# Optimization of Electric Vehicle Routes Considering Multi-Temperature Co-Distribution in Cold Chain Logistics with Soft Time Windows

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Vehicle Routing Problem with Time Windows

#### 2.2. Vehicle Routing Problem of EVs

#### 2.3. Multi-Temperature Co-Distribution Problem

#### 2.4. Algorithm Optimization

## 3. Problem Description and Model Formulation for EVRP-MTCD-STW

#### 3.1. Problem Description

- (1)
- The demand of each customer and the load capacity of the distribution vehicle do not exceed the maximum load capacity of the vehicle. Additionally, all vehicles are of the same type.
- (2)
- The vehicle departs from the depot in a fully charged state. If the power is insufficient to support its rush to the next customer during transportation, it should be recharged at the nearest charging station by replacing the battery.
- (3)
- Vehicles do not consume electricity when serving customers, that is, the impact of unloading operations on electricity consumption is not taken into consideration.
- (4)
- The power consumption of the vehicle is linearly related to the distance traveled.
- (5)
- Customers have a soft time window requirement, with incentives for early arrival and penalties for late arrival.
- (6)
- Each vehicle can carry the same number of insulation box with a known capacity.
- (7)
- The insulation box and cooler used in the vehicle have the same specifications, and the cost of cold storage is only related to the number of insulation boxes and coolers.

#### 3.2. Cost Analysis

- (1)
- Transportation costs

- (2)
- Refrigeration costs

- (3)
- Charging costs

- (4)
- Incentive costs

#### 3.3. Model Formulation

## 4. IACO Algorithm for EVRP-MTCD-STW

#### 4.1. Modification of State Transfer Rules

#### 4.2. Improved Volatility Factor

#### 4.3. Local Search Optimization

#### 4.4. The Main Steps of IACO

## 5. Computational Experiments

#### 5.1. Parameter Setting

#### 5.2. Efficiency Assessment of IACO

#### 5.3. Computational Results for EVRP-MTCD-STW Instance

- (1)
- Results of solving adapted dataset R101

- (2)
- Influence of distribution mode

- (3)
- Influence of the width of the time window

## 6. Conclusions and Future Research

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 7.**Comparison of vehicle distribution routes for STD and MTCD. (

**a**) Normal temperature goods; (

**b**) Refrigerated goods; (

**c**) Frozen goods; (

**d**) Multi-temperature co-distribution.

Description | |
---|---|

Sets | |

$V$ | Set of depot and customers |

$C$ | Set of charging station |

$K$ | Set of distribution vehicles |

$M$ | Set of fresh produce categories |

$A$ | Set of arcs |

Parameters | |

$f$ | Cost of using the vehicle |

$e$ | Cost of transporting the vehicle per unit of time |

$g$ | Cost of using the insulation box |

$\omega $ | Charging cost rate of the vehicle |

${P}_{1}$ | Early arrival reward factor, ${P}_{1}<0$ |

${P}_{2}$ | Delayed arrival penalty factor, ${P}_{2}>0$ |

$Q$ | Maximum load of the vehicle |

$B$ | Vehicle battery capacity |

$h$ | Number of insulation box that can be accommodated per vehicle |

$L$ | Maximum capacity of insulation box |

$\xi $ | Power consumption of the vehicle per unit mile |

$\delta $ | Loss rate of goods |

$F$ | Maximum acceptable goods loss rate |

Variables | |

${x}_{ijk}$ | Binary variable, equals 1 if vehicle $k$ is transported from node $i$ to $j$ |

${Y}_{c}$ | Binary variable, equals 1 if vehicle is charged at $c$ |

${Z}_{jmk}$ | Binary variable, equals 1 if vehicle $k$ delivers $m$ products to node $j$ |

${d}_{ij}$ | Distance from node $i$ to $j$ |

${N}_{m}^{k}$ | Number of insulation box required to put the product of the $m$ temperature layer into the vehicle $k$. If there is less than one box, it will be counted as one box. |

