What is the meaning of this math formulation?

Question

I have been wondering what is the meaning of this sigma with delta negative or plus in there (if my read is correct).

$$ \sum_{i \in \Delta^{-}(j)} x_{i j k}-\sum_{i \in \Delta^{+}(j)} x_{j i k}=0 \quad \forall k \in K, j \in N $$

Answer 1

It looks like a standard flow conservation constraint. In network models, it is somewhat common to use either $\Delta^-(v)$ or $\delta^-(v)$ to denote the set of nodes $u$ for which there is an arc from $u$ to $v$, and $\Delta^+(v)$ or $\delta^+(v)$ to denote the set of nodes $u$ for which there is an arc from $v$ to $u.$ So the constraint may be saying that for every node $j$ and every commodity / vehicle type / whatever $k,$ the flow of $k$ entering $j$ equals the flow of $k$ exiting $j.$