Orlin's algorithm is known to solve minimum cost maximum flow problems in $O(|E|^2 \log |V| + |E| \; |V| \log^2 |V|)$ time, where $|E|$ and $|V|$ respectively denote the cardinalities of the edge and the node sets of the graph $G(V, E)$ in question.
If the graph $G(V = V_1 \cup V_2, E)$ is known to be bipartite (with $V_1$ and $V_2$ denoting the "left" and "right" node sets), can one compute the minimum cost maximum flow any faster? Here the flow is between an additional source that is connected to the nodes in $V_1$ and an additional sink that is connected to the nodes in $V_2$.
I'm also interested to hear about algorithms that do not have better time complexity, but perform well in practice.
You can assume that all capacities and costs are non-negative integers. There can be both limited-capacity and unlimited-capacity edges in the graph. Also, assume that both the maximum non-infinite capacity $c$, and the maximum edge cost $w$ is small; i.e. one can consider both as $O(1)$ terms for complexity purposes.
Edit: My current-best solution is to use a minimum cost augmentation algorithm, which solves the problem in $O(|E| \; F \log |V|)$ time, where $F$ is the value of the maximum flow. Since $F$ is bounded by $c \;|V|$ (which is $O(|V|)$ under our assumptions), this approach results in an overall time complexity of $O(|E| \; |V| \; \log |V|)$. Is it possible to beat this?