Multi-Objective Two-Stage Stochastic Programming Model for a Proposed Casualty Transportation System in Large-Scale Disasters: A Case Study
Abstract
:1. Introduction
2. Literature Review
3. Methodology
3.1. Problem Definition
3.2. A Multi-Objective Two-Stage Stochastic Programming Formulation
- In the first stage, the ambulances are assigned to the EMS according to the existing number of ambulances.
- Before the disaster, ambulances are only available at emergency stations.
- Ambulances may leave EMS, but casualties are not transported to the EMS, but to the hospitals.
- At the beginning of the first period, while emergency stations send ambulances only to the triage points assigned to the station, ambulances can serve to each point within the period and in the following periods.
- Additional ambulances can come in every period, and the arriving ambulance will serve in the next period.
- Ambulances can work throughout the periods.
- RPM scores of the patients do not change.
3.3. Solution Methodology
Algorithm 1. | Definitions of algorithm steps |
Create the payoff table | |
Calculate ranges , | |
Define = number of intervals | |
Divide into intervals | |
Initialize counter = 0 = 0; : the number of Pareto optimal solutions | |
Do (Until reach to ) | |
… | |
Update and solve the Problem P for equations (37)-(41) | |
If the solution is feasible then; | |
, calculate , ; (/) | |
If < then, | |
repeat to | |
else, | |
then, | |
If < then, | |
repeat to | |
else, | |
then, | |
If < then, | |
repeat to | |
else, | |
End if | |
End if | |
End if | |
End if | |
The algorithm is completed, and the results obtained by creating the Pareto optimal solution table are evaluated. |
4. Computational Study
Case Study and Data Collection
5. Results and Discussion
- While making the coverage decisions, the population of the region, existing resources and the expected rare events must be considered. Besides, making multi objectives decisions for disaster relief will make planning more effective.
- It is necessary to plan ambulance allocation based on scenarios for disaster relief. Adding ambulances can decrease the number of unserved casualties by considering RPM scores. Because of the hospital capacities, the increasing number of ambulances cannot significantly decrease the value of the T1 and T2 casualties transported to the hospitals after a certain level.
- If the severity of the disaster is great, hospital capacities will be insufficient even in the first critical hours. A centralized transportation system will play a major role in case detection so that emergency cases can be handled with priority. The prior arrival of the most urgent cases to the hospitals prevents the usage and exhaustion of the hospital capacities by the relatively less urgent cases.
- In order to reduce the RPM-weighted number of unserved casualties, ambulances must be dispatched according to the obtained real-time data from the information/decision support system. Choosing only the nearest distances prevents both the transportation of urgent casualties and the damages the equity in service provided to the demand points.
- If the optimistic scenario occurs, all T1 and T2 group casualties can be transported to the hospitals with the number of correctly planned ambulances. However, more ambulance services and medical care points will be needed in other scenarios, especially after the second period.
- In the study, it was observed that the ambulance assignment, according to only the nearest locations, had a negative effect on the number of unserved casualties. If the dispatching strategy is developed according to the RPM of the casualties, the transportation time will increase; however, the number of transported casualties will increase. However, the number of transported casualties will be more.
