1 exam scheduling problem: an ahp model for parameter estimation zehra kamiŞli ÖztÜrk anadolu...
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EXAM SCHEDULING PROBLEM: AN AHP MODEL FOR
PARAMETER ESTIMATION
Zehra KAMIŞLI ÖZTÜRKAnadolu University, Open Education Faculty
Eskisehir/TURKEY [email protected]
Assoc.Prof. Dr. Mujgan SAĞIR ÖZDEMİREskişehir Osmangazi University
Industrial Engineering DepartmentEskisehir/[email protected]
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Outline
• The Goal
• Timetabling Problems
• Educational Timetabling
• Invigilator-Exam Scheduling
• The AHP
• Conclusions and Future Works
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GOAL
Constructing a valid multi cirteria decison model.
– Robustness
– Appropriate method
– Qualitative and quantitative factors
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Timetabling Problems
• Timetabling problems are a kind of scheduling problems that deal with allocationallocation of given resourcesresources to objects being placed in space timespace time, in such a way as to satisfy as nearly as possible a set of desirable objectivesobjectives, subject to constraints. constraints.
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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”
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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
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which invigilators will take part on which exam
Invigilator-Exam Assignment
Time Slots (TS) ExamsInvigilators
S1 S2 S3 . . .
TS1
Exam1 ? ? ? ?
Exam2 ? ? ? ?
TS2
Exam3 ? ? ? ?
Exam4 ? ? ? ?
Exam5 ? ? ? ?
TS3 Exam6 ? ? ? ?
. . ? ? ? ?
. . ? ? ? ?
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The context diagram of automated invigilator assignment system
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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
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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,
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Mathematical Model
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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 tangibletangible and intangibleintangible criteria that influence the decision problems.
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AHP
• In the AHP process decision makers give judgments judgments about relative importance for each criterion, and then they specify preferences 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 pair-wise comparisons, the comparison matrices of criteria and decision alternatives are constructed.
• By making the comparisons, the weightsweights (importance) of each criterion are obtained. In the final step, by hierarchical synthesis, the weights (priorities) of the alternatives are obtained.
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AHP Model of the ProblemGoal: Find the most important criteria of invigilator-exam assignment problem
Invigilator Requirements Exam parameters
Assignments to undesired time
slots
Equally loaded exam schedules
Time slot Day Type
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
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Weights of all criteria
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Sensitivity Analysis
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Sensitivity Analysis
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Conclusions and Future Works
Considering preferences affect the overall performance of the system
Considering preferences affect the overall performance of the system
Exam scheduling problem is a time consuming task that is usually solved manually
Exam scheduling problem is a time consuming task that is usually solved manually
The parameters of invigilator-exam assignment problem are evaluated
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Future work
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Future Work
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21
An integer programming approach to classification problems
based on polyhedral conic functions
Thank you …Thank you …
EXAM SCHEDULING PROBLEM: AN AHP MODEL FOR
PARAMETER ESTIMATION
Zehra KAMIŞLI ÖZTÜRKAnadolu University, Open Education Faculty
Eskisehir/TURKEY [email protected]
Assoc.Prof. Dr. Mujgan SAĞIR ÖZDEMİREskişehir Osmangazi University
Industrial Engineering DepartmentEskisehir/[email protected]