Linear programming application according to assignment model

	Linear programming application according to assignment model
Muthanna Journal of Administrative and Economic Sciences
Article 1, Volume 2, Issue 3, 2012, Pages 50-61
Abstract
The second special purpose linear programming (L. P ) algorithm discussed in the research is assignment model . Each assignment problem has associated with a matrix Generally, the rows contain the objects or problem we wish to assign, and the columns comprise the takes we want them assigned to The numbers in the matrix 0r the costs associated with each particular assignment . An assignment problem can be viewed as a transportation problem in which capacity from each source ( m ) or person to be assigned is ( 1 ) and the demand at each destination ( n ) or job to be done is ( 1 ) also to get of the objective function ( max or min ) if assigned a sources ( i = 1 , 2 , ………, m ) to done a jobs ( j = 1 , 2 , ………, n ) to reach for objective function ( maximization or minimization ) . The assignment problem must be square matrix ( n n ) . Hanes assignment one source to one job and this means number of (m) equal (n) , if ( m > n ) or ( m < n ) here in this case must addition dummy source or dummy destination depend of which more or leas between ( m and n ) . The mathematical assignment model by using a linear programming as following : 1 – Suppose if assigned a sources ( i ) to job ( j) . 2 – Suppose if don’t assigned a source ( i ) to job ( j ) . From above we reach to the following model :

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