Designing Mathematical Model for Examinations Timetable in Universities and its Solutions Analysis
In this research, optimization of examinations' timetable for university courses, based on a real problem in one of the universities in Iran is studied. The objective function defined for this problem is more practical and realistic than the other objective functions that have been utilized by...
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| Format: | Article |
| Language: | fas |
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Allameh Tabataba'i University Press
2017-03-01
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| Series: | Muṭāli̒āt-i Mudīriyyat-i Ṣan̒atī |
| Subjects: | |
| Online Access: | https://jims.atu.ac.ir/article_7337_dcc8b6dced75d63c482b28b015d891a1.pdf |
| _version_ | 1797367686502547456 |
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| author | Hossein Shams Shemirani1 Mahdi Bashiri Mohammad Modarres |
| author_facet | Hossein Shams Shemirani1 Mahdi Bashiri Mohammad Modarres |
| author_sort | Hossein Shams Shemirani1 |
| collection | DOAJ |
| description | In this research, optimization of examinations' timetable for university courses, based on a real problem in one of the universities in Iran is studied. The objective function defined for this problem is more practical and realistic than the other objective functions that have been utilized by previous researchers in literature and effectively reflects the real objective of the problem. In order to define the objective function, we have made use of Coulomb's law in electricity that says the magnitude of the electrostatic force of interaction between two point charges is directly proportional to the scalar multiplication of the magnitudes of the charges and inversely proportional to the square of the distance between them. We have defined a repulsive force between any pair of Examinations. The optimum solution is achieved when the sum of all forces is minimized. Hence, the obtained mathematical model is a non-linear programming with binary variables, similar to the quadratic assignment problem (QAP) which is an NP-Hard problem. This sort of problems can be solved exactly only if they are in small sizes. For solving this problem in medium and large scale, some methods are used based on Simulated Annealing (SA) algorithm and Imperialist Competitive algorithm (ICA). These algorithms can reach good sub-optimal solutions in a short period of time. Practical results of this mathematical model are already used in one of the national universities in Iran. The practical results demonstrate the high efficiency and effectiveness of this model. |
| first_indexed | 2024-03-08T17:21:45Z |
| format | Article |
| id | doaj.art-683833b2bc284505b6e1a358d05bd172 |
| institution | Directory Open Access Journal |
| issn | 2251-8029 2476-602X |
| language | fas |
| last_indexed | 2024-03-08T17:21:45Z |
| publishDate | 2017-03-01 |
| publisher | Allameh Tabataba'i University Press |
| record_format | Article |
| series | Muṭāli̒āt-i Mudīriyyat-i Ṣan̒atī |
| spelling | doaj.art-683833b2bc284505b6e1a358d05bd1722024-01-03T04:44:42ZfasAllameh Tabataba'i University PressMuṭāli̒āt-i Mudīriyyat-i Ṣan̒atī2251-80292476-602X2017-03-011544275010.22054/jims.2017.73377337Designing Mathematical Model for Examinations Timetable in Universities and its Solutions AnalysisHossein Shams Shemirani10Mahdi Bashiri1Mohammad Modarres2مربی، گروه مهندسی صنایع، دانشکده فنی و مهندسی گلپایگاناستاد، گروه مهندسی صنایع، دانشگاه شاهداستاد، دانشکده مهندسی صنایع، دانشگاه صنعتی شریفIn this research, optimization of examinations' timetable for university courses, based on a real problem in one of the universities in Iran is studied. The objective function defined for this problem is more practical and realistic than the other objective functions that have been utilized by previous researchers in literature and effectively reflects the real objective of the problem. In order to define the objective function, we have made use of Coulomb's law in electricity that says the magnitude of the electrostatic force of interaction between two point charges is directly proportional to the scalar multiplication of the magnitudes of the charges and inversely proportional to the square of the distance between them. We have defined a repulsive force between any pair of Examinations. The optimum solution is achieved when the sum of all forces is minimized. Hence, the obtained mathematical model is a non-linear programming with binary variables, similar to the quadratic assignment problem (QAP) which is an NP-Hard problem. This sort of problems can be solved exactly only if they are in small sizes. For solving this problem in medium and large scale, some methods are used based on Simulated Annealing (SA) algorithm and Imperialist Competitive algorithm (ICA). These algorithms can reach good sub-optimal solutions in a short period of time. Practical results of this mathematical model are already used in one of the national universities in Iran. The practical results demonstrate the high efficiency and effectiveness of this model.https://jims.atu.ac.ir/article_7337_dcc8b6dced75d63c482b28b015d891a1.pdfexamination schedulingoptimization examinationsmathematical modelingquadratic assignmentsimulated annealingimperialist competitive algorithm |
| spellingShingle | Hossein Shams Shemirani1 Mahdi Bashiri Mohammad Modarres Designing Mathematical Model for Examinations Timetable in Universities and its Solutions Analysis Muṭāli̒āt-i Mudīriyyat-i Ṣan̒atī examination scheduling optimization examinations mathematical modeling quadratic assignment simulated annealing imperialist competitive algorithm |
| title | Designing Mathematical Model for Examinations Timetable in Universities and its Solutions Analysis |
| title_full | Designing Mathematical Model for Examinations Timetable in Universities and its Solutions Analysis |
| title_fullStr | Designing Mathematical Model for Examinations Timetable in Universities and its Solutions Analysis |
| title_full_unstemmed | Designing Mathematical Model for Examinations Timetable in Universities and its Solutions Analysis |
| title_short | Designing Mathematical Model for Examinations Timetable in Universities and its Solutions Analysis |
| title_sort | designing mathematical model for examinations timetable in universities and its solutions analysis |
| topic | examination scheduling optimization examinations mathematical modeling quadratic assignment simulated annealing imperialist competitive algorithm |
| url | https://jims.atu.ac.ir/article_7337_dcc8b6dced75d63c482b28b015d891a1.pdf |
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