Given the following sequences
$$\begin{aligned} a_1 + a_2 + \cdots + a_n = A \\ b_1 + b_2 + \cdots + b_{n'} = B\\ c_1 + c_2 + \cdots + c_n = C \\ d_1 + d_2 + \cdots + d_{n'} = D\end{aligned}$$
let
$$e_{ij} = \min(a_i + b_j, c_i + d_j)$$
$$ e = \sum_{j = 1}^{n} \sum_{i = 1}^{n'} e_{ij} $$
Does there exist any bound on $e$ in terms of $A, B, C, D$?