A New Integer Model for Selecting Students at Higher Education Institutions: Preparatory Classes of Engineers as Case Study
Abstract
:1. Introduction
2. Problem Statement
3. Objective and Methodology
3.1. Main Objective of Our Work
3.2. Methodology
3.2.1. Organizational Structure of Higher Education Institutions
- Higher education institution: This entity is generally responsible for the management of academic programs and specialty streams. It often develops selection criteria specific to their programs and reviews applications.
- Departments: Academic departments within institutions may be responsible for defining more specific selection criteria related to their specific areas. They may also be involved in the assessment of candidates.
- Selection Committees: Some institutions set up selection committees composed of teaching staff members and experts in the field. These committees evaluate applications and recommend candidates for admission to specialty streams.
- Admission Services: In many institutions, a centralized admissions service processes student applications and coordinates the selection process.
- Academic Advisors: Academic advisors can play an advisory role to students, helping them choose the appropriate specialty streams based on their academic and career goals.
- The Governance Bodies of the institution: In some cases, the governance bodies of the institution, such as boards of directors or management committees, may define general policies concerning selection criteria and specialty streams.
3.2.2. Rules of Selection
- Consistency of applications must be respected. Each student must apply to the appropriate streams in a given higher education institution.
- Selection twice is not permitted. Each student shall be assigned at most to a seat in a chosen academic stream in a given higher education institution. In fact, a student chooses a fixed number of streams belonging to a higher education institution and they are assigned at most to one seat from them.
- Collisions shall not be permitted. In a given higher education institution and in a particular academic stream, a seat is assigned at most to one student who has already chosen this stream.
- The maximum number of seats in a particular stream belonging to a higher education institution must be respected. In fact, each stream has its own number of seats that defines the capacity of the stream; then, the number of admitted students in each stream must not exceed the number of available seats.
- The quotas of students having a particular series of bachelor’s degree in each stream must be respected. In fact, in a given higher education institution, each available stream opens access to students with several series of bachelor’s degrees with different quotas.
- Priority is given to the first choices if possible. In fact, each student has the right to choose more than one stream in a given higher education institution and is assigned at most to one from these choices.
3.2.3. Methodology Adopted
4. The Mathematical Model of Student Selection Problem
4.1. General Features of the Model
- The student who has the right to apply for a seat in an academic stream to pursue their studies. The set of all these students is denoted by S, e.g.,
- The seat to which an admitted student is assigned to pursue their studies. The set of all available seats is denoted A, e.g.,
- The academic stream in which a student will pursue their studies. The set of all available streams in the higher education institution is denoted by B, e.g.,
- The type of Baccalaureate tokens from which each student graduates; the set of all these baccalaureate types is denoted by T, e.g.,
- The quota of students having a particular type of baccalaureate in a specific stream. The set of all possible quotas in the different streams is denoted by Q, e.g.,
- The number of seats available in an academic stream that represent the capacity of stream. The set of all these numbers is denoted by N, e.g.,
4.2. Special Features of the Model
- seat available in the stream }.
- student applying for the stream to pursue their studies}.
- student having the series of the baccalaureate}.
- .
- a stream chosen by the student .
- a stream open for students having the baccalaureate series .
- a baccalaureate series required to apply for the stream whose quota of seats devoted to students with this type of baccalaureate is exhausted.
- a baccalaureate series required to applying for the stream whose quota of seats devoted to students with this type of baccalaureate is not exhausted.
- a baccalaureate series required to apply for the stream }.
- is the number of available seats in the academic stream
- the quota of seats devoted to bachelors having the series of baccalaureate in the academic stream }.
- a priori assignment in which the student is assigned to the academic stream }.
4.3. Objective Function
- B: the set of all available streams belonging to the higher education institution;
- : the set of student applying for the stream b;
- : the set of available seats in the stream b.
4.4. Constraints of the Model
4.4.1. Uniqueness Constraints
- This set of constraints ensures that, in a higher education institution, each student shall be assigned at most to one seat in a stream of their choices. This constraint is given by the following equation:
- –
- S: the set of all students;
- –
- : the set of streams chosen by the student s.
- This set of constraints ensures that, in each stream b, a seat is assigned to one and only one student who has applied for the stream b. This rule is formulated by the following equation:
4.4.2. Capacity Constraints
- In a specified stream, the number of admitted students is limited. So, the number of assigned students to a stream shall not exceed the number of available seats in this stream.
- –
- : the number of available seats in the stream b.
