Optimal distributions for multiplex logistic networks

Abstract

This paper presents some mathematical models for distribution of goods in logistic networks based on spectral analysis of complex networks. Given a steady distribution of a finished product, some numerical algorithms are presented for computing the weights in a multiplex logistic network that reach the equilibrium dynamics with high convergence rate. As an application, the logistic networks of Germany and Spain are analyzed in terms of their convergence rates.
We are living in a global-scale world. Globalization is the process of international integration of products, ideas, culture, and science that has changed our way of understanding the world. Advances in communication and transportation that took place along the last Century allowed shortening the distances and making that our society moved from the local-scale to a global scale, generating new interdependences of economic, political, social, and cultural activities along the world. This process also has affected the business and commerce processes and the way that traditional trade is performed, changing from buying and selling to our closest neighbors to exchanging products with costumers in any country in the world. This change in the commerce's scales forces a new way of distributing the goods that has shifted from the direct supplier to costumer perspective to a new distributed point of view. Supply chain management (SCM),11 which is also known as Logistics Network Analysis, is a part of the Operational Research that has been extensively studied in recent years to analyze the newly distributed perspective of commerce arises from the Globalization. In this new approach, the classic point-to-point distribution that directly connects the supplier (the factory) with the final costumer is replaced by the use of logistic networks and distributed global-scale transportation. This paper presents some mathematical models for distribution of several products simultaneously by using multiplex networks analysis, and some effective algorithms are included in order to spot the optimal logistic network, in terms of distribution rate.