A survey of dynamic network flows
Annals of Operations Research
Linear programming and network flows (2nd ed.)
Linear programming and network flows (2nd ed.)
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Efficient dynamic network flow algorithms
Efficient dynamic network flow algorithms
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Here we are dealing with minimum cost flow problem on dynamic network flows with zero transit times and a new arc capacity, horizon capacity, which denotes an upper bound on the total flow traversing through on an arc during a pre-specified time horizon T. We develop a simple approach based on mathematical modelling attributes to solve the min-cost dynamic network flow problem where arc capacities and costs are time varying, and horizon capacities are considered. The basis of the method is simple and relies on the appropriate defining of polyhedrons, and in contrast to the other usual algorithms that use the notion of time expanded network, this method runs directly on the original network.