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Various network flow models, such as a flow maximization, a time minimization, a cost minimization, or a combination of them, have already been investigated. In most of the cases, they are considered subject to the flow conservation constraints. Here, we investigate the network flow models with intermediate storage, i.e., the inflow may be greater than the outflow at intermediate nodes. We introduce a maximum static and a maximum dynamic flow problem where an intermediate storage is allowed.doi:10.1007/s43069-020-00033-0 fatcat:dfyoh2u5cjaxtffnlfwkzyek5e