- For each stream , the number of students having a particular series of baccalaureate and assigned to seats in the stream b shall not exceed the quota of seats devoted to students having this series of baccalaureate in the stream b, described as follows:
- –
- : the set of all baccalaureate series required to applying for the stream b;
- –
- : the set of students applying for the stream and having the series t of baccalaureate;
- –
- : the quota of seats devoted to bachelors having the baccalaureate series t in the stream b.
- In several cases, some students hold some types of baccalaureates in some streams that cannot exceed their quotas of seats, which can generate some unoccupied seats in such streams. In order to maximize the use of the academic resources, we redistribute these unoccupied seats among the other students holding other types of baccalaureate whose quotas of seats are exhausted. This property can be added by replacing the constraints (5) with the following constraints (6):
- –
- For and , we calculate the number of unoccupied seats in the stream b devoted to students holding the baccalaureate type t:
- –
- Then, we calculate the total number of unoccupied seats in the stream b:
- –
- Therefore, we redistribute this number of unoccupied seats among students holding the type of baccalaureate using the following equation:
- –
- The integer division generates a reminder denoted , which is also redistributed among students holding the baccalaureate type using the following equation:
4.4.3. Consecutiveness Constraints
- Consecutiveness of student choices: For every student, priority to first choices must be considered. In fact, each student wishes satisfy their first choice before the second, etc. This rule can be formulated by the following equation:
- Consecutiveness of competent students: This set of constraints ensures that priority is given to competent students. In this sense, students who have the higher weight coefficient will be assigned to a seat from their chosen streams. The following constraint formulates this rule:
- –
- : the weight coefficient of the student s.
In this equation, the term takes two possible values: It takes the 1 value if the student r is assigned to one of the streams b and —in this case, the student s can be assigned to a seat in the stream b; otherwise, it takes the 0 value if the student r is not assigned to any stream—in this case, and given that , the student r should not assigned to any stream.
4.4.4. Pre-Assignment Constraints
- This set of constraints ensures that certain students will be assigned to a seat in a stream of their choices and could be used either for the pre-allocation of students or for better handling and reducing complexity and computational difficulties. These constraints are formulated by the following equation:
- –
- : the set of a priori assignments to the list of students .
4.5. Determination of Weight Coefficients
5. Real Case Study
5.1. Presentation of the Moroccan Preparatory Classes
- Appropriate a work methodology based on organization, investigation, personal initiative, and perseverance.
- Develop autonomy and skills for thinking and reasoning as well as communication.
- Adapt to different problem situations.
- Gradually familiarize themselves with situations requiring sustained effort that may arise during their subsequent training and during execution of their professions.
5.2. Ways of Access to Preparatory Classes
- For holders of a Moroccan baccalaureate, access to preparatory classes is regulated by a ministerial letter. It specifies the procedures and steps to be followed for the application as well as all the selection and registration procedures.
- For students of Moroccan nationality and holding a foreign baccalaureate, application files are assessed at the central service level by a special committee. About twenty places, all courses combined, are reserved each year for this category of candidates.
- For students of foreign nationality with a foreign baccalaureate, the Moroccan Agency for International Cooperation (AMCI) centralizes application files. It also manages the quota reserved for this category of candidates. Around one hundred places are reserved for these candidates across the study streams.
5.3. Statement of the Student Selection Problem at Preparatory Classes
5.4. Organizational Structure of the Preparatory Classes
- The number of repeated years in the baccalaureate phase;
- Age, specialty, and the total mark of the student;
- A mark awarded by the class council;
- A qualifying average of subjects, calculated in terms of the educational streams chosen.
5.5. Data Description
- Streams available in this center;
- Type of Baccalaureate series required to access each stream;
- Quota of seats devoted to holders of each Baccalaureate series;
- Number of seats available in each stream in this center.
- where
- –
- The passing rate achieved in the first year of the Baccalaureate cycle;
- –
- The passing rate achieved in the second year of the Baccalaureate cycle.
- The qualifying average of subjects for each stream. For example, for the stream MPSI, the parameter is calculated using the equationwhere M, , , , and are the marks attained in the final exam of the second year, namely, in the subjects considered for accessing the MPSI stream:
- –
- the math mark;
- –
- the physics mark;
- –
- the Arabic mark;
- –
- the french mark;
- –
- the English mark.
- a grade attributable by the class council (rated on 25).
- a grade that takes into account the range of the stream chosen, where is the number of possible choices.
