In recent years, the application of civil drone technology for island transport has gained significant attention due to its flexibility, cost-effectiveness, and reduced human risk. Civil drones are increasingly deployed for emergency logistics, such as delivering medical supplies, ammunition, and equipment to remote islands with complex terrains. However, evaluating the transport efficiency of various civil drone models under specific conditions like island environments remains challenging. Traditional methods, such as expert judgment, mathematical modeling, simulation, and machine learning, often face limitations like subjectivity, complexity, or data scarcity. To address this, I propose a data-driven approach based on super-efficiency parallel network data envelopment analysis (DEA). This method incorporates the internal structure of civil drones, decomposing transport capability into parallel components, and enables a comprehensive ranking of civil drone efficiency for island logistics. By integrating shared input adjustments and super-efficiency concepts, this approach provides a more nuanced and interpretable assessment, supporting the selection of optimal civil drone models for military applications.
The core of this research lies in modeling civil drone transport efficiency as a multi-input, multi-output system. I consider 30 different models of industry-grade civil drones as decision-making units (DMUs). Each civil drone’s transport capability is divided into two parallel subcomponents: flight platform base capability and mission environment adaptation capability. This decomposition allows for a detailed analysis of how internal factors, such as endurance and environmental resilience, contribute to overall performance. The inputs include variables like deployable quantity, maintenance cost, procurement cost, and repair投入, while outputs encompass metrics such as endurance time, payload capacity, cruise speed, operational radius, and environmental resistance. To handle shared inputs, I introduce proportionality factors, optimizing their allocation across subcomponents. Subsequently, I apply a super-efficiency parallel network DEA model, which excludes the evaluated DMU from the reference set, enabling a full ranking of all civil drones, including those on the efficiency frontier.
The parallel network DEA model structure for civil drone island transport efficiency is illustrated in the figure above. It consists of two parallel subcomponents: flight platform base capability and mission environment adaptation capability. Inputs are shared between these subcomponents, with proportionality factors adjusting their distribution. For example, maintenance投入 and procurement cost are allocated using factors α and β (where 0 < α, β < 1). The flight platform subcomponent uses α times maintenance投入 and β times procurement cost, while the adaptation subcomponent uses the remainder. This setup captures the interdependencies within civil drone systems, providing a more accurate efficiency measurement compared to traditional “black-box” models.
Mathematically, the classic CCR DEA model evaluates the efficiency of a DMU0 by solving the following linear programming problem:
$$ \text{Maximize } \theta^* = \sum_{r=1}^{s} \mu_r y_{r0} $$
Subject to:
$$ \sum_{r=1}^{s} \mu_r y_{rj} – \sum_{i=1}^{m} v_i x_{ij} \leq 0, \quad j = 1, 2, \dots, n $$
$$ \sum_{i=1}^{m} v_i x_{i0} = 1 $$
$$ \mu_r, v_i \geq 0, \quad r = 1, 2, \dots, s; \quad i = 1, 2, \dots, m $$
However, this model ignores internal structures. In the parallel network DEA for civil drones, I extend this by incorporating constraints for each subcomponent. Let \( x_{ij}^{(p)} \) and \( y_{rj}^{(p)} \) denote the inputs and outputs for subcomponent \( p \) (where \( p = 1 \) for flight platform and \( p = 2 \) for environment adaptation). The model becomes:
$$ \text{Maximize } \theta^* = \sum_{r=1}^{s} \mu_r y_{r0} $$
Subject to:
$$ \sum_{r=1}^{s} \mu_r y_{rj} – \sum_{i=1}^{m} v_i x_{ij} \leq 0, \quad j = 1, 2, \dots, n $$
$$ \sum_{r=1}^{s} \mu_r y_{rj}^{(p)} – \sum_{i=1}^{m} v_i x_{ij}^{(p)} \leq 0, \quad j = 1, 2, \dots, n; \quad p = 1, 2 $$
$$ \sum_{i=1}^{m} v_i x_{i0} = 1 $$
$$ \mu_r, v_i \geq 0, \quad r = 1, 2, \dots, s; \quad i = 1, 2, \dots, m $$
To address shared inputs, I define allocation factors. For instance, maintenance投入 \( x_{2j} \) is split as \( \alpha x_{2j} \) for the flight platform and \( (1 – \alpha) x_{2j} \) for environment adaptation. Similarly, procurement cost \( x_{3j} \) is divided using β. This refinement allows for a more realistic representation of how resources are utilized in civil drone operations.
