This setup came to me from power distribution in electrical panels.
I have $n$ loads, each one with a power $X_i$ which is a Random Variable $X_i\sim N(\mu_i,\sigma_i)$, $i=1...n$, sorted as $\mu_1>...>\mu_n$.
I have to distribute these loads into three disjoint groups, $K=\{R,S,T\}$ (the phases), so that for the sum of each group, $X^k\sim N(\mu^k,\sigma^k)$, the means $\mu^R\sim\mu^S\sim\mu^T$ and deviations $\sigma^R\sim\sigma^S\sim\sigma^T$ be "similar", in the best rough way possible.
Normally people do this at hand, assuming deterministic values, assigning $X_1\to R$, $X_2\to S$, $X_3\to T$, $X_4\to R$, etc. and then reassigning manually at the end "some" indexes to adjust the sums to be "similar". But having the Random Variables as defined above, how should I proceed, anyway, if there could be a better way than trial and error?
