EXAM SCHEDULING PROBLEM: AN AHP MODEL FOR PARAMETER ESTIMATION

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EXAM SCHEDULING PROBLEM AN AHP MODEL FOR
PARAMETER ESTIMATION
Zehra KAMISLI ÖZTÜRK Anadolu University, Open
Education Faculty Eskisehir/TURKEY
zkamisli_at_anadolu.edu.tr Assoc.Prof. Dr. Mujgan
SAGIR ÖZDEMIR Eskisehir Osmangazi
University Industrial Engineering
Department Eskisehir/TURKEY msagir_at_ogu.edu.tr
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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
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Invigilator-Exam Assignment

• which invigilators will take part on which exam

Time Slots (TS) Exams Invigilators Invigilators Invigilators Invigilators
Time Slots (TS) Exams S1 S2 S3 . . .
TS1 Exam1 ? ? ? ?
TS1 Exam2 ? ? ? ?
TS2 Exam3 ? ? ? ?
TS2 Exam4 ? ? ? ?
TS2 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
subject to
C1
C2
C3
C4
C5
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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
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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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An integer programming approach to classification
problemsbased on polyhedral conic functions
EXAM SCHEDULING PROBLEM AN AHP MODEL FOR
PARAMETER ESTIMATION
Thank you
Zehra KAMISLI ÖZTÜRK Anadolu University, Open
Education Faculty Eskisehir/TURKEY
zkamisli_at_anadolu.edu.tr Assoc.Prof. Dr. Mujgan
SAGIR ÖZDEMIR Eskisehir Osmangazi
University Industrial Engineering
Department Eskisehir/TURKEY msagir_at_ogu.edu.tr