provided solution technique
should enable the launch of new production
orders in real time. 

Physical model of MDF boards
Aims to provide a physical
model of MDF boards used in the manufacture of
kitchen furniture doors. The existence of a
board physical model and handling process
(smoothing, drilling, and painting/lacquering)
will allow computing (numerically) the board
behavior when subject to the multiple physical
phenomena taking place. The ability to
numerically simulate the occurrence of defects
would allow the determination of optimum
parameters to be used in the different
processing phases (e.g. environment temperature
and humidity), leading to the minimization of
rejection doors due to manufacture defects.
Setting the Reserve Fleet
An urban transportation
company has a reserve fleet of buses, which
allows replacement of the active fleet in case
of breakdown or maintenance. Through the survey
of the maintenance data and reliability of the
fleet it is intended to determine the optimal
reserve fleet (number of buses). 

Surgical cases packages
The hospital
holds currently more than 27,000
surgeries/year in operating room,
involving a series of material and
significant human resources. To achieve
a high standard clinical quality a
continuous and regular improvement in
delivering operational efficiency is
mandatory.
A study on the composition of standard
surgical packages, to optimize the
grouping of surgical instruments that
make up each box according to the
surgical specialty, is to be made. The
packages should be made according to a
set of similar characteristics in
different dimensions (e.g., surgical
team and surgery), taking into
consideration the type of materials used
in a historical database.
The aim of this approach is to identify
groups of materials to be included in
surgical boxes, meeting minimum
difference in usage profile (high
internal consistency) and with
significant differences between
different groups of boxes (high external
heterogeneity, i.e. between groups of
boxes).


Prediction
model to textile parameters (mathematical
formulae are in LaTeX, see
here for a PDF
version of the text)
The challenge consists in
the use of a big quantity of available data to
predict textile parameters, by developing a
prediction model that considers different
material conditions – greige and dipped.
Mathematically, the problem can be described as
given $x\in[(R,Z)]^n$ and $y\in[(R,Z)]^m$, $n>m$, related
by an unknown function $f:R^n\rightarrow R^m$, an approximate
function (prediction model) $\tilde{f}^{1}$ of
$f^{1}$
is to be obtained. The available of a big
quantity of data for $x$ and $y$ allows to obtain
$\tilde{f}^{1}$ (or $\tilde{f}$) by using approximation
techniques (e.g., neural networks). The
approximate function $\tilde{f}^{1}$ is to be used to
predict $\bar{x}$ values, obtained from $\tilde{f}^{1}$ ($\bar{y}$). Given $\bar{y}$, the possible non injectivity of
$f$
may result in several values for $\bar{x}$, which may
require to solve the optimization problem
$\{\min_x g(x), s.t. \tilde{f}(x)=\bar{y}\}$, so a unique
solution is to be obtained. The objective
function $g(x)$ is a performance measure, like,
for example, the textile shrinkage.


Stock and production planning
Production planning of a
production line with different rates in
operations. The production line of study has
(among others) an assembly operation with high
rate with respect to the next treatment step,
which in turn is followed by the finishing step
with a higher rate. The existence of an
intermediate stage of lower production rate
leads to the need to have entry and exit stocks
at the lowest rate step. The aim is to calculate
the size of intermediate stocks and the
development of a mathematical model that allowed
the production planning.

