# Designing the Distribution Network of Essential Items in the Critical Conditions of Earthquakes and COVID-19 Simultaneously

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## Abstract

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## 1. Introduction

- What could happen and what factors need to be considered when creating a distribution network for necessities in the event of COVID-19 and earthquakes occurring simultaneously?
- How can a distribution network be made more efficient to guarantee prompt and effective delivery of necessities when COVID-19 and earthquakes occur simultaneously?

## 2. Literature Review

#### 2.1. Related Work

#### 2.1.1. Location and Allocation

#### 2.1.2. Transportation

#### 2.1.3. Location and Transportation

#### 2.2. Research Gap and Contributions

- Considering reliable support DCs for affected population centres to improve reliability.
- Providing a bi-objective mathematical model to minimize the time spent transporting relief goods and related logistics costs is also considered.
- The uncertainties related to earthquake probability, earthquake magnitude, and the probability of DC destruction are considered using a scenario-based approach.
- Public facilities and establishments are considered DCs.
- Turkey has been used as a case study to describe the model’s performance and the application of the described method.
- Considering distance restriction between people at the demand point.
- Reusing vehicles during the time horizon and in each period is considered.

## 3. Problem Statement

#### 3.1. Assumptions

- The capacity of distribution and backup centers is specified, but the capacity of central warehouses is considered unlimited.
- The uncertainties of the model, including the probability of an earthquake, the likelihood of failure of local DCs, and demand, were modeled using a probabilistic scenario-based approach.
- If the supply of goods through the main DC is not possible, goods will be supplied through backup centers.
- Goods have priority, reflected in the cost of a shortage of goods.
- Each vehicle can make multiple trips during the time horizon and in each period.
- Two methods of land and air transportation are used to transport goods.
- Vehicles are homogeneous in each transportation mode.
- The number and location of affected areas are identified.
- The possibility of shortages exists.
- The capacity of vehicles is specified.
- The distances between nodes are identified.
- Multiple periods are considered in the model.
- Multiple types of goods are considered in the model.

#### 3.2. Sets

$i$ | Set of warehouses during both earthquakes and COVID-19 disasters $i\in \left\{1,2,\dots ,I\right\}$; |

$g$ | Set of DCs during the both earthquakes and COVID-19 disasters $g\in \left\{1,2,\dots ,G\right\}$; |

${g}^{\prime}$ | Set of reliable DCs that can be used as a backup during both earthquakes and COVID-19 disasters $g\prime \u03f5\left\{1,2,\dots ,G\prime \right\};$ |

$o$ | Set of damaged points for earthquake and COVID-19 disasters $o\in \left\{1,2,\dots ,O\right\}$; |

$m$ | Set of vehicles $m\in \left\{1,2,\dots ,M\right\}$; |

${V}_{im}$ | Set of vehicles of type $m$ in the warehouse $i\text{};$ |

${V}_{gm}$ | Set of vehicles of type $m$ in the DC $g\in G\cup G\prime ;$ |

${n}_{m}$ | Set of number of trips of each vehicle type $m$ in each period t $n\in \left\{1,2,\dots ,N\right\};$ |

$s$ | Set of scenarios $s\in \left\{1,2,\dots ,S\right\}$; |

$t$ | Set of time periods for earthquakes and COVID-19 disaster; $t\in \left\{1,2,\dots ,T\right\}$ |

$l$ | Set of goods $l\in \left\{1,2,\dots ,L\right\}$; |

#### 3.3. Model Parameters

${\theta}_{i}$ | Fixed cost of establishing a warehouse $i$; |

${\theta}_{g}$ | Fixed cost of establishing the DC $g\in G\cup {G}^{\prime};$ |

${a}_{l}$ | Size of the product, which includes the volume and weight of the product; |

${d}_{olst}$ | The demand of good $l$ in damaged point $o$ in scenario $s$ in period $t$ during the earthquakes and COVID-19 disasters; |

${b}_{g}$ | The capacity of DC $g\in G\cup G\prime $; |

${c}_{igm}$ | The cost of each transportation unit from warehouse $i$ to the DC $g\in G\cup G\prime $ by vehicle type $m;$ |

${c}_{gom}$ | The cost of each transportation unit from DC $g\in G\cup G\prime $ to the damaged point $o$ by vehicle type $m$; |