${g}_{m}$ | Cost of the cooler required for the $m$ temperature layer |

${b}_{c}$ | Power of the vehicle arriving at the charging station $c$ |

$\left({e}_{i},{l}_{i}\right)$ | Customer expectation time window |

$\left({E}_{i},{L}_{i}\right)$ | Customer tolerable time window |

${t}_{i}^{1}$ | Time for the vehicle to arrive at node $i$ |

${s}_{jm}$ | Demand for goods $m$ at node $j$ |

${t}_{ijk}$ | Time taken by vehicle $k$ to travel from node $i$ to $j$ |

${w}_{ij}$ | Load from depot to the node $j$,$i=0$ |

${t}_{i}^{2}$ | Time of the vehicle leaving the node $i$ |

${P}_{ck}^{1}$ | Power of the vehicle $k$ leaving the charging station $c$ |

${P}_{jk}^{2}$ | Remaining power of the vehicle $k$ arriving at the node $j$ |

Parameter | Description | Value |
---|---|---|

Algorithm | ||

$m$ | Ant number | 100 |

$\alpha $ | Pheromone importance | 1 |

$\beta $ | Heuristic factor importance | 5 |

$\rho $ | Initial pheromone volatility factor | 0.2 |

$Nc\_\mathit{max}$ | Iteration number | 200 |

Model | ||

${P}_{1}$ | Reward coefficient | −0.5 |

${P}_{2}$ | Penalty coefficient | 1 |

${f}_{1}$ | Cost of using normal temperature vehicle (CNY) | 500 |

${f}_{2}$ | Cost of using refrigerated vehicle (CNY) | 550 |

${f}_{3}$ | Cost of using frozen vehicle (CNY) | 575 |

$e$ | Vehicle unit transportation cost (CNY/km) | 2 |

$g$ | Insulation box cost (CNY) | 0.5 |

${g}_{2}$ | Refrigerated cooler cost (CNY) | 1 |

${g}_{3}$ | Frozen cooler cost (CNY) | 1.6 |

$\omega $ | Vehicle charging cost (CNY/kWh) | 0.747 |

$B$ | Vehicle battery capacity (kWh) | 80 |

$\xi $ | Unit mileage power consumption (kWh/km) | 0.055 |

$Q$ | Maximum load of the vehicle (kg) | 200 |

$h$ | Number of insulation box that can be accommodated per vehicle | 15 |

$L$ | Maximum capacity of insulation box (kg) | 12 |

$\delta $ | Loss rate of goods | 0.03 |

$F$ | Maximum acceptable goods loss rate | 20% |

Dataset | BKS | TP-TS | SARS | IACO | ∆x% | ||||
---|---|---|---|---|---|---|---|---|---|

NV | TD | NV | TD | NV | TD | NV | TD | ||

C101 | 10 | 828.94 | 10 | 829.01 | 10 | 828.94 | 10 | 828.94 | 0 |

C102 | 10 | 828.94 | 10 | 832.56 | 10 | 828.94 | 10 | 828.94 | 0 |

C201 | 3 | 591.56 | 3 | 591.58 | 3 | 591.56 | 3 | 591.56 | 0 |

C202 | 3 | 591.56 | 3 | 591.58 | 3 | 591.56 | 3 | 591.56 | 0 |

R101 | 19 | 1645.79 | 20 | 1653.54 | 20 | 1644.26 | 16 | 1425.82 | −13.29 |

R102 | 17 | 1486.12 | 19 | 1488.00 | 19 | 1481.9 | 15 | 1367.56 | −7.72 |

R201 | 4 | 1252.37 | 5 | 1216.33 | 9 | 1167.53 | 7 | 1098.56 | −5.91 |

R202 | 3 | 1191.70 | 4 | 1131.75 | 9 | 1053.5 | 7 | 1019.24 | −3.25 |

RC101 | 14 | 1696.94 | 16 | 1653.06 | 17 | 1664.06 | 14 | 1513.66 | −8.43 |

RC102 | 12 | 1554.75 | 14 | 1502.16 | 15 | 1489.22 | 12 | 1336.57 | −10.25 |

RC201 | 4 | 1406.91 | 4 | 1470.12 | 9 | 1287.05 | 8 | 1232.67 | −4.23 |

RC202 | 3 | 1367.09 | 4 | 1208.10 | 9 | 1109.51 | 7 | 1099.10 | −0.94 |

No. | X (km) | Y (km) | Demand (kg) | D1 (kg) | D2 (kg) | D3 (kg) | T1 (min) | T2 (min) |
---|---|---|---|---|---|---|---|---|

