All-sizes Network Simplex

Question

I am currently using Network Simplex to find the min-cost flow to send $x$ units of goods from source $s$ to sink $t$ given a capacitated graph.

I would now like to solve the problem for all $x \in [1, 2, 3, \ldots, N]$. I could run network simplex $N$ times (once for each $x$) but that is proving to be slow for large $N$ (e.g. $N=200)$.

Does anyone know of some optimized way to do this?

Answer 1

Try Ant methods / critical path analysis on the problem.

Ant Method

Critical Path method

I am not able to advise on efficiency of these algorithms compared to Network Simplex