# An Extended Model for Disaster Relief Operations Used on the Hagibis Typhoon Case in Japan

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Research on Humanitarian Logistics

#### 2.2. The Hierarchical Compromise Model

#### 2.3. Dynamic Flow Model

#### 2.4. Compromise Programming Model

## 3. Model Description

_{p}represents the total amount of aid desired to be distributed. The equation assures that at the end of the operation the sum of delivered goods in all the nodes that have a demand for a particular product should be equal to the quantity of products planned to the distribution, summarized over all products. If the condition is not fulfilled, then a positive value, equal to the amount of aid that could not be delivered, will be assigned to the deviation variable $DVQ$. If the condition is satisfied, the variable will be equal to zero.

## 4. Case Description

#### Case Study Data

## 5. Computational Experiments

#### Solution Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

From | To | Length (km) | Speed (km/h) | Arc Reliability |
---|---|---|---|---|

D1 | D3 | 25 | 90 | 0.88 |

D1 | N2 | 35 | 90 | 0.85 |

D1 | N5 | 4 | 50 | 0.78 |

D1 | N9 | 50 | 90 | 0.89 |

D1 | N10 | 20 | 90 | 0.97 |

D2 | D4 | 51 | 90 | 0.79 |

D2 | N2 | 45 | 50 | 0.99 |

D2 | N9 | 35 | 90 | 0.8 |

D3 | D1 | 25 | 90 | 0.88 |

D3 | N1 | 26 | 50 | 0.99 |

D3 | N5 | 20 | 70 | 0.98 |

D3 | N6 | 50 | 70 | 0.29 |

D4 | D2 | 51 | 90 | 0.79 |

D4 | N2 | 67 | 90 | 0.1 |

D4 | N3 | 52 | 90 | 0.52 |

D4 | N10 | 70 | 90 | 0.87 |

N1 | D3 | 26 | 50 | 0.99 |

N1 | N6 | 55 | 70 | 0.59 |

N1 | N7 | 130 | 90 | 0.61 |

N1 | N5 | 9 | 50 | 0.99 |

N2 | D1 | 35 | 90 | 0.85 |

N2 | D2 | 45 | 50 | 0.99 |

N2 | D4 | 67 | 90 | 0.1 |

N2 | N9 | 17 | 50 | 0.89 |

N2 | N10 | 22 | 70 | 0.99 |

N3 | D4 | 52 | 90 | 0.52 |

N3 | N4 | 40 | 90 | 0.97 |

N3 | N8 | 20 | 50 | 0.56 |

N3 | N10 | 50 | 70 | 0.24 |

N4 | N3 | 40 | 90 | 0.97 |

N4 | N7 | 150 | 90 | 0.79 |

N4 | N8 | 20 | 50 | 0.89 |

N4 | N10 | 50 | 70 | 0.21 |

N5 | D1 | 4 | 50 | 0.78 |

N5 | D3 | 20 | 70 | 0.98 |

N5 | N1 | 9 | 50 | 0.99 |

N5 | N10 | 19 | 90 | 0.79 |

N6 | D3 | 50 | 70 | 0.29 |

N6 | N1 | 55 | 70 | 0.59 |

N6 | N7 | 98 | 90 | 0.88 |

N6 | N10 | 50 | 70 | 0.53 |

N7 | N1 | 130 | 90 | 0.61 |

N7 | N4 | 150 | 90 | 0.79 |

N7 | N6 | 98 | 90 | 0.88 |

N8 | N3 | 20 | 50 | 0.56 |

N8 | N4 | 20 | 50 | 0.9 |

N8 | N10 | 30 | 90 | 0.2 |

N9 | D1 | 50 | 90 | 0.89 |

N9 | D2 | 35 | 90 | 0.8 |

N9 | N2 | 17 | 50 | 0.89 |

N10 | D1 | 20 | 90 | 0.97 |

N10 | D4 | 70 | 90 | 0.87 |

N10 | N2 | 22 | 70 | 0.99 |

N10 | N3 | 50 | 70 | 0.24 |

N10 | N4 | 50 | 70 | 0.21 |

N10 | N5 | 19 | 90 | 0.79 |

N10 | N6 | 50 | 70 | 0.53 |

N10 | N8 | 30 | 90 | 0.2 |

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**Figure 1.**The path of typhoon Hagibis over time [26].