0 | 35 | 35 | 0 | 0 | 0 | 0 | 0 | 230 |

1 | 5 | 5 | 25 | 5 | 13 | 7 | 167 | 187 |

2 | 4 | 18 | 16 | 4 | 4 | 8 | 36 | 56 |

3 | 10 | 43 | 20 | 6 | 10 | 4 | 90 | 110 |

4 | 15 | 10 | 19 | 5 | 8 | 6 | 148 | 168 |

5 | 6 | 68 | 26 | 5 | 12 | 9 | 29 | 49 |

6 | 2 | 60 | 24 | 12 | 3 | 9 | 89 | 109 |

7 | 27 | 69 | 13 | 3 | 7 | 3 | 46 | 66 |

8 | 20 | 50 | 9 | 2 | 3 | 4 | 146 | 66 |

9 | 30 | 60 | 25 | 8 | 9 | 8 | 119 | 139 |

10 | 41 | 49 | 34 | 8 | 12 | 14 | 93 | 103 |

11 | 49 | 73 | 18 | 8 | 3 | 7 | 62 | 82 |

12 | 40 | 60 | 35 | 8 | 9 | 18 | 66 | 86 |

13 | 62 | 77 | 23 | 7 | 6 | 10 | 156 | 176 |

14 | 57 | 48 | 28 | 10 | 10 | 8 | 27 | 47 |

15 | 65 | 35 | 19 | 6 | 5 | 8 | 78 | 98 |

16 | 67 | 5 | 30 | 9 | 9 | 12 | 177 | 197 |

17 | 53 | 12 | 26 | 7 | 9 | 10 | 163 | 183 |

18 | 45 | 10 | 33 | 13 | 8 | 12 | 125 | 145 |

19 | 32 | 12 | 17 | 4 | 6 | 7 | 96 | 116 |

20 | 22 | 27 | 38 | 7 | 16 | 15 | 29 | 49 |

21 | 50 | 35 | 30 | 8 | 13 | 9 | 58 | 78 |

22 | 65 | 20 | 36 | 9 | 12 | 15 | 87 | 107 |

23 | 23 | 3 | 29 | 9 | 7 | 13 | 127 | 147 |

24 | 49 | 58 | 28 | 12 | 5 | 11 | 103 | 123 |

25 | 15 | 30 | 32 | 9 | 15 | 8 | 130 | 150 |

26 | 50 | 20 | 0 | 0 | 0 | 0 | 0 | 230 |

27 | 16 | 56 | 0 | 0 | 0 | 0 | 0 | 230 |

28 | 35 | 12 | 0 | 0 | 0 | 0 | 0 | 230 |

29 | 15 | 35 | 0 | 0 | 0 | 0 | 0 | 230 |

30 | 40 | 55 | 0 | 0 | 0 | 0 | 0 | 230 |

Vehicle | Route |
---|---|

Vehicle 1 | 0-5-7-10-24-13-30-0 |

Vehicle 2 | 0-20-2-6-3-25-0 |

Vehicle 3 | 0-14-15-22-4-1-0 |

Vehicle 4 | 0-21-11-12-9-8-0 |

Vehicle 5 | 0-19-23-18-17-16-0 |

Method | Cost (CNY) | Transportation (CNY) | Refrigeration (CNY) | Charging (CNY) | Incentive (CNY) |
---|---|---|---|---|---|

Single | 8941.16 | 8340.18 | 480 | 93.46 | 27.52 |

Multi | 4520.2 | 3941.12 | 572.9 | 41.39 | −35.21 |

Expands | Cost (CNY) | Incentive (CNY) | Vehicle |
---|---|---|---|

0% | 6234.21 | 28.48 | 8 |

50% | 5120.73 | 6.8 | 6 |

100% | 4520.20 | −35.21 | 5 |

150% | 4460.52 | −52.52 | 5 |

200% | 4432.88 | −61.09 | 5 |

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## Share and Cite

**MDPI and ACS Style**

He, M.; Yang, M.; Fu, W.; Wu, X.; Izui, K.
Optimization of Electric Vehicle Routes Considering Multi-Temperature Co-Distribution in Cold Chain Logistics with Soft Time Windows. *World Electr. Veh. J.* **2024**, *15*, 80.
https://doi.org/10.3390/wevj15030080

**AMA Style**

He M, Yang M, Fu W, Wu X, Izui K.
Optimization of Electric Vehicle Routes Considering Multi-Temperature Co-Distribution in Cold Chain Logistics with Soft Time Windows. *World Electric Vehicle Journal*. 2024; 15(3):80.
https://doi.org/10.3390/wevj15030080

**Chicago/Turabian Style**

He, Meiling, Mei Yang, Wenqing Fu, Xiaohui Wu, and Kazuhiro Izui.
2024. "Optimization of Electric Vehicle Routes Considering Multi-Temperature Co-Distribution in Cold Chain Logistics with Soft Time Windows" *World Electric Vehicle Journal* 15, no. 3: 80.
https://doi.org/10.3390/wevj15030080