Assignment Problem/Examples/Workers to Jobs

Example of Assignment Problem

Let an industrial firm have $n$ workers who are each to be assigned to one of $n$ jobs.

Let it be possible to specify the value $v_{i j}$, measured in suitable units, of the $i$th worker when assigned to the $j$th job.

The values could then be displayed in a square matrix:

$\begin {pmatrix} v_{1 1} & v_{1 2} & \cdots & v_{1 n} \\ v_{2 1} & v_{2 2} & \cdots & v_{2 n} \\ \vdots & \vdots & \ddots & \vdots \\ v_{n 1} & v_{n 2} & \cdots & v_{n n} \end {pmatrix}$

which would allow the resulting assignment problem to be interpreted as an exercise in linear programming.

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): assignment problem
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): assignment problem