- a grade that takes into account the exact date of students candidature, where
- –
- deadline for submission of candidature on the web site;
- –
- starting date for submission of candidature on the web site;
- –
- exact submission date of candidature of student s on the web site.
6. Results and Discussion
6.1. Computational Environment
6.2. Results Presentation
6.3. Comparative Study
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Basic Selection Rules |
---|
|
Poles | Stream | Abbreviation |
---|---|---|
Scientific and Technological | Mathematics, Physics, and Engineering science | MPSI |
Physics, Chemistry, and Engineering science | PCSI | |
Technology and Industrial Sciences | TSI | |
Economic and Commercial | Economics and Trade, Scientific option | ECS |
Economy and Trade, Technological option | ECT |
Streams | MPSI | PCSI | TSI | ECS | ECT | Total Number of Students | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Year | Requests | Assigned | Requests | Assigned | Requests | Assigned | Requests | Assigned | Requests | Assigned | Requests | Assigned |
2014 | 26,356 | 1775 | 30,409 | 743 | 2096 | 484 | 19,736 | 70 | 20,066 | 789 | 98,663 | 3861 |
2015 | 25,515 | 1779 | 29,677 | 709 | 2147 | 520 | 22,544 | 62 | 21,051 | 978 | 100,934 | 4048 |
2016 | 31,060 | 1804 | 31,937 | 723 | 2556 | 551 | 23,513 | 68 | 24,177 | 937 | 113,243 | 4083 |
2017 | 22,323 | 1822 | 25,966 | 729 | 1887 | 557 | 20,306 | 62 | 18,306 | 1017 | 88,788 | 4187 |
2018 | 28,200 | 1858 | 26,933 | 682 | 1833 | 549 | 26,041 | 350 | 3812 | 713 | 86,819 | 4152 |
2019 | 33,366 | 1914 | 32,243 | 693 | 1922 | 600 | 30,892 | 383 | 4691 | 793 | 103,114 | 4383 |
2020 | 31,646 | 1899 | 31,518 | 693 | 2363 | 594 | 24,892 | 405 | 5276 | 743 | 95,695 | 4334 |
Center | Available Streams | Requests Number |
---|---|---|
High school Moulay Idriss (Fez) | MPSI | 4532 |
PCSI | 6725 | |
ECT | 799 | |
High school Mohmmed V (Casablanca) | MPSI | 7503 |
PCSI | 7974 | |
High school Moulay Ismael (Meknes) | ECS | 5290 |
ECT | 812 | |
Technical high school (Mohammedia) | MPSI | 7271 |
TSI | 728 |
Designation | Parameter | Signification |
---|---|---|
Streams | MPSI | Mathematics, Physics, and Engineering Sciences |
PCSI | Physics, Chemistry, and Engineering Sciences | |
TSI | Technology and Industrial Sciences | |
ECT | Economics and Trade, Technology Option | |
ECS | Economics and Trade, Scientific Option | |
Baccalaureate series | SM | Mathematical Sciences |
SX-SP | Experimental Sciences-Physical Sciences | |
SX-SVT | Experimental Sciences-Life and Earth Sciences | |
SX-SA | Experimental Sciences-Agricultural Sciences | |
SE | Economic Sciences | |
STE | Electrical Science and Technology | |
STM | Technology and Mechanical Sciences | |
SGC | Accounting Management Sciences |
Center | Stream | Capacity | Requests Number | Baccalaureate Series | Requests Number | Quotas of Seats | Availability |
---|---|---|---|---|---|---|---|
High school Moulay Idriss (Fez) | MPSI | 140 | 15,281 | SM | 1328 | 90% | 126 |
SX-SP | 13953 | 10% | 14 | ||||
PCSI | 68 | 6724 | SM | 1234 | 40% | 27 | |
SX-PC | 5328 | 40% | 27 | ||||
SX-SVT and SX-SA | 162 | 20% | 14 | ||||
ECT | 72 | 799 | SE | 721 | 75% | 54 | |
SGC | 78 | 25% | 18 | ||||