**Figure 2.**Transport network for the operation (https://yandex.com/maps/-/CCQ2F8edtD, accessed on 10 June 2021).

$N$ | : | Set of demand nodes and depots |

$A$ | : | Set of arcs represents existing links between nodes |

$T$ | : | Planned time horizon to complete the operation |

$V$ | : | Set of vehicles, defined by types |

$P$ | : | Set of products |

$G$ | : | Set of goals/objectives |

$i,j$ | : | $\mathrm{Indices}\mathrm{referring}\mathrm{to}\mathrm{nodes}\left(i,j\right)\in A$$\mathrm{being}i,j\in N$ |

$t,s$ | : | $\mathrm{Indices}\mathrm{referring}\mathrm{to}\mathrm{time}\mathrm{periods}t,s\in \left\{1,\dots ,T\right\}$ |

$p,d$ | : | $\mathrm{Indices}\mathrm{referring}\mathrm{to}\mathrm{any}\mathrm{products}p,d\in P$ |

$f,m$ | : | $\mathrm{Indices}\mathrm{referring}\mathrm{to}\mathrm{food}\mathrm{and}\mathrm{medicine}\mathrm{products}f,m\in P$, respectively |

$k$. | : | $\mathrm{Index}\mathrm{referring}\mathrm{to}\mathrm{vehicle}\mathrm{types}k\in V$ |

$g$ | : | $\mathrm{Index}\mathrm{referring}\mathrm{to}\mathrm{goals}g\in G$ |

$de{m}_{ip}$ | : | Demand of product $p\in P$ at node $i\in N,$ in tons |

$av{q}_{ip}$ | : | Available supply of product $p\in P$ at node $i\in N,$ in tons |

$dis{t}_{ij}$ | : | Length of arc $\left(i,j\right)\in A,$ in km |

$vel{r}_{ij}$ | : | Maximum velocity on arc $\left(i,j\right)\in A,$ in km per hour |

$re{l}_{ij}$ | : | Probability of crossing the arc $\left(i,j\right)\in A,re{l}_{ij}\in \left[0,1\right]$ |

$ca{p}_{k}$ | : | Capacity of vehicle type $k\in V,$ in tons |

$ve{l}_{k}$ | : | Maximum velocity of vehicle type $k\in V,$ in km per hour |

$ave{h}_{ki}$ | : | Number of available vehicles of type $k\in V$ at node $i\in N$ |

$tve{h}_{k}$ | : | Total number of vehicle types $k\in V$ available for the operation |

$t{r}_{ijk}$ | : | Travel time of arc $\left(i,j\right)\in A$ using vehicle of type $k\in V$ |

$c{f}_{ijk}$ | : | Empty travel cost, i.e., fixed cost of using arc $\left(i,j\right)\in A$ with vehicle of type $k\in V,$ per km |

$c{v}_{ijkp}$ | : | Load travel cost, i.e., variable cost of using arc $\left(i,j\right)\in A$ with vehicle of type $k\in V$, per km, and ton of product $p\in P$ |

$pr{i}_{i}$ | : | Priority level of node $i\in N,$ $pr{i}_{i}\in \left[0,1\right]$ |

$t{\mathrm{g}}_{\mathrm{g}}$ | : | Target for criterion $\mathrm{g}\in G$; $t{\mathrm{g}}_{\mathrm{g}}\ne 0$ defined by decision maker |

${w}_{\mathrm{g}}$ | : | Weight of criterion $\mathrm{g}\in G$ defined by decision maker |

$tm$ | : | Time measure helping adjust the length of time period |

$bd$ | : | Large value to create bounds for some constraints |

$dvQ$ | : | Fixed deviation of delivered aid, in tons |

${q}_{p}$ | : | Total amount of product $p\in P$ desired to be distributed in the operation, in tons |

$b$ | : | Budget available to perform the operation |

$Q{C}_{ijkpt}$ | : | Load of product $p\in P$ carried from $i\in N$ to $j\in N$ using vehicle of type $k\in V$ and starting in period $t\in \left\{1,..,T\right\}$, in tons |

