1 EXAM SCHEDULING PROBLEM: AN AHP MODEL FOR PARAMETER ESTIMATION Zehra KAMIŞLI ÖZTÜRK Anadolu University, Open Education Faculty Eskisehir/TURKEY zkamisli@anadolu. edu. tr Assoc. Prof. Dr. Mujgan SAĞIR ÖZDEMİR Eskişehir Osmangazi University Industrial Engineering Department Eskisehir/TURKEY msagir@ogu. edu. tr
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 • Timetabling problems are a kind of scheduling problems that deal with allocation of given resources to objects being placed in space time, time in such a way as to satisfy as nearly as possible a set of desirable objectives, subject to objectives 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 period and that room capacities are not exceeded”
6 Educational Timetabling Problems Course Scheduling Exam Scheduling Course-timeslot assignment Exam-timeslot assignment Course-room assignment Exam-room assignment Course-lecturer assignment Exam-room-timeslot assignment Course-lecturer-room-timeslot assignment Exam-invigilator assignment
7 Invigilator-Exam Assignment which invigilators will take part on which exam Time Slots (TS) Exams Invigilators S 1 S 2 S 3 . . . Exam 1 ? ? Exam 2 ? ? Exam 3 ? ? Exam 4 ? ? Exam 5 ? ? TS 3 Exam 6 ? ? . . ? ? TS 1 TS 2
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 • 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, … continue
11 Mathematical Model subject to C 1 C 2 C 3 C 4 C 5
12 AHP 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 • In 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. • To make the pair-wise comparisons, the comparison matrices of criteria and decision alternatives are constructed. • By 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 Requirements Assignments to undesired time slots Equally loaded exam schedules Exam parameters Duration Time slot Day Type 60 minutes 9 am -11 am Monday Open book 90 minutes 11 am- 1 pm Tuesday Test based 120 minutes 2 pm- 4 pm Wednesday Paper based 4 pm- 6 pm Thursday Without answer sheet Friday Saturday
15 Weights of all criteria
16 Sensitivity Analysis
17 Sensitivity Analysis
18 Conclusions and Future Works Exam scheduling problem is a time consuming task that is usually solved manually Considering preferences affect the overall performance of the system The parameters of invigilator-exam assignment problem are evaluated
19 Future work database User interface (FLASH) GAMS & C++ optimisation
20 Future Work 20
21 EXAM SCHEDULING PROBLEM: An integer. AHP MODELapproach to AN programming FOR classification problems PARAMETER ESTIMATION based on polyhedral conic functions Thank you … Zehra KAMIŞLI ÖZTÜRK Anadolu University, Open Education Faculty Eskisehir/TURKEY zkamisli@anadolu. edu. tr Assoc. Prof. Dr. Mujgan SAĞIR ÖZDEMİR Eskişehir Osmangazi University Industrial Engineering Department Eskisehir/TURKEY msagir@ogu. edu. tr
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