$k$ firends are living in a living community. There are $n$ houseworks that have to be allocated. The estimated time for each housework is $t_1, t_2, \dots , t_n$ respectively. The friends want to share the houseworks so that each of them will finish with the work in the time $T$.
I want to show that the problem is NP-complete.
To prove this do we maybe reduce the Bin Packing Problem to the above one?
At the Bin Packing Problem a set of numbers $a_1,\dots ,a_n,B,k$ is given. It asks if $a_1,\dots ,a_n$ can be allocated into the $k$ bins of size $B$ , so that the sum in each bin is $\leq B$.
For the reduction we consider the numbers $a_i$ as the times $t_i$, the $k$ bins as the $k$ students and the size $B$ as the time $T$.
Is my idea correct?
If $k=2$ and $t_1+\ldots+t_n=2T$, your problem becomes an instance of the NP-complete Partition problem, so your problem is NP-complete as well.