Stable Matching Algorithm Approach to Resolving Institutional
Projects Allocation and Distribution Optimization Problems
ISMAIL OLANIYI MURAINA
Department of Computer Science
Lagos State University of Education
Otto/Ijanikin Lagos
NIGERIA
Abstract: - The manual approach to resolving assignment issues involving the distribution or assignment of
graduate students to lecturers for projects or thesis studies continues to be difficult and time-consuming for both
the involved departments and the students. Even though it is evident that a student must be paired with a
lecturer, there are significant problems with matching due to individual preferences, specializations, interests,
prior student-teacher relationships, and other factors directly or indirectly related to the distribution process.
This study uses a reliable matching technique to address issues with project allocation and distribution
optimization problems, ten lecturers and ten graduate students participated. A matching algorithm is provided
randomly, with students favouring a lecturer (although these roles are reversible). The lists of preferences for
students and lecturers are input into the algorithm. Students and lecturers are split into two categories
throughout the algorithm: those previously selected and those who have not yet been determined (free). Both
instructors and students are initially accessible. The method chooses one student X randomly from the group of
free students, provided that the group is not empty. Student X prefers a lecturer (let's say lecturer Y) who he
rates among the top lecturers he has never previously picked. The Python programming language created and
executed the stable matching algorithm. The stable matching algorithm makes the allocation faster, more
accurate and timely compared to manual methods.
Key-Words: - Stable Machine, Algorithm, Optimization, Project Allocation, Optimization Problems, Matching
Algorithm
Received: June 29, 2023. Revised: March 17, 2024. Accepted: May 21, 2024. Published: June 21, 2024.
1 Introduction
A With the help of technology, working in isolation
is no more needed. Better decision is always made
when people come in unison to share and combine
ideas [11]. The distribution and allocation of
students for project work should not be stressful. A
student and institution should take project writing
seriously because it enables students to develop a
curious mind, always wanting to know why things
happen the way they do; it also allows the student to
be organised in his approach to solving the research
problem, it causes the student to stop relying on
rule-of-thumb but to be scientifically minded, and it
also enables the student to be more organised with
his work and do things in an orderly manner, It also
helps pupils acquire a sense of proportion and the
habit of tenaciously following goals to a successful
conclusion, which is the realisation of results.
Scheduling is one of the most important tools for
resolving educational allocation/resource issues
between teachers and students [2]. A project can
take weeks, months, or even a semester. Writing
projects necessitate a lecturer supervising one or
more students per session (usually final-year
students). The findings from scholars have
established their concerns about institutions and the
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process of selecting students for particular courses
of study[3]. Many students, particularly graduating
students, find it inconvenient that they must do
project work. They feel stressed by the cognitive
weight of the educational system, and project work
adds to it. Because the project is a requirement for
students to graduate, they must complete it. For
appropriate allocation and distribution, students
and lecturers must allow for preferences; if
students can prioritize the professor, they prefer to
supervise them, and lecturers should be allowed to
do the same. Appropriate allocation of projects will
result in a high level of interest and understanding
between students and professors during the project
writing process. The stable matching method is one
approach to solving student-lecturer
allocation/distribution difficulties.
2 Related Literature
Using a stable matching algorithm has been
acknowledged as a problem-solving strategy for
various societal and organizational difficulties.
Among the researchers are:
Many researchers have examined variants of the
benchmark resource leveling and allocation
optimization issues using various scheduling
approaches, according to [4], because it makes
scheduling techniques easier and faster. As
educational projects get more complicated, multiple
obstacles develop, such as appropriately deploying
human and material resources or selecting
alternative investments within a portfolio. Because
answers based on intuition are risky due to the
complexity, there is a search for less intuitive and
more dependable approaches to handling
educational challenges. An engineering approach to
the problem may lead to operations research
mathematical modeling to aid in timetabling
solution discovery [5]. [6] also observed that the
issue of class distribution among available teachers
was time-consuming and attracted various
constraints that must be met, such as preventing a
teacher from teaching in two different locations at
the same time and avoiding solutions which some
teachers have more class hours than others.
In most cases, this is done manually, which is time-
consuming and does not allow teachers to see
different combinations of class assignments.
Furthermore, it is frequently prone to errors.