High school Mohmmed V (Casablanca) | MPSI | 175 | 7544 | SM | 5474 | 90% | 157 |
SX-PC | 2070 | 10% | 18 | ||||
PCSI | 70 | 7975 | SM | 1346 | 40% | 28 | |
SX-PC | 6428 | 40% | 28 | ||||
SX-SVT and SX-SA | 201 | 20% | 14 | ||||
High school Moulay Ismael (Meknes) | ECS | 72 | 5137 | SM | 982 | 50% | 36 |
SX-SP | 4155 | 50% | 36 | ||||
ECT | 72 | 812 | SE | 728 | 75% | 54 | |
SGC | 84 | 25% | 18 | ||||
Technical high school (Mohammedia) | MPSI | 64 | 7271 | SM | 1830 | 90% | 57 |
SX-SP | 5441 | 10% | 7 | ||||
TSI | 96 | 727 | STE | 486 | 70% | 67 | |
STM | 241 | 30% | 29 |
Center | Stream | Capacity | Requests Number | Baccalaureate Series | Availability | Assigned Number | Assignment Rate | E-Time (s) |
---|---|---|---|---|---|---|---|---|
High school Moulay Idriss (Fez) | MPSI | 140 | 15,281 | SM | 126 | 126 | 100% | 153,561.72 |
SX-SP | 14 | 14 | 100% | |||||
PCSI | 68 | 6724 | SM | 27 | 27 | 100% | ||
SX-PC | 27 | 27 | 100% | |||||
SX-SVT and SX-SA | 14 | 13 | 92.85% | |||||
ECT | 72 | 799 | SE | 54 | 54 | 100% | ||
SGC | 18 | 18 | 100% | |||||
High school Mohmmed V (Casablanca) | MPSI | 175 | 7544 | SM | 157 | 157 | 100% | 86,278.98 |
SX-PC | 18 | 17 | 94.44% | |||||
PCSI | 70 | 7975 | SM | 28 | 28 | 100% | ||
SX-PC | 28 | 28 | 100% | |||||
SX-SVT and SX-SA | 14 | 14 | 100% | |||||
High school Moulay Ismael (Meknes) | ECS | 72 | 5137 | SM | 36 | 36 | 100% | 19,118.04 |
SX-SP | 36 | 36 | 100% | |||||
ECT | 72 | 812 | SE | 54 | 54 | 100% | ||
SGC | 18 | 18 | 100% | |||||
Technical high school (Mohammedia) | MPSI | 64 | 7271 | SM | 57 | 57 | 100% | 27,858.45 |
SX-SP | 7 | 6 | 85.71% | |||||
TSI | 96 | 727 | STE | 67 | 67 | 100% | ||
STM | 29 | 28 | 96.55% |
Center | Stream | Baccalaureate Series | Availability | Our Method | Traditional Method |
---|---|---|---|---|---|
High school Moulay Idriss (Fez) | MPSI | SM | 126 | 126 | 126 |
SX-SP | 14 | 14 | 14 | ||
PCSI | SM | 27 | 27 | 27 | |
SX-PC | 27 | 27 | 27 | ||
SX-SVT and SX-SA | 14 | 13 | 14 | ||
ECT | SE | 54 | 54 | 54 | |
SGC | 18 | 18 | 18 | ||
High school Mohmmed V (Casablanca) | MPSI | SM | 157 | 157 | 157 |
SX-PC | 18 | 17 | 18 | ||
PCSI | SM | 28 | 28 | 28 | |
SX-PC | 28 | 28 | 28 | ||
SX-SVT and SX-SA | 14 | 14 | 14 | ||
High school Moulay Ismael (Meknes) | ECS | SM | 36 | 36 | 36 |
SX-SP | 36 | 36 | 36 | ||
ECT | SE | 54 | 54 | 54 | |
SGC | 18 | 18 | 18 | ||
Technical high school (Mohammedia) | MPSI | SM | 57 | 57 | 57 |
SX-SP | 7 | 6 | 7 | ||
TSI | STE | 67 | 67 | 67 | |
STM | 29 | 28 | 29 |
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Majdoub, S.; Loqman, C.; Boumhidi, J. A New Integer Model for Selecting Students at Higher Education Institutions: Preparatory Classes of Engineers as Case Study. Information 2024, 15, 529. https://doi.org/10.3390/info15090529
Majdoub S, Loqman C, Boumhidi J. A New Integer Model for Selecting Students at Higher Education Institutions: Preparatory Classes of Engineers as Case Study. Information. 2024; 15(9):529. https://doi.org/10.3390/info15090529
Chicago/Turabian StyleMajdoub, Soufyane, Chakir Loqman, and Jaouad Boumhidi. 2024. "A New Integer Model for Selecting Students at Higher Education Institutions: Preparatory Classes of Engineers as Case Study" Information 15, no. 9: 529. https://doi.org/10.3390/info15090529