# Supported Evacuation for Disaster Relief through Lexicographic Goal Programming

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## Abstract

**:**

## 1. Introduction and Literature Review

- The introduction of dynamism into the supported evacuation model regarding the arrival of potential evacuees to the pick up points, since we consider their arrival may happen at different of points of time during the planning horizon.
- The classification of affected people requiring evacuation according to their particular situation and/or medical condition, leading to several priority levels, so that each group can be treated accordingly.
- The joint consideration of objectives such us number of evacuated people, operation time and cost within a lexicographic approach, in such a way that there is no trade off among them.
- The validation of the proposed model on a realistic case study based on the earthquake and tsunami that hit Indonesia in September 2018.

## 2. Problem Description

## 3. The Proposed Evacuation Model

#### 3.1. Parameters of the Model and Decision Variables

**Sets and indices**

$\mathcal{N}:$ | Set of nodes or involved areas ($i,j\in \mathcal{N}$: $\mathcal{N}=\mathcal{NA}\cup \mathcal{NS}\cup \mathcal{NH}\cup \mathcal{NT}$). |

$\mathcal{E}:$ | Set of edges or arcs between nodes ($(i,j)=\left(ij\right)\in \mathcal{E}$). |

$\mathcal{T}:$ | Discretized time periods ($t,{t}^{\prime}\in \{1,...,\mathcal{T}\}$). |

$\mathcal{H}:$ | Set of types of people to be evacuated ($h\in \mathcal{H}$). |

$\mathcal{K}:$ | Set of types of vehicles available for the evacuation ($k\in \mathcal{K}$). |

$\mathcal{M}:$ | Set of goals to be achieved ($m\in \mathcal{M}$). |

**Parameters**

${d}_{ij}^{k}:$ | Distance from node $i\in \mathcal{N}$ to node $j\in \mathcal{N}$ (or length of arc/edge $(i,j)\in \mathcal{E})$ when traversed by a vehicle of type $k\in \mathcal{K}$. |

$a{v}_{ij}^{k}:$ | Average velocity of arc/edge $(i,j)\in \mathcal{E}$ for a vehicle of type $k\in \mathcal{K}$. |

$b:$ | Budget limitation. |

$q{p}_{it}^{h}:$ | Amount of people of type $h\in \mathcal{H}$ to be evacuated from node $i\in \mathcal{NA}$ at the beginning of period $t\le \mathcal{T}$. |

$ty{p}^{h}:$ | Priority of people of type $h\in \mathcal{H}$ (high or normal). |

$w{p}^{h}:$ | Space that a person of type $h\in \mathcal{H}$ occupies in a vehicle to be transported or in a node of the secure area. |

$c{p}_{i}^{h}:$ | Capacity for people of type $h\in \mathcal{H}$ at node $i\in \mathcal{NS}\cup \mathcal{NH}$. |

$vp{c}^{k}:$ | Capacity of a vehicle of type $k\in \mathcal{K}$. |

$v{a}_{i}^{k}:$ | Number of vehicles of type $k\in \mathcal{K}$ that are available at node $i\in \mathcal{N}$ at the beginning of the operation. |

$f{c}_{ij}^{k}:$ | Fixed cost to traverse the arc/edge $(i,j)\in \mathcal{E}$ with a vehicle of type $k\in \mathcal{K}$, by unit of distance. |

$v{c}_{ij}^{k}:$ | Variable cost to traverse the arc/edge $(i,j)\in \mathcal{E}$ with a vehicle of type $k\in \mathcal{K}$, by unit of distance and cargo transported. |

$v{v}^{k}:$ | Maximum velocity that a vehicle of type $k\in \mathcal{K}$ may reach. |

${\tau}_{ij}^{k}:$ | Time required to travel the arc/edge $(i,j)\in \mathcal{E}$ with a vehicle of type $k\in \mathcal{K}$, calculated as follows: ${\tau}_{ij}^{k}=max\{\frac{{d}_{ij}^{k}}{v{v}^{k}},\frac{{d}_{ij}^{k}}{a{v}_{ij}^{k}}\}$ |

