Customer momentum factor based on centrality weighting - a single-layer customer relationship perspective
factor.formula
Weighted Customer Momentum based on centrality:
In the formula:
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Represents the customer momentum factor value of company i in the past month based on centrality weighting. The higher the value, the better the overall performance of company i's customers and the stronger the momentum effect.
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Represents the profitability of customer j of company i in the past month. This is an indicator to measure the short-term performance of customer j, with positive values representing an increase and negative values representing a decrease.
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represents the centrality weight of customer j to company i. This weight is determined by the closeness of the connection between customer j and company i in the supply chain network. It is calculated as: $w_{ij}^{centrality} = \frac{c_{ij}}{ \sum_{k=1}^{N_i} c_{ik}}$, where $k$ is all customers of company i, ensuring that the sum of the weights is 1.
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It represents the edge betweenness centrality of the supply chain network between customer j and company i. Specifically, it measures the number of shortest paths in the network that pass through the edge between customer j and company i. A higher betweenness centrality means that the relationship between customer j and company i is more important in the supply chain network and has a greater impact on information transfer and resource flow.
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represents the total number of customers of company i
factor.explanation
Traditional customer momentum factors usually use the customer's sales share as a weight, however, this method is easily affected by missing or incomplete sales data. This factor innovatively introduces the edge betweenness centrality of the supply chain graph network as a weight. Betweenness centrality captures the structural importance of each node in the supply chain network and can better reflect the influence of customers on suppliers. Empirical studies have shown that edge betweenness centrality and sales share are significantly positively correlated, which provides theoretical support for the use of centrality measures instead of sales share. In addition, the use of edge betweenness centrality can also help avoid the problem of factor failure caused by missing sales data, and enhance the robustness and applicability of the factor. This factor measures customer momentum through network structure, which more accurately reflects the importance and transmission effect of customer relationships in the supply chain.