$tim{e}_{igm}$ | Transfer time of products from the warehouse $i$ to the DC $g\in G\cup G\prime $ by vehicle type $m;$ |

$tim{e}_{gom}$ | Transfer time of products from the DC $g\in G\cup G\prime $ to the damaged point $o$ by vehicle type $m$ |

${p}_{s}$ | Probability of scenarios during both earthquakes and COVID-19 disasters; |

${p}_{gs}$ | Probability of destruction of the DC $g\in G$ under scenario $s;$ |

${\Phi}_{l}$ | Shortage cost of products $l$ during the two earthquakes and COVID-19 disasters; |

${q}_{m}$ | The capacity of vehicle type $m$, which includes the volume and weight capacity of the vehicle; |

${\alpha}_{ig}$ | Distance from warehouse $i$ to DC $g\in G\cup G\prime $; |

${\alpha}_{go}$ | Distance between the DC $g\in G\cup G\prime $ to the damaged point $o$; |

$m{d}_{o}$ | Maximum allowable distance between people in damaged point $o;$ |

$dis{s}_{o}$ | Distance between people in damaged point $o;$ |

$\psi $ | Large positive number; |

#### 3.4. Decision Variables

${z}_{ist}$ | If the central is selected in the scenario s in the period $t$ is 1; otherwise, 0 |

$z{z}_{gst}$ | If DC $g\in \text{}G\cup G\prime $ is selected in scenario s in period $t$ is 1; otherwise, 0 |

${y}_{igst}$ | If DC $j\in J\cup J\prime $ is selected to the warehouse $i$ in scenario $s$ in period $t$ is 1; otherwise, 0 |

${x}_{gost0}$ | If the damaged point $o$ be assigned to the DC $g\in G$ in scenario $s$ in the period $t$ 1; otherwise, 0 |

${x}_{gost0}^{\prime}$ | If the damaged point $o$ is assigned to the DC $g\in G\prime $ as the leading supplier in scenario $s$ in period $t$ is 1; otherwise, 0 |

${x}_{gost1}$ | If damaged $o$ is assigned to the DC $g\in G\prime $ as a backup supplier in scenario $s$ in period $t\text{}\mathrm{is}\text{}1$; otherwise, 0 |

${q}_{iglst}^{mnv}$ | The quantity of product $l$ that transfers from the central warehouse $i$ to the DC $g\in G\cup G\prime $ by vehicle type $m$ around $n\in {N}_{m}$ with vehicle $v\in {V}_{mi}$ in scenario $s$ in period $t$; |

${q}_{iglst}^{\prime mnv}$ | The quantity of the backup product $l$ that is transported from the warehouse $i$ to the DC $g\in G\prime $ by vehicle type $m$ in round $n\in {N}_{m}$ and by vehicle $v\in {V}_{mi}$ in scenario $s$ in period $t$; |

${q}_{glost}^{mnv}$ | The quantity of the product $l$ that is transported from the DC $g\in G\cup G\prime $ to the damaged point $o$ by vehicle type $m$ in round $n\in {N}_{m}$ and by Vehicle $v\in {V}_{mi}$ in scenario $s$ in period $t$; |

${B}_{olst}$ | Shortage amount of commodity $l$ at incident point $k$ in scenario $s$ in period $t$; |

${w}_{golst}^{mnv}$ | If the route $g\in G\cup G\prime $ is taken by vehicle type $m$ in round $n\in {N}_{m}$ or with vehicle $v\in {V}_{mi}$ in scenario $s$ in period $t$ is 1; otherwise, 0 |

${w}_{iglst}^{mnv}$ | If the route $i$ to $g\in G\cup G\prime $ is taken by vehicle type ‘$m$ at round $n\in {N}_{m}$ or by Vehicle $v\in {V}_{mi}$ in scenario $s$ in period $t$ is 1; otherwise, 0 |