$Q{S}_{ipt}$ | : | Load of product $p\in P$ stored at node $i\in N$ at the beginning of period $t\in \left\{1,..,T\right\},$ in tons |

$NT{V}_{ijkt}$ | : | Number of vehicles of type $k\in V$ that start traveling from $i\in N$ to $j\in N$ in period $t\in \left\{1,..,T\right\}$ |

$N{V}_{ikt}$ | : | Number of vehicles of type $k\in V$ available at node $i\in N$ at the beginning of period $t\in \left\{1,..,T\right\}$ |

$B{T}_{ijk}$ | : | Binary variable taking value 1 if a vehicle of type $k\in V$ uses arc $\left(i,j\right)\in A$, 0 otherwise |

$B{A}_{ij}$ | : | Binary variable taking value 1 if any vehicle uses arc $\left(i,j\right)\in A$, 0 otherwise |

$B{Q}_{t}$ | : | Binary variable taking value 1 if load has been delivered in period $t\in \left\{1,..,T\right\}$, 0 otherwise |

$D{V}_{\mathrm{g}}$ | : | Variable showing unwanted deviation of the criterion $\mathrm{g}\in G$ from its target, in units of criterion |

$DVQ$ | : | Variable showing unwanted deviation from desired amount of delivered aid, in tons |

$Cost$ | : | Total cost of the operation, in US dollars. |

$Time$ | : | Number of time periods required to complete the operation. |

$TP$ | : | Time penalties variable adding higher penalties to long operations. |

$EqF$ | : | Criterion of equity of food distribution. 0 if food demand of all nodes is completely fulfilled and positive otherwise. |

$EqM$ | : | Criterion of equity of medicine distribution. 0 if medicine demand of all nodes is completely fulfilled and positive otherwise. |

$Prio$ | : | Demand satisfaction priority criterion in the specific nodes. 0 if demand of priority nodes is completely fulfilled and positive otherwise. |

$Rel$ | : | Reliability criterion indicates the most unreliable arc used in the operation. |

$GR$ | : | Global route reliability criterion shows reliability of the whole set of arcs used in the operation. |

Name | Nodes | Demand (Tons) | Supply (Tons) | Availability of Vehicles of Each Type | Priority | ||||
---|---|---|---|---|---|---|---|---|---|

Food | Medicine | Food | Medicine | Small | Medium | Large | |||

Haneda Airport | D1 | 1100 | 200 | 50 | 30 | 20 | |||

Narita Airport | D2 | 440 | 80 | 12 | 8 | 2 | |||

Yokohama Port | D3 | 230 | 80 | 7 | 13 | 2 | |||

Tsuchiura DC | D4 | 1270 | 0 | 50 | 30 | 20 | |||

Fujisawa | N1 | 75 | 10 | ||||||

Funabashi | N2 | 105 | 20 | ||||||

Kasukabe | N3 | 40 | 5 | ||||||

Kawagoe | N4 | 60 | 10 | ||||||

Kawasaki | N5 | 255 | 45 | ||||||

Hachioji | N6 | 95 | 20 | ||||||

Kofu | N7 | 35 | 5 | 1 | |||||

Saitama | N8 | 225 | 25 | ||||||

Chiba | N9 | 165 | 30 | ||||||

Tokyo | N10 | 1530 | 270 | 0.8 |

Vehicle Types | Vehicle Capacity (tons) | Speed (km/h) | Fixed Cost (US$/km) | Variable Cost (US$/(km·Ton·Product)) | |
---|---|---|---|---|---|

Food | Medicine | ||||

small | 5 | 100 | 20 | 1 | 1 |

medium | 15 | 90 | 50 | 1.1 | 1 |

large | 25 | 80 | 70 | 1.3 | 1 |

Criterion | Cost, $ | Time, Hour | TP | EqF | EqM | Prio | Rel | GR | |
---|---|---|---|---|---|---|---|---|---|