6. Conclusions and Future Research
Author Contributions
Funding
Conflicts of Interest
Appendix A
The Experiment Number | The Experiment Number | ||||||
---|---|---|---|---|---|---|---|
#1 | 77,792.98 | 75.49 | 31,947.17 | #20 | 60,403.07 | 177.86 | 60,602.37 |
#2 | 63,778.53 | 109.54 | 44,229.66 | #21 | 68,471.09 | 194.93 | 31,946.71 |
#3 | 63,763.61 | 109.48 | 52,423.86 | #22 | 64,658.91 | 194.86 | 36,032.81 |
#4 | 69,199.93 | 126.62 | 31,947.08 | #23 | 62,154.57 | 194.90 | 40,137.83 |
#5 | 65,225.87 | 126.68 | 36,041.47 | #24 | 60,915.48 | 194.92 | 44,231.90 |
#6 | 68,761.43 | 143.75 | 31,947.17 | #25 | 60,409.34 | 194.92 | 48,327.80 |
#7 | 60,642.11 | 143.75 | 52,424.20 | #26 | 60,401.57 | 183.60 | 52,420.97 |
#8 | 60,642.00 | 143.73 | 60,614.98 | #27 | 60,402.71 | 194.87 | 56,519.15 |
#9 | 68,532.64 | 160.79 | 31,946.00 | #28 | 60,401.57 | 194.92 | 60,610.92 |
#10 | 64,648.71 | 160.73 | 36,042.06 | #29 | 79,871.20 | 212.00 | 27,851.75 |
#11 | 62,353.25 | 160.80 | 40,137.88 | #30 | 68,348.07 | 212.00 | 31,941.25 |
#12 | 61,030.86 | 160.80 | 44,232.76 | #31 | 64,550.41 | 212.00 | 36,039.83 |
#13 | 68,375.21 | 177.84 | 31,947.12 | #32 | 62,069.27 | 212.00 | 40,136.89 |
#14 | 64,493.62 | 177.85 | 36,042.49 | #33 | 60,875.88 | 212.00 | 44,232.77 |
#15 | 62,250.23 | 177.74 | 40,137.26 | #34 | 60,407.61 | 212.00 | 48,325.51 |
#16 | 60,969.67 | 177.81 | 44,232.74 | #35 | 60,402.65 | 212.00 | 52,423.90 |
#17 | 60,582,86 | 177.87 | 48,328.79 | #36 | 60,401.57 | 212.00 | 56,519.20 |
#18 | 60,413.51 | 177.83 | 52,420.47 | #37 | 60,401.57 | 212.00 | 60,610.15 |
#19 | 60,419.43 | 177.78 | 56,517.04 |
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Scenario | Occurrence Probability of Scenarios | Magnitude of Earthquake | Proportion of Expected Type-T1 Casualty (%) | Proportion of Expected Type-T2 Casualty (%) | Proportion of Expected Type-T3 Casualty (%) | Expected Damage of Road | Expected Damage of Hospital |
---|---|---|---|---|---|---|---|
Scenario 1 | 0.06 | 7.7 | 2 | 2.7 | 3.3 | 65% | 35% |
Scenario 2 | 0.08 | 7.7 | 1.8 | 2.4 | 3 | 62% | 33% |
Scenario 3 | 0.09 | 7.7 | 1.7 | 2.3 | 2.8 | 60% | 32% |
Scenario 4 | 0.1 | 7.7 | 1.5 | 2 | 2.5 | 60% | 30% |
Scenario 5 | 0.16 | 7.5 | 1.3 | 1.7 | 2.2 | 55% | 27% |
Scenario 6 | 0.11 | 7.4 | 1.1 | 1.4 | 1.9 | 45% | 25% |
Scenario 7 | 0.1 | 6.9 | 0.9 | 1.1 | 1.6 | 30% | 7% |
Scenario 8 | 0.16 | 7.5 | 0.09 | 0.42 | 0.74 | 25% | 18% |
Scenario 9 | 0.14 | 7.5 | 0.054 | 0.264 | 0.502 | 20% | 10% |
The Minimized Objective Function | |||
---|---|---|---|
Min (The number of unserved casualties) | 60,401.57 | 212 | 60,615 |
Min (The number of ambulances) | 85,069 | 75.49 | 28,873 |
Min (The total time) | 91,342 | 212 | 27,851.78 |
Emergency Medical Service Stations | Assigned Demand Points | Located Number of Ambulances |