$t{g}_{m}:$ | Aspiration level of goal $m\in \mathcal{M}$. |

**Decision variables**

$B{T}_{t}:$ | 1 if population with high priority has been evacuated in period t and 0, otherwise. |

$B{T}_{t}^{\prime}:$ | 1 if population with normal priority has been evacuated in period t and 0, otherwise. |

$T:$ | Total time required to evacuate population with high priority. |

${T}^{\prime}:$ | Total time required to evacuate the rest of the population. |

${P}_{it}^{h}:$ | Number of people of type $h\in \mathcal{H}$ located at node $i\in \mathcal{N}$ at the beginning of period $t\le \mathcal{T}$. |

$P{L}_{ijt}^{hk}:$ | Number of people of type $h\in \mathcal{H}$ who started to be transported from node $i\in \mathcal{N}$ to node $j\in \mathcal{N}$ in a vehicle of type $k\in \mathcal{K}$ at the beginning of period $t\le \mathcal{T}$. |

${V}_{it}^{k}:$ | Number of vehicles of type $k\in \mathcal{K}$ located at node $i\in \mathcal{N}$ at the beginning of period $t\le \mathcal{T}$. |

$V{L}_{ijt}^{k}:$ | Number of vehicles of type $k\in \mathcal{K}$ that started to move from node $i\in \mathcal{N}$ to node $j\in \mathcal{N}$ at the beginning of period $t\le \mathcal{T}$. |

**Attribute and deviation variables**

$E:$ | Number of people with high priority that are evacuated depending on the characteristics of the particular instance. |

${E}^{\prime}:$ | Number of people with normal priority that are evacuated depending on the characteristics of the particular instance. |

$TM:$ | Total time required to evacuate all the population (max. of T and ${T}^{\prime}$). |

$Cost:$ | Total cost of the operation. |

$D{V}_{m}:$ | Deviation variable with respect to the aspiration level of goal $m\in \mathcal{M}$. |

${P}_{m}:$ | Slack variable with respect to the aspiration level of goal $m\in \mathcal{M}$. |

#### 3.2. Mathematical Model

## 4. Case Study: Palu, Indonesia

#### 4.1. Data

- 16 pickup nodes (R) located at the affected area, easily recognized by the local population and the Search & Rescue Teams, such as mosques, schools, cafes or shopping centers in relatively unaffected or lightly affected streets. The total number of affected nodes and their locations have been established according to the data of affected buildings and affected population obtained from Copernicus, [52].
- 23 temporary shelter nodes (S) are real evacuation sites corresponding to real temporary shelters enabled by BASARNAS (the National Search and Rescue Agency of Indonesia), whose locations and capacities have been obtained from reports of the Government of Indonesia [53,54,55]. Initially, there were only 24 evacuation sites, which amounted to 41 and, finally, to 141 on 4 October 2018. According to the time horizon and the total area of this case study, we have considered 5 large shelters, 6 medium ones and 12 small.
- Hospitals and medical center nodes (H) correspond to real locations of hospitals and medical centers obtained from the same reports used to compile the data regarding temporary shelters. These nodes are the destination of severely injured people and pregnant women, especially.
- Palu airport (A) is a node that corresponds to the real location of Mutiara SIS Al-Jufrie, the airport of the city. For the case study, this airport was a destination point for population to be evacuated by plane to other safer cities, especially for severely injured people that could not be treated at the available hospitals due to a lack of medical supplies or appropriate facilities.

