E-commerce platforms increasingly rely on multi-warehouse fulfillment networks, which speed delivery but also expose them to systemic stockout risk, the network-wide loss of fulfillment capability caused by persistent demand shocks. Such persistence is common in digital commerce, where viral promotions and platform-wide campaigns produce demand surges with long memory that Markovian models cannot capture. We embedded long-memory demand pressure, modeled by fractional Brownian motion, in a continuous-time inventory network and obtained four results. First, we derived a closed-form expression for the systemic stockout risk of a benchmark network, defined as the probability that its average inventory of a critical item ends the period below its safety threshold, and identified the exact conditions under which this risk rises with demand persistence, the time horizon, and volatility. Its validity was proven rather than assumed; the result is exact under a common shock, asymptotically exact under correlated shocks, and with a quantified error under independent shocks. Companion measures capture the expected shortfall and the risk of breaching the threshold at any time, not only at the period's end. Second, the internal work of keeping the network balanced can be split into two quantities that should not be confused: a pressure index measuring how unevenly stock is spread and the actual volume of goods moved between warehouses. This distinction separates stock health from the logistics cost of maintaining it. Third, within a class of feedback policies based on the observed inventory gap, we obtained the optimal emergency-replenishment rule, which acts earlier and harder when demand is more persistent and is proved optimal by an elementary argument that sidesteps the difficulties associated with fractional noise. Fourth, when demand shocks are shared across warehouses, the network's overall risk does not fall to zero as it grows but settles at a strictly positive floor, so adding or diversifying warehouses removes location-specific risk but not the risk shared across all locations. Overall, the paper provides e-commerce platforms with a practical framework for quantifying systemic stockout risk under long-memory demand, calibrating that memory from data, and dynamically deploying emergency fulfillment capacity through a computable optimal feedback rule.
Citation: Hui Sun. Systemic stockout risk in e-commerce fulfillment networks: A fractional stochastic control approach[J]. Journal of Industrial and Management Optimization, 2026, 22(9): 4387-4421. doi: 10.3934/jimo.2026153
E-commerce platforms increasingly rely on multi-warehouse fulfillment networks, which speed delivery but also expose them to systemic stockout risk, the network-wide loss of fulfillment capability caused by persistent demand shocks. Such persistence is common in digital commerce, where viral promotions and platform-wide campaigns produce demand surges with long memory that Markovian models cannot capture. We embedded long-memory demand pressure, modeled by fractional Brownian motion, in a continuous-time inventory network and obtained four results. First, we derived a closed-form expression for the systemic stockout risk of a benchmark network, defined as the probability that its average inventory of a critical item ends the period below its safety threshold, and identified the exact conditions under which this risk rises with demand persistence, the time horizon, and volatility. Its validity was proven rather than assumed; the result is exact under a common shock, asymptotically exact under correlated shocks, and with a quantified error under independent shocks. Companion measures capture the expected shortfall and the risk of breaching the threshold at any time, not only at the period's end. Second, the internal work of keeping the network balanced can be split into two quantities that should not be confused: a pressure index measuring how unevenly stock is spread and the actual volume of goods moved between warehouses. This distinction separates stock health from the logistics cost of maintaining it. Third, within a class of feedback policies based on the observed inventory gap, we obtained the optimal emergency-replenishment rule, which acts earlier and harder when demand is more persistent and is proved optimal by an elementary argument that sidesteps the difficulties associated with fractional noise. Fourth, when demand shocks are shared across warehouses, the network's overall risk does not fall to zero as it grows but settles at a strictly positive floor, so adding or diversifying warehouses removes location-specific risk but not the risk shared across all locations. Overall, the paper provides e-commerce platforms with a practical framework for quantifying systemic stockout risk under long-memory demand, calibrating that memory from data, and dynamically deploying emergency fulfillment capacity through a computable optimal feedback rule.
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Figures(11) / Tables(3)
Hui Sun. Systemic stockout risk in e-commerce fulfillment networks: A fractional stochastic control approach[J]. Journal of Industrial and Management Optimization, 2026, 22(9): 4387-4421. doi: 10.3934/jimo.2026153
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