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ABSTRACT
This paper describes a project of designing general departmental plan of study
using zero-one goal programming. First, a model that uses multiple objective
programming is built, and then it was used to construct the plan of study of industrial
engineering department at the Islamic University-Gaza. The output of the model is the
assignment of courses to semesters according to the goals and constraints associated.
The resulting plan of study clearly outperforms the manually designed plan of study
that is normally based on experience. Furthermore, formulation of the problem
systematically revealed that some constraints are usually unaccounted for in the plan.
The model was then solved using LP-Solve software. The overall objective function
could be decreased by an average of 53%. Finally, the model can be easily extended
and applied to other departments.
1- INTRODUCTION
The process of devising a plan of study requires that the plan satisfy several
objectives at varying degrees according to the importance of these objectives. Thus, it
is a difficult and time- consuming task, the complexity of which is conveyed through
the different levels of constraints imposed on it. In addition to the fact that experience
alone may not yield optimal solution. To date, the course assignment of college study
plans were carried out manually and repeatedly and thus consuming a substantial
amount of time and effort. With an increasing number of colleges and departments,
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there are greater needs to computerized models and programming algorithms to
perform such complex processes.
Goal programming is a widely used methodology that is especially suitable for
cases of multiple objective programming models. Goal programming does provide a
way of striving towards more than one objective simultaneously. It establishes a
specific numeric goal for each objective and then seeks for a solution that minimizes
the deviations of the objectives from their corresponding goals (Taha, 1987;
Lieberman and Hillier, 1990). Applications of goal programming cover wide range of
areas from academic resource planning (Albright, 1975; Joiner, 1980), accounting
(Killough and Sounders, 1973), agricultural planning (Wheeler, and Russel, 1977),
portfolio management (Kumar et. al, 1979) , library management (Hannan, 1978), and
media scheduling (Kluyver, 1979). Plan of study design, with its different levels
objectives renders the problem solvable using goal programming.
Most of what has been done in this area is that students are normally asked to design
their plans of study based on the general plan of study provided by the department
which is the topic of this paper. In other words, students select from the general study
plan courses that suit them. (Kokstal and Egitman, 1998) used quality function
deployment to improve the education quality of industrial engineering. While (Shea
and West, 1996) used a linear additive multi-objective model that was built based on
analytic hierarchy process to rank the importance of these objectives. Some of these
objectives include integration, communication, people skill, time between courses and
problem solving. The following sections briefly discuss applying zero-one goal
programming to generate department study plans. Finally, the study plan of the
Industrial Engineering Department at the Islamic University-Gaza is generated using
the given model as a case a study.
2- GENERAL PLANS OF STUDY
A general plan of study is a plan that includes all the courses required to be
successfully passed by students before they can get their degrees. A plan of study is
normally designed by assigning courses to semesters. In these plans of study, several
objectives need to be achieved and several constraints are required to be met. In
general, any plan of study includes three types of courses. These courses are
university requirements, college requirements and finally department requirements.
Each of these requirements has a certain number of credit hours. University
requirements are normally offered every semester. While, college requirements are
normally offered once a year in a given semester. The department requirements, in
most cases, include: 1) courses taken from the department of major, and 2) courses
taken from other departments (supporting courses). In this paper, the focus will be on
assigning department courses to semesters.
2.1-Variables definition
The decision variables are defined as
otherwise
if course i is assigned to semester j
yij 0
1 " " ::
To simplify the formulation, major courses are represented by the variable 'Y ',
whereas supporting courses are designated by 'X'.
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2.2 Objectives:
Five objectives are considered in this model. These objectives include
1- Number of credit hours in each semester may not exceed a given number of
credit hours in the first years. (University requirements are not included since
they are available all year round during the semesters). Normally this is done
to avoid overloading the students.
2- Number of credit hours taken during the last two semesters may not exceed a
given number credit hours. Normally, this objective is added in order to give
students some time to work on their senior projects in addition to the daunting
job search process.
3- To minimize the time interval among parts of the same fields. For example
(manufacturing I and manufacturing II)
4- To maximize the number of different fields courses taken during the first years.
In other words, to minimize the number of semesters required to cover classes
from different fields (e.g. Operations Research, Manufacturing…). This is
done in order to expose students to the different specialties in the department
so that they can discover their interests at an early stage of their study.
5- To minimize the difference between total numbers of credit hours offered
during the odd and even semesters in order to make sure that faculty loads are
equally distributed. In other words, faculty members are not overloaded at a
given semester and have no load during the other.