#### 4.2. Results

## 5. Concluding Remarks

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Özdamar, L.; Ertem, M.A. Models, solutions and enabling technologies in humanitarian logistics. Eur. J. Oper. Res.
**2015**, 244, 55–65. [Google Scholar] [CrossRef] - Tomasini, R.; Van Wassenhove, L. Humanitarian Logistics; Springer: Berlin/Heidelberg, Germany, 2009. [Google Scholar]
- Vitoriano, B.; Montero, J.; Ruan, D. Decision Aid Models for Disaster Management and Emergencies; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2013. [Google Scholar]
- Wu, H.C.; Lindell, M.K.; Prater, C.S. Logistics of hurricane evacuation in Hurricanes Katrina and Rita. Transp. Res. Part F Traffic Psychol. Behav.
**2012**, 15, 445–461. [Google Scholar] [CrossRef] - Peizhuang, W.; Xihui, L.; Sanchez, E. Set-valued statistics and its application to earthquake engineering. Fuzzy Sets Syst.
**1986**, 18, 347–356. [Google Scholar] [CrossRef] - Sherali, H.D.; Carter, T.B.; Hobeika, A.G. A location-allocation model and algorithm for evacuation planning under hurricane/flood conditions. Transp. Res. Part B Methodol.
**1991**, 25, 439–452. [Google Scholar] [CrossRef] - Shahparvari, S.; Chhetri, P.; Abareshi, A.; Abbasi, B. Multi-Objective Decision Analytics for Short-Notice Bushfire Evacuation: An Australian Case Study. Aust. J. Inf. Syst.
**2015**, 19. [Google Scholar] [CrossRef] [Green Version] - Dong, W.; Chiang, W.; Shah, H. Fuzzy information processing in seismic hazard analysis and decision making. Soil Dyn. Earthq. Eng.
**1987**, 6, 220–226. [Google Scholar] [CrossRef] - Monzón, J.; Liberatore, F.; Vitoriano, B. A Mathematical Pre-Disaster Model with Uncertainty and Multiple Criteria for Facility Location and Network Fortification. Mathematics
**2020**, 8, 529. [Google Scholar] [CrossRef] [Green Version] - Vitoriano, B.; Ortuño, M.T.; Tirado, G.; Montero, J. A multi-criteria optimization model for humanitarian aid distribution. J. Glob. Optim.
**2011**, 51, 189–208. [Google Scholar] [CrossRef] - Ortuño, M.T.; Tirado, G.; Vitoriano, B. A lexicographical goal programming based decision support system for logistics of Humanitarian Aid. Top
**2011**, 19, 464–479. [Google Scholar] [CrossRef] - Tirado, G.; Martín-Campo, F.J.; Vitoriano, B.; Ortuño, M.T. A lexicographical dynamic flow model for relief operations. Int. J. Comput. Intell. Syst.
**2014**, 7, 45–57. [Google Scholar] [CrossRef] [Green Version] - Fahy, R.F. EXIT89: An evacuation model for high-rise buildings. Fire Saf. Sci.
**1991**, 3, 815–823. [Google Scholar] [CrossRef] - Dhamala, T.N. A survey on models and algorithms for discrete evacuation planning network problems. J. Ind. Manag. Optim.
**2015**, 11, 265–289. [Google Scholar] - UN Office for Disaster Risk Reduction. Terminology on Disaster Risk Reduction. 2017. Available online: https://www.unisdr.org/we/inform/terminology (accessed on 1 March 2020).
- Sharma, S.; Singh, H.; Prakash, A. Multi-agent modeling and simulation of human behavior in aircraft evacuations. IEEE Trans. Aerosp. Electron. Syst.
**2008**, 44, 1477–1488. [Google Scholar] [CrossRef] - Shi, J.; Ren, A.; Chen, C. Agent-based evacuation model of large public buildings under fire conditions. Autom. Constr.
**2009**, 18, 338–347. [Google Scholar] [CrossRef] - Manley, M.; Kim, Y.S.; Christensen, K.; Chen, A. Modeling emergency evacuation of individuals with disabilities in a densely populated airport. Transp. Res. Rec.
**2011**, 2206, 32–38. [Google Scholar] [CrossRef] - Hamacher, H.W.; Tjandra, S.A. Mathematical Modelling of Evacuation Problems: A State of Art; Fraunhofer-Institut für Techno- und Wirtschaftsmathematik: Kaiserslautern, Germany, 2001. [Google Scholar]
- London Resilience Partnership. Mass Evacuation Framework. 2018. Available online: https://www.london.gov.uk (accessed on 1 March 2020).
