Cities can benefit from complex supply chains

The study investigates whether and how the architecture of urban supply networks—specifically their complexity—relates to cities’ exposure to and resistance against supply chain shocks. Contrary to the common perception that complexity necessarily exacerbates disruptions, the authors hypothesize, by analogy with ecological systems, that complexity linked to diversity (supplier variety) can stabilize urban supply chains. They address gaps in prior research by moving beyond firm-level analyses to the city scale and by explicitly considering both topological and interaction-strength dimensions of supply networks. The purpose is to quantify vertical (strength-based) and horizontal (connection-based) supply chain complexity for U.S. cities, identify common architectural patterns across cities, and test how these complexities associate with measured shock intensities in 2012–2015.

The paper situates its contribution within several strands of literature: (1) Supply chain management research that links complexity, just-in-time practices, and vulnerability to disruptions, largely at the firm level. (2) Ecological and network science findings that show complexity and diversity can enhance stability and resilience in ecological and social systems. (3) Urban scaling literature showing systematic relationships between city size and socioeconomic characteristics, while noting prior work often overlooks intercity networked interactions. (4) Economic complexity research using dimensionality reduction on bipartite product–place networks to characterize technological sophistication and predict growth or specialization. The authors leverage these insights to propose and compute city-level supply chain complexity indices and test their relationship to empirically measured shocks.

Data: Annual commodity flow data from the Freight Analysis Framework version 4 (FAF4) for 2012–2015, covering 115 U.S. domestic regions (69 metropolitan areas aggregated from 85 FAF4 cities plus remainders of states and state-level regions) and 8 international regions. Flows are in tons or U.S. dollars. Product coverage spans 39 out of 41 FAF4 commodity categories (excluding unclassified and waste). In total, 156 product-specific spatial supply networks (39 products × 4 years), comprising over 1 million annual flows, are analyzed.

Supply chain complexity indices: Two indices are defined at the city level for each year using a bipartite product–region representation constructed from the set of product-specific supply networks.

• Vertical complexity (SCI): Captures interaction strength patterns using each region’s share of total inflow value by product (in-strength). Conceptually linked to upstream depth/strength.
• Horizontal complexity (SCI’): Captures topological patterns using each region’s share of the number of distinct supplier connections by product (in-degree). Conceptually linked to the breadth/relative diversity of immediate suppliers.

Bipartite network construction: For each year, the 39 product networks are combined into a 115 × 39 unweighted, undirected product–region bipartite matrix using a location quotient (LQ) assignment. For a product–region pair, the region’s concentration of inflows (for SCI) or supplier connections (for SCI’) is compared to the national share for that product. Pairs with LQ ≥ 1 are set to 1 (dominant inflows/suppliers), others 0, yielding the binary matrix M. Column and row sums give regional diversity (number of products with LQ ≥ 1) and product ubiquity. Similarity matrices are computed as M̃ = D^−1 M U^−1 Mᵗ (region–region, diversity-weighted) and à = U^−1 M D^−1 Mᵗ (product–product, ubiquity-weighted), where D and U are diagonal matrices of diversity and ubiquity. Following the eigenvalue approach of Mealy et al., SCI is the eigenvector associated with the second largest right eigenvalue of M̃; product complexity ranking is the eigenvector associated with the second largest right eigenvalue of Ã. The same procedure is repeated using supplier-connection shares to obtain SCI’. The approach is interpretable as spectral clustering; SCI or SCI’ ≈ 0 partitions regions into two main groups. The ranking of product complexity used to derive SCI and SCI’ has a moderate Spearman rank correlation (R = 0.53, P < 0.001), enabling comparisons between the indices.

Shock intensity and alternative stability metric: For each city–product pair, shock intensity over 2012–2015 is computed as S = [1 − min(I_t)/avg(I_t)] × 100, where I_t is the annual inflow series. Most series (≈75%) are stationary (no significant linear trend at 5% level). As a robustness alternative, average fluctuation is computed as the mean absolute year-to-year change across 2012–2013, 2013–2014, and 2014–2015.

Statistical analysis: Ordinary least squares regressions with ln(shock intensity) as the response. Three core analyses and an extended sensitivity analysis are conducted:

• Analysis I (n = 69): Response is the city’s average shock intensity for main inflow products (LQ ≥ 1). Predictors: SCI, SCI’, their interaction, and controls: ln(population), ln(GMP), economic complexity index (ECI, computed from outflows), and ln(average shipment distance). R² and coefficient significance are reported.
• Analysis II (n = 69): Response is the city’s average shock intensity across all imported products; same predictors/controls as Analysis I.
• Analysis III (n ≈ 2512 city–product pairs): Response is city–product shock intensity; predictors include city-level SCI, SCI’, interaction, controls ln(population), ln(GMP), ECI, ln(average distance), and product-category dummies.
• Analysis IV (sensitivity): Repeats Analysis III with additional controls (percent foreign-sourced inflows, percent urban-sourced inflows, total product outflows as a production proxy) and computes indices using 2012 (IV.a) and 2015 (IV.b) networks to assess year sensitivity. Multicollinearity (VIF), residual diagnostics for homoscedasticity/normality, and leverage/influence are assessed. Robustness checks also include restricting to stationary series and replacing shock intensity with average fluctuation as the response.

