1 EXAM SCHEDULING PROBLEM: AN AHP MODEL FOR PARAMETER ESTIMATION Zehra KAMIŞLI ÖZTÜRK Anadolu University, Open Education Faculty Eskisehir/TURKEY Assoc.Prof. Dr. Mujgan SAĞIR ÖZDEMİR Eskişehir Osmangazi University Industrial Engineering Department Eskisehir/TURKEY

2 Outline The Goal Timetabling Problems Educational Timetabling Invigilator-Exam Scheduling The AHP Conclusions and Future Works

3 GOAL Constructing a valid multi cirteria decison model. –Robustness –Appropriate method –Qualitative and quantitative factors

4 Timetabling Problems allocation resourcesspace time objectives constraints.Timetabling problems are a kind of scheduling problems that deal with allocation of given resources to objects being placed in space time, in such a way as to satisfy as nearly as possible a set of desirable objectives, subject to constraints.

5 Educational Timetabling The problem of constructing course timetables for academic institutions consists of “allocating the set of courses offered by the university to time periods and classrooms in such a way that no teacher, student or room is used more than once per period and that room capacities are not exceeded”

6 Educational Timetabling Educational Timetabling Problems Exam Scheduling Exam-invigilator assignment Course-timeslot assignment Course-room assignment Course-lecturer-room-timeslot assignment Course Scheduling Course-lecturer assignment Exam-timeslot assignment Exam-room assignment Exam-room-timeslot assignment

7 which invigilators will take part on which exam Invigilator-Exam Assignment Time Slots (TS)Exams Invigilators S1S1 S2S2 S3S3... TS 1 Exam 1 ???? Exam 2 ???? TS 2 Exam 3 ???? Exam 4 ???? Exam 5 ???? TS 3 Exam 6 ????..????..????

8 The context diagram of automated invigilator assignment system

9 Multiobjective Structure Simultaneous minimization of total assignment cost, the total deviation from average exam weights the total deviation from average number of exams in undesired time slots

10 Constraints … continue Hard Constraints One invigilator must be assigned to maximum one exam at time slot t required number of invigilators must be assinged to exactly each exam Pre assignments must be satisfied Soft Constraints (description of user’ whishes) balancing of the total exam weights of each invigilators number of exams in undesired time slots,

11 Mathematical Model subject to C1C1C1C1 C2C2C2C2 C3C3C3C3 C4C4C4C4 C5C5C5C5

12 AHP tangibleintangible An Analytic Hierarchy Process (AHP) model is developed to weigh different criteria of the problem. AHP has been a popular research and application tool for multicriteria decision-making. The AHP was developed by Saaty [Saaty, 1986; Saaty, 1980] and has been identified as an important approach to multi-criteria decision making problems of choose and prioritization. There can be several tangible and intangible criteria that influence the decision problems.

13 AHP judgments preferencesIn the AHP process decision makers give judgments about relative importance for each criterion, and then they specify preferences on each criterion for each decision alternative. The first step of AHP is the definition of decision problem and determination of its objective. Then, the decision criteria are defined in the form of a hierarchy. pair-wiseTo make the pair-wise comparisons, the comparison matrices of criteria and decision alternatives are constructed. weightsBy making the comparisons, the weights (importance) of each criterion are obtained. In the final step, by hierarchical synthesis, the weights (priorities) of the alternatives are obtained.

14 AHP Model of the Problem Goal: Find the most important criteria of invigilator-exam assignment problem Invigilator RequirementsExam parameters Assignments to undesired time slots Equally loaded exam schedules Time slotDayType Monday Tuesday Wednesday Thursday Friday Saturday 9 am -11 am 11 am- 1 pm 2 pm- 4 pm 4 pm- 6 pm Open book Test based Paper based Without answer sheet Duration 60 minutes 120 minutes 90 minutes

15 Weights of all criteria

16 Sensitivity Analysis

17 Sensitivity Analysis

18 Conclusions and Future Works Considering preferences affect the overall performance of the system Exam scheduling problem is a time consuming task that is usually solved manually The parameters of invigilator-exam assignment problem are evaluated

19 Future work

20 Future Work 20

21 An integer programming approach to classification problems based on polyhedral conic functions Thank you … EXAM SCHEDULING PROBLEM: AN AHP MODEL FOR PARAMETER ESTIMATION Zehra KAMIŞLI ÖZTÜRK Anadolu University, Open Education Faculty Eskisehir/TURKEY Assoc.Prof. Dr. Mujgan SAĞIR ÖZDEMİR Eskişehir Osmangazi University Industrial Engineering Department Eskisehir/TURKEY