Assignment problem By Munther Mouzaneh - PowerPoint Presentation

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Assignment problem

By Munther Mouzaneh

139252

Mechanical Engineering Department

introduction

In

mathematics

and

computer

science

,

an optimization problem is the

problem

of

finding the best solution from all feasible

solutions.

Types of Optimization problems =

Optimization problems can be divided into two categories depending on whether the

variables

are continuous

or

discrete.

Types of optimization problem

An optimization problem with

discrete

variables

is known as a combinatorial optimization problem.

In

a combinatorial optimization problem, we are looking for an object such as an integer, permutation or graph from a

finite

(or possibly accountably infinite) set. Problems with continuous variables include constrained problems and multimodal problems.

Way to solve optimization problem

Assignment problem

Assignment problem definition

The assignment problem is one of the fundamental

combinatorial optimization

problems in the branch of

optimization

or operations research

in

mathematics.

It consists of finding a maximum weight matching (or minimum weight perfect matching) in a

weighted bipartite graph.

Assignment problem

mathematical form

ij

x

ij

Such that:

ij

= 1

ij = 1 Xij >= 0; For (i,j = 1,…,m)

Network model of the assignment

problem

generally

The Assignment problem is a feasible problem. That’s mean; we can find a feasible solution for a problem by assigning one Task for each one Agent.

conclusion

Assignment

Problem that used in optimization problem solving.

Assignment

problem is popular used to solve complicate problem in our life. However, this type of solving the optimization problem is one of many ways to solve such a problem

.

Thank you

Sincerely