# Optimization of Sustainable Bi-Objective Cold-Chain Logistics Route Considering Carbon Emissions and Customers’ Immediate Demands in China

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Problem Description and Modeling

#### 2.1. Problem Description

**Supposition**

**1:**

**Supposition**

**2:**

**Supposition**

**3:**

**Supposition**

**4:**

**Supposition**

**5:**

**Supposition**

**6:**

#### 2.2. Distribution Cost Function

- (1)
- Vehicle fixed cost

- (2)
- Vehicle Transportation Costs

- (3)
- Temperature cost

- (4)
- Cost of carbon emissions

- (5)
- Time window penalty cost

#### 2.3. Customer Satisfaction Function

#### 2.4. Mathematical Models

## 3. Algorithm Design

#### 3.1. Algorithm for Initial Distribution Path Planning

#### 3.1.1. Principle of Ant Colony Algorithm

#### 3.1.2. Improved Ant Colony Algorithm

- (1)
- Adopt a saving matrix to guide the ant search

- (2)
- Improvement of the heuristic function

- (3)
- Improvement of pheromone

- (4)
- Multi-strategy improvementThis paper uses a multi-strategy approach to adjust the solutions obtained from each iteration. Moreover, we add a sequential exchange strategy [25], 2-OPT algorithm [26], and a sequential insertion strategy to the ant colony algorithm [27], in which each strategy is a neighborhood to avoid local optima to enhance the ergodicity of the ant colony algorithm search.
- (1)
- Sequential exchange strategy: Each customer point is passed through in sequence, and a customer point within the current line is exchanged with a customer on the same line or another line for the location.
- (2)
- The 2-OPT algorithm: Two points on the route are randomly selected, and the order of the remaining points remains the same, only the points between them are flipped in reverse order, which belongs to a local search algorithm.
- (3)
- Sequential insertion strategy: Insert customer points in different routes.

#### 3.1.3. Improved Ant Colony Algorithm Flow

- (1)
- Initialization parameters. Let time $t=0$, iteration number $iter=0$, set maximum iteration number $ite{r}_{\mathrm{max}}$, input specific data such as the distribution center and customer geographic location, set the distribution center node as the starting point of the ant, and enable chaos initialization.
- (2)
- Under the restriction of satisfying multiple constraints, each ant selects the next node $j$ according to Equation (26), records it in the forbidden table, and updates the load information of the vehicle.
- (3)
- Determine whether all ants visit all customer points. If not, repeat the step; if yes, put all customer points into the forbidden table and return to the logistics distribution center.
- (4)
- Multi-strategy improvement is performed.
- (5)
- Update the pheromone using the pheromone update rule Formula (29) of chaotic perturbation.
- (6)
- When the number of loops reaches the set maximum number of loops, the algorithm is terminated, and the optimal result of the algorithm is output. Conversely, the taboo table is emptied, and a new round of loops is started, $iter=iter+1$.
- (7)
- Output the calculation results.

#### 3.2. Delivery Path Algorithm for Immediate Customer Demand Phase

## 4. Example Analysis of the Calculation

#### 4.1. Background Analysis and Parameter Setting

_{2}emission factor $e$ is 2.61 kg/L. This paper assumed that the outdoor temperature is constant at 18 °C. The temperature inside the refrigerated vehicle compartment is set at 0 °C, and the cooling cost of the logistics vehicle during the transportation is 35 yuan/h. The temperature inside the compartment increases by 3 °C when the distribution point carries out unloading, the additional cooling cost due to the temperature difference is 6 yuan (°C/h), and the speed of the distribution vehicle is 60 km/h. The basic parameters of the improved ant colony algorithm are: $\alpha =1$, $\beta =2$, $\rho =0.75$, $Q=100$, and $\theta =2$, the number of ants $m=40$, and the maximum number of iterations $ite{r}_{\mathrm{max}}=200$ [22]. In addition, the weight of the lowest transportation cost is 0.75, and the lowest customer dissatisfaction is 0.25.

#### 4.2. Analysis of Results

- (1)
- Solving under the initial distribution demand

- (2)
- Problem solving under immediate customer demand

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Relationship between customer satisfaction and time window of trapezoidal membership function.

Variable Classification | Symbol | Connotation and Unit |
---|---|---|

Parametric variable | $K$ | A collection of vehicles providing fresh produce delivery services, $k\in K\mathrm{and}k=(1,2,\dots m)$; |

$I$ | The collection of distribution points where transportation is required. $i,j\in I$ and $i,j=(0,1,2\dots n)$, where 0 is the distribution center, and the others are the demand points; | |

${f}_{k}$ | Fixed cost of using any of the delivery vehicles; | |

${F}_{k}$ | Transportation cost per unit distance; | |

${d}_{ij}$ | The distance between client $i$ and client $j$; | |

${t}_{ij}^{k}$ | The time it takes for the $k$ vehicle to travel from distribution point $i$ to distribution point $j$; | