Abstract
The flow maximization problem being a leading problem in network optimization is widely studied with many applications. In this work, we find the maximum flow pulled out from the source and sent to the sink using the uncertainty theory. We develop a flow function to get maximum flow for the network having uncertain arc capacities and sufficient storage capacities at the intermediate vertices. The centiles-method is used to find the maximum flow value and an algorithm is proposed to get non-conservative maximum flow. The result is also illustrated by an example. The flow values are compared graphically to see the dominance of the non-conservative maximum flow over the conservative maximum flow.
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