Graph-theoretic Approach to Optimal Synthesis of Supply Networks: Distribution of Gasoline from a Refinery

The synthesis of a supply network is profoundly convoluted because of its combinatorial complexity. Global or even near optimal solutions are, more often than not, unobtainable through the heuristic methods. On the other hand, the majority of the algorithmic methods, which mainly resort to mixed integer programming, in theory, can give rise to global optima; however, they are effective only for relatively minute networks. Obviously, it is highly desirable that a novel paradigm be established for optimally synthesizing supply networks; the adoption of the graph-theoretic method based on P-graphs (process graphs) is proposed herein for the synthesis of optimal supply networks. The proposed method is illustrated with examples. Each example has yielded simultaneously the optimal and near optimal structures of the supply network performing a specific task in the ranked order. The example reveals a unique feature of the method.