#### 3.5. Mathematical Model

s.t | ||

${\displaystyle \sum}_{i}}{\displaystyle {\displaystyle \sum}_{m}}{\displaystyle {\displaystyle \sum}_{n\in {N}_{m}}}{\displaystyle {\displaystyle \sum}_{\nu \in {V}_{mi}}}{q}_{iglst}^{mn\nu}+{\displaystyle {\displaystyle \sum}_{i}}{\displaystyle {\displaystyle \sum}_{m}}{\displaystyle {\displaystyle \sum}_{n\in {N}_{m}}}{\displaystyle {\displaystyle \sum}_{\nu \in {V}_{mi}}}{{q}^{\prime}}_{iglst}^{mn\nu$ $={\displaystyle {\displaystyle \sum}_{o}}{\displaystyle {\displaystyle \sum}_{m}}{\displaystyle {\displaystyle \sum}_{n\in {N}_{m}}}{\displaystyle {\displaystyle \sum}_{\nu \in {V}_{mg}}}{q}_{golst}^{mn\nu}$ | $\forall g\in {G}^{\text{'}},l,s,t$ | (3) |

${\displaystyle \sum}_{i}}{\displaystyle {\displaystyle \sum}_{m}}{\displaystyle {\displaystyle \sum}_{n\in {N}_{m}}}{\displaystyle {\displaystyle \sum}_{\nu \in {V}_{mi}}}{q}_{iglst}^{mn\nu}={\displaystyle {\displaystyle \sum}_{o}}{\displaystyle {\displaystyle \sum}_{m}}{\displaystyle {\displaystyle \sum}_{n\in {N}_{m}}}{\displaystyle {\displaystyle \sum}_{\nu \in {V}_{mg}}}{q}_{golst}^{mn\nu$ | $\forall g\in G{,}^{}l,s,t$ | (4) |

$\displaystyle \sum}_{m}}{\displaystyle {\displaystyle \sum}_{n\in {N}_{m}}}{\displaystyle {\displaystyle \sum}_{\nu \in {V}_{mg}}}{q}_{golst}^{mn\nu}\le {d}_{olst}.{x}_{gost0}^{\text{'$ | $\forall g\in G,o,l,s,{t}^{}$ | (5) |

${\displaystyle \sum}_{i}}{\displaystyle {\displaystyle \sum}_{m}}{\displaystyle {\displaystyle \sum}_{n\in {N}_{m}}}{\displaystyle {\displaystyle \sum}_{\nu \in {V}_{mg}}}{{q}^{\prime}}_{iglst}^{mn\nu}\le {\displaystyle {\displaystyle \sum}_{o}}{\displaystyle {\displaystyle \sum}_{g\in G}}{x}^{}{}_{gost0}.{x}_{{g}^{\prime}ost1}.{d}_{olst}.{p}_{gs$ | $\forall g\in {G}^{\text{'}},l,s,t$ | (6) |

${B}_{olst}=\mathrm{max}\left(0.{d}_{olst}-{\displaystyle {\displaystyle \sum}_{g\in G\cup {G}^{\prime}}}{\displaystyle {\displaystyle \sum}_{m}}{\displaystyle {\displaystyle \sum}_{n\in {N}_{m}}}{\displaystyle {\displaystyle \sum}_{{V}_{mg}}}{q}_{golst}^{mn\nu}\right),$ | $\forall g\in {G}^{},l,s,t$ | (7) |

${\displaystyle \sum}_{i}}{\displaystyle {\displaystyle \sum}_{m}}{\displaystyle {\displaystyle \sum}_{n\in {N}_{m}}}{\displaystyle {\displaystyle \sum}_{\nu \in {V}_{mg}}}{\displaystyle {\displaystyle \sum}_{l}}{q}_{iglst}^{mn\nu}+{\displaystyle {\displaystyle \sum}_{i}}{\displaystyle {\displaystyle \sum}_{m}}{\displaystyle {\displaystyle \sum}_{n\in {N}_{m}}}{\displaystyle {\displaystyle \sum}_{\nu \in {V}_{mi}}}{\displaystyle {\displaystyle \sum}_{l}}{{q}^{\prime}}_{iglst}^{mn\nu}={b}_{g$ | $\forall g\in {G}^{\text{'}},s,t$ | (8) |

${\displaystyle \sum}_{i}}{\displaystyle {\displaystyle \sum}_{m}}{\displaystyle {\displaystyle \sum}_{n\in {N}_{m}}}{\displaystyle {\displaystyle \sum}_{\nu \in {V}_{mi}}}{\displaystyle {\displaystyle \sum}_{l}}{q}_{iglst}^{mn\nu}\le {b}_{g$ | $\forall g\in G,s,{t}^{}$ | (9) |