- Smith, J.M. State-dependent queueing models in emergency evacuation networks. Transp. Res. Part B Methodol.
**1991**, 25, 373–389. [Google Scholar] [CrossRef] - Sbayti, H.; Mahmassani, H.S. Optimal scheduling of evacuation operations. Transp. Res. Rec.
**2006**, 1964, 238–246. [Google Scholar] [CrossRef] - Brown, C.; White, W.; van Slyke, C.; Benson, J.D. Development of a strategic hurricane evacuation–dynamic traffic assignment model for the Houston, Texas, Region. Transp. Res. Rec.
**2009**, 2137, 46–53. [Google Scholar] [CrossRef] - Sun, D.; Kang, J.; Batta, R.; Song, Y. Optimization of Evacuation Warnings Prior to a Hurricane Disaster. Sustainability
**2017**, 9, 2152. [Google Scholar] [CrossRef] [Green Version] - Özdamar, L.; Aksu, D.T.; Yasa, E.; Ergunes, B. Disaster relief routing in limited capacity road networks with heterogeneous flows. J. Ind. Manag. Optim.
**2018**, 14, 1367–1380. [Google Scholar] [CrossRef] [Green Version] - Houston, N.; Easton, A.; Davis, E.; Mincin, J.; Phillips, B.; Leckner, M. Evacuating Populations with Special Needs: Routes to Effective Planning Primer Series; US Department of Transportation: Washington, DC, USA, 2009.
- Amideo, A.E.; Scaparra, M.P.; Kotiadis, K. Optimising shelter location and evacuation routing operations: The critical issues. Eur. J. Oper. Res.
**2019**, 279, 279–295. [Google Scholar] [CrossRef] - Pyakurel, U.; Nath, H.N.; Dhamala, T.N. Efficient contraflow algorithms for quickest evacuation planning. Sci. China Math.
**2018**, 61, 2079–2100. [Google Scholar] [CrossRef] - Pyakurel, U.; Nath, H.N.; Dempe, S.; Dhamala, T.N. Efficient Dynamic Flow Algorithms for Evacuation Planning Problems with Partial Lane Reversal. Mathematics
**2019**, 7, 993. [Google Scholar] [CrossRef] [Green Version] - Pillac, V.; Van Hentenryck, P.; Even, C. A conflict-based path-generation heuristic for evacuation planning. Transp. Res. Part B Methodol.
**2016**, 83, 136–150. [Google Scholar] [CrossRef] [Green Version] - Bish, D.R. Planning for a bus-based evacuation. OR Spectr.
**2011**, 33, 629–654. [Google Scholar] [CrossRef] - Shahparvari, S.; Abbasi, B. Robust stochastic vehicle routing and scheduling for bushfire emergency evacuation: An Australian case study. Transp. Res. Part A Policy Pract.
**2017**, 104, 32–49. [Google Scholar] [CrossRef] - Shahparvari, S.; Abbasi, B.; Chhetri, P. Possibilistic scheduling routing for short-notice bushfire emergency evacuation under uncertainties: An Australian case study. Omega
**2017**, 72, 96–117. [Google Scholar] [CrossRef] - Shahparvari, S.; Abbasi, B.; Chhetri, P.; Abareshi, A. Fleet routing and scheduling in bushfire emergency evacuation: A regional case study of the Black Saturday bushfires in Australia. Transp. Res. Part D Transp. Environ.
**2019**, 67, 703–722. [Google Scholar] [CrossRef] - Dhamala, T.; Pyakurel, U. Significance of Transportation Network Models in Emergency Planning of Cities. Cities People Places Int. J. Urban Environ.
**2016**, 2, 58–76. [Google Scholar] [CrossRef] [Green Version] - Miller-Hooks, E.; Patterson, S.S. On solving quickest time problems in time-dependent, dynamic networks. J. Math. Model. Algorithms
**2004**, 3, 39–71. [Google Scholar] [CrossRef] - Gutjahr, W.J.; Nolz, P.C. Multicriteria optimization in humanitarian aid. Eur. J. Oper. Res.
**2016**, 252, 351–366. [Google Scholar] [CrossRef] - Ferrer, J.M.; Ortuño, M.T.; Tirado, G. A New Ant Colony-Based Methodology for Disaster Relief. Mathematics
**2020**, 8, 518. [Google Scholar] [CrossRef] [Green Version] - Mejia-Argueta, C.; Gaytán, J.; Caballero, R.; Molina, J.; Vitoriano, B. Multicriteria optimization approach to deploy humanitarian logistic operations integrally during floods. Int. Trans. Oper. Res.