log | % | ||||||||

Cost | 799,342 | 2.5 | 5525 | 1 | 1 | 1.8 | 0.52 | −2.4 | 9.4 |

Operation Time | 998,942 | 1.7 | 1240 | 1 | 1 | 1.79 | 0.1 | −6.9 | 0.11 |

Time Penalty | 974,028 | 0.7 | 14 | 1 | 1 | 1.8 | 0.52 | −1.9 | 13.8 |

Equity Food | 999,112 | 2.5 | 5525 | 0 | 1 | 0.25 | 0.1 | −7.2 | 0.07 |

Equity Medicine | 997,901 | 2.5 | 5525 | 1 | 0.2 | 1.49 | 0.29 | −4.7 | 0.84 |

Priority | 991,038 | 2.5 | 5525 | 1 | 1 | 0 | 0.29 | −3.7 | 2.5 |

Reliability | 998,680 | 2.5 | 5525 | 1 | 1 | 0.82 | 0.87 | −0.37 | 69.3 |

Global Route Rel. | 997,824 | 2.5 | 5525 | 1 | 1 | 0.76 | 0.87 | −0.21 | 81.1 |

Criteria | Cost, $ | Time, Hour | TP | EqF | EqM | Prio | Rel | GR | |
---|---|---|---|---|---|---|---|---|---|

log | % | ||||||||

Cost and Time and TP | 799,802 | 1.7 | 14 | 1 | 1 | 1.76 | 0.52 | −1.61 | 19.8 |

Cost and Rel and GR | 987,939 | 2.5 | 5525 | 1 | 1 | 0.74 | 0.87 | −0.21 | 81.1 |

Cost and EqF and EqM and Prio | 936,175 | 2.5 | 5525 | 0.002 | 0.2 | 0 | 0.1 | −8.5 | 0.02 |

Cost and Time and TP and EqF and EqM | 993,456 | 1.8 | 1785 | 0 | 0.2 | 0.024 | 0.1 | −10.1 | 0.001 |

EqF and EqM and Prio | 999,967 | 2.5 | 5525 | 0.002 | 0.2 | 0 | 0.1 | −11.4 | 0.001 |

Rel and GR | 999,973 | 6 | 5525 | 1 | 1 | 0.74 | 0.87 | −0.21 | 81.1 |

Optimal solution | 995,107 | 1.8 | 1785 | 0 | 0.2 | 0 | 0.52 | −3.7 | 2.5 |

Node | N1 | N2 | N3 | N4 | N5 | N6 | N7 | N8 | N9 | N10 |
---|---|---|---|---|---|---|---|---|---|---|

Demand, tons | 75 | 105 | 40 | 60 | 255 | 95 | 35 | 225 | 165 | 1530 |

Criteria | Demand satisfaction, % | |||||||||

Cost | 140 | 66 | 2037 | 0 | 480 | 0 | 0 | 0 | 224 | 0 |

Operation Time | 286 | 804 | 487 | 0 | 372 | 0 | 0 | 0 | 212 | 1 |

Time Penalty | 0 | 0 | 2762 | 0 | 521 | 0 | 0 | 0 | 90 | 0 |

Equity Food | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |

Equity Medicine | 0 | 57 | 1412 | 0 | 413 | 0 | 0 | 0 | 396 | 16 |

Priority | 224 | 671 | 2062 | 0 | 329 | 0 | 134 | 0 | 0 | 0 |

Reliability | 0 | 123 | 0 | 0 | 90 | 0 | 0 | 0 | 133 | 131 |

Global Route Rel | 266 | 176 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 143 |

Aggregated criteria | Demand satisfaction, % | |||||||||

Cost and Time and TP | 666 | 414 | 2925 | 0 | 98 | 0 | 0 | 0 | 90 | 5 |

Cost and Rel and GR | 266 | 190 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 142 |

Cost and EqF and EqM and Prio | 100 | 100 | 100 | 100 | 101 | 100 | 100 | 100 | 100 | 99 |

Cost and Time and TP and EqF and EqM | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |

EqF and EqM and Prio | 100 | 100 | 100 | 100 | 101 | 100 | 100 | 100 | 100 | 99 |

Rel and GR | 253 | 190 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 143 |

Nodes | N1 | N2 | N3 | N4 | N5 | N6 | N7 | N8 | N9 | N10 |
---|---|---|---|---|---|---|---|---|---|---|