${\displaystyle \sum}_{g\in G}}{x}_{gost0}+{\displaystyle {\displaystyle \sum}_{g\in g\text{'}}}{x}_{gost0}^{\text{'}}=1$ | $\forall o,s,{t}^{}$ | (10) |

${\displaystyle \sum}_{g\in G\text{'}}}{x}_{gost1}={\displaystyle {\displaystyle \sum}_{g\in G}}{x}_{gost0$ | $\forall {o}^{},s,t$ | (11) |

${\displaystyle \sum}_{g\in G\cup {G}^{\prime}}}{y}_{igst}\le \psi {z}_{ist$ | ${\forall}^{}i,s,t$ | (12) |

${\displaystyle \sum}_{I}}{y}_{igst}\le z{z}_{gst$ | $\forall g\in G\cup {G}^{\prime},s,t$ | (13) |

${q}_{iglst}^{mn\nu}\le \psi {y}_{igst}$ | $\forall i,g\in G\cup {G}^{\prime},l,s,t,m,n\in {N}_{m},v\in {V}_{mi}$ | (14) |

${{q}^{\prime}}_{iglst}^{mn\nu}\le \psi {y}_{igst}$ | $\forall i,g\in G\cup {G}^{\prime},l,s,t,m,n\in {N}_{m},v\in {V}_{mi}$ | (15) |

${\displaystyle \sum}_{l}}{a}_{l}{q}_{iglst}^{mn\nu}\le {q}_{m$ | $\forall i,g\in G\cup {G}^{\prime},l,s,t,m,n\in {N}_{m},v\in {V}_{mi}$ | (16) |

${\displaystyle \sum}_{l}}{a}_{l}{{q}^{\prime}}_{iglst}^{mn\nu}\le {q}_{m$ | $\forall i,g\in G\cup {G}^{\prime},l,s,t,m,n\in {N}_{m},v\in {V}_{mi}$ | (17) |

${\displaystyle \sum}_{l}}{a}_{l}{q}_{golst}^{mn\nu}\le {q}_{m},$ | $\forall k,g\in G\cup {G}^{\prime},l,s,t,m,n\in {N}_{m},v\in {V}_{mi}$ | (18) |

${w}_{golst}^{mnv}\le \psi {q}_{golst}^{mn\nu},$ | $\forall k,g\in G\cup {G}^{\prime},l,s,t,m,n\in {N}_{m},v\in {V}_{mi}$ | (19) |

${w}_{golst}^{mnv}\le {q}_{golst}^{mn\nu}\frac{1}{\psi}$ | $\forall k,g\in G\cup {G}^{\prime},l,s,t,m,n\in {N}_{m},v\in {V}_{mi}$ | (20) |

${w}_{iglst}^{mnv}\le \psi {q}_{iglst}^{mn\nu}$ | $\forall i,g\in G\cup {G}^{\prime},l,s,t,m,n\in {N}_{m},v\in {V}_{mi}$ | (21) |

${w}_{iglst}^{mnv}\le {q}_{iglst}^{mn\nu}\frac{1}{\psi}$ | $\forall i,g\in G\cup {G}^{\prime},l,s,t,m,n\in {N}_{m},v\in {V}_{mi}$ | (22) |

$dis{s}_{o}.{x}_{gost0}^{\text{'}}\le m{d}_{o}$ | $\forall g,o,s,t$ | (23) |

${x}_{gost0},{x}_{gost0}^{\text{'}},{z}_{ist},z{z}_{gst,}{y}_{igst}\in \left\{0,1\right\}$ | $\forall i,g\in G\cup {G}^{\prime},l,s,t$ | (24) |

${q}_{iglst}^{mn\nu},{q}_{golst}^{mn\nu},{{q}^{\prime}}_{iglst}^{mn\nu},{B}_{olst}\ge 0$ | $\forall i,g\in G\cup {G}^{\prime},o,l,s,t$ | (25) |

#### 3.6. Linearity

- In issues related to optimization, the method is used to linearize nonlinear functions.
- A matching auxiliary equality constraint and an auxiliary variable are introduced for each intermediate nonlinear component of the function [44].
- A nonlinear optimization problem can be made linear by using this strategy.
- Linearization based on an auxiliary variable is a commonly employed method in optimization.

