Developing the Page Rank Algorithm in Social Network Analysis for Cross-docking Location Problem

Cross-docking is a strategy in logistics management in which products from one or more suppliers are distributed directly to customers with a minimum loading or storage time. Cross docks act more as an inventory coordinator than as a storage warehouse. Finding a proper location is a critical issue in cross-docking. The page rank algorithm in social networks is one of the methods used to locate the accessible nodes in urban-networks. However, in the application of page rank algorithm in the location problems, only location access to the other nodes of the network has been considered, whereas, in cross docks’ location problem, the distance between the nodes, directly and indirectly, is of high importance due to the one-way nature of some routes and the average closeness of the cross docks to all nodes of the network in general. Thus, this research aims to develop the page rank algorithm in cross docks’ location problem, recognizing the distance between nodes with a weighted distanced adjacency matrix, besides considering the access and closeness to the different nodes of the network.  

The page rank algorithm developed by Agryzkov et al. (2012) in a way that the binary adjacency matrix of the path between nodes is changed into a weighted adjacency matrix, in which each element of the matrix in a row ‘i’ and column ‘j’ denotes the distance between ith and jth locations in the map. Besides, the main criteria of the Social Network Analysis (SNA) approach, such as Closeness centrality and Eigenvector centrality, also used to develop the model. Finally, the maximum covering location model in the network has been created by considering the output of the developed page rank algorithm as the input. To investigate the validity of the developed algorithm, it is applied in a practical cross docking problem and is solved by using the GAMS software.  

The developed page rank algorithm was applied to find the best locations of cross docks for an online store in the western half of district 3 in Tehran. The location points identified by the algorithm seem reasonable since they have access to the main highways allowing for easy and timely delivery of orders to customers distributed all over the investigated area.

Authors did not consider limitations such as the cost of renting and purchasing warehouse and the physical and traffic feasibility of the location points in the developed model. As a suggestion for future study, the model can be further developed by considering such features.   Practical implications: By using the developed algorithm, the time of delivering goods and services to the customers by online stores would reduce, which not only increases the customers’ satisfaction but it also declines the company’s costs, significantly.  

Timely delivery of orders to customers elevates customers’ feeling of safety and trust. Thus, it augments the online shopping habit of customers, leading to saving time, energy, and cost.  

Previously, the page ranking algorithm used in finding the best locations of advertising billboards in the urban map. Regarding the nature of a billboard location problem, only access/lack of access to a point determines the importance of a place, while in cross-docking location problem, in addition to access points, the distance of these warehouses, directly and indirectly, and the average proximity of them to all points of the network is of great importance. The algorithm developed in this study, in comparison with the previous version, not only considers the access of location points but also reflects the proximity of points through direct or indirect paths.