Demand, tons | 10 | 20 | 5 | 10 | 45 | 20 | 5 | 25 | 30 | 270 |

Criteria | Demand satisfaction, % | |||||||||

Cost | 0 | 25 | 0 | 0 | 622 | 0 | 0 | 0 | 250 | 0 |

Operation Time | 800 | 400 | 0 | 0 | 56 | 0 | 0 | 0 | 583 | 0 |

Time Penalty | 800 | 1000 | 0 | 0 | 0 | 0 | 0 | 0 | 267 | 0 |

Equity Food | 0 | 0 | 0 | 0 | 622 | 0 | 0 | 0 | 267 | 0 |

Equity Medicine | 100 | 80 | 80 | 80 | 80 | 105 | 80 | 80 | 80 | 80 |

Priority | 0 | 275 | 0 | 0 | 567 | 0 | 500 | 0 | 83 | 0 |

Reliability | 0 | 400 | 0 | 0 | 178 | 0 | 0 | 0 | 0 | 74 |

Global Route Rel | 800 | 650 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 56 |

Aggregated criteria | Demand satisfaction, % | |||||||||

Cost and Time and TP | 300 | 0 | 0 | 0 | 556 | 0 | 0 | 0 | 267 | 0 |

Cost and Rel and GR | 800 | 400 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 74 |

Cost and EqF and EqM and Prio | 80 | 80 | 80 | 80 | 87 | 95 | 120 | 80 | 80 | 80 |

Cost and Time and TP and EqF and EqM | 80 | 100 | 80 | 90 | 80 | 80 | 100 | 84 | 83 | 80 |

EqF and EqM and Prio | 80 | 80 | 80 | 80 | 91 | 80 | 120 | 80 | 83 | 80 |

Rel and GR | 800 | 400 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 74 |

Node | Demand, tons | Satisfaction, % | Completion Time, Hours | ||
---|---|---|---|---|---|

Food | Medicine | Food | Medicine | ||

N1 | 75 | 10 | 100 | 80 | 1.08 |

N2 | 105 | 20 | 100 | 100 | 1.75 |

N3 | 40 | 5 | 107 | 80 | 1.42 |

N4 | 60 | 10 | 100 | 80 | 1.83 |

N5 | 255 | 45 | 100 | 82 | 1.83 |

N6 | 95 | 20 | 100 | 80 | 1.83 |

N7 | 35 | 5 | 100 | 120 | 1.83 |

N8 | 225 | 25 | 100 | 80 | 1.83 |

N9 | 165 | 30 | 100 | 83 | 1.83 |

N10 | 1530 | 270 | 99 | 80 | 1.83 |

Period | Hours Elapsed | D1 | D2 | D3 | D4 | N1 | N2 | N3 | N4 | N5 | N6 | N7 | N8 | N9 | N10 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

0 | 0.00 | 1300 | 520 | 310 | 1270 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

1 | 0.08 | 1041 | 375 | 295 | 1225 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

2 | 0.17 | 1041 | 370 | 295 | 1180 | 0 | 0 | 0 | 0 | 166 | 0 | 0 | 0 | 0 | 0 |

3 | 0.25 | 1041 | 320 | 295 | 1180 | 0 | 0 | 0 | 0 | 166 | 0 | 0 | 0 | 0 | 0 |

4 | 0.33 | 1041 | 320 | 280 | 1180 | 0 | 0 | 0 | 0 | 166 | 0 | 0 | 0 | 0 | 23 |

5 | 0.42 | 1041 | 320 | 230 | 1180 | 29 | 0 | 0 | 0 | 181 | 0 | 0 | 0 | 0 | 23 |

6 | 0.50 | 1041 | 320 | 205 | 1180 | 29 | 0 | 0 | 0 | 181 | 0 | 0 | 0 | 95 | 23 |

7 | 0.58 | 1041 | 320 | 85 | 820 | 4 | 0 | 0 | 0 | 166 | 0 | 0 | 0 | 120 | 23 |

8 | 0.67 | 1056 | 320 | 85 | 820 | 4 | 0 | 0 | 0 | 166 | 0 | 0 | 0 | 165 | 23 |

9 | 0.75 | 1056 | 320 | 85 | 650 | 4 | 0 | 45 | 0 | 166 | 0 | 0 | 0 | 165 | 23 |

10 | 0.83 | 1056 | 290 | 40 | 630 | 4 | 0 | 0 | 0 | 166 | 0 | 0 | 0 | 165 | 23 |

11 | 0.92 | 1056 | 195 | 40 | 385 | 19 | 0 | 0 | 0 | 207 | 0 | 0 | 0 | 165 | 23 |

