Q.Give mathematical form of Assignment Problem.

The assignment problem minimises $\sum\sum c_{ij}x_{ij}$ with each row-sum and column-sum equal to $1$ and $x_{ij}\in\{0,1\}$.

Suppose $n$ workers (facilities) are to be assigned to $n$ jobs, and $c_{ij}$ is the cost of assigning worker $i$ to job $j$. Let

$x_{ij} = \begin{cases} 1, & \text{if worker } i \text{ is assigned to job } j, \\ 0, & \text{otherwise.} \end{cases}$

Mathematical form:

$\text{Minimise } \quad Z = \sum_{i=1}^{n} \sum_{j=1}^{n} c_{ij}\,x_{ij}$

subject to

$\sum_{j=1}^{n} x_{ij} = 1 \quad (i = 1, 2, \dots, n) \qquad \text{[each worker does exactly one job]},$ …