# Optimization of Green Vehicle Paths Considering the Impact of Carbon Emissions: A Case Study of Municipal Solid Waste Collection and Transportation

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## Abstract

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## 1. Introduction

_{2}) emissions into the vehicle routing problem. Their proposed model aimed to resolve the trade-off between cost and emission reduction, resulting in a substantial decrease in the total cost. Ziaei and Jabbarzadeh [21] considered the impact of carbon emissions on a multi-modal transport network for hazardous materials. Sherif et al. [22] incorporated the cost of carbon emissions into the objective function and built a multi-depot heterogeneous green vehicle routing optimization model for the battery supply chain network. Madden et al. [23] built a model to estimate carbon emissions from curbside organic waste collection based on waste collection route data, which showed that curbside collection was the largest contributor to overall transport emissions. Guo, Qian, et al. [24] proposed a three-dimensional ant colony optimization algorithm (TDACO) to solve the multi-compartment vehicle routing problem (MCVRP) in industries such as waste collection and incorporated carbon emissions into the state transition rules in the TDACO. Dayanara, Arvitrida, and Siswanto [25] constructed a vehicle routing optimization model with the number of waste collections, time windows, and carbon emissions as constraints. Liu and Liao [26] considered different types of vehicles working together for waste collection and built an optimization model to minimize economic costs and carbon emissions. Li et al. [27] comprehensively considered the fixed vehicle costs, early and delayed penalty costs, fuel costs, and the impacts of vehicle speed, load, and road gradient on fuel consumption and developed a hybrid genetic algorithm solution with variable neighborhood search. Zhou, Li, and Wang [28] took into account how vehicle load affects carbon emissions and constructed a model that they then tested for robustness to find the shortest route and reduce carbon emissions. Wang and Shan [29] established a multi-objective waste collection model combining transport distance, fuel consumption, and carbon emission and demonstrated the effectiveness and practicality of the algorithm. Lu [30] constructed a mathematical model with the optimization objective of minimizing economic cost and carbon emission cost to meet the low-carbon demand for waste collection and transportation. Li, Song, and Guo [31] established a cold chain logistics multi-temperature co-distribution path optimization model consisting of transportation cost, carbon emission cost, refrigeration cost, and loss cost with the lowest total cost as the objective function to achieve low-carbon collection and transportation. Martyushev et al. [32] studied the operational performance of electric vehicles and developed a simulation model to determine the range of an electric vehicle by cycles of movement. The effects of operating speed, drag, and mechanical forces on the operation of electric vehicles were considered in the modeling process.

_{2}emissions in order to minimize costs. The aim of this paper is to reduce business costs and increase environmental benefits by optimizing the routes of sanitation vehicles. This study is based on real case data from Huzhou, Zhejiang, China. Firstly, the waste collection network in the study area is divided into five sub-areas by investigating the current situation of MSW collection and transportation, analyzing the distribution of waste nodes, and studying the waste generation pattern. A model is established for vehicle matching and path optimization with time window constraints and capacity constraints. An improved ant colony algorithm is designed to solve the model and compare the results with those of the other two algorithms.

## 2. Model Formulation

#### 2.1. Research Data

#### 2.2. Problem Description

#### 2.3. Mathematical Model

_{2}emission coefficient, and ${F}_{e}$ is the fuel consumption per km.

## 3. Methodology

## 4. Results

#### 4.1. Spatial Clustering of Waste Collection Points

#### 4.2. The Optimized Scheme of Collection and Transport Vehicle Dispatching

#### 4.3. Scheme Comparison

## 5. Conclusions

#### 5.1. Results

#### 5.2. Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Block Number | Daily Average (kg) | Block Number | Daily Average (kg) |
---|---|---|---|