12 | 1.00 | 1060 | 195 | 40 | 285 | 4 | 0 | 0 | 0 | 207 | 0 | 0 | 0 | 165 | 23 |

13 | 1.08 | 1060 | 195 | 40 | 285 | 8 | 0 | 0 | 0 | 207 | 0 | 0 | 0 | 165 | 23 |

14 | 1.17 | 1060 | 195 | 40 | 285 | 83 | 0 | 0 | 45 | 252 | 0 | 0 | 0 | 165 | 23 |

15 | 1.25 | 1060 | 195 | 40 | 285 | 83 | 0 | 0 | 45 | 252 | 0 | 0 | 45 | 165 | 23 |

16 | 1.33 | 1060 | 195 | 40 | 285 | 83 | 0 | 0 | 45 | 252 | 0 | 0 | 45 | 165 | 23 |

17 | 1.42 | 595 | 170 | 40 | 285 | 83 | 0 | 177 | 45 | 252 | 25 | 0 | 45 | 165 | 383 |

18 | 1.50 | 595 | 170 | 40 | 285 | 83 | 0 | 47 | 45 | 252 | 25 | 0 | 45 | 165 | 383 |

19 | 1.58 | 350 | 170 | 0 | 285 | 83 | 0 | 47 | 45 | 252 | 25 | 0 | 45 | 165 | 383 |

20 | 1.67 | 0 | 170 | 0 | 285 | 83 | 0 | 47 | 45 | 252 | 25 | 0 | 45 | 165 | 848 |

21 | 1.75 | 0 | 170 | 0 | 285 | 83 | 30 | 47 | 45 | 252 | 25 | 0 | 45 | 165 | 848 |

22 | 1.83 | 0 | 170 | 0 | 285 | 83 | 125 | 47 | 45 | 252 | 90 | 0 | 45 | 165 | 1293 |

23 | 1.92 | 0 | 170 | 0 | 285 | 83 | 125 | 47 | 68 | 292 | 111 | 41 | 245 | 190 | 1743 |

From | To | Vehicle Type | Time Period | |||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |||

