As shown by Figure 1, the problem is to determine an optimal transportation scheme that is to
minimize the total of the shipments cost between the nodes in the network model, subject to
supply and demand constraints. As well as, this structure arises in many applications such as; the
sources represent warehouses and the sinks represent retail outlets.
Moreover, Ad-hoc networks are designed dynamically by group of mobile devices. In Ad-hoc
network, nodes between source and destination act as a routers so that source node can
communicate with the destination node [7].