A Dynamic Shelter Location and Victim Resettlement Model Considering Equitable Waiting Costs
Abstract
:1. Introduction
- We simultaneously consider waiting cost and fairness in the DMPLA problem.
- We consider fairness from two aspects. Firstly, we consider the unit waiting cost gap between two different disaster areas over the whole victim resettlement process. Secondly, we set an allocation percentage (or service level) threshold in each time period.
- We formulate a mixed integer linear programming model and a numerical example is investigated to explain the model. Furthermore, a case study is conducted to demonstrate the applicability of the DMPLA model to practical problems.
2. Literature Review
2.1. Shelter Location and Victim Resettlement
2.2. Human Suffering
2.3. Fairness
3. Problem Description
3.1. Shelter Location
3.2. Victim Allocation
4. Formulation
- (1)
- Indices
- (2)
- Parameters
- (3)
- Decision variables
4.1. Waiting Cost
4.2. Fairness
4.2.1. Waiting Cost Equity
4.2.2. Service Level Equity
4.3. Mathematical Model
5. Illustrative Example
5.1. Fairness Interpretation
5.2. Waiting Cost Verification
6. Case Study
6.1. Case Background and Data Estimation
6.1.1. Initial Demand of Each Disaster Site
6.1.2. Initial Distance between a Demand Point and a Candidate Shelter Location Point
6.1.3. Monetary Costs
6.1.4. Periodic Capacities for Victim Transportation and Building Shelters
6.1.5. Weight for Equity
6.1.6. Periodic Service Level
6.2. Numerical Results
7. Conclusions
- The DMPLA model reduces people’s waiting time for resettlement through minimizing victims’ waiting costs. This improves the performance of post-disaster operations significantly from a perspective of humanism, and at the same time with an acceptable increase of monetary costs.
- The proposed DMPLA model provides an equitable decision, which is important to improve people’s satisfaction. Appropriate weight value settings can bring an obvious improvement in fairness without significantly increasing waiting costs.
- The tradeoffs between waiting cost and equity can be easily controlled by adjusting the values of weight under the support of Pareto analysis.
- Transportation capacity and building capacity significantly impact the decision. In addition, they have different binding force. Thus, it is very important to assign limited resources to purchase shelters and deliver victims in a scientific way.
- An appropriate periodic service level requirement will not lead to an obvious increase of objective value and related costs while guaranteeing the periodic equity.
Author Contributions
Funding
Conflicts of Interest
References
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Parameter | Value |
---|---|
1, 2, 3, 4 | |
1, 2, 3, 4, 5 | |
1, 2, 3, 4, 5 | |
, , , , | |
, , , | |
, , , , | |
(km) | , , , , |
, , , , | |
250 | |
70 | |
0.5 | |
(yuan) | 400,000 |
(yuan) | 2 |
1 | 2 | 3 | 4 | 5 | ||
---|---|---|---|---|---|---|
i | 1 | 15 | 10 | 20 | 15 | 15 |
2 | 8 | 20 | 40 | 25 | 8 | |
3 | 5 | 35 | 40 | 25 | 5 | |
4 | 30 | 50 | 20 | 18 | 30 |
No. | Purposes | Experimental steps |
---|---|---|
(I) | Test the sensitivities of equity weight and analyze the tradeoffs for the waiting cost and equity | (1) Use the base setting of parameters (except E). (2) Generate 101 values for equity weight from 0 to 1 × 105 by a step size of 0.01 × 105. Solve each scenario. (3) Draw and analyze the Pareto fronts between WC and equity. |
(II) | Test the sensitivities of periodic building capacities | (1) Use the base setting of parameters. (2) For the parameter of building capacities, adjust the value by −100% … −10%, −5% … 0 … +5%, 10% … +100%. (3) For each adjustment, consider three scenarios (equity weight equals to 0, 0.12 × 105, 1 × 105). Solve DMPLA. |
(III) | Test the sensitivities of periodic transportation capacities | (1) Use the base setting of parameters. (2) For the parameter of periodic capacities, adjust the value by −100% … −20%, −10% … 0 … +10%, +20% … +100%. (3) For each adjustment, consider three scenarios (equity weight equals to 0, 0.12 × 105, 1 × 105). Solve DMPLA. |
(IV) | Test the sensitivities of periodic service level | (1) Use the base setting of parameters. (2) Generate 10 sets of service level constraints by a step size of 0.5%. (3) For each adjustment, solve DMPLA. |
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Share and Cite
Wang, D.; Xi, M.; Chen, Y. A Dynamic Shelter Location and Victim Resettlement Model Considering Equitable Waiting Costs. Int. J. Environ. Res. Public Health 2020, 17, 471. https://doi.org/10.3390/ijerph17020471
Wang D, Xi M, Chen Y. A Dynamic Shelter Location and Victim Resettlement Model Considering Equitable Waiting Costs. International Journal of Environmental Research and Public Health. 2020; 17(2):471. https://doi.org/10.3390/ijerph17020471
Chicago/Turabian StyleWang, Donghai, Menghao Xi, and Yingzhen Chen. 2020. "A Dynamic Shelter Location and Victim Resettlement Model Considering Equitable Waiting Costs" International Journal of Environmental Research and Public Health 17, no. 2: 471. https://doi.org/10.3390/ijerph17020471