DESIGNING MATHEMATICAL MODEL FOR EXAMINATIONS TIMETABLE IN UNIVERSITIES AND ITS SOLUTIONS ANALYSIS

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SHAMS SHEMIRANI HOSSEIN; BASHIRI MAHDI; MODARRES MOHAMMAD

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Journal: JOURNAL OF INDUSTRIAL MANAGEMENT STUDIES Year:2017 | Volume:15 | Issue:44 Page(s): 27-50

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Title

DESIGNING MATHEMATICAL MODEL FOR EXAMINATIONS TIMETABLE IN UNIVERSITIES AND ITS SOLUTIONS ANALYSIS

Author(s)

SHAMS SHEMIRANI HOSSEIN | BASHIRI MAHDI | MODARRES MOHAMMAD | Issue Writer Certificate

Keywords

EXAMINATION SCHEDULINGQ1

OPTIMIZATION EXAMINATIONSQ1

MATHEMATICAL MODELINGQ1

QUADRATIC ASSIGNMENTQ1

SIMULATED ANNEALINGQ1

IMPERIALIST COMPETITIVE ALGORITHMQ1

Abstract

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.

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APA: Copy

SHAMS SHEMIRANI, HOSSEIN, BASHIRI, MAHDI, & MODARRES, MOHAMMAD. (2017). DESIGNING MATHEMATICAL MODEL FOR EXAMINATIONS TIMETABLE IN UNIVERSITIES AND ITS SOLUTIONS ANALYSIS. JOURNAL OF INDUSTRIAL MANAGEMENT STUDIES, 15(44 ), 27-50. SID. https://sid.ir/paper/213243/en

Vancouver: Copy

SHAMS SHEMIRANI HOSSEIN, BASHIRI MAHDI, MODARRES MOHAMMAD. DESIGNING MATHEMATICAL MODEL FOR EXAMINATIONS TIMETABLE IN UNIVERSITIES AND ITS SOLUTIONS ANALYSIS. JOURNAL OF INDUSTRIAL MANAGEMENT STUDIES[Internet]. 2017;15(44 ):27-50. Available from: https://sid.ir/paper/213243/en

IEEE: Copy

HOSSEIN SHAMS SHEMIRANI, MAHDI BASHIRI, and MOHAMMAD MODARRES, “DESIGNING MATHEMATICAL MODEL FOR EXAMINATIONS TIMETABLE IN UNIVERSITIES AND ITS SOLUTIONS ANALYSIS,” JOURNAL OF INDUSTRIAL MANAGEMENT STUDIES, vol. 15, no. 44 , pp. 27–50, 2017, [Online]. Available: https://sid.ir/paper/213243/en

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