# Last-Mile Logistics Network Design under E-Cargo Bikes

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Problem Description

#### 2.2. Solution Method

#### 2.2.1. Solution Representation and Initialization

#### 2.2.2. Fitness Function Value

#### 2.2.3. Genetic Operators

**7 4 11**13 ] → [ 10 14

**21 20 19**13 ],

**21 20 19**24 8 ] → [ 2 12

**7 4 11**24 8 ].

#### 2.2.4. Route Extraction

#### 2.2.5. Genetic Algorithm Termination

## 3. Results

#### 3.1. Overview

^{TM}was used to determine road grades. The gradient threshold for e-bike deployment was assumed as 8% [29,30]. The battery capacity of the e-cargo bikes was assumed as 450 Wh (2). Average energy consumption was assumed as 10 Wh/km [2] and adjusted according to the gradient of segments [31]. The usable capacity is assumed as 80%, while the tolerance rate used for workload balancing was assumed as 20%. Finally, packages to be delivered are homogeneous, with specific dimensions and similar weight, not exceeding 2 kg. Capacity of e-cargo bikes is expressed in terms of parcels [7]. For this analysis, it is assumed that the maximum load of bicycles is 20 parcels [13].

#### 3.2. GA Parameters and Fine Tuning

#### 3.3. Results

#### 3.4. Sensitivity Analysis

#### 3.5. GA Performance Validation

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Impact of capacity on number of routes (

**top**), average distance (

**center**) and energy consumption (

**bottom**).

**Figure 4.**Impact of demand on number of routes (

**top**), average distance (

**center**) and energy consumption (

**bottom**).

Description | |
---|---|

Sets | |

V | $\mathrm{Set}\mathrm{of}\mathrm{delivery}\mathrm{points}I,j,V=\left\{1,2,\dots N\right\}$ |

${V}_{0}$ | $\mathrm{Set}\mathrm{of}\mathrm{delivery}\mathrm{points}\mathrm{including}\mathrm{depot}0,{V}_{0}$$=\left\{0,1,2,\dots N\right\}$ |

${V}_{N+1}$ | $\mathrm{Set}\mathrm{of}\mathrm{delivery}\mathrm{points}\mathrm{including}\mathrm{depot}N+1,$ ${V}_{N+1}=\left\{1,2,\dots N,N+1\right\}$ |

${V}_{0,N+1}$ | Set of delivery points including depot 0 and depot N+1 (starting and ending point), ${V}_{0,N+1}$$=\left\{0,1,2,\dots N,N+1\right\}$$=V\cup \left\{0\right\}\cup \left\{N+1\right\}$ |

B | $\mathrm{Set}\mathrm{of}\mathrm{e}\text{-}\mathrm{cargo}\mathrm{bikes},\mathsf{{\rm B}}=\left\{1,2,\dots b\right\}$ |

Q | Set of packages for delivery |

Parameters | |

N | Number of delivery points |

q_{i} | Number of packages to be delivered at point i |

C | Capacity of the e-cargo bike (in packages) |

b | Ε-cargo bike |

d_{ij} | Distance between delivery points (i,j) (km) |

e_{ij} | Energy consumption for link (i,j) |

L | Battery Capacity for each e-cargo bike |

r | Usable capacity factor |

α | Tolerance for workload allocation |

Decision Variable | |

x_{ijb} | Binary variable equal to 1 if the vehicle b is traveling on arc (i,j), $0\mathrm{otherwise}(i\in {V}_{0},j\in {V}_{N+1},i\ne j)$ |

Set of Experiments | POP | CR | MR | Best Objective Function Value (Wh) | Average | Standard Deviation |
---|---|---|---|---|---|---|

1 | 25 | 0.2 | 0.05 | 685.25 | 782.75 | 58.12 |

2 | 0.15 | 828.46 | 889.904 | 77.01 | ||

3 | 0.25 | 835.36 | 866.548 | 25.77 | ||

4 | 0.6 | 0.05 | 790.24 | 842.862 | 44.12 | |

5 | 0.15 | 771.81 | 907.45 | 99.96 | ||

6 | 0.25 | 877.54 | 905.056 | 31.30 | ||

7 | 0.8 | 0.05 | 678.71 | 779.924 | 92.43 | |

8 | 0.15 | 816.55 | 845.22 | 20.19 | ||

9 | 0.25 | 838.55 | 909.574 | 102.79 | ||

10 | 50 | 0.2 | 0.05 | 784.98 | 891.39 | 78.83 |

11 | 0.15 | 888.74 | 929.058 | 43.19 | ||

12 | 0.25 | 867.45 | 893.08 | 19.63 | ||

13 | 0.6 | 0.05 | 836.39 | 855.262 | 13.45 | |

14 | 0.15 | 832.02 | 890.702 | 36.36 | ||

15 | 0.25 | 941.46 | 1018.814 | 57.91 | ||

16 | 0.8 | 0.05 | 834.1 | 834.56 | 57.87 | |

17 | 0.15 | 849.77 | 876.99 | 42.07 | ||

18 | 0.25 | 942.1 | 1013.29 | 194.39 |

Travelled Distance (m) | Packages Per Route | Delivery Points Per Route | |
---|---|---|---|

Route 1 | 14,689 | 20 | 7 |

Route 2 | 18,581 | 18 | 6 |

Route 3 | 16,856 | 19 | 6 |

Route 4 | 14,351 | 19 | 6 |

Objective Function | 634 Wh |

Algorithm | Best Objective Function Value (Wh) | Average | Standard Deviation |
---|---|---|---|

GA | 678.71 | 779.924 | 92.43 |

ACO | 699.12 | 740.818 | 24.9 |

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**MDPI and ACS Style**

Papaioannou, E.; Iliopoulou, C.; Kepaptsoglou, K.
Last-Mile Logistics Network Design under E-Cargo Bikes. *Future Transp.* **2023**, *3*, 403-416.
https://doi.org/10.3390/futuretransp3020024

**AMA Style**

Papaioannou E, Iliopoulou C, Kepaptsoglou K.
Last-Mile Logistics Network Design under E-Cargo Bikes. *Future Transportation*. 2023; 3(2):403-416.
https://doi.org/10.3390/futuretransp3020024

**Chicago/Turabian Style**

Papaioannou, Eleni, Christina Iliopoulou, and Konstantinos Kepaptsoglou.
2023. "Last-Mile Logistics Network Design under E-Cargo Bikes" *Future Transportation* 3, no. 2: 403-416.
https://doi.org/10.3390/futuretransp3020024