**2018**, 25, 1053–1079. [Google Scholar] [CrossRef] [Green Version] - Alçada-Almeida, L.; Tralhao, L.; Santos, L.; Coutinho-Rodrigues, J. A multiobjective approach to locate emergency shelters and identify evacuation routes in urban areas. Geogr. Anal.
**2009**, 41, 9–29. [Google Scholar] [CrossRef] - Valkaniotis, S.; Ganas, A.; Tsironi, V.; Barberopoulou, A. A Preliminary Report on the M7.5 Palu Earthquake Co-Seismic Ruptures and Landslides Using Image Correlation Techniques on Optical Satellite Data; Zenodo: Genève, Switzerland, 2018. [Google Scholar] [CrossRef]
- Humanitarian Country Team. Central Sulawesi Earthquake and Tsunami; Technical Report 01; Humanitarian Country Team: Jakarta, Indonesia, 2018. [Google Scholar]
- World Health Organization/Indonesia. Situation Report 01 Sulawesi Earthquake and Tsunami, Indonesia; Technical report; WHO: Geneva, Switzerland, 2018. [Google Scholar]
- AHA Centre. Situation Update No. 1 M 7.4 Earthquake & Tsunami; Sulawesi, Indonesia; Technical Report 01; AHA Centre: Jakarta, Indonesia, 2018. [Google Scholar]
- AHA Centre. Situation Update No. 2 M 7.4 Earthquake & Tsunami; Sulawesi, Indonesia; Technical Report 02; AHA Centre: Jakarta, Indonesia, 2018. [Google Scholar]
- AHA Centre. Situation Update No. 3 M 7.4 Earthquake & Tsunami; Sulawesi, Indonesia; Technical Report 03; AHA Centre: Jakarta, Indonesia, 2018. [Google Scholar]
- AHA Centre. Situation Update No. 4 M 7.4 Earthquake & Tsunami; Sulawesi, Indonesia; Technical Report 04; AHA Centre: Jakarta, Indonesia, 2018. [Google Scholar]
- AHA Centre. Situation Update No. 5 M 7.4 Earthquake & Tsunami; Sulawesi, Indonesia; Technical Report 05; AHA Centre: Jakarta, Indonesia, 2018. [Google Scholar]
- AHA Centre. Situation Update No. 6 M 7.4 Earthquake & Tsunami; Sulawesi, Indonesia; Technical Report 06; AHA Centre: Jakarta, Indonesia, 2018. [Google Scholar]
- AHA Centre. Situation Update No. 7 M 7.4 Earthquake & Tsunami; Sulawesi, Indonesia; Technical Report 07; AHA Centre: Jakarta, Indonesia, 2018. [Google Scholar]
- AHA Centre. Situation Update No. 9 M 7.4 Earthquake & Tsunami; Sulawesi, Indonesia; Technical Report 09; AHA Centre: Jakarta, Indonesia, 2018. [Google Scholar]
- European Commission (EC); European Space Agency (ESA); European Environment Agency (EEA). Emergency Management Service—Mapping. 2018. Available online: https://emergency.copernicus.eu/mapping (accessed on 1 March 2020).
- Badan Nasional Penanggulangan Bencana. Laporan Harian No.1 Gempa M.7,4 dan Tsunami Sulawesi Tengah; Technical Report 01; Badan Nasional Penanggulangan Bencana: Jakarta, Indonesia, 2018. [Google Scholar]
- Badan Nasional Penanggulangan Bencana. Laporan Harian Penanganan Gempa Bumi dan Tsunami Palu dan Donggala; Technical Report 02; Badan Nasional Penanggulangan Bencana: Jakarta, Indonesia, 2018. [Google Scholar]
- Badan Nasional Penanggulangan Bencana. Penanganan Bencana Gempabumi M7,4 dan Tsunami di Kota Palu dan Donggala Sulawesi Tengah; Technical Report 03; Badan Nasional Penanggulangan Bencana: Jakarta, Indonesia, 2018. [Google Scholar]
- Indonesia Humanitarian Country Team. Central Sulawesi Earthquake Response Plan (October 2018–December 2018); Technical report; Indonesia Humanitarian Country Team: Jakarta, Indonesia, 2018. [Google Scholar]
- Stepanov, A.; Smith, J.M. Multi-objective evacuation routing in transportation networks. Eur. J. Oper. Res.
**2009**, 198, 435–446. [Google Scholar] [CrossRef] - International Civil Aviation Organization of OCHA. Airport Situation Report; Technical Report 04; International Civil Aviation Organization of OCHA: Geneva, Switzerland, 2018. [Google Scholar]