According to [7], an assignment problem is a
particular type of linear programming that is a well-
studied optimization problem in practically every
job of life. The fundamental goal of using an
optimization problem algorithm is to assign a given
number of people to an equal number of positions
on a one-to-one basis so that the overall cost of
accomplishing that task is minimized or maximized
for efficiency. According to [8], the essence of using
an assignment problem is due to the fluctuating
capacity of a human or machine to accomplish the
assigned work or job. The use of classical
Assignment Problems to solve real-world problems
has some limitations. Stable Matching can
undoubtedly help to alleviate these constraints. Over
the years, certain scholars, such as [4], have
employed a simple scheduling technique known as
resource histogram to utilize the allocation and
leveling of available resources. According to the
findings, resource constraints substantially impact
performance and lead the project to be extended
beyond its scheduled term. [5] also employed a
mathematical model (software) to solve a
timetabling problem as valuable software to
maximize the utilization of human resources. The
software was built on a mathematical model that
determined the timetable while limiting the number
of students with conflicting schedules. [6]
developed a decision support tool for assigning
professors to university classrooms by appreciating
the simple technique to address assignment
challenges. The research comprised the creation of
computer software that used object orientation
notions to build a search technique called Beam
Search, which investigates the combinatorial nature
of the problem. The programming language utilized
was Java, and the program included a graphical
interface for inserting and manipulating data.
Similarly, [7] conducted a a study on the placement
of the right individual for the correct position, which
they found to be highly challenging due to
ambiguity and imprecise information. To tackle the
challenge, they adopted a fuzzy assignment problem
approach. The findings obtained were compared to
effectively apply the placement of the right
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candidate for the suitable job. Further research by
[9] examined the criteria for assigning practice
teachers to supervise prospective senior teachers
during school experience and practice courses. The
study's findings indicated some criteria for giving
practice teachers, such as informal comments from
students and faculty mentors, informal perspectives
of school and university coordinators, and
participant ideas about the assignment procedure. In
2021, [10] offered an optimal solution to a wide
range of assignment problems, directly employing
numerical illustration to determine the optimality of
the model's output. The appealing model required
simple arithmetic and logical computations to
generate output.
The usual way of solving the general assignment
problem by most institutions is to manually examine
the full list of courses in some predefined order and
for each course to a lecturer or lecturers of best-
fitting [10]. In line with this, [11] studied
departmental course distribution in a university
system over a specific period. The distribution
considered the limits imposed by lecturers' contact
hours and teaching load per week, as well as
individual lecturers' choices for courses offered in
the department per semester. The goal was to create
a framework to allocate methods to lecturers based
on their choices optimally. The Gomory cutting
plane algorithm was used to solve the course
allocation problem, which was then implemented in
MATLAB. Similarly, other scholars have used
stable matching algorithms for similar allocation
and distribution concerns [12], [8], [13]. For
example, [12] provides a private stable matching
algorithm based on the well-known Gale and
Shapley method. Several independent parties,
known as Matching Authorities, were used in the
secret algorithm.
When Matching Authorities are truthful, the
protocol correctly produces a stable match. It
provides no information other than what can be
learned from that match and the participants'
preferences controlled by the adversary. The
protocol's security and privacy were built on re-
encryption mix networks and an additively
homomorphic semantically secure public-key
encryption technique. [8], like other academics, did
research on the student-Project Allocation problem
(SPA) to solve a generalization of the traditional
Hospitals / Residents problem (HR). The study
included a group of students, projects, and
instructors. A lecturer is assigned a task, and both
the lecturer and the project have capacity
constraints. The results of stable Matching provided
by the first algorithm are the best for all students,
whereas the results produced by the second
algorithm are the best for all instructors.
Furthermore, it was demonstrated that some
structural insights involving the set of stable
matchings in a given instance of SPA were quite
general and could be applied to various settings
other than student-project allocation. [13] employed
stable Matching in economics to resolve conflicts of
interest among selfish market agents in their study.
Sub-problem agents might express their preferences
over solution agents in the study, and vice versa.
The Stable Matching Model (STM) produced a
single solution for each sub-problem.
Similarly, [14] discovered that stable matching
problems are the same as problems involving stable
X-network setups. [12] said that the absence of any
odd party is both a necessary and sufficient
condition for the presence of a complete stable
matching. A "stable partition," a new structure that
generalized the concept of a whole stable matching,
showing that every case of the stable roommate's
dilemma has at least one such design. A stable
partition also contained all of the odd parties.
