Location Optimization of Emergency Station for Dangerous Goods Accidents Considering Risk
Abstract
:1. Introduction
2. Literature Review
3. Optimization Modeling of Emergency Station for Hazardous Chemical Accidents
3.1. A Risk Assessment Method for Hazard Source Area
3.2. Problem Description
- (1)
- All emergency stations can provide rescue services for the demand point;
- (2)
- The demand point requires a k-level demand coverage level, and each level of demand coverage level is provided by at most one emergency station, which is shown in Figure 1;
- (3)
- The coverage satisfaction of the emergency station decreases with the distance to the demand point.
3.3. Notations
- Sets:
- is the set of demand points, indexed by i;
- is the emergency station, indexed by j.
- Parameters:
- is the number of the emergency station to be set;
- is the construction cost of the emergency station j;
- is the weight of the demand point i;
- is the distance from the emergency station j to demand point i;
- is the risk value of the emergency station j;
- is the emergency material demand of demand point I;
- is the total reserves of materials at emergency station j;
- k is the coverage level of emergency station to demand points;
- is the coverage attenuation function of facility point j and demand point i providing k-level service.
- Decision variables:
- is 1 if the emergency station is set, ; 0, otherwise;
- is 1 if the emergency station j provides k-level coverage for demand point i, , ; 0, otherwise;
- is the quantity of emergency materials transported from emergency station j to demand point i; , .
3.4. Formulation
- (1)
- Upper-level planning model:
- (2)
- Lower-level planning model
4. Solution Procedure
5. Numerical Example
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Number | Central Point Coordinate | Category of Hazardous Substances | Maximum Influence Radius (m) | Risk Value (P/a) | Weight | Forecast Demand for Emergency Materials (t) |
---|---|---|---|---|---|---|
1 | (3, 9) | Hydrocarbons and combustion volatiles | 6280 | 0.000808 | 0.16 | 52.8 |
2 | (2, 3) | Hydrogen sulfide and other poisons | 6260 | 0.000932 | 0.17 | 55.8 |
3 | (4, 14) | Hydrocarbons and combustion volatiles | 6240 | 0.000808 | 0.15 | 48.6 |
4 | (6, 7) | Strong corrosive liquid | 6260 | 0.000932 | 0.13 | 43.8 |
5 | (12, 10) | Fuel oil and combustion volatiles | 6260 | 0.000932 | 0.11 | 47.8 |
6 | (15, 13) | Hydrocarbons and combustion volatiles | 5000 | 0.000048 | 0.09 | 48.8 |
7 | (10, 2) | Strong corrosive liquid | 5500 | 0.000044 | 0.08 | 46.4 |
8 | (18, 4) | Hydrocarbons and combustion volatiles | 6000 | 0.000068 | 0.12 | 44.8 |
Emergency Station Demand Point | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|
1 | 3.2 | 9.2 | 2 | 5.3 | 8.2 | 11 | 11.7 | 16.1 |
2 | 7.2 | 12.2 | 5.1 | 6.7 | 4.2 | 6 | 11 | 12.7 |
3 | 15.3 | 18.3 | 14.1 | 13 | 6.3 | 3 | 12.9 | 8 |
4 | 13.3 | 14.3 | 14.4 | 10 | 5.6 | 7.1 | 7.2 | 2.8 |
5 | 8.2 | 9.8 | 9.8 | 5 | 3.1 | 7.2 | 5.1 | 7.6 |
6 | 5.6 | 5.4 | 9.4 | 2.2 | 7 | 11.3 | 4.2 | 11 |
7 | 6 | 2 | 11 | 4.4 | 10 | 14.9 | 6.1 | 14 |
Emergency Station | 1 | 2 | 3 | 4 | 5 | 6 | 7 | |
---|---|---|---|---|---|---|---|---|
Demand point | 1 | 0.000431 | 0 | 0 | 0 | 0 | 0.000095 | 0.000039 |
2 | 0 | 0 0 | 0 | 0 | 0 | 0.000139 | 0.000689 | |
3 | 0.000597 | 0.000160 | 0 | 0 | 0 | 0 | 0 | |
4 | 0.000155 | 0 | 0 | 0 | 0.000204 | 0.000657 | 0.000301 | |
5 | 0 | 0.000333 | 0 | 0.000107 | 0.000511 | 0 | 0 | |
6 | 0 | 0 | 0.000021 | 0 | 0 | 0 | 0 | |
7 | 0 | 0 | 0 | 0 | 0.000004 | 0.000011 | 0 | |
8 | 0 | 0 | 0 | 0.000040 | 0 | 0 | 0 | |
Total risk value (P/a) | 0.001183 | 0.000494 | 0.000021 | 0.000146 | 0.000719 | 0.000903 | 0.001029 |
Emergency Station | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|