1 | 16.2874 | 15 | 25.19309 |

2 | 38.20596 | 16 | 43.59313 |

3 | 116.1029 | 17 | 7.240346 |

4 | 82.4291 | 18 | 36.31804 |

5 | 27.22089 | 19 | 110.6039 |

6 | 125.5312 | 20 | 297.0145 |

7 | 43.59113 | 21 | 57.20373 |

8 | 28.9518 | 22 | 569.5574 |

9 | 152.7669 | 23 | 177.8744 |

10 | 69.16793 | 24 | 274.5275 |

11 | 27.14389 | 25 | 381.2409 |

12 | 52.62627 | 26 | 1412.876 |

13 | 51.00258 | 27 | 844.055 |

14 | 52.5404 | 28 | 28.06824 |

Longitude | Latitude | Speed (km/h) | Time | Status |
---|---|---|---|---|

120.2348 | 30.84301 | 27 | 4:00 | In operation |

120.2348 | 30.84527 | 30 | 4:00 | In operation |

120.2349 | 30.84772 | 18 | 4:01 | In operation |

120.2349 | 30.84777 | 18 | 4:01 | In operation |

120.2351 | 30.84779 | 20 | 4:01 | In operation |

120.2418 | 30.84807 | 28 | 4:02 | In operation |

120.2447 | 30.84797 | 0 | 4:03 | Stalled |

120.2447 | 30.84797 | 0 | 4:03 | Stalled |

120.2456 | 30.84817 | 30 | 4:03 | In operation |

120.2526 | 30.84888 | 30 | 4:04 | In operation |

120.2554 | 30.84918 | 30 | 4:05 | In operation |

120.2569 | 30.84937 | 0 | 4:05 | Stalled |

120.257 | 30.8494 | 10 | 4:06 | In operation |

120.2572 | 30.84955 | 16 | 4:06 | In operation |

120.2573 | 30.8498 | 14 | 4:06 | In operation |

120.2573 | 30.85002 | 6 | 4:07 | In operation |

Element | Description |
---|---|

$N$ | Set of waste collection points, $i=1,2,\dots ,N$ |

$K$ | Set of vehicles, $k=1,2,\dots ,K$ |

$Q$ | Maximum load of the vehicle |

${d}_{ij}$ | Distance between points “$i,j$“ |

${f}_{k}$ | Fixed costs for vehicle $k$ |

${t}_{ik}$ | Time when vehicle $k$ arrives at customer $i$ |

${c}_{k}$ | Cost per unit distance transported for vehicle $k$ |

$\alpha $ | Transport costs per unit distance |

$\beta $ | Time window penalty factor |

$\mathrm{E}$ | Costs of carbon emissions |

${F}_{e}$ | Fuel consumption per km |

$\mathsf{\delta}$ | Carbon emission factor |

${q}_{i}$ | Quantity demanded at waste collection point $i$ |

$\left[{a}_{i},{b}_{i}\right]$ | Working time window for collection point $i$ |

$\left[{S}_{1},{S}_{2}\right]$ | Waste collection time window |

${x}_{\mathit{ijk}}$ | $1\text{}\mathrm{if}\text{}\mathrm{vehicle}\text{}k\text{}\mathrm{from}\text{}\mathrm{collection}\text{}\mathrm{point}\text{}i\text{}\mathrm{to}\text{}j;\text{}0\text{}\mathrm{otherwise}$ |

${y}_{\mathit{ik}}$ | $1\text{}\mathrm{if}\text{}\mathrm{vehicle}\text{}k\text{}\mathrm{at}\text{}\mathrm{collection}\text{}\mathrm{point}\text{}i\text{}\mathrm{for}\text{}\mathrm{waste}\text{}\mathrm{collection};\text{}0\text{}\mathrm{otherwise}$ |

Element | Description | Value | Unit |
---|---|---|---|

$Q$ | Maximum load of the vehicle | 5 | t |

${f}_{k}$ | Fixed costs for vehicle $k$ | — | 10,000 RMB |

${\mathrm{f}}_{\mathrm{p}}$ | Acquisition costs of the vehicle | 54.9 | CNY/vehicle/day |

${\mathrm{f}}_{\mathrm{m}}$ | Maintenance costs of the vehicle | 50 | CNY/vehicle/day |

${\mathrm{f}}_{\mathrm{w}}$ | Cost of vehicle insurance | 3.79 | CNY/vehicle/day |

${\mathrm{f}}_{\mathrm{i}}$ | Cost of staff salary | 170 | CNY/person/day |

${c}_{k}$ | Cost per unit distance transported for vehicle $k$ | — | 10,000 CNY |

${\mathrm{c}}_{\mathrm{f}}$ | Fuel cost per kilometer | 3 | CNY/km |

$\mathrm{v}$ | Average vehicle travel speed | 30 | km/h |

${t}_{i}$ | Average operating time at collection points | 0.1 | h |

$\alpha $ | Non-linear coefficient | 1.4 | — |

$\beta $ | Road congestion factor | 1.5 | — |

${F}_{e}$ | Fuel consumption per km | 0.45 | L/km |

$\mathsf{\delta}$ | Carbon emission factor | 3.096 | — |

${C}_{m}$ | Carbon tax | 0.6 | CNY/kg |

Area | Vehicle Number | Waste Collection Sequence | Distance Traveled (km) | Assignment Time (h) |
---|---|---|---|---|

