Consider the problem of assigning n jobs to n machines (one job to one machine).

**Definition
and formulation**

Consider the problem of
assigning *n* jobs to *n* machines (one job to one machine). Let *C _{ij}*
be the cost of assigning

* x _{ij} *is missing in any cell
means that no assignment is made between the pair of job

*x _{ij} *presents in any cell
means that an assignment is made their.In such cases

The assignment model can
be written in LPP as follows

Subject to the
constrains

**Note**

The optimum assignment
schedule remains unaltered if we add or subtract a constant from all the
elements of the row or column of the assignment cost matrix.

**Note**

If for an assignment
problem all C_{ij} > 0 then an assignment schedule (x_{ij})
which satisfies âˆ‘ C_{ij} x_{ij}
= 0 must be optimal.

Tags : Operations Research , 12th Business Maths and Statistics : Chapter 10 : Operations Research

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12th Business Maths and Statistics : Chapter 10 : Operations Research : Definition and formulation of Assignment Problem | Operations Research

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