This paper presents new algorithms for solving the maximum flow problem, the Hitchcock transportation problem, and the general minimum-cost flow problem. The authors derive upper bounds on the number of steps required by these algorithms, which are shown to be more efficient than previous methods. For the maximum flow problem, the paper introduces a labeling method that avoids computational difficulties by choosing flow augmenting paths with the minimum number of arcs. It is proven that this method requires no more than $\frac{1}{4}(n^3 - n)$ augmentations, where $n$ is the number of nodes. Another refinement of the labeling method chooses flow augmenting paths that maximize the increase in flow value, leading to a bound of $1 + \log_{M/(M-1)} f^*(t, s)$ augmentations, where $f^*(t, s)$ is the value of the maximum flow and $M$ is the maximum number of arcs across a cut. For the minimum-cost flow problem, the paper proposes a labeling method that performs all shortest-path calculations on networks with nonnegative weights. This method is then extended to a scaling technique that solves a sequence of problems with scaled-down capacities, approximating the original problem. The scaling method is shown to require at most $(n + 2) \log_2 (B / m)$ augmentations for a Hitchcock transportation problem with $m$ sources and $n$ sinks, where $B$ is the maximum flow value and $M$ is the maximum number of arcs across a cut. The paper also discusses the efficiency of the scaling method for the minimum-cost flow problem, showing that it requires a number of steps proportional to the number of binary digits in the capacities. This makes the scaling method a "good" algorithm in terms of computational complexity.This paper presents new algorithms for solving the maximum flow problem, the Hitchcock transportation problem, and the general minimum-cost flow problem. The authors derive upper bounds on the number of steps required by these algorithms, which are shown to be more efficient than previous methods. For the maximum flow problem, the paper introduces a labeling method that avoids computational difficulties by choosing flow augmenting paths with the minimum number of arcs. It is proven that this method requires no more than $\frac{1}{4}(n^3 - n)$ augmentations, where $n$ is the number of nodes. Another refinement of the labeling method chooses flow augmenting paths that maximize the increase in flow value, leading to a bound of $1 + \log_{M/(M-1)} f^*(t, s)$ augmentations, where $f^*(t, s)$ is the value of the maximum flow and $M$ is the maximum number of arcs across a cut. For the minimum-cost flow problem, the paper proposes a labeling method that performs all shortest-path calculations on networks with nonnegative weights. This method is then extended to a scaling technique that solves a sequence of problems with scaled-down capacities, approximating the original problem. The scaling method is shown to require at most $(n + 2) \log_2 (B / m)$ augmentations for a Hitchcock transportation problem with $m$ sources and $n$ sinks, where $B$ is the maximum flow value and $M$ is the maximum number of arcs across a cut. The paper also discusses the efficiency of the scaling method for the minimum-cost flow problem, showing that it requires a number of steps proportional to the number of binary digits in the capacities. This makes the scaling method a "good" algorithm in terms of computational complexity.