Furthermore, to achieve a full ranking of civil drones, I introduce the super-efficiency concept. The super-efficiency parallel network DEA model modifies the constraints by excluding the DMU under evaluation from the reference set:
$$ \text{Maximize } \theta^* = \sum_{r=1}^{s} \mu_r y_{r0} $$
Subject to:
$$ \sum_{r=1}^{s} \mu_r y_{rj} – \sum_{i=1}^{m} v_i x_{ij} \leq 0, \quad j = 1, 2, \dots, n; \quad j \neq j_0 $$
$$ \sum_{r=1}^{s} \mu_r y_{rj}^{(p)} – \sum_{i=1}^{m} v_i x_{ij}^{(p)} \leq 0, \quad j = 1, 2, \dots, n; \quad j \neq j_0; \quad p = 1, 2 $$
$$ \sum_{i=1}^{m} v_i x_{i0} = 1 $$
$$ \mu_r, v_i \geq 0, \quad r = 1, 2, \dots, s; \quad i = 1, 2, \dots, m $$
This model computes efficiency scores that can exceed 1, enabling differentiation among efficient civil drones. I implement this with a step size ε (e.g., 0.05) for the proportionality factors, iterating over possible values to average the results for robustness.
The evaluation指标体系 for civil drone island transport efficiency includes multiple inputs and outputs, as summarized in the table below. Inputs measure resource consumption, while outputs reflect performance metrics. For example, deployable quantity is inversely related to the space occupied on a vessel, affecting cluster operations. Environmental resistance outputs, such as anti-salt spray and anti-electromagnetic interference, are rated on a 1–10 scale to quantify adaptation capabilities.
| Variable Type | Indicator | Definition and Unit |
|---|---|---|
| Input | Deployable Quantity (I1) | Space occupied per civil drone, in m² (smaller values allow more units) |
| Maintenance投入 (I2) | Average maintenance cost per 100 km, in currency units | |
| Procurement Cost (I3) | Market price of the civil drone, in 10,000 currency units | |
| Repair投入 (I4) | Average repair cost based on failure rate, in currency units | |
| Output | Endurance Time (O1) | Maximum flight time with full load, in hours |
| Payload Capacity (O2) | Maximum cargo mass per trip, in kg | |
| Cruise Speed (O3) | Average transport speed, in km/h | |
| Operational Radius (O4) | Maximum delivery distance, in km | |
| Anti-Salt Spray (O5) | Resistance to corrosion in marine environments, scale 1–10 | |
| Anti-Rain and Wind (O6) | Tolerance to adverse weather, scale 1–10 | |
| Anti-Electromagnetic Interference (O7) | Ability to operate in noisy electromagnetic conditions, scale 1–10 | |
| Delivery Accuracy Rate (O8) | Percentage of successful deliveries to target locations |
In my analysis, I collected data for 30 civil drone models, focusing on industry-grade variants suitable for island transport. The data includes values for all inputs and outputs, as shown in the subsequent table. For instance, civil drone models vary significantly in deployable quantity, with some occupying as little as 1.3 m², enabling higher deployment density. Outputs like endurance time range from 0.7 to 19 hours, highlighting the diversity in civil drone capabilities.
