Emergency resource allocation considering the heterogeneity of affected areas during the COVID-19 pandemic in China

The COVID-19 pandemic caused extensive human and socio-economic losses, placing high demands on governments to make effective emergency management decisions. Emergency resource allocation is central to successful epidemic response but is complicated by multi-period dynamics and simultaneous demand across multiple affected areas. This study emphasizes that affected areas exhibit heterogeneity—captured by a disaster coefficient (reflecting severity via indicators like mortality and infection rates) and demand urgency (based on vulnerability, age, and infection rates). Allocating scarce resources without accounting for such heterogeneity can worsen outcomes, particularly early in an outbreak. To address this, the paper introduces a multi-period resource allocation model that simultaneously considers efficiency (time), economy (cost), and equity (loss), and validates it through a simulation study of medical resource allocation during COVID-19 in Hubei Province, China.

Recent humanitarian logistics research on emergency resource allocation commonly uses optimization models with varying decision objectives grouped into three categories: efficiency (minimizing delivery time), economy (minimizing cost), and equity (minimizing system loss). Prior work has examined each criterion separately and in combinations (e.g., efficiency–economy; efficiency–equity). A few studies considered all three simultaneously but mainly in natural disaster contexts (e.g., earthquakes), which differ from pandemics in transmission dynamics, resource types, and transport conditions. Gaps identified include limited integration of all three criteria in pandemic settings and insufficient attention to heterogeneity among affected areas (e.g., differing disaster coefficients and demand urgency), potentially preventing optimal allocations.

Study design: The authors develop a multi-period emergency resource allocation optimization model that incorporates heterogeneity of affected areas via disaster coefficient and demand urgency and jointly optimizes three criteria: equity (loss minimization), efficiency (time minimization), and economy (cost minimization). Model formulation: Objective functions: (1) minimize total loss due to resource shortfalls over all periods (equity); (2) minimize total allocation/delivery time over all periods (efficiency); (3) minimize total allocation cost (including procurement, loading/unloading, and transport fixed/variable costs) over all periods (economy). Key constraints include: demand satisfaction dynamics (shortfall carryover), supply availability, minimum satisfaction rate, transport capacity, inventory capacity at supply centers, vehicle usage under mixed loading, shortfall evolution per period, and a policy to satisfy as much demand as possible given supply. Decision variables include allocated quantities by center–area–resource–period and end-period shortfalls. Solution method: A weighted-sum approach aggregates the three objectives into a single objective with weights set by decision-makers/experts based on situational factors (e.g., vulnerability, demand urgency, supply–demand). To handle differing units, objectives are normalized to [0,1] using 0–1 transformation for cost- and benefit-oriented measures. The transformed single-objective model is solved using LINGO 12.0. Simulation study: Case context is Hubei Province, China (March 1–28, 2020; four weekly periods). Affected areas (D): Wuhan (WH), Huanggang (HG), Suizhou (SZ), Xiaogan (XG), Jingzhou (JZ). Rescue centers (R): Nanchang (NCS, Jiangxi) and Zhengzhou (ZZS, Henan). Resources (M): m1 disposable protective clothing (10^4 pieces), m2 disinfectant (10^4 bottles). Periods (N): 4. Data sources combine official statistics and expert consultations where needed. Inputs include: epidemiological status per period (Table 2) to estimate demands; period-start new demands by area/resource (Table 3); transit times and vehicle fixed/variable costs by route (Table 4); procurement costs per resource and period (Table 5); new supplies at centers per period (Table 6); resource attributes (volume, loading/unloading time and cost; Table 7); route-specific maximum transport capacities and disturbance coefficients per period (Table 8); inventory capacities at centers per period (Table 9); heterogeneity parameters per area and period: disaster coefficient and demand urgency (Table 10). Assumptions include daily use rates for protective clothing (one per diagnosed person per day; max 24 h use) and disinfectant coverage (100 m^2 per bottle; applied thrice daily).

• Incorporating heterogeneity improves outcomes: Allocation schemes that account for disaster coefficient and demand urgency yield consistently higher satisfaction rates across areas and periods than schemes that ignore heterogeneity. The benefits are most pronounced in early periods with scarce supply. Wuhan, with the highest disaster and urgency coefficients, appropriately receives priority, reducing system loss risk. • Trade-offs across decision criteria: Optimizing each criterion alone minimizes its own objective (equity minimizes loss, efficiency minimizes time, economy minimizes cost), but leads to significant differences in total loss, time, and cost across strategies. • Weight sensitivity: As the equity weight increases (examined across weight sets W1–W6), loss declines while time and cost increase, indicating clear trade-offs between fairness and operational efficiency/economy. • Temporal dynamics: Across all criteria, system loss decreases over periods and eventually reaches zero as supply catches up, while total time and cost rise initially (as more resources are moved) and then fall later (as demand declines and conditions improve). • Balanced strategy performance: Under the balance criterion with equal weights W* = (1/3, 1/3, 1/3), satisfaction rates increase period by period and reach 100% by the end of the planning horizon; aggregate loss, time, and cost outcomes are superior to single-criterion extremes, indicating better overall performance for large-scale, multi-period epidemic response.

The findings confirm that modeling heterogeneity among affected areas substantially enhances the effectiveness and equity of emergency allocations, particularly under early-stage scarcity. The results also demonstrate that different decision criteria produce markedly different global allocation strategies, necessitating explicit trade-off management. In practice, prioritizing equity early can mitigate severe losses in high-need, high-severity areas, while shifting progressively toward efficiency and economy as supplies stabilize aligns with operational realities. The balanced approach offers robust overall performance by preventing extreme allocations and simultaneously reducing loss, time, and cost, making it well-suited for sustained epidemic response. These insights inform policy by guiding when and how to weigh equity, efficiency, and economy and by highlighting the importance of incorporating heterogeneity in planning parameters.

This study introduces a multi-period emergency resource allocation model for COVID-19 that explicitly incorporates affected-area heterogeneity via disaster coefficients and demand urgency and jointly optimizes equity, efficiency, and economy. A Hubei Province simulation validates feasibility and effectiveness, showing that considering heterogeneity improves satisfaction and reduces losses, and that an equal-weighted balance among objectives yields strong overall performance with satisfaction reaching 100% by the end of the horizon. The approach is applicable to other large-scale public health emergencies and can guide governmental and managerial policy-making for multi-period, large-scale resource allocation.

Limitations include the need to incorporate additional heterogeneous factors beyond disaster coefficient and demand urgency; reliance on some estimated values due to limited official data, underscoring the value of real-time dynamic data on costs and supplies; and scalability challenges that motivate development of more efficient solution methods for larger, more complex instances.