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EXAM SCHEDULING PROBLEM:
AN AHP MODEL FOR
PARAMETER ESTIMATION
Zehra KAMIŞLI ÖZTÜRK
Anadolu University, Open Education Faculty
Eskisehir/TURKEY
[email protected]
Assoc.Prof. Dr. Mujgan SAĞIR ÖZDEMİR
Eskişehir Osmangazi University
Industrial Engineering Department
Eskisehir/TURKEY
[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 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.
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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
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
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Invigilator-Exam Assignment
which invigilators will take part on which exam
Time Slots (TS)
Exams
Invigilators
S1
S2
S3
...
Exam1
?
?
?
?
Exam2
?
?
?
?
Exam3
?
?
?
?
Exam4
?
?
?
?
Exam5
?
?
?
?
TS3
Exam6
?
?
?
?
.
.
?
?
?
?
.
.
?
?
?
?
TS1
TS2
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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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… continue
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,
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Mathematical Model
min

i
cit xit 
 d
t

4i
 d 4i  d 5i  d 5i

i
subject to
C1
 yij s jt  1,
i  I , t  T
j
C2
 yij  g j ,
j  J
i
C3
C4
xit  mit ,
i  I , t  T
 y ij a j  d 4i  d 4i
j
C5
 y ij s jt  d 5i  d 5i
j


  wi


 a j g j 
j
  r4i ,
w
 i 
i

  g j s jt 
 j


  r5i ,
ns




i  I , t  T
i  I , t  T
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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 tangible and intangible criteria that influence the
decision problems.
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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.
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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
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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
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
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Future work
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Future Work
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EXAM SCHEDULING PROBLEM:
An integer
programming
to
AN AHP
MODELapproach
FOR
classification problems
PARAMETER
ESTIMATION
based on polyhedral conic functions
Thank you …
Zehra KAMIŞLI ÖZTÜRK
Anadolu University, Open Education Faculty
Eskisehir/TURKEY
[email protected]
Assoc.Prof. Dr. Mujgan SAĞIR ÖZDEMİR
Eskişehir Osmangazi University
Industrial Engineering Department
Eskisehir/TURKEY
[email protected]