| DMU | I1 (m²) | I2 (currency) | I3 (10k units) | I4 (currency) | O1 (h) | O2 (kg) | O3 (km/h) | O4 (km) | O5 | O6 | O7 | O8 (%) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 8.8 | 6.5 | 200 | 200 | 3.3 | 40.0 | 50 | 5 | 4 | 2 | 4 | 85 |
| 2 | 2.2 | 5.0 | 210 | 210 | 1.5 | 20.0 | 40 | 4 | 6 | 4 | 4 | 72 |
| 3 | 3.2 | 17.0 | 400 | 400 | 0.9 | 2.7 | 35 | 8 | 6 | 6 | 6 | 84 |
| 4 | 5.4 | 10.0 | 300 | 300 | 1.5 | 4.0 | 40 | 10 | 4 | 6 | 6 | 80 |
| 5 | 3.3 | 7.0 | 300 | 300 | 3.4 | 10.0 | 30 | 4 | 4 | 6 | 6 | 78 |
| 6 | 2.4 | 4.0 | 200 | 200 | 0.7 | 2.0 | 20 | 4 | 2 | 4 | 6 | 75 |
| 7 | 10.2 | 20.0 | 450 | 450 | 3.0 | 40.0 | 45 | 15 | 8 | 10 | 10 | 83 |
| 8 | 12.3 | 30.0 | 350 | 350 | 5.0 | 4.0 | 60 | 40 | 8 | 6 | 8 | 90 |
| 9 | 12.4 | 35.0 | 250 | 250 | 5.5 | 5.0 | 70 | 30 | 10 | 6 | 10 | 98 |
| 10 | 10.5 | 22.0 | 230 | 230 | 4.0 | 5.0 | 60 | 25 | 10 | 8 | 8 | 82 |
| 11 | 7.4 | 17.0 | 220 | 220 | 2.0 | 6.0 | 50 | 30 | 8 | 10 | 8 | 78 |
| 12 | 8.2 | 15.0 | 140 | 140 | 4.0 | 5.0 | 40 | 28 | 6 | 4 | 8 | 83 |
| 13 | 5.4 | 21.0 | 210 | 210 | 12.0 | 25.0 | 50 | 26 | 8 | 8 | 10 | 88 |
| 14 | 3.5 | 23.0 | 250 | 250 | 10.0 | 27.0 | 55 | 35 | 8 | 8 | 10 | 84 |
| 15 | 5.4 | 32.0 | 450 | 450 | 15.0 | 50.0 | 70 | 45 | 10 | 6 | 8 | 94 |
| 16 | 1.3 | 7.0 | 150 | 150 | 2.0 | 5.0 | 35 | 5 | 2 | 4 | 4 | 75 |
| 17 | 7.1 | 6.8 | 150 | 150 | 3.2 | 4.0 | 30 | 5 | 4 | 2 | 4 | 78 |
| 18 | 6.8 | 8.0 | 500 | 500 | 3.4 | 5.0 | 35 | 6 | 4 | 4 | 4 | 80 |
| 19 | 7.8 | 12.0 | 150 | 150 | 6.5 | 6.0 | 40 | 8 | 6 | 8 | 4 | 82 |
| 20 | 8.6 | 16.0 | 200 | 200 | 6.8 | 7.0 | 50 | 10 | 6 | 8 | 6 | 86 |
| 21 | 7.4 | 14.0 | 230 | 230 | 6.2 | 7.0 | 40 | 12 | 6 | 8 | 6 | 88 |
| 22 | 3.6 | 18.0 | 240 | 240 | 5.8 | 6.0 | 35 | 15 | 8 | 6 | 8 | 80 |
| 23 | 4.5 | 19.0 | 200 | 200 | 8.0 | 8.0 | 50 | 16 | 6 | 8 | 6 | 90 |
| 24 | 12.2 | 21.0 | 390 | 390 | 7.0 | 20.0 | 60 | 16 | 8 | 6 | 8 | 92 |
| 25 | 14.6 | 25.0 | 380 | 380 | 10.0 | 28.0 | 50 | 20 | 10 | 8 | 10 | 88 |
| 26 | 12.2 | 27.0 | 250 | 250 | 12.0 | 25.0 | 70 | 25 | 10 | 10 | 8 | 94 |
| 27 | 15.6 | 26.0 | 220 | 220 | 11.0 | 28.0 | 60 | 30 | 8 | 10 | 10 | 91 |
| 28 | 7.6 | 24.0 | 210 | 210 | 12.0 | 24.0 | 50 | 28 | 10 | 8 | 8 | 88 |
| 29 | 5.6 | 23.0 | 180 | 180 | 10.0 | 18.0 | 55 | 26 | 8 | 10 | 8 | 90 |
| 30 | 3.5 | 21.0 | 260 | 260 | 19.0 | 15.0 | 40 | 18 | 10 | 8 | 10 | 87 |
I applied three DEA models to evaluate the island transport efficiency of these civil drones: the classic CCR model, the parallel network DEA model with improved shared proportionality, and the super-efficiency parallel network DEA model. The results are summarized in the following table. The classic CCR model identified 17 out of 30 civil drones as efficient (score 1.000), indicating poor discrimination. The parallel network DEA reduced this to 10 efficient units by incorporating internal structures. Finally, the super-efficiency version achieved a full ranking, with efficiency scores ranging above and below 1, providing clear differentiation.