${t}_{g{g}^{\prime}ost}^{\prime}$ | Binary auxiliary variable for linearization |

${S}_{olst}^{+}$ | Continuous auxiliary variable for linearization |

${S}_{olst}^{-}$ | Continuous auxiliary variable for linearization |

${\xdf}_{olst}$ | Binary auxiliary variable for linearization |

${t}_{gost}^{\text{'}}\le \frac{1}{2}\left({x}_{gost}+{x}_{go1st}^{\text{'}}\right)$ | $\forall g\in G,{g}^{\prime}\in {G}^{\text{'}},o,s,t$ | (26) |

${t}_{g.{g}^{\prime}.o.s.t}^{\text{'}}\le \left({x}_{gost}+{x}_{go1st}^{\text{'}}\right)-1$ | $\forall g\in G,{g}^{\prime}\in {G}^{\text{'}},o,s,t$ | (27) |

${\displaystyle \sum}_{i}}{\displaystyle {\displaystyle \sum}_{m}}{\displaystyle {\displaystyle \sum}_{n\in {N}_{m}}}{\displaystyle {\displaystyle \sum}_{v\in {V}_{mi}}}{{q}^{\prime}}_{iglst}^{mn\nu}\le {\displaystyle {\displaystyle \sum}_{k}}{\displaystyle {\displaystyle \sum}_{j\in J}}{t}_{g{g}^{\prime}ost}^{\text{'}}.{d}_{kolst}.{p}_{gs$ | $\forall g\in {G}^{\text{'}},l,s,t$ | (28) |

${B}_{olst}={S}_{olst}^{+},$ | $\forall o,s,l,{t}^{}$ | (29) |

${S}_{olst}^{+}-{S}_{olst}^{-}={d}_{olst}-{\displaystyle {\displaystyle \sum}_{g\in G\cup {G}^{\prime}}}{\displaystyle {\displaystyle \sum}_{m}}{\displaystyle {\displaystyle \sum}_{n\in {N}_{m}}}{\displaystyle {\displaystyle \sum}_{\nu \in {V}_{mg}}}{q}_{golst}^{mn\nu}$ | $\forall o,s,l,{t}^{}$ | (30) |

${S}_{olst}^{+}\le \psi .{\xdf}_{olst}$ | $\forall o,s,l,{t}^{}$ | (31) |

${S}_{olst}^{-}\le \psi .\left(1-{\xdf}_{olst}\right)$ | $\forall o,s,l,{t}^{}$ | (32) |

## 4. Solution Methods

#### 4.1. Goal Programming

- Ascertain the resources needed to accomplish a desired set of goals.
- Assess the extent to which the objectives have been met in relation to the resources at hand.
- Offer the most fulfilling solution given the different resources available and the goals’ relative importance.

