Conversion of Network Problem with Transfer Nodes, and Condition of Supplying the Demand of any Sink from the Particular Source to the Transportation Problem

In this article we present an algorithm for converting a network problem with several sources and several sinks including several transfer nodes and condition of supplying the demand of any sink from a particular source to the transportation problem. Towards this end, and considering the very special structure of transportation algorithm, after implementing the shortest path algorithm or solving model 2 and determining the paths by the minimum cost, we let the algorithm to behave with any of these shortest paths as an arc. Although this problem is soluble by linear programming with network structure, but by converting it to transportation problem an efficient method may be proposed for solving it.