Construction cost (CNY 10,000) | 3000 | 4900 | 2500 | 5530 | 5400 | 5900 | 2300 |
Risk value (10−3 P/a) | 1.183 | 0.494 | 0.021 | 0.146 | 0.719 | 0.903 | 1.029 |
Reserves of emergency materials | 21.12 | 20.32 | 19.44 | 17.52 | 15.12 | 21.52 | 20.56 |
Number of Emergency Station | Site Location Scheme | Total Risk Value | Total Cost (CNY 10,000) | Total Weighted Distance | Coverage Satisfaction |
---|---|---|---|---|---|
4 | 1, 2, 3, 7 | 2.727 | 12,700.6069 | 21.774 | 84.94% |
1, 3, 4, 7 | 2.379 | 13,330.6203 | 23.647 | 81.86% | |
2, 3, 4, 6 | 1.564 | 18,830.6279 | 24.126 | 80.96% | |
2, 3, 4, 7 | 1.69 | 15,230.6421 | 24.342 | 80.92% | |
2, 3, 5, 7 | 1.263 | 15,100.6020 | 21.608 | 78.57% | |
Recommended scheme | 2, 3, 5, 7 | 1.263 | 15,100.6020 | 21.608 | 78.57% |
Demand Point Number | Level 1 Emergency Station | Quantity of Supplies | Level 2 Emergency Station | Quantity of Supplies | Level 3 Emergency Station | Quantity of Supplies |
---|---|---|---|---|---|---|
1 | 5 | 12.7 | 2 | 19.6 | 7 | 20.5 |
2 | 7 | 20.6 | 5 | 15.1 | 2 | 20.1 |
3 | 5 | 15.0 | 2 | 19.6 | 7 | 14.0 |
4 | 2 | 8.6 | 5 | 14.8 | 7 | 20.5 |
5 | 5 | 14.9 | 2 | 18.9 | 3 | 14.3 |
6 | 3 | 19.3 | 5 | 14.3 | 2 | 15.3 |
7 | 2 | 10.9 | 7 | 20.4 | 5 | 15.1 |
8 | 2 | 10.3 | 5 | 15.1 | 3 | 19.4 |
Number of Emergency Station | Site Location Scheme | Total Risk Value | Total Cost (CNY 10,000) | Total Weighted Distance | Coverage Satisfaction |
---|---|---|---|---|---|
5 | 1, 2, 3, 4, 7 | 1.873 | 18,230.5286 | 19.433 | 94.33% |
1, 2, 3, 5, 7 | 3.446 | 18,100.5207 | 18.766 | 88.72% | |
2, 3, 4, 5, 6 | 2.283 | 24,230.5432 | 19.866 | 86.45% | |
2, 3, 4, 5, 7 | 2.409 | 20,630.5577 | 20.03 | 87.41% | |
Recommended scheme | 1, 2, 3, 4, 7 | 1.873 | 18,230.5286 | 19.433 | 94.33% |
Demand Point Number | Level 1 Emergency Station | Quantity of Supplies | Level 2 Emergency Station | Quantity of Supplies | Level 3 Emergency Station | Quantity of Supplies |
---|---|---|---|---|---|---|
1 | 1 | 21.1 | 2 | 13.1 | 7 | 18.6 |
2 | 7 | 20.6 | 5 | 14.3 | 1 | 21.0 |
3 | 5 | 7.5 | 2 | 20.2 | 1 | 20.9 |
4 | 5 | 15.0 | 1 | 8.7 | 7 | 20.3 |
5 | 2 | 19.1 | 5 | 15.0 | 3 | 13.8 |
6 | 3 | 19.1 | 5 | 11.3 | 2 | 18.5 |
7 | 2 | 11.1 | 5 | 14.8 | 7 | 20.5 |
8 | 2 | 10.3 | 5 | 15.1 | 3 | 19.4 |
Number of Emergency Station | Site Location Scheme | Total Risk Value | Total Cost (CNY 10,000) | Total Weighted Distance | Coverage Satisfaction |
---|---|---|---|---|---|
6 | 1, 2, 3, 4, 5, 7 | 2.592 | 23,630.4794 | 17.188 | 97.59% |
2, 3, 4, 5, 6, 7 | 3.312 | 26,530.4813 | 17.393 | 94.62% | |
Recommended scheme | 1, 2, 3, 4, 5, 7 | 2.592 | 23,630.4794 | 17.188 | 97.59% |
Demand Point Number | Level 1 Emergency Station | Quantity of Supplies | Level 2 Emergency Station | Quantity of Supplies | Level 3 Emergency Station | Quantity of Supplies |
---|---|---|---|---|---|---|
1 | 1 | 20.8 | 2 | 11.5 | 7 | 20.6 |
2 | 5 | 14.9 | 7 | 20.6 | 1 | 20.3 |
3 | 5 | 8.7 | 1 | 19.9 | 2 | 20.1 |
4 | 1 | 8.3 | 5 | 15.0 | 7 | 20.5 |
5 | 2 | 19.3 | 5 | 14.7 | 4 | 13.9 |
6 | 3 | 18.9 | 4 | 12.6 | 2 | 17.4 |
7 | 4 | 11.9 | 7 | 20.4 | 5 | 14.1 |
8 | 4 | 17.5 | 5 | 15.1 | 3 | 12.4 |
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Lu, J.; Yang, Q. Location Optimization of Emergency Station for Dangerous Goods Accidents Considering Risk. Sustainability 2022, 14, 6088. https://doi.org/10.3390/su14106088
Lu J, Yang Q. Location Optimization of Emergency Station for Dangerous Goods Accidents Considering Risk. Sustainability. 2022; 14(10):6088. https://doi.org/10.3390/su14106088
Chicago/Turabian StyleLu, Jianfeng, and Qiang Yang. 2022. "Location Optimization of Emergency Station for Dangerous Goods Accidents Considering Risk" Sustainability 14, no. 10: 6088. https://doi.org/10.3390/su14106088