Maximum flow in hybrid network with intermediate storage

When uncertain and random arcs coexist with non-deterministic arc capacities in network optimization issues, chance space is used as the product of uncertain and probability space to arrive at the required answer. In order to determine the maximum flow in the hybrid network in this study, the intermediate storage at the vertices together with both uncertain and random arcs are introduced. The maximum flow model based on chance measure is first transformed into its deterministic equivalent by using the self dual and measure inversion properties, as well as a theorem on inverse uncertain distribution and the same qualities for probability measure. The intermediate vertices’ deterministic storing capability to the extent that it allows them to record the flow that is headed toward them is taken into account. As a generic solution to the issue, an algorithm for the maximum flow is then developed using the maximum flow distribution theorem. An illustrative example is provided to demonstrate the models’ and algorithms’ efficacy and level of efficiency. Additionally, a graphic comparison of the change in maximum flow values with and without intermediate storage is included.