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# Definition and formulation of Assignment Problem

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 Cij be the cost of assigning ith job to the jth machine and xij represents the assignment of ith job to the jth machine. xij is missing in any cell means that no assignment is made between the pair of job and machine.(i.e) xij = 0.

xij presents in any cell means that an assignment is made their.In such cases xij = 1

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 Cij > 0 then an assignment schedule (xij) which satisfies Ōłæ Cij xij  = 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