Finally, an O(n2) algorithm discovers one stable
division, which yields all the uncommon parties. In
the same vein, [12] examined stable matching
problems from an algorithmic standpoint, with some
problems derived from new stable matching models
and others from existing stable matching models
involving ties and incomplete lists, with additional
natural constraints on the problem instance. The
application of the stable matching algorithm in
addressing matching-related issues has grown in
popularity. [15] employed the stable matching
algorithm to resolve difficulties in discovering a b-
matching of the highest weight while observing
lower quotas. They demonstrated in their study that
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obtaining such a maximum weight matching is an
NP-complete task even if all students mark at most
two projects and all projects have upper and lower
quotas of three. Furthermore, it was demonstrated
that if no upper percentage is greater than two, the
issue is automatically polynomially tractable. In a
general situation, an approximation approach that
achieved the best possible ratio described in several
forms was presented. Anytime we are crucial with
time, accuracy, and error free of processing data,
using machine learning tactic to handle the
necessary procedures always prove encouraging and
convenient than manual methods. The usual way of
solving the general assignment problem by most
institutions is to manually examine the full list of
courses in some predefined order and for each
course to find a corresponding shortlist of best-
fitting lecturers, and then assign one of those
lecturers to the course [16].
3 Methodology
The stable matching technique is used in this
work to handle project allocation and
distribution optimization problems. There were
ten graduate students and ten lecturers engaged.
A matching algorithm is provided at random,
with students preferring a professor (these roles
are reversible). The algorithm is fed lists of
student and professor preferences as input.
Students and professors are divided into two
groups throughout the algorithm: those who
have already been picked and those who have
yet to be chosen (free). All students and
lecturers are initially free. As long as the group
of free students is not empty, the algorithm
chooses one student X at random from the
group of free students. Student X prefers a
lecturer whom he ranks top among instructors
whom he has never previously preferred (let us
call him lecturer Y). The Python programming
language was used to create and run the stable
matching algorithm. The Gale-Shapley
technique was modified to address the current
issue (See Fig. 1).
Fig. 1: Gale-Shapley Algorithm Adapted
4 Results
The hypothesized model for Matching was built
in which all students were freely matched with
all professors without regard for the students' or
lecturers' preferences (See Fig. 2).
Figure 2: Hypothesized Model for Matching
Students and Lecturers
In order to take preferences into account, the tables
(Tables 1 and 2) indicate student and professor
preferences.
Table 1: Table of Preferences for students
Stu
1st
2nd
3rd
5th
6th
7st
8th
9th
10th
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According to the students' preferences table (Table
1), student one chooses lecturer 1 initially, and if
lecturer 1 is unavailable, he prefers lecturer 2. It
proceeds in this order to the final speaker he selects
based on his preference - which could be based on
interest, knowledge, area of specialization, or other
instinctual reasons. Similarly, lecturers have
preferences for the types of students they want to
supervise based on previous relationships or
observations of such lecturers during class activities
(See Table 2).
Table 2: Table of Preferences for Lecturers
Stud
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1st
Pref
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2nd
Pre
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The code was written in Python and yielded the
following results.
Fig. 3: Results generated from the codes
According to the allocation results, there were
certain occasions when two or more students were
assigned to a professor, which could generate
confusion (see Fig. 4). When two or more students
are unable to attach to a single professor, there
should be a break between students and lecturers,
and any possible matching should be considered.
Fig. 4: Students that are to break for effective
allocation
Finally, the best allocation and distribution were
found. In this case, all 10 students were assigned to
all instructors without any conflicts. As a result, Fig.
5 shows the final allocation with 100%
optimization.
Fig. 5: Successful allocation of students to lecturers
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As a result, the results of the Python code allocation
are supported by Fig. 6. This also means that the
project allocation/distribution has been optimized.
Fig. 6: Optimal Allocation Obtained
Expanded Optimization
Stu
den
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1st
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INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS,
COMPUTATIONAL SCIENCE AND SYSTEMS ENGINEERING
DOI: 10.37394/232026.2024.6.9
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E-ISSN: 2766-9823
106
Volume 6, 2024
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Stud
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INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS,
COMPUTATIONAL SCIENCE AND SYSTEMS ENGINEERING
DOI: 10.37394/232026.2024.6.9
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E-ISSN: 2766-9823
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Volume 6, 2024
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INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS,
COMPUTATIONAL SCIENCE AND SYSTEMS ENGINEERING
DOI: 10.37394/232026.2024.6.9
Ismail Olaniyi Muraina
E-ISSN: 2766-9823
108
Volume 6, 2024
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Student6 is breaking with Lecturer10.
