Preferences Based Decision Making Mathematical Model for Faculty Course Assignment using Linear and Exponential Membership Functions

Abstract

Abstract-This paper gives a general model for the faculty course assignment problem that is a zero-one nonlinear multiobjective programming problem. Because of the nonconvexity of the problem, linear membership function and exponential membership function are used to find optimal solutions. The model with fuzzy methods provides a more satisfactory solution to a course assignment problem than assigning with arbitrary weights. Keywords-Preferences based decision makers, zero-one multiobjective programming, faculty course problem; scalarization. I. INTRODUCTIONThe employee assignment problem is becoming more intricate now a day. Specially schools, colleges, industries, organizations, etc are facing scheduling problem for assigning task. For example, scheduling or assigning work means matching people, places, time slots, and facilities. Further it is very difficult to solve problems having so many constraints. Generally, constraint is two types hard and soft. The problem of faculty course assignment means to satisfy all the constraints like one subject to one teacher only, teacher preference to teach course, not exceeding load, all course is distributed according to preferences of teachers as well as administrator. So many researchers have carried out research in the field of assigning courses to faculty. [3]. Two-stage optimization model to maximize faculty course preferences in assigning faculty members to courses (stage 1) and then maximize faculty time preferences by allocating courses to time blocks (stage 2). These constraints, which are computationally more complex than the others, are recovered during the second stage, and a number of sub-problems, one for each day of the week, are solved for local optima by Badri [7]. Bloomfield and McShary [1] also considered faculty preferences in their heuristic approach. Kara and Ozdemir [8] developed a minimax approach to the faculty course assignment problem by considering faculty preferences. Asratian and Werra [13] considered a theoretical model which extends the basic class teacher model of timetabling. This model corresponds to some situations which occur frequently in the basic training programs of universities and schools. It has been shown that this problem is NP complete when founded in some sufficient conditions for the existence of a timetable. Kara and Ozdemir presented a min-max approach to the faculty course assignment problem by considering faculty preferences. This study is a continuation and generalization of the faculty-course assignment problem considered earlier by Ozdemir and Gasimov [14]. They constructed a multi objective 0-1 nonlinear model for the problem, considering participants' average preferences and explained an effective way for its solution.To optimal fuzzy classification of students, Amintoosi & Haddadnia [18] has used a fuzzy function to solve university course timetable by genetic programming problem. A hybrid fuzzy evolutionary algorithm has been presented by Rachmawati & Srinivasan [20] to multi objective resource allocation pro...