---|---|---|
EMS-1 | D2-D5-D16 | 2 |
EMS-2 | D15 | 1 |
EMS-3 | D3-D8-D10-D11-D12-D18-D20 | 3 |
EMS-4 | D7 | 1 |
EMS-5 | D1-D4-D6-D9-D13-D14-D17 | 4 |
EMS-6 | D19 | 1 |
Scenario | Number of Unserved Casualties (RPM Score 1–4) | Number of Unserved Casualties (RPM Score 5–8) | Number of Unserved Casualties (RPM Score 9–12) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
t = 1 | t = 2 | t = 3 | % | t = 1 | t = 2 | t = 3 | % | t = 1 | t = 2 | t = 3 | % | |
Scenario 1 | 0 | 1150 | 2766 | 20.8 | 1544 | 3812 | 5940 | 60.0 | 2352 | 5176 | 7836 | 81.6 |
Scenario 2 | 0 | 873 | 2321 | 18.8 | 1260 | 3296 | 5220 | 57.7 | 2112 | 4648 | 7060 | 81.5 |
Scenario 3 | 0 | 708 | 2064 | 17.4 | 1122 | 3038 | 4846 | 56.5 | 1992 | 4380 | 6644 | 81.7 |
Scenario 4 | 0 | 557 | 1761 | 16.4 | 722 | 2418 | 4018 | 50.7 | 1764 | 3880 | 5880 | 81.6 |
Scenario 5 | 0 | 140 | 1180 | 10.8 | 526 | 1966 | 3326 | 47.5 | 1560 | 3424 | 5184 | 83.1 |
Scenario 6 | 0 | 0 | 884 | 8.5 | 247 | 1251 | 2375 | 37.4 | 1348 | 2952 | 4472 | 84.7 |
Scenario 7 | 0 | 0 | 549 | 6.5 | 0 | 242 | 1126 | 16.1 | 904 | 2260 | 3532 | 79.0 |
Scenario 8 | 0 | 0 | 0 | 0.0 | 0 | 0 | 0 | 0.0 | 0 | 0 | 54 | 1.8 |
Scenario 9 | 0 | 0 | 0 | 0.0 | 0 | 0 | 0 | 0.0 | 0 | 0 | 0 | 0.0 |
Scenario | To Minimize the Number of Unserved Casualties (According to 26th Solution) | |||
---|---|---|---|---|
t = 1 | t = 2 | t = 3 | Total | |
Scenario 1 | 200 | 0 | 0 | 200 |
Scenario 2 | 200 | 0 | 0 | 200 |
Scenario 3 | 194 | 0 | 0 | 194 |
Scenario 4 | 200 | 0 | 0 | 200 |
Scenario 5 | 187 | 0 | 0 | 187 |
Scenario 6 | 176 | 24 | 0 | 200 |
Scenario 7 | 171 | 18 | 11 | 200 |
Scenario 8 | 96 | 26 | 21 | 143 |
Scenario 9 | 53 | 15 | 13 | 81 |
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Caglayan, N.; Satoglu, S.I. Multi-Objective Two-Stage Stochastic Programming Model for a Proposed Casualty Transportation System in Large-Scale Disasters: A Case Study. Mathematics 2021, 9, 316. https://doi.org/10.3390/math9040316
Caglayan N, Satoglu SI. Multi-Objective Two-Stage Stochastic Programming Model for a Proposed Casualty Transportation System in Large-Scale Disasters: A Case Study. Mathematics. 2021; 9(4):316. https://doi.org/10.3390/math9040316
Chicago/Turabian StyleCaglayan, Nadide, and Sule Itir Satoglu. 2021. "Multi-Objective Two-Stage Stochastic Programming Model for a Proposed Casualty Transportation System in Large-Scale Disasters: A Case Study" Mathematics 9, no. 4: 316. https://doi.org/10.3390/math9040316
APA StyleCaglayan, N., & Satoglu, S. I. (2021). Multi-Objective Two-Stage Stochastic Programming Model for a Proposed Casualty Transportation System in Large-Scale Disasters: A Case Study. Mathematics, 9(4), 316. https://doi.org/10.3390/math9040316