AbstractGiven a network having costs and upper bound constraints on the flows in its arcs, the minimum‐cost network flow problem is that of finding flows which satisfy a flow‐conservation constraint at each node and minimize the total cost of the flow. If the arc capacities vary as functions of time, and storage is permitted at the nodes of the network, then the problem becomes an infinitedimensional linear program with a network structure. We describe an algorithm to solve such problems. This algorithm is a continuuous‐time version of the network simplex algorithm.