Controls: Population proxies city size and correlates with many urban characteristics; shipment distance proxies transport costs; GMP proxies competitiveness/scale; ECI captures specialization/diversity; additional controls capture sourcing structure (foreign vs domestic, urban vs non-urban) and production scale.

Visualization and interpretation: Similarity matrices illustrate clustering by SCI and SCI’. Spatial maps of normalized indices highlight heterogeneity across regions. Relationships with local city and network metrics (degree/strength) are examined via linear fits with 90% confidence intervals.

• Trade-off architecture: Across cities, vertical complexity (SCI) tends to increase as horizontal complexity (SCI’) decreases, indicating a trade-off in supply network architecture. This pattern holds across local city characteristics (population, GMP, population density, ECI) and local supply network metrics (in-/out-degree and in-/out-strength).
• City size relationships: SCI is positively related to population (slope ≈ 0.8, R² = 0.20, P < 0.001), while SCI’ is negatively related to population (slope ≈ −0.43, P = 0.012), implying larger cities concentrate inflow shares in higher-complexity products but maintain greater relative diversity of suppliers for low-complexity products.
• Product complexity ranking consistency: The product complexity rankings used for SCI and SCI’ are moderately consistent (Spearman R = 0.53, P < 0.001).
• Shock reduction with horizontal complexity: Horizontal complexity (SCI’) is strongly and negatively associated with shock intensity across multiple model specifications and levels of aggregation. • Analysis I (average shocks for main inflows): Model explains 72% of variance (R² = 0.72, P < 0.001). Population and SCI’ have strong negative coefficients; cities that are larger and/or have higher SCI’ experience less intense shocks on average. • Analysis II (average shocks for all inflows): R² = 0.61 (P < 0.001). A 10% increase in population reduces average shock intensity by about 6%; a one standard deviation increase in SCI’ reduces average shock intensity by about 13%. • Analysis III (city–product level, n ≈ 2512): R² = 0.34 (P < 0.001). A 10% increase in population reduces shock intensity by about 5.6%; a one standard deviation increase in SCI’ reduces shock intensity by about 13%. Vertical complexity (SCI) shows a slightly positive association with shock intensity in this specification.
• Robustness: Results persist when (i) restricting to stationary series, (ii) using average fluctuation instead of shock intensity (R² slightly improves; SCI’ remains significantly negative), and (iii) adding controls for sourcing structure and production. The negative association between SCI’ and shock intensity is consistent and strongly significant across models (P < 0.01).
• Practical implication: Increasing supplier relative diversity for technologically sophisticated products can buffer cities against supply chain shocks; network (SCI’) and local size effects complement each other, with network effects particularly salient for medium-sized cities.

The findings support the central hypothesis that certain forms of supply chain complexity—specifically horizontal complexity reflecting supplier diversity—enhance cities’ resistance to disruptions. The empirically observed trade-off between vertical and horizontal complexity characterizes urban supply network architecture across diverse cities. Higher horizontal complexity systematically associates with lower shock intensity, even after controlling for city size, competitiveness, specialization, and distance. This indicates that diversity functions as a stabilizing mechanism for urban supply chains, akin to ecological systems. Larger cities benefit from local effects (size and partial self-reliance), while medium-sized cities can achieve resilience gains by increasing horizontal complexity, particularly for high-complexity products. While cross-sectional constraints limit causal inference, multiple robustness checks and consistent negative coefficients on SCI’ across specifications strengthen confidence that supplier diversity is a key lever for urban supply chain risk management.

The paper introduces network-based city-level indices of supply chain complexity—vertical (SCI) and horizontal (SCI’)—derived from observed first-tier supplier data using a bipartite LQ-based, eigenvector approach. It documents a trade-off between vertical and horizontal complexity across U.S. cities and demonstrates that greater horizontal complexity (supplier relative diversity) is associated with reduced shock intensity and improved stability of inflows. Policy and design implications include fostering supplier diversity for technologically sophisticated products and adopting holistic, multisector strategies to balance diversity across sectors. The approach is generalizable to other scales (firms to countries) and can leverage emerging smart data sources. Future research could extend the time horizon, incorporate causal designs, refine product granularity, and explore dynamic responses and recovery behavior following shocks.

• Temporal scope: Only four years of data (2012–2015) limits longitudinal inference; analyses are cross-sectional regarding the complexity–shock relationship, precluding strong causal claims.
• Data aggregation: Product categories are coarse (39 classes), potentially masking within-category heterogeneity in complexity and supply risks.
• Upstream visibility: Indices infer higher-tier complexity from first-tier inflows and product sophistication; actual upstream structures may differ, introducing measurement error.
• Stationarity and short series: Shock metric is best suited to stationary series; although most series are stationary, short time series constrain alternative shock/stability estimators and higher-order statistics.
• Geographic scope: Results pertain to U.S. cities and FAF4-defined regions; generalizability to other countries or different urban systems may require validation.
• Potential omitted variables: Despite multiple controls, unobserved factors (e.g., governance quality, inventory policies, sector-specific regulations) could influence both complexity and shock outcomes.