There was a problem at work and I couldn't solve it due to the computational cost involved.
Well, for example, I have 5 locations, named A to E, keeping their respective quantities: 174, 215, 74, 210 and 210.
I have to put them together in such a way that the resulting new locations are as close as possible to 425.
I think it can be solved with linear (or integer) programming, but due to time I won't be able to solve it in time.
I would like some suggestion, idea, book me a light.
Thinking here I arrived at the following modeling, the problem boils down to
Let $\Omega = \{\omega_1, \omega_2, \cdots, \omega_n\}$
Find a partition $$s_j = \cup_{i=1}^{j_k}\{\omega_i\},\: s_i \cap s_j = \emptyset$$
such that
$$\min \sum_{j=1}^{J}\left(\sum_{i=1}^{j_k}(Q(s_i) - c) \right)$$
where
$$Q(S_i) = \sum_{\omega_j \in s_i}Q(\{\omega_j\})$$
and
$$Q(\{\omega_j\}) = \begin{cases} a_1, & j = 1\\ a_2, & j = 2\\ \vdots\\ a_n, & j = n\\ \end{cases}\\$$
Thanks in advance!