Industrial Management Studies

Designing Mathematical Model for Examinations Timetable in Universities and its Solutions Analysis

Document Type : Research Paper

Authors

Hossein Shams Shemirani1
Mahdi Bashiri
Mohammad Modarres
https://doi.org/10.22054/jims.2017.7337
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.

Keywords

Examination Scheduling
optimization Examinations
Mathematical Modeling
Quadratic Assignment
Simulated Annealing
imperialist competitive algorithm
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05 مطالعات مدیریت صنعتی – سال پانزدهم، شماره 44 ، بهار 69
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Industrial Management Studies
Volume 15, Issue 44
Spring 2017
Pages 27-50

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