I want to put the following in formula-form: "$ T_i$ should be the sum of the $ b $ smallest durations out of all durations of the predecessors of $i$ (which is the set $P_i$)"
Does a mathematical formulation exist to describe the "$n$-th smallest element of a set"?
This was my trial:
$$T_i = \sum\limits_{n=0}^{b} \min\limits_{n}\{ t_j \mid j \in P_i \} $$
Thank you in advance!