OAR@UM Collection:https://www.um.edu.mt/library/oar/handle/123456789/66422026-05-02T18:56:13Z2026-05-02T18:56:13ZOptimizing scheduling in a pharmaceutical companyhttps://www.um.edu.mt/library/oar/handle/123456789/939002022-04-18T09:05:15Z2015-01-01T00:00:00ZTitle: Optimizing scheduling in a pharmaceutical company
Abstract: Scheduling is very important task which is used on a daily basis. A "good" schedule will
increase the company's' profit and customers will be more willing to buy products as they
are being satisfied in the shortest period of time. It is also important as it may solve many
different objective functions such as minimization of makespan; minimization of delays;
and minimization of total completion time. There has been an extensive research about
algorithms to solve such problems. An overview of these algorithms both from a
deterministic theoretical part and stochastic theoretical part is provided.
This dissertation mainly focuses on solving the minimization of makespan on identical
parallel machines scheduling problem. A mixed integer linear program (MILP) is built to
solve this scheduling problem by using real live data from a local pharmaceutical
company. In addition, the Longest Processing Time (LPT) heuristic algorithm which is
one of the famous and oldest scheduling algorithms is used to compare its results with the
MILP problem results and the original schedule by the company.
Description: B.SC.(HONS)STATS.&OP.RESEARCH2015-01-01T00:00:00ZParameter estimation of Lévy processeshttps://www.um.edu.mt/library/oar/handle/123456789/938992022-04-18T09:03:19Z2015-01-01T00:00:00ZTitle: Parameter estimation of Lévy processes
Abstract: Levy processes have become increasingly popular in mathematical finance because of
their ability to capture the leptokurtic shape of stock returns and also the jumps
observed in stock prices.
In this dissertation we will present some of the theory and major results of Levy
processes. In particular we shall focus on the Normal Inverse Gaussian and the Meixner
process. Then we shall be looking at different parameter estimation methods for Levy
processes, which can be split into two major categories: the parametric approach and
nonparametric approach. For the nonparametric approach we shall consider a projection
estimator proposed by Comte and Genon-Catalot [14] and also an estimator introduced
by Rubin and Tucker [ 44]. In the parametric approach we consider the Integrated Sum
of Squared Estimation proposed by Heathcote [28] and a Stochastic Programming
method presented by Sant and Caruana [ 45]. Finally these methods of estimation are
implemented on the Malta Stock Exchange Index and some results are compared were
possible.
Description: B.SC.(HONS)STATS.&OP.RESEARCH2015-01-01T00:00:00ZAnalyzing dichotomous and multichotomous categorical responses to assess self-esteem using response modelshttps://www.um.edu.mt/library/oar/handle/123456789/938972022-04-18T08:58:17Z2015-01-01T00:00:00ZTitle: Analyzing dichotomous and multichotomous categorical responses to assess self-esteem using response models
Abstract: Item Response Theory (IRT) is a statistical procedure, typically used in psychological
measurement, with specific reference to the attitudes, abilities, achievement levels and
personality traits of individuals. Its main aim is that of constructing and analyzing
scores on a person's latent trait using questionnaires, personality assessments and
surveys. IRT assesses the person's probability of rating an item in a particular manner
according to a number of factors, namely the respondent's trait level (qualities of the
individual), the item difficulty and the item discrimination (qualities of the item).
Dichotomous IRT models have been developed to cater for two-category responses.
The Rasch model establishes the probability of rating an item with a specific difficulty
by a person having a particular trait level. If the item discrimination varies, then the
Two-Parameter Logistic (2-PL) model is used. The Three-Parameter Logistic (3-PL)
model generalizes the 2-PL model by introducing a guessing parameter.
Multichotomous IRT models have been developed to cater for rating responses with
more than two categories. The Rating Scale model (RSM) and the Partial Credit model
(PCM) which belong to the polytomous family of Rasch models are also described.
The 1- and 2- PL models as well as the RSM and the PCM are fitted to a data set related
to self-esteem and are implemented using the facilities of STATA's subroutine gllamm.
The questionnaire, which was distributed to 303 individuals, comprised ten items, each
of which was rated on a 4-point Likert scale. A summary of the main findings is
provided for each fitted model.
Description: B.SC.(HONS)STATS.&OP.RESEARCH2015-01-01T00:00:00ZParametric and non-parametric estimation methods for latent variableshttps://www.um.edu.mt/library/oar/handle/123456789/938962022-04-18T08:50:25Z2015-01-01T00:00:00ZTitle: Parametric and non-parametric estimation methods for latent variables
Abstract: The aim of this dissertation is to compare two estimation methods - the Maximization
Expectation (EM) and the Non-Parametric Maximum Likelihood Estimation (NPMLE)
approach to estimate a number of unobserved groups or latent classes. A medical data
set related to patients suffering from schizophrenia was used to compare these two
methods.
The nonparametric maximum likelihood estimator of an unspecified distribution is a
discrete distribution with nonzero mass probabilities at a finite number of mass points
(locations). The true number of locations is determined when the likelihood is
maximized using the concept of a directional derivative, called Gateaux derivative.
The NPMLE algorithm is initialized by setting the number of mass-points (latent
variable) to 1 and then searches for a new mass point over a fine grid covering a wide
range of values. The algorithm is terminated if the directional derivative is non positive
for all mass points. The method was applied to the medical data set and implemented
using the facilities of GLLAMM, which is a subroutine of STATA. The approach
yields posterior means, which are probabilities that a patient belong to each of the
latent classes. Patients are then allocated to the latent class (segment) with the largest
posterior mean.
The EM algorithm uses a different approach in which observed data is augmented by
the inclusion of unobserved data, which are 0-1 indicators indicating whether a patient
belongs to a particular latent class. The posterior probabilities are the expected values
of this unobserved data and are calculated using Bayes theorem. The EM algorithm
was applied to the data set and implemented using the facilities of GLIM. Similar to
the NPMLE approach, patients are then allocated to the latent class with the largest
posterior probability. In this approach, both the clustering and estimation procedures
are carried out simultaneously, where a regression model is fitted for each segment.
Both the EM (parametric) and NPMLE (non-parametric) approach showed that the 2-
segment model is the best model for the dataset. Both methods yielded similar parameter
estimates for the regression models and similar allocation of patients to the two latent
classes. The two estimation methods were compared for execution time. It was found
that for a small number of latent classes the two methods yielded similar execution
times; however as the number of segments is increased the EM approach converges at
a faster rate than the NPMLE approach. The main advantage of the NPMLE approach is
that it guarantees convergence to a global maximum; while the EM algorithm only
guarantees convergence to a local maximum.
Description: B.SC.(HONS)STATS.&OP.RESEARCH2015-01-01T00:00:00Z