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This paper consists in constructing and modeling Dynamic Multi Generative Network Flows in which the flow commodities is dynamically generated at source nodes and dynamically consumed at sink nodes. It is assumed that the source nodes produce the flow commodities according to k time generative functions and the sink nodes absorb the flow commodities according to k time consumption functions. The minimum cost dynamic flow problem in such networks that extend the classical optimal flow problems on static networks, for a pre-specified time horizon T is defined and mathematically formulated. Moreover, it is showed that the dynamic problem on these networks can be formulated as a linear program whose special structure permits efficient computations of its solution and can be solved by one minimum cost static flow computation on an auxiliary time-commodity expanded network. By using flow …