2
Student3 is breaking with Lecturer7.
3
Student5 is breaking with Lecturer3.
4
Student10 is breaking with Lecturer10.
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Student8 is breaking with Lecturer8.
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Student14 is breaking with Lecturer9.
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Student15 is breaking with Lecturer5.
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Student20 is breaking with Lecturer6.
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Student4 is breaking with Lecturer4. …
5 Discussion
There are hundreds of grudges among students in
traditional project allocations between students and
professors due to inadequate clues as a result of the
lecturer assigned to such student. Due to time limits,
the difficulty of distribution, and allocation loops,
several students did not complete their projects or
sought the assistance of an expert to assist them.
The basic goal of using an optimization problem
method is to assign a given number of people to an
equal number of jobs on a one-to-one basis in such a
way that the overall time/cost of doing that work is
minimized or the total efficiency/profit of allocation
is maximized. According to Akpan and Abraham
(2016), the essence of using assignment problem is
due to the fluctuating capacity of a human or
machine to accomplish the assigned work or job.
The use of classical Assignment Problems to solve
real-world problems has some limitations. Stable
Matching can certainly help to alleviate these
constraints. The model was appealing and required
extremely simple arithmetic and logical
computations to produce results. It should be
emphasized that the model was provided properly
INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS,
COMPUTATIONAL SCIENCE AND SYSTEMS ENGINEERING
DOI: 10.37394/232026.2024.6.9
Ismail Olaniyi Muraina
E-ISSN: 2766-9823
109
Volume 6, 2024
and accurately in order to achieve the desired
output. Researchers such as [13] used stable
Matching in economics to resolve conflicts of
interest among selfish market actors, and [15] used
stable matching algorithm to resolve challenges to
identify a b-matching of highest weight while
observing lower quotas. [11] conducted a study on
departmental course allocation problem in a
university system over a definite period of time, and
[4] used a simple scheduling technique called
resource histogram to utilize the allocation and
leveling of the available resources.
6 Conclusion
It goes without saying that project allocation and
distribution are crucial in final year project writing.
As a result, it can be inferred that the approach
(Stable Matching Algorithm) delivers an optimal
solution to an Assignment Problem in less rounds.
This strategy will be highly useful for departmental
academic staff/decision makers dealing with
allocation/distribution concerns because it takes less
time and is very simple to grasp and execute. Future
studies may investigate using another programming
language to achieve similar outcomes.
References:
[1]. Muraina I O, Aiyegbusi E A& Lesi B O
(2021). Ensuring Team Building Learning
with the Use of Relevant Collaborative
Tools. Middle East International
Conference on Contemporary Scientific
Studies-VI, September 20-22, 2021
Beirut, Lebanon. Pp 264-270
[2]. Muraina, I O (2023). Youth
Empowerment, Green Skills Acquisition,
and Environmental Needs &
Sustainability: Analysis and Emphasis on
Correlational and Influential Factors.
CUKUROVA 11th International Scientific
Researches Conference, August 22-24,
2023/ Adana, Turkey, 844-851
[3]. Muraina I O, Lesi B O, Oladapo W O &
Hamzat I O (2021). Artificial Neural
Network Model to Predict Students
‘Relevant Courses of Study on Getting
Into Higher Institutions. International
Siirt Scientific Research Congress 5-7
November 2021 SIIRT, Turkey. Pp 364-
370
[4]. Eirgash, M. A. (2020). Resource
Allocation and Leveling in Construction
Management Projects with Resource
Histogram. American Journal of
Engineering and Technology
Management. Vol. 5, No. 6, pp. 91-95.
doi: 10.11648/j.ajetm.20200506.11
[5]. Azevedo, A. T; Kameyama, A; Amorim,
J. A & Gustavsson, P M (2013a) A
Mathematical Model for Determining
Timetables that Minimizes the Number of
Students with Conflicting Schedules. A
Conference Paper. Retrieved from
https://www.researchgate.net
[6]. Azevedo, Anibal Tavares de; Kameyama,
Alexander; Amorim, Joni A &
Gustavsson, Per M (2013b) A
Mathematical Model for Determining
Timetables that Minimizes the Number of
Students with Conflicting Schedules. A
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