On Ranking the Relative Importance of Nodes in Physical Distribution Networks
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Physical distribution networks are integral parts of modern supply chains. When faced with a question of which node in a network is more important, cost immediately jumps to mind. However, in a world of uncertainty, there are other significant factors which should be considered when trying to answer such a question. The integrity of a network, as well as its robustness are factors that we consider, in making a judgement of importance. We develop algorithms to measure several properties of a class of networks. To accelerate the optimization of multiple related linear programs, we develop a modification of the revised simplex method, which exploits several key aspects to gain efficiency. We combine these algorithms and methods, to give rankings of the relative importance of nodes in networks. In order to better understand the usefulness of our method, we analyse the effect parameter changes have on the relative importance of nodes. We present a large, realistic network, whose nodes we rank in importance. We then vary the network's parameters and observe the impact of each change.