Fragility of a multilayer network of intranational supply chains

Abstract

Supply chains enable the flow of goods and services within economic systems. When mapped for the entire economy and geographic locations of a country, supply chains form a spatial web of interactions among suppliers and buyers. One way to characterize supply chains is through multiregional input-output linkages. Using a multiregional input-output dataset, we build the multilayer network of supply chains in the United States. Together with a network cascade model, the multilayer network is used to explore the propagation of economic shocks along intranational supply chains. We find that the effect of economic shocks, measured using the avalanche size or total number of collapsed nodes, varies widely depending on the geographic location and economic sector of origin of a shock. The response of the supply chains to shocks reveals a threshold-like behavior. Below a certain failure or fragility level, the avalanche size increases relatively quickly for any node in the network. Based on this result, we find that the most fragile regions tend to be located in the central United States, which are regions that tend to specialize in food production and manufacturing. The most fragile layers are chemical and pharmaceutical products, services and food-related products, which are all sectors that have been disrupted by the Coronavirus Disease 2019 (COVID-19) pandemic in the United States. The fragility risk, measured by the intersection of the fragility level of a node and its exposure to shocks, varies across regions and sectors. This suggests that interventions aiming to make the supply-chain network more robust to shocks are likely needed at multiple levels of network aggregation.

Keywords: COVID-19; Cascading failure; Diffusion; Economic networks; Multiplex; Multiregional input-output; Shock.

Fig. 1

Illustration of the multilayer network of supply chains in the United States obtained using the multiregional input-output dataset. The illustration shows five different layers obtained from the actual data (intralayer flows) and a few hypothetical interlayer flows (red arrows). The nodes in each layer represent the 115 geographic locations or regions in the dataset. The same set of nodes are shared by all the layers

Fig. 2

Spatial evolution of a shock initiated in the government sector of New York City (a-d), Chicago (e-h), and Los Angeles (i-l) for Ω = 0.06. The colors show the number of collapsed nodes within each geographical region at the specified level of propagation. The shock is shown at the 25 (a, e, i), 50 (b, f, j), 75 (c, g, i) and 100% (d, h, l) level of propagation relative to the total number of time steps or iterations required for the shock to be completely absorbed. The total number of time steps is 2, 25 and 12 for New York City, Chicago and Los Angeles, respectively. The avalanche size is 3, 1622 and 156 for New York City, Chicago and Los Angeles, respectively

Fig. 3

Complementary cumulative distribution function (ccdf) of avalanche sizes for the 115 regions (a) and 37 layers (b) in our multilayer network. The ccdfs are for Ω = 0.04

Fig. 4

Average avalanche size for the top 30 regions (a) and layers (b) in the multilayer network (Ω = 0.04)

Fig. 5

Avalanche sizes for each node in the meat (a), government services (b), pharmaceuticals (c) and retailers layer (d) versus the failure threshold Ω. Each curve represents the avalanche size-failure threshold relationship for a node in the layer

Fig. 6

Ranking of all the regions from high to low (1–115) based on the average fragility level Ω_c of the nodes belonging to each region (a). Groups of layers with high and low fragility based on the average fragility level Ω_c of the nodes belonging to each layer (b). The layers in the food-related group include cereal grains, milled grains, fruits and vegetables, meat, animal feed, live animals, manufactured food, and fertilizers. The layers in the chemicals and pharmaceuticals group include basic chemicals, chemical products and pharmaceutical products. The layers in the services group include government, food services (e.g., restaurants), wholesalers, retailers, transportation services, government and utilities. The group labeled other industrial sectors includes the rest of the layers that are not part of the high-fragility groups. In the box-and-whisker plots, the box represents the first and third quartile, the red line is the median and the whiskers show the range of the values

Fig. 7

Average exposure of nodes versus the fragility level (a). The error bars indicate ± 1 standard deviation. Exposure of regions (b) and layers (c) to shocks versus the fragility level