| DMU | CCR Total Efficiency | Parallel Network DEA Total Efficiency | Base Capability Min | Base Capability Max | Adaptation Capability Min | Adaptation Capability Max | Super-Efficiency Parallel Network DEA Total Efficiency |
|---|---|---|---|---|---|---|---|
| 1 | 1.000 | 0.992 | 1.000 | 1.000 | 0.708 | 0.969 | 1.480 |
| 2 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.839 |
| 3 | 0.764 | 0.516 | 0.478 | 0.478 | 0.544 | 0.544 | 0.516 |
| 4 | 0.803 | 0.743 | 0.750 | 0.750 | 0.706 | 0.737 | 0.743 |
| 5 | 1.000 | 0.882 | 0.811 | 0.811 | 0.936 | 0.936 | 0.882 |
| 6 | 1.000 | 0.966 | 0.833 | 0.833 | 1.000 | 1.000 | 1.342 |
| 7 | 0.875 | 0.696 | 0.648 | 0.648 | 0.729 | 0.729 | 0.696 |
| 8 | 0.763 | 0.666 | 0.726 | 0.726 | 0.202 | 0.568 | 0.666 |
| 9 | 0.916 | 0.896 | 0.916 | 0.916 | 0.770 | 0.875 | 0.896 |
| 10 | 1.000 | 0.943 | 0.895 | 0.895 | 0.998 | 0.998 | 0.943 |
| 11 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.047 |
| 12 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.334 |
| 13 | 1.000 | 0.995 | 0.998 | 0.998 | 0.946 | 0.990 | 1.035 |
| 14 | 1.000 | 1.000 | 1.000 | 1.000 | — | — | 1.224 |
| 15 | 1.000 | 1.000 | 1.000 | 1.000 | — | — | 1.157 |
| 16 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.512 |
| 17 | 1.000 | 0.968 | 0.799 | 0.799 | 1.000 | 1.000 | 1.030 |
| 18 | 0.846 | 0.694 | 0.782 | 0.782 | 0.340 | 0.600 | 0.694 |
| 19 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.143 |
| 20 | 0.936 | 0.877 | 0.894 | 0.894 | 0.828 | 0.875 | 0.877 |
| 21 | 0.905 | 0.823 | 0.756 | 0.756 | 0.862 | 0.862 | 0.823 |
| 22 | 0.921 | 0.800 | 0.639 | 0.639 | 0.878 | 0.878 | 0.800 |
| 23 | 0.937 | 0.886 | 0.929 | 0.929 | 0.537 | 0.823 | 0.886 |
| 24 | 0.683 | 0.642 | 0.657 | 0.657 | 0.552 | 0.627 | 0.642 |
| 25 | 0.760 | 0.711 | 0.666 | 0.666 | 0.735 | 0.735 | 0.711 |
| 26 | 0.974 | 0.919 | 0.954 | 0.954 | 0.736 | 0.886 | 0.919 |
| 27 | 1.000 | 0.978 | 1.000 | 1.000 | 0.823 | 0.958 | 1.012 |
| 28 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.074 |
| 29 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.189 |
| 30 | 1.000 | 1.000 | 1.000 | 1.000 | — | — | 1.902 |
The results demonstrate that the super-efficiency parallel network DEA model offers superior discrimination. For instance, civil drone models like DMU30, DMU2, and DMU16 rank highest with scores of 1.902, 1.839, and 1.512, respectively. These civil drones excel in both base capability and environment adaptation, making them ideal for island transport. In contrast, models with lower scores, such as DMU3 (0.516), exhibit deficiencies in one or both subcomponents. The parallel decomposition also reveals insights for improvement; for example, DMU23 has a total efficiency of 0.886, with base capability at 0.929 but adaptation capability between 0.537 and 0.823, suggesting that enhancing environmental resilience could boost overall performance.
In conclusion, the super-efficiency parallel network DEA model provides a robust framework for evaluating civil drone island transport efficiency. By accounting for internal structures and enabling full ranking, it addresses limitations of traditional methods. This approach aids in the selection of optimal civil drone models for military logistics, ensuring efficient and reliable operations in challenging environments. Future work could focus on refining the shared input allocation and extending the model to dynamic scenarios involving multiple missions. The versatility of this method also suggests applications in other domains where civil drones are deployed, such as disaster response or agricultural monitoring.