Abstract: The agenda of showing the scheduled time for
performing certain tasks is known as timetabling. It is widely used in
many departments such as transportation, education, and production.
Some difficulties arise to ensure all tasks happen in the time and
place allocated. Therefore, many researchers invented various
programming models to solve the scheduling problems from several
fields. However, the studies in developing the general integer
programming model for many timetabling problems are still
questionable. Meanwhile, this thesis describes about creating a
general model which solves different types of timetabling problems
by considering the basic constraints. Initially, the common basic
constraints from five different fields are selected and analyzed. A
general basic integer programming model was created and then
verified by using the medium set of data obtained randomly which is
much similar to realistic data. The mathematical software, AIMMS
with CPLEX as a solver has been used to solve the model. The model
obtained is significant in solving many timetabling problems easily
since it is modifiable to all types of scheduling problems which have
same basic constraints.
Abstract: In this article, we deal with a variant of the classical
course timetabling problem that has a practical application in many
areas of education. In particular, in this paper we are interested in
high schools remedial courses. The purpose of such courses is to
provide under-prepared students with the skills necessary to succeed
in their studies. In particular, a student might be under prepared in
an entire course, or only in a part of it. The limited availability
of funds, as well as the limited amount of time and teachers at
disposal, often requires schools to choose which courses and/or which
teaching units to activate. Thus, schools need to model the training
offer and the related timetabling, with the goal of ensuring the
highest possible teaching quality, by meeting the above-mentioned
financial, time and resources constraints. Moreover, there are some
prerequisites between the teaching units that must be satisfied. We
first present a Mixed-Integer Programming (MIP) model to solve
this problem to optimality. However, the presence of many peculiar
constraints contributes inevitably in increasing the complexity of
the mathematical model. Thus, solving it through a general-purpose
solver may be performed for small instances only, while solving
real-life-sized instances of such model requires specific techniques
or heuristic approaches. For this purpose, we also propose a heuristic
approach, in which we make use of a fast constructive procedure
to obtain a feasible solution. To assess our exact and heuristic
approaches we perform extensive computational results on both
real-life instances (obtained from a high school in Lecce, Italy) and
randomly generated instances. Our tests show that the MIP model is
never solved to optimality, with an average optimality gap of 57%.
On the other hand, the heuristic algorithm is much faster (in about the
50% of the considered instances it converges in approximately half of
the time limit) and in many cases allows achieving an improvement
on the objective function value obtained by the MIP model. Such an
improvement ranges between 18% and 66%.
Abstract: Timetabling problems are often hard and timeconsuming
to solve. Most of the methods of solving them concern
only one problem instance or class. This paper describes a universal
method for solving large, highly constrained timetabling problems
from different domains. The solution is based on evolutionary
algorithm-s framework and operates on two levels – first-level
evolutionary algorithm tries to find a solution basing on given set of
operating parameters, second-level algorithm is used to establish
those parameters. Tabu search is employed to speed up the solution
finding process on first level. The method has been used to solve
three different timetabling problems with promising results.