The COVID-19 pandemic caused significant human and socioeconomic losses globally. Effective emergency management and resource allocation are crucial for mitigating these losses. The allocation of emergency resources significantly impacts the success of pandemic relief efforts. However, the sudden onset and rapid spread of COVID-19, especially in its early stages, created a critical need for simultaneous resource allocation across multiple affected areas with varying needs. The efficient and equitable distribution of limited resources became a significant challenge. This study focuses on the heterogeneity of affected areas, acknowledging that different regions experienced varying levels of impact and urgency of need. This heterogeneity, characterized by factors like disaster coefficient (reflecting the severity of the epidemic) and demand urgency (based on victim characteristics and infection rates), significantly influences resource allocation decisions. Inefficient allocation can lead to major infections and losses in severely affected areas, underscoring the need for a model that considers these factors to optimize the equitable, efficient, and economical allocation of limited emergency resources over multiple periods. The existing literature primarily focuses on single decision criteria (efficiency, economy, or equity) in emergency resource allocation, with limited research exploring the simultaneous optimization of all three criteria, especially in the context of a pandemic. This study aims to bridge this gap by developing a multi-period optimal allocation model that considers both the heterogeneity of affected areas and the simultaneous optimization of equity, efficiency, and economic criteria. The model's effectiveness is then verified through a simulation study focusing on the allocation of emergency medical resources in Hubei Province, China, a region significantly impacted by the early stages of the pandemic.

Existing research on emergency resource allocation in humanitarian logistics has grown significantly due to increasing disaster frequency and impact. Most studies use optimization models to derive resource allocation schemes, focusing on different objectives: efficiency (shortest delivery time), economy (lowest allocation cost), and equity (minimum system loss). Efficiency-oriented studies typically minimize the maximum or average arrival time of resources. Economy-oriented studies minimize the total cost of allocation, encompassing factors such as facility costs, deprivation costs, inventory costs, and transportation costs. Equity-oriented studies emphasize fair distribution to minimize deprivation or disutility loss caused by resource shortages. While some studies combine two criteria (e.g., efficiency and economy, efficiency and equity), research simultaneously considering efficiency, economy, and equity is relatively rare, especially for pandemic scenarios. The characteristics of the COVID-19 pandemic (rapid spread, specific resource needs, generally good transportation conditions) differ from natural disasters, requiring a specific model tailored to the pandemic context. This study addresses these gaps by proposing a model that incorporates all three criteria and considers the unique challenges posed by the COVID-19 pandemic.

This study employs a multi-period optimization model for emergency resource allocation that considers efficiency, economy, and equity criteria simultaneously, while explicitly acknowledging the heterogeneity of affected areas. The model is formulated using a set of notations (Table 1) defining sets, indices, parameters, and variables. The objective function minimizes the total loss due to resource shortfall (equity), total delivery time (efficiency), and total allocation cost (economy). Several constraints are incorporated, including demand constraints, supply constraints, resource satisfaction rate constraints, transport capacity constraints, and inventory capacity constraints. The model accounts for resource mixed loading and expresses resource shortfall at the end of each time period. A constraint ensures maximum demand satisfaction within available supply. Non-negativity constraints are applied to decision variables. The model is a multi-objective optimization problem, solved using the weighted sum method. This method integrates the three objectives into a single objective function using weight coefficients (ωy) determined by decision-makers and experts, considering factors such as victim vulnerability and demand urgency. The (0-1) interval transformation method is used for normalization of objective functions with different units. Lingo 12.0 software is used to solve the transformed single-objective model. A simulation study is conducted using Hubei Province, China, as a case study due to its early and severe impact from the pandemic. Five severely affected cities are selected as affected areas, and two nearby cities serve as rescue centers. Two types of emergency resources (disposable protective clothing and disinfectant) are considered, using a combination of real and hypothetical data to reflect the situation in March 2020. Data on accumulated confirmed cases, deaths, cured cases, and existing confirmed cases in each affected area over four emergency periods (Table 2) are used to estimate resource demand (Table 3). Transportation time and costs (Table 4), procurement costs (Table 5), initial resource supply (Table 6), resource attribute parameters (Table 7), transport capacity and time disturbance coefficients (Table 8), rescue center inventory capacity (Table 9), and heterogeneity parameters (disaster coefficient and demand urgency) (Table 10) are determined based on available data and expert consultation.

The simulation results demonstrate the significant impact of considering heterogeneity in emergency resource allocation. Figure 2 compares resource satisfaction rates with and without considering heterogeneity. The results show that the satisfaction rate is consistently higher when heterogeneity is considered, especially for resource m1 and m2. Wuhan City (WH), with the highest disaster coefficient and demand urgency, consistently shows the highest satisfaction rate, highlighting the model's ability to prioritize areas with the most critical needs. Figure 3 shows that different decision criteria (equity, efficiency, economy) significantly affect total loss, total time, and total cost. Optimizing for a single criterion leads to extreme results; for example, prioritizing equity minimizes losses but may increase time and cost. Figure 4 illustrates the trade-offs between these criteria with different weight combinations (W1-W6). Increasing the weight on equity reduces losses but increases time and cost. Figure 5 compares the effects of considering each criterion separately and simultaneously (balance criterion). The balance criterion shows a decrease in system loss and a trend of initially increasing and then decreasing time and cost, aligning with the reality of multi-period emergency resource allocation. Figure 6 shows that, under the balance criterion, the resource satisfaction rate gradually increases, reaching 100% by the end of the emergency period. Figure 7 details the loss, time, and cost at each affected area under the balance criterion, showing that losses decline while time and cost initially rise and then fall. This demonstrates the model’s ability to balance multiple objectives.

The findings directly address the research question by demonstrating the benefits of a multi-period emergency resource allocation model that incorporates the heterogeneity of affected areas and balances efficiency, economy, and equity criteria. The results highlight the importance of considering heterogeneity, particularly during the initial phases of a crisis when resources are scarce. The model's ability to prioritize areas with the most critical needs and achieve high satisfaction rates demonstrates its practical value. The analysis of different decision criteria emphasizes the need for a balanced approach, avoiding the pitfalls of extreme optimization focused on a single criterion. The balance criterion offers a more robust and sustainable approach to resource allocation in multi-period emergency situations. The successful application of the model to the COVID-19 pandemic in Hubei Province suggests its broader applicability to other large-scale public health emergencies.

This study contributes a multi-period emergency resource allocation model that effectively balances efficiency, economy, and equity while explicitly addressing the heterogeneity of affected areas. The model's performance in a simulation of the COVID-19 pandemic in Hubei Province validates its practical value. Future research could explore incorporating additional heterogeneity factors, utilizing real-time dynamic data, and developing more efficient solution methods for larger-scale problems. The model provides valuable insights for policymakers in developing more effective and equitable emergency resource allocation strategies.

This study has certain limitations. First, the model currently incorporates only two heterogeneity factors (disaster coefficient and demand urgency). Future research could incorporate more comprehensive factors reflecting the complex realities of disaster situations. Second, the model relies on a combination of real and hypothetical data. Acquiring real-time dynamic data on costs and supply would improve the model's accuracy and generalizability. Finally, as the scale and complexity of the problem increase, more advanced solution methods could improve the efficiency and scalability of the model.