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7.05 Assignment allocation

Interactive practice questions

Three people, Elise, Poppy and Richard, are each to be given $1$1 task ($T1$T1, $T2$T2 or $T3$T3) to complete on their own.

Each person is able to complete the $3$3 tasks that are available in a set time. These times, in minutes, are shown in the network diagram below.

Represent this data in a matrix.

      $T1$T1 $T2$T2 $T3$T3    
$E$E     $\editable{}$ $\editable{}$ $\editable{}$    
$P$P     $\editable{}$ $\editable{}$ $\editable{}$    
$R$R     $\editable{}$ $\editable{}$ $\editable{}$    
Easy
1min

A physiotherapy company receives requests for $3$3 home visits ($V1$V1, $V2$V2 and $V3$V3) in the same area.

There are $3$3 workers ($W1$W1, $W2$W2 and $W3$W3) in that area who are available.

The network below shows the travel cost for each worker to get to each house in dollars.

Easy
< 1min

Three friends, Adam, Ben and Christie, decide to have a picnic together. They each agree to buy either snacks, sandwiches or drinks from their local shopping centre and bring them to share at the picnic.

The table below shows the price of these products at each friend’s local shopping centre, in dollars.

Easy
3min

A courier company needs to make multiple pick-ups across several stores.

The lengths of the roads (in km) linking these stores are shown in the diagram below.

Easy
2min
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Outcomes

4.3.4.1

use a bipartite graph and its tabular or matrix form to represent an assignment/allocation problem, e.g. assigning four swimmers to the four places in a medley relay team to maximise the team’s chances of winning

4.3.4.2

determine the optimum assignment/s for small-scale problems by inspection, or by use of the Hungarian algorithm (3 × 3) for larger problems

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