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Assignment  Problems Hazırlayanlar:  Ali Evren Erdin Arzu Çalık  Hilal Demirhan
INDEX ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Description of the Assignment Problems ,[object Object]
What can be the objectives? ,[object Object],[object Object],[object Object],[object Object]
What are the Applications of Assignment Problems? ,[object Object],[object Object],[object Object],[object Object],[object Object]
A Simple Example...  ,[object Object],[object Object]
The network Representation of Example (continued...) 2 3 1 2 3 1 c 11 c 12 c 13 c 21 c 22 c 23 c 31 c 32 c 33 Agents Tasks
Mathemetical Explanation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
 “ An Application of Genetic Algorithm Methods for Teacher Assignment Problems” The ARTICLE
What is the Problem?? ,[object Object],[object Object],[object Object]
What is Genetic Algorithm? ,[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],The Datas for the Problem
The Questionnarie
20 points 19 points minlimit upperlimit
 
 
The objection function for  the  problem will be :
[object Object]
The Lingo Formulation
SETS : teachers  / A B C D E F G H I J K L M N O P    Q R S T /:   upperlimit, minlimit; c ourses   / C1A C2A  .................... C45A    C1B C2B  .................... C45B /:   hours; chromosomes  ( teachers, courses ) :     willingness, match; ENDSETS
DATA: willingness =  (The matrix taken from  the   given table B1 ) hours = 4 4 5 3 3 3 3 3 3 4 4 2 3 3 3 2 4 3 3 3 3 3 3    3 3 3 3 3 2 3 3 3 2 2 3 3 3 3 3 3 3 2 3 3 3 4    4 5 3 3 3 3 3 3 4 4 2 3 3 3 2 4 3 3 3 3 3 3 3    3 3 3 3 2 3 3 3 2 2 3 3 3 3 3 3 3 2 3 3 3; minlimit = 12 12 11 12 14 12 14 12 12 12 14 12 12    12 12 9 12 12 4 12; upperlimit = 13 13 12 18 15 18 15 18 18 18 15 18  18 18 18 15 13 13 11 13; ENDDATA
Matrix of Willingness J=1 0 0 14 15 16 E 0 11 20 19 12 D 0 0 0 15 16 C 0 0 0 0 0 B 0 0 0 0 0 A C5A C4A C3A C2A C1A Courses Teachers
OBJECTIVE FUNCTION ,[object Object],[object Object],[object Object]
CONSTRAINTS ,[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],CONSTRAINTS
Objective value
REPORT -18 1 MATCH( A, C27B) -19 1 MATCH( A, C26B) -18 1 MATCH( A, C27A) -19 1 MATCH( A, C26A) Reduced Cost Value Variable
The teacher  A is going to teach  : ,[object Object],[object Object],[object Object]
REDUCED COSTS ,[object Object],[object Object],[object Object]
REPORT -17 1 MATCH( T, C38B) -16 1 MATCH( T, C34B) -20 1 MATCH( T, C7B) -16 1 MATCH( T, C34A) -20 1 MATCH( T, C7A) Reduced Cost Value Variable
THANKS!

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Assingment Problem3

  • 1. Assignment Problems Hazırlayanlar: Ali Evren Erdin Arzu Çalık Hilal Demirhan
  • 2.
  • 3.
  • 4.
  • 5.
  • 6.
  • 7. The network Representation of Example (continued...) 2 3 1 2 3 1 c 11 c 12 c 13 c 21 c 22 c 23 c 31 c 32 c 33 Agents Tasks
  • 8.
  • 9. “ An Application of Genetic Algorithm Methods for Teacher Assignment Problems” The ARTICLE
  • 10.
  • 11.
  • 12.
  • 13.
  • 15. 20 points 19 points minlimit upperlimit
  • 16.  
  • 17.  
  • 18. The objection function for the problem will be :
  • 19.
  • 21. SETS : teachers / A B C D E F G H I J K L M N O P Q R S T /: upperlimit, minlimit; c ourses / C1A C2A .................... C45A C1B C2B .................... C45B /: hours; chromosomes ( teachers, courses ) : willingness, match; ENDSETS
  • 22. DATA: willingness = (The matrix taken from the given table B1 ) hours = 4 4 5 3 3 3 3 3 3 4 4 2 3 3 3 2 4 3 3 3 3 3 3 3 3 3 3 3 2 3 3 3 2 2 3 3 3 3 3 3 3 2 3 3 3 4 4 5 3 3 3 3 3 3 4 4 2 3 3 3 2 4 3 3 3 3 3 3 3 3 3 3 3 2 3 3 3 2 2 3 3 3 3 3 3 3 2 3 3 3; minlimit = 12 12 11 12 14 12 14 12 12 12 14 12 12 12 12 9 12 12 4 12; upperlimit = 13 13 12 18 15 18 15 18 18 18 15 18 18 18 18 15 13 13 11 13; ENDDATA
  • 23. Matrix of Willingness J=1 0 0 14 15 16 E 0 11 20 19 12 D 0 0 0 15 16 C 0 0 0 0 0 B 0 0 0 0 0 A C5A C4A C3A C2A C1A Courses Teachers
  • 24.
  • 25.
  • 26.
  • 28. REPORT -18 1 MATCH( A, C27B) -19 1 MATCH( A, C26B) -18 1 MATCH( A, C27A) -19 1 MATCH( A, C26A) Reduced Cost Value Variable
  • 29.
  • 30.
  • 31. REPORT -17 1 MATCH( T, C38B) -16 1 MATCH( T, C34B) -20 1 MATCH( T, C7B) -16 1 MATCH( T, C34A) -20 1 MATCH( T, C7A) Reduced Cost Value Variable