# Facility Location Problem Approach for Distributed Drones

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## Abstract

**:**

## 1. Introduction

#### 1.1. Motivation for Distributed Drone Ports

#### 1.2. Related Work

#### 1.3. Challenges

#### 1.4. Facility Location Problem

#### 1.5. K-Means Clustering Algorithms

## 2. Materials and Methods

#### 2.1. Central Controller

#### 2.2. Drone Port

#### 2.3. Objective

#### 2.4. Tasks

#### 2.5. Energy Consumption

#### 2.6. Facility Location Problem

#### 2.7. Capital Expenditure

#### 2.8. Operational Expenditure

#### 2.9. Drone Port Placement Algorithm

Algorithm 1 Facility Location Problem for Drones |

procedure Drone Port Placement and Shortest Route |

$i\leftarrow \mathrm{max}\phantom{\rule{4.pt}{0ex}}\mathrm{number}\phantom{\rule{4.pt}{0ex}}\mathrm{of}\phantom{\rule{4.pt}{0ex}}\mathrm{droneports}$ |

$T\leftarrow \mathrm{Task}\phantom{\rule{4.pt}{0ex}}\mathrm{Locations}\phantom{\rule{4.pt}{0ex}}\mathrm{array}$ |

$P\leftarrow \mathrm{Set}\phantom{\rule{4.pt}{0ex}}\mathrm{of}\phantom{\rule{4.pt}{0ex}}\mathrm{drone}\phantom{\rule{4.pt}{0ex}}\mathrm{ports}\phantom{\rule{4.pt}{0ex}}\mathrm{array}$ |

${P}_{max}\leftarrow \mathit{\text{max number of droneports}}$ |

$p\leftarrow \mathit{\text{Initial number of droneports}}$ |

while $p\le {P}_{max}$ do |

$clusters\leftarrow GenerateCluster(Tasks,p)$ |

$shortestroute\leftarrow TSP(tasks,droneport)$ |

$e\leftarrow f({d}_{i}j)$ |

if $e\ge \theta $ then |

Break |

else |

$p\leftarrow p+1$ |

return Drone Port location |

return Shortest Routes |

#### 2.10. Traveling Salesman Problem

## 3. Performance Evaluation

#### 3.1. Coverage Size effect on the Combinatorial Search Space

#### 3.2. Average Round Trip Distance

#### 3.3. Infrastructure and Energy Cost

#### 3.4. Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

Notation | Explanation |

${e}_{c}$ | Set of drone ports |

${t}_{p}$ | Set of drones |

${d}_{i}$ | Drone i |

$v\ast $ | Vector |

$\gamma $ | Drone energy level |

${d}_{ij}$ | Distance between task j and drone port i |

${c}_{i}$ | Cost to build drone port |

${z}_{i}$ | Decision variable to build drone port |

${x}_{j}$ | Decision variable for drone i to complete task j |

${y}_{ij}$ | Task completion state $\{0,1\}$ |

${x}_{0}$ | Drone initial position |

${x}_{0}$ | Drone final position |

${\tau}_{j}$ | Calculated task completion delay |

$\widehat{{\tau}_{j}}$ | Earliest deadline first constraint |

$f\left({d}_{ij}\right)$ | Power Function |

${\tau}_{complete}$ | Drone energy function |

${\tau}_{arrival}$ | Minimum drone energy |

$\eta $ | Task’s drone energy consumption |

$\eta $ | Task’s drone energy consumption |

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**Figure 4.**Average round trip for drones based on k-means clustering and Traveling Salesman Approximation.

Category Name | Mass [kg] | Range [km] | Flight Altitude [m] | Endurance [Hours] |
---|---|---|---|---|

Micro | <5 | <10 | 250 | 1 |

Mini | <20/30/150 | <10 | 150/250/300 | <2 |

Close Range | 25–150 | 10–30 | 3000 | 2–4 |

Medium Range | 50–250 | 30–70 | 3000 | 3–6 |

High Alt. Long Endurance | >250 | >70 | >3000 | >6 |

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**MDPI and ACS Style**

Lynskey, J.; Thar, K.; Oo, T.Z.; Hong, C.S.
Facility Location Problem Approach for Distributed Drones. *Symmetry* **2019**, *11*, 118.
https://doi.org/10.3390/sym11010118

**AMA Style**

Lynskey J, Thar K, Oo TZ, Hong CS.
Facility Location Problem Approach for Distributed Drones. *Symmetry*. 2019; 11(1):118.
https://doi.org/10.3390/sym11010118

**Chicago/Turabian Style**

Lynskey, Jared, Kyi Thar, Thant Zin Oo, and Choong Seon Hong.
2019. "Facility Location Problem Approach for Distributed Drones" *Symmetry* 11, no. 1: 118.
https://doi.org/10.3390/sym11010118