Minimum cost network flows: Problems, algorithms, and software

Minimum Convex Cost Dynamic Network Flows

This paper presents and solves in polynomial time the minimum convex cost dynamic network flow problem, an infinite horizon integer programming problem which involves network flows evolving over time. The model is a finite network in which each arc has an associated transit time for flow to pass through it. An integral amount of flow is to be sent through arcs of the network in each period over...

On Minimum Concave Cost Network Flow Problems

Minimum concave Cost Network Flow Problems (MCNFPs) arise naturally in many practical applications such as communication, transportation, distribution, and manufacturing, due to economic considerations. In addition, it has been shown that every MCNFP with general nonlinear cost functions can be transformed into a concave MCNFP on an expanded network. It must also be noted, that multiple source ...

Minimum cost flows

G Minimum - Cost Flows

In this final chapter on flows, we consider a significant generalization of the maximumflow problem that (as far as we know) cannot be solved by modifying the graph and applying a standard flow algorithm. The input to our problem consists of a flow network without special source and target vertices, where each edge e has a cost $(e), in addition to the usual edge capacities and vertex balances....

New polynomial-time cycle-canceling algorithms for minimum-cost flows

The cycle-canceling algorithm is one of the earliest algorithms to solve the minimum cost flow problem. This algorithm maintains a feasible solution x in the network G and proceeds by augmenting flows along negative cost directed cycles in the residual network G(x) and thereby canceling them. For the minimum cost flow problem with integral data, the generic version of the cycle-canceling algori...