Type | Capacity | Mean Velocity | Fixed Cost | Variable Cost | Quantity Available |
---|---|---|---|---|---|

Helicopter | 3 | 153 km/h | 0.50 $/km | 1.20 $/(km×u.l.) | 8 |

Truck | 18 | 80 km/h | 0.20 $/km | 0.80 $/(km×u.l.) | 410 |

Ambulance | 9 | 80 km/h | 0.10 $/km | 0.50 $/(km×u.l.) | 40 |

Raft | 6 | 3 km/h | 0.05 $/km | 0.12 $/(km×u.l.) | 48 |

AoI 7 | AoI 11 | All AoI | |
---|---|---|---|

Number of inhabitants | 110,265 | 76,176 | 608,521 |

Affected in AoI | 37,776 | 136 | 60,424 |

Type | Priority | Required Space | AoI 7 | AoI 11 |
---|---|---|---|---|

Severely injured adults (SIA) | High | 3 | 171 | 6 |

Pregnant women (PW) | High | 1.5 | 85 | 2 |

Susc. to gender violence (GBV) | High | 1 | 153 | 3 |

Unaccompanied minors (UM) | High | 1 | 98 | 2 |

Rest of the population (RP) | Normal | 1 | 476 | 11 |

**Table 4.**Shelter characteristics and capacity distributions. PW: pregnant women. UM: unaccompanied minors. GBV: women susceptible to gender violence. RP: rest of the population.

ID | Name | Capacity | Classif. | Type | PW | UM | GBV | RP |
---|---|---|---|---|---|---|---|---|

