Hossein Shams Shemirani1; Mahdi Bashiri; Mohammad Modarres
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 ...
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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.
Mehdi Yazdani; Bahman Naderi
Abstract
In the scheduling problems, it is commonly assumed that processing times are fixed and known. In the literature of project scheduling emphasizes that the time of each activity/operation can be multi-mode and by assigning more resources, the activity time can be reduced. In these problems, in addition ...
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In the scheduling problems, it is commonly assumed that processing times are fixed and known. In the literature of project scheduling emphasizes that the time of each activity/operation can be multi-mode and by assigning more resources, the activity time can be reduced. In these problems, in addition to activity scheduling, allocation of available limited resources to the activities should also be carried out. This assumption that processing time of activities is fixed is a weakness in scheduling literature. This paper develops the classic problem flow shop scheduling to multi-mode resource-cosntrainted flow shop scheduling problem. This paper discusses comprehensively about mathematical modeling. In this regard, two mixed integer linear programming models with two differnet concepts are presented. The first model is location-based model and the second is sequence-based. The performance of the models are evaluated by comparing their size and computational complexities. In the size complexity, the first model requires more variables but less constraints than second Model. In the computational complexity, the first model significantly outperforms than the second Model. Also, the first model, besides solving more problems as optimally, requires less time to solve than the second model
S.M. Ali Khatami Fivouzabadi; Mohsen Rahimi; Ali Mohtashami
Volume 5, Issue 14 , December 2006, , Pages 29-54
Abstract
In this paper, we will consider the problem of courses timetabling in a small educational institute. We will present the mathematical model considering six hard constraints (compelling constraints) and five soft constraints (constraints that are lot compelling, but regarding them results increasing the ...
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In this paper, we will consider the problem of courses timetabling in a small educational institute. We will present the mathematical model considering six hard constraints (compelling constraints) and five soft constraints (constraints that are lot compelling, but regarding them results increasing the utility of timetable). To formulating the model we will use a type of goal programming. In this paper we will try to define decision variables, hard constraints, soft constraints and objective function in a step by step direction. Afterward we will test the model on a mathematical example.