The states | The variables deviating from the ideal | Description |

First | ${d}_{i}^{+}={d}_{i}^{-}=0$ | Full achievement of the goal |

Second | ${d}_{i}^{+}\ne 0,{d}_{i}^{-}=0$ | Overtaking of the goal. |

Third | ${d}_{i}^{+}=0,{d}_{i}^{-}\ne 0$ | Failure to achieve the goal |

Fourth | ${d}_{i}^{+}\ne 0,{d}_{i}^{-}\ne 0$ | This is not possible |

#### 4.2. Lp-Metrics Approach

## 5. Case Study

## 6. Comparing Solution Methods

## 7. Sensitivity Analysis

#### 7.1. Demand

#### 7.2. Transportation Cost

#### 7.3. Failure Rate Percentage

#### 7.4. Maximum Allowable Distance between People

## 8. Managerial Insights

- In the event of a crisis, it is essential to give first priority to the distribution of resources like labour, supplies, and tools. The author can make recommendations for creating a system for allocating resources that takes into account things like population density, the extent of the damage, and the urgent needs of impacted communities. As a result, resources may be distributed by the government where they are most needed.
- Effective inter-stakeholder collaboration is crucial to disaster management. The management might suggest a strong communication system that facilitates real-time information exchange between governmental institutions, relief groups, and communities that were impacted. Coordination, decision-making, and the efficient use of resources may all benefit from this.
- The manager can stress how crucial it is for local government officials and non-governmental organizations (NGOs) to work together on disaster assistance. These organizations frequently possess important information about the surroundings, available resources, and impacted areas. Government agencies can better understand local conditions and enable more specialized assistance efforts by forming partnerships.
- The manager might emphasize the importance of making data-driven decisions while managing a crisis. The government can learn about the level of damage, population relocation, and resource needs by utilizing technologies like satellite photography, remote sensing, and data analytics. Better decision-making, resource planning, and efficient allocation may all be aided by this data-driven strategy.
- Regulatory roadblocks and ineffective bureaucracy can impede aid operations in times of crisis. By reducing paperwork, simplifying procedures, and using effective approval mechanisms, the author can recommend streamlining administrative operations. This can hasten relief efforts and guarantee that impacted populations receive aid on time.
- Finally, management should emphasize how crucial it is to make investments in catastrophe preparedness measures. The government may reduce the effect of future catastrophes by investing in early warning systems, holding exercises, and proactively creating disaster response plans. When comparable situations develop, having a long-term outlook on disaster management can assist in expeditiously and suitably arranging resources.

## 9. Conclusions and Future Suggestion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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Authors | Objective Functions | Kind of Parameters | Number of Products | Decision Level | Time Window | Kind of Disaster | Case Study | Solution Method | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Cost | Time | Unmet Demand | Certain | Uncertain | Single | Multi | Location | Allocation | Transportation | Distribution | |||||

Tofighi et al. (2016) [12] | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | - | ✓ | Meta-Heuristic | ||||||

Cotes and Cantillo (2019) [23] | ✓ | ✓ | ✓ | - | Exact | ||||||||||

Yang and Wang (2020) [19] | ✓ | ✓ | ✓ | ✓ | COVID-19 | Exact | |||||||||

Maghfiroh et al. (2020) [33] | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | - | ✓ | Heuristic | ||||||

Shokr et al. (2021) [38] | ✓ | ✓ | ✓ | ✓ | - | Exact | |||||||||

Zokaee et al. (2021) [39] | ✓ | ✓ | ✓ | ✓ | ✓ | Earthquake | ✓ | Exact | |||||||

Babaee-Tirkolaee et al. (2022) [29] | ✓ | ✓ | ✓ | ✓ | ✓ | COVID-19 | ✓ | Meta-Heuristic | |||||||

Hosseini-Motlagh et al. (2023) [40] | ✓ | ✓ | ✓ | ✓ | COVID-19 | ✓ | Exact | ||||||||

Li et al. (2023) [41] | ✓ | ✓ | ✓ | ✓ | ✓ | COVID-19 | Meta-Heuristic | ||||||||

Ehsani et al. (2023) [42] | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | COVID-19 | ✓ | Exact | ||||||

This Study | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | Earthquake COVID-19 | ✓ | Exact |

Earthquake Scenario | Scenario1 | Scenario2 | Scenario3 | Scenario4 |
---|---|---|---|---|

Fault | Location 1 | Location 2 | Location 3 | Location 3 |

Length | 68 | 74 | 32 | 20 |

Width | 22 | 45 | 12 | 9 |

Severity of occurrence | 3.5 | 8.5 | 60.1 | 7.1 |

Probability of occurrence | 0.40 | 0.66 | 0.14 | 0.5 |

Commodity | Volume (${\mathbf{m}}^{3}$) | Weight (kg) | Shortage Cost ($) | Discharge Time/Loading Time (Minutes) |
---|---|---|---|---|

Non-consumable | 0.2 | 38 | 25 | 0.1 |

Consumable | 0.17 | 5 | 77 | 0.03 |

Vehicles | Weight Capacity (tons) | $\mathbf{Volumetric}\text{}\mathbf{Capacity}\text{}\mathbf{(}{\mathbf{m}}^{3}$) | Speed (km/h) | Cost ($) |
---|---|---|---|---|

Kind of one | 1.2 | 30 | 100 | 8 |

Kind of two | 5 | 61 | 70 | 3 |

Central Warehouse | Local DC | Backup DC | |
---|---|---|---|

Capacity | 2 | 5000 | 4000 |

Construction cost | 1.1 | 0.20 | 0.8 |

Earthquake Scenario | Scenario1 | Scenario2 | Scenario3 | Scenario4 |
---|---|---|---|---|

District 15 | 22 | 17 | 21 | 15 |

District 16 | 30 | 10 | 15 | 12 |

District 18 | 40 | 20 | 30 | 15 |

District 19 | 30 | 10 | 20 | 16 |

District 20 | 60 | 40 | 56 | 39 |

Damaged Points | Scenario1 | Scenario2 | Scenario3 | Scenario4 |
---|---|---|---|---|