S01 | Silae (Miners) | 500 | medium | normal | 0 | 0 | 0 | 500 |

S02 | Makorem (area) | 3000 | large | normal | 0 | 0 | 0 | 3000 |

S03 | Mako Sabhara P. | 5000 | large | safe | 600 | 1600 | 2800 | 0 |

S04 | Perumahan M.R. | 150 | small | normal | 0 | 0 | 0 | 150 |

S05 | GOR Siranindi | 200 | small | normal | 0 | 0 | 0 | 200 |

S06 | Halaman D. | 100 | small | normal | 0 | 0 | 0 | 100 |

S07 | Masjid Raya | 300 | small | normal | 0 | 0 | 0 | 300 |

S08 | Lap. Anoa | 100 | small | normal | 0 | 0 | 0 | 100 |

S09 | Masjid B.A. | 1500 | large | safe | 180 | 480 | 840 | 0 |

S10 | Bundaran STQ | 500 | medium | normal | 0 | 0 | 0 | 500 |

S11 | Lap. Dayodara | 700 | medium | normal | 0 | 0 | 0 | 700 |

S12 | Samping M.A.F. | 880 | medium | normal | 0 | 0 | 0 | 880 |

S13 | Lagarutu | 511 | medium | normal | 0 | 0 | 0 | 511 |

S14 | Lap Vatulemo | 1000 | large | safe | 120 | 320 | 560 | 0 |

S15 | Jalan Swadaya | 157 | small | normal | 0 | 0 | 0 | 157 |

S16 | Malao Atas | 150 | small | normal | 0 | 0 | 0 | 150 |

S17 | Jalan Maleo | 100 | small | normal | 0 | 0 | 0 | 100 |

S18 | Hal. Perkantoran | 2000 | large | normal | 0 | 0 | 0 | 2000 |

S19 | Sepanjang J.G. | 250 | small | normal | 0 | 0 | 0 | 250 |

S20 | BTN Lasoani | 300 | small | normal | 0 | 0 | 0 | 300 |

S21 | Lap. Kawatuna | 300 | small | normal | 0 | 0 | 0 | 300 |

S22 | Sekitar J.B.R. | 120 | small | normal | 0 | 0 | 0 | 120 |

S23 | Lap. Faqih R. | 500 | medium | normal | 0 | 0 | 0 | 500 |

Constraints | Variables | Non-Zeroes | Discrete Var. | |
---|---|---|---|---|

Level 1 | 25,854 | 87,411 | 1,960,669 | 87,409 |

Level 2 | 25,856 | 87,414 | 1,960,694 | 87,410 |

Level 3 | 25,957 | 87,467 | 1,972,821 | 87,458 |

Level 4 | 25,959 | 87,470 | 2,050,729 | 87,458 |

**Table 6.**Distribution of evacuees at the end of the operation by category. SIA: Severely injured adults. PW: pregnant women. UM: unaccompanied minors. GBV: women susceptible to gender violence. RP: rest of the population.

SIA | PW | UM | GBV | RP | |
---|---|---|---|---|---|

R09 | 1 | ||||

R11 | 144 | 521 | |||

S01 | 500 | ||||

S02 | 2997 | ||||

S03 | 600 | 1565 | 2433 | ||

S04 | 150 | ||||

S05 | 200 | ||||

S06 | 100 | ||||

S07 | 300 | ||||

S09 | 180 | 167 | 198 | ||

S10 | 270 | ||||

S12 | 863 | ||||

S14 | 12 | ||||

S18 | 107 | ||||

H01 | 750 | 250 | |||

H02 | 750 | 230 | |||

H03 | 727 | 250 | |||

H04 | 527 | ||||

A01 | 6 | 1 | 1333 |

% Critical Evacuees | % Non-Critical Evacuees | Evacuation Time (h) | Operation Cost ($) | |
---|---|---|---|---|

Base case | 98.36 | 92.89 | 72 | 54,956 |

No Airport | 97.85 | 92.94 | 72 | 59,019 |

No Hospitals | 88.33 | 95.84 | 72 | 56,204 |

No Helicopters | 97.01 | 93.01 | 72 | 57,792 |

No rafts | 95.81 | 92.99 | 69 | 70,142 |

No trucks | 40.52 | 2.06 | 72 | 5292 |

Split in two | 75.92 | 51.23 | 39 | 34,992 |

Asp. Levels 75–50 | 75.00 | 50.00 | 30 | 151,340 |

Asp. Levels 50–75 | 50.00 | 75.00 | 36 | 171,516 |

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**MDPI and ACS Style**

Flores, I.; Ortuño, M.T.; Tirado, G.; Vitoriano, B.
Supported Evacuation for Disaster Relief through Lexicographic Goal Programming. *Mathematics* **2020**, *8*, 648.
https://doi.org/10.3390/math8040648

**AMA Style**

Flores I, Ortuño MT, Tirado G, Vitoriano B.
Supported Evacuation for Disaster Relief through Lexicographic Goal Programming. *Mathematics*. 2020; 8(4):648.
https://doi.org/10.3390/math8040648

**Chicago/Turabian Style**

Flores, Inmaculada, M. Teresa Ortuño, Gregorio Tirado, and Begoña Vitoriano.
2020. "Supported Evacuation for Disaster Relief through Lexicographic Goal Programming" *Mathematics* 8, no. 4: 648.
https://doi.org/10.3390/math8040648