Assignment Problems Hazırlayanlar: Ali Evren Erdin Arzu Çalık Hilal Demirhan
Description Of The Assignment Problems
Uses of The Assignment Problems
Explanation of the Article
The Solution of the Problem in Lingo
Description of the Assignment Problems
The problems that their goal is to find an optimal assignment of agents to tasks without assigning an agent more than once and ensuring that all tasks are completed
What can be the objectives?
M inimize the total time to complet e set of tasks
M aximize skill ratings
M inimize the cost of the assignments
What are the Applications of Assignment Problems?
A ssigning e mployees to tasks
Assigning machines to production jobs
A ssign fleets of aircrafts to particular t rips
A ssigning school buses to routes
N etworking computers
A Simple Example...
An assignment problem seeks to minimize the total cost assignment of m workers to m jobs, given that the cost of worker i performing job j is c ij .
It assumes all workers are assigned and each job is performed.
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
Min ∑∑ c ij x ij
s.t. ∑ x ij = 1 for each agent i
∑ x ij = 1 for each task j
x ij = 0 or 1 for all i and j
“ An Application of Genetic Algorithm Methods for Teacher Assignment Problems” The ARTICLE
What is the Problem??
“ What are the most suitable teacher and course assignments ?”
What is Genetic Algorithm?
The Genetic Algorithm is optimization procedure based on the natural law of evolution!
The Key Idea of Genetic Algorithm is Survival of the Fittest!
It is an Heuristic Approach based on Darwin’s Theory of Evolution
Teacher Assignment Problem include multiple constraints
Teachers willingness need to be considered,
There should be a fair distribution of over time
Teacher satisfaction has to be maximized
One course should not be appointed to different teachers.
There are 20 teachers.
There are 45 courses. Each course has two classes: A and B.
Each teacher have an upper and minimum workhour limits
Each Teacher rank the courses that they want to teach
The Datas for the Problem
20 points 19 points minlimit upperlimit
The objection function for the problem will be :
Upper And Lower Limits for teacher work Hours
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