A | 1 | 0→95→94→93→83→82→81→98→97→0 | 9.43 | [0,1.27] |

B | 2 | 0→90→91→92→89→78→79→77→87→88→85→86→76→80→84→15→17→5→20→19→60→61→96→0 | 17.97 | [0,3.09] |

C | 3 | 0→22→9→6→1→8→7→3→2→10→13→14→11→12→0 | 19.65 | [0,2.68] |

C | 4 | 0→16→18→21→47→41→42→44→45→43→40→35→36→31→32→37→33→34→38→39→46→30→29→54→4→0 | 20.21 | [0,3.31] |

D | 5 | 0→58→68→69→66→67→23→27→28→25→26→24→53→52→49→51→50→48→64→65→63→70→72→71→0 | 19.23 | [0,3.26] |

E | 1 | 0→56→74→62→59→55→73→75→0 | 12.35 | [1.27,2.59] |

Area | Vehicle Number | Waste Collection Sequence | Distance Traveled (km) | Assignment Time (h) |
---|---|---|---|---|

A | 1 | 0→95→94→93→83→82→81→98→97→0 | 9.43 | [0,1.27] |

B | 2 | 0→96→90→91→92→89→78→79→77→87→88→80→76→86→85→84→15→17→5→20→19→60→61→0 | 21.73 | [0,3.17] |

C | 3 | 0→12→9→1→6→8→7→3→2→10→13→14→16→18→21→54→0 | 21.65 | [0,2.73] |

C | 4 | 0→22→11→47→41→42→44→45→43→40→35→36→31→32→37→33→34→38→39→46→30→29→4→0 | 22.70 | [0,3.43] |

D | 5 | 0→58→68→69→66→67→23→27→28→25→26→24→52→53→49→50→51→48→64→65→63→70→72→71→0 | 20.95 | [0,3.37] |

E | 1 | 0→56→74→62→59→55→73→75→0 | 12.35 | [1.27,2.59] |

Area | Vehicle Number | Waste Collection Sequence | Distance Traveled (km) | Assignment Time (h) |
---|---|---|---|---|

A | 1 | 0→95→94→93→83→82→81→98→97→0 | 9.43 | [0,1.27] |

B | 2 | 0→79→77→78→87→88→80→76→86→85→84→15→17→5→20→19→60→61→96→90→91→92→89→0 | 22.38 | [0,3.24] |

C | 3 | 0→9→1→6→8→7→44→42→41→47→21→18→16→4→0 | 21.63 | [0,2.78] |

C | 4 | 0→22→12→11→14→13→10→2→3→45→43→40→35→36→31→32→37→33→34→46→39→38→30→29→54→0 | 22.06 | [0,3.46] |

D | 5 | 0→58→68→69→66→67→23→27→28→25→24→26→52→53→49→50→51→48→64→65→63→72→70→71→0 | 22.39 | [0,3.37] |

E | 1 | 0→56→74→62→59→55→73→75→0 | 12.35 | [1.27,2.59] |

Improved ACO (km) | GA (km) | PSO (km) | ACO (km) | Practical Application (km) | |
---|---|---|---|---|---|

Vehicle_1 | 21.78 | 21.78 | 21.78 | 20.62 | 13.56 |

Vehicle_2 | 17.97 | 21.73 | 22.38 | 18.87 | 22.47 |

Vehicle_3 | 19.65 | 21.65 | 21.63 | 21.13 | 14.19 |

Vehicle_4 | 20.21 | 22.7 | 22.06 | 17.75 | 13.83 |

Vehicle_5 | 19.23 | 20.95 | 22.39 | 18.92 | 18.89 |

Vehicle_6 | / | / | / | 18.46 | 17.57 |

Vehicle_7 | / | / | / | / | 11.7 |

Vehicle_8 | / | / | / | / | 20.13 |

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**MDPI and ACS Style**

Li, T.; Deng, S.; Lu, C.; Wang, Y.; Liao, H.
Optimization of Green Vehicle Paths Considering the Impact of Carbon Emissions: A Case Study of Municipal Solid Waste Collection and Transportation. *Sustainability* **2023**, *15*, 16128.
https://doi.org/10.3390/su152216128

**AMA Style**

Li T, Deng S, Lu C, Wang Y, Liao H.
Optimization of Green Vehicle Paths Considering the Impact of Carbon Emissions: A Case Study of Municipal Solid Waste Collection and Transportation. *Sustainability*. 2023; 15(22):16128.
https://doi.org/10.3390/su152216128

**Chicago/Turabian Style**

Li, Tingting, Shejun Deng, Caoye Lu, Yong Wang, and Huajun Liao.
2023. "Optimization of Green Vehicle Paths Considering the Impact of Carbon Emissions: A Case Study of Municipal Solid Waste Collection and Transportation" *Sustainability* 15, no. 22: 16128.
https://doi.org/10.3390/su152216128