1 | 3300 | 2088 | 7176 | 5621 |

2 | 5791 | 1122 | 6611 | 2011 |

3 | 4210 | 1081 | 8058 | 6344 |

4 | 1010 | 520 | 7622 | 5031 |

5 | 1329 | 850 | 5445 | 4310 |

First OF | Second OF |
---|---|

1.75 × 10^{10} | 7.62 × 10^{12} |

2.13 × 10^{10} | 5.40 × 10^{12} |

3.55 × 10^{10} | 4.30 × 10^{12} |

3.92 × 10^{10} | 3.20 × 10^{12} |

4.90 × 10^{10} | 2.00 × 10^{12} |

5.80 × 10^{10} | 2.09 × 10^{12} |

6.80 × 10^{10} | 1.01 × 10^{12} |

8.81 × 10^{10} | 1.00 × 10^{12} |

First OF | Second OF |
---|---|

1.33 × 10^{10} | 9.62 × 10^{12} |

2.10 × 10^{10} | 8.20 × 10^{12} |

4.15 × 10^{10} | 7.30 × 10^{12} |

5.98 × 10^{10} | 6.27 × 10^{12} |

7.10 × 10^{10} | 4.03 × 10^{12} |

7.89 × 10^{10} | 4.09 × 10^{12} |

8.82 × 10^{10} | 2.81 × 10^{12} |

9.82 × 10^{10} | 1.99 × 10^{12} |

Number of Test Problem | Size of Test Problem | ${\mathbf{Z}}_{\mathbf{G}\mathbf{P}}\left({\mathbf{f}}_{1}^{*}\right)$ | ${\mathbf{Z}}_{\mathbf{G}\mathbf{P}}\left({\mathbf{f}}_{2}^{*}\right)$ | ${\mathbf{Z}}_{\mathbf{L}\mathbf{P}}\left({\mathbf{f}}_{1}^{*}\right)$ | ${\mathbf{Z}}_{\mathbf{G}\mathbf{P}}\left({\mathbf{f}}_{2}^{*}\right)$ | CPU Time (for GP.) | CPU Time (for Lp.) |
---|---|---|---|---|---|---|---|

${P}_{1}$ | Small | 8.27631 × 10^{5} | 54,640.18 | 8.2893 × 10^{10} | 45,483.172 | 14.8 | 12.4 |

${P}_{2}$ | Small | 4.27232 × 10^{6} | 158,069 | 2.11 × 10^{11} | 115,527.3 | 15.1 | 12.5 |

${P}_{3}$ | Medium | 2.56632 × 10^{8} | 190,281.2 | 4.13 × 10^{11} | 226,506.2 | 17.4 | 13.7 |

${P}_{4}$ | Medium | 4.32509 × 10^{7} | 617,904.7 | 5.14 × 10^{11} | 281,904.7 | 18 | 15 |

${P}_{5}$ | Medium | 5.70672 × 10^{7} | 785,247 | 6.79 × 10^{11} | 372,507.2 | 23 | 20 |

Methods | SAW Criteria | Ranking |
---|---|---|

Lp-metric | 0.441206 | 1 |

GP | 0.371205 | 2 |

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## Share and Cite

**MDPI and ACS Style**

Abbasi, S.; Vlachos, I.; Rekabi, S.; Talooni, M.
Designing the Distribution Network of Essential Items in the Critical Conditions of Earthquakes and COVID-19 Simultaneously. *Sustainability* **2023**, *15*, 15900.
https://doi.org/10.3390/su152215900

**AMA Style**

Abbasi S, Vlachos I, Rekabi S, Talooni M.
Designing the Distribution Network of Essential Items in the Critical Conditions of Earthquakes and COVID-19 Simultaneously. *Sustainability*. 2023; 15(22):15900.
https://doi.org/10.3390/su152215900

**Chicago/Turabian Style**

Abbasi, Sina, Ilias Vlachos, Shabnam Rekabi, and Mohammad Talooni.
2023. "Designing the Distribution Network of Essential Items in the Critical Conditions of Earthquakes and COVID-19 Simultaneously" *Sustainability* 15, no. 22: 15900.
https://doi.org/10.3390/su152215900