D1 | N5 | small | 25 | |||||||||||||||||||

medium | 3 | |||||||||||||||||||||

large | 3 | |||||||||||||||||||||

N10 | small | 25 | ||||||||||||||||||||

medium | 31 | 3 | ||||||||||||||||||||

large | 1 | 8 | 9 | |||||||||||||||||||

D2 | D4 | small | 1 | 1 | ||||||||||||||||||

medium | ||||||||||||||||||||||

large | 1 | |||||||||||||||||||||

N2 | small | 1 | ||||||||||||||||||||

medium | 2 | 6 | ||||||||||||||||||||

large | ||||||||||||||||||||||

N9 | small | 1 | 9 | |||||||||||||||||||

medium | 6 | |||||||||||||||||||||

large | 1 | 1 | ||||||||||||||||||||

D3 | N1 | small | ||||||||||||||||||||

medium | 1 | 5 | ||||||||||||||||||||

large | 2 | 1 | ||||||||||||||||||||

N5 | small | 8 | ||||||||||||||||||||

medium | 1 | 3 | 3 | |||||||||||||||||||

large | ||||||||||||||||||||||

D4 | N3 | small | 9 | |||||||||||||||||||

medium | 3 | 3 | ||||||||||||||||||||

large | 8 | 1 | ||||||||||||||||||||

N10 | small | |||||||||||||||||||||

medium | 24 | |||||||||||||||||||||

large | 8 | 4 | ||||||||||||||||||||

N1 | N6 | small | ||||||||||||||||||||

medium | 1 | |||||||||||||||||||||

large | 1 | 2 | 1 | |||||||||||||||||||

N7 | small | |||||||||||||||||||||

medium | 3 | |||||||||||||||||||||

large | ||||||||||||||||||||||

N3 | N4 | small | ||||||||||||||||||||

medium | 3 | |||||||||||||||||||||

large | 1 | |||||||||||||||||||||

N8 | small | |||||||||||||||||||||

medium | 3 | |||||||||||||||||||||

large | 8 | |||||||||||||||||||||

N5 | D1 | small | ||||||||||||||||||||

medium | 1 | 3 | 3 | |||||||||||||||||||

large | 1 | |||||||||||||||||||||

D3 | small | 1 | ||||||||||||||||||||

medium | ||||||||||||||||||||||

large | 1 | |||||||||||||||||||||

N1 | small | |||||||||||||||||||||

medium | 3 | |||||||||||||||||||||

large | 1 | |||||||||||||||||||||

N9 | D2 | small | 1 | |||||||||||||||||||

medium | 6 | |||||||||||||||||||||

large | 1 |

From | To | Vehicle Type | Time Period | ||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 17 | 18 | 19 | 20 | |||

D1 | N5 | small | 125 | ||||||||||||||||

medium | 45 | ||||||||||||||||||

large | 66 | ||||||||||||||||||

N10 | small | 125 | |||||||||||||||||

medium | 465 | 45 | |||||||||||||||||

large | 23 | 200 | 225 | ||||||||||||||||

D2 | D4 | small | 5 | 5 | |||||||||||||||

medium | |||||||||||||||||||

large | 25 | ||||||||||||||||||

N2 | small | 5 | |||||||||||||||||

medium | 30 | 90 | |||||||||||||||||

large | |||||||||||||||||||

N9 | small | 5 | 45 | ||||||||||||||||

medium | 90 | ||||||||||||||||||

large | 25 | 25 | |||||||||||||||||

D3 | N1 | small | |||||||||||||||||

medium | 15 | 75 | |||||||||||||||||

large | 50 | 25 | |||||||||||||||||

N5 | small | 40 | |||||||||||||||||

medium | 15 | 45 | 45 | ||||||||||||||||

large | |||||||||||||||||||

D4 | N3 | small | 45 | ||||||||||||||||

medium | 45 | 45 | |||||||||||||||||

large | 200 | 25 | |||||||||||||||||

N10 | small | ||||||||||||||||||

medium | 360 | ||||||||||||||||||

large | 200 | 100 | |||||||||||||||||

N1 | N6 | small | |||||||||||||||||

medium | 15 | ||||||||||||||||||

large | 25 | 50 | 25 | ||||||||||||||||

N7 | small | ||||||||||||||||||

medium | 41 | ||||||||||||||||||

large | |||||||||||||||||||

N3 | N4 | small | |||||||||||||||||

medium | 45 | ||||||||||||||||||

large | 23 | ||||||||||||||||||

N8 | small | ||||||||||||||||||

medium | 45 | ||||||||||||||||||

large | 200 | ||||||||||||||||||

N5 | D1 | small | |||||||||||||||||

medium | 15 | 0 | 0 | ||||||||||||||||

large | 0 | ||||||||||||||||||

D3 | small | 0 | |||||||||||||||||

medium | |||||||||||||||||||

large | 0 | ||||||||||||||||||

N1 | small | ||||||||||||||||||

medium | 45 | ||||||||||||||||||

large | 25 | ||||||||||||||||||

N9 | D2 | small | 0 | ||||||||||||||||

medium | 0 | ||||||||||||||||||

Large | 0 |

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## Share and Cite

**MDPI and ACS Style**

Hrydziushka, D.; Pasha, U.; Hoff, A.
An Extended Model for Disaster Relief Operations Used on the Hagibis Typhoon Case in Japan. *Logistics* **2021**, *5*, 39.
https://doi.org/10.3390/logistics5020039

**AMA Style**

Hrydziushka D, Pasha U, Hoff A.
An Extended Model for Disaster Relief Operations Used on the Hagibis Typhoon Case in Japan. *Logistics*. 2021; 5(2):39.
https://doi.org/10.3390/logistics5020039

**Chicago/Turabian Style**

Hrydziushka, Darya, Urooj Pasha, and Arild Hoff.
2021. "An Extended Model for Disaster Relief Operations Used on the Hagibis Typhoon Case in Japan" *Logistics* 5, no. 2: 39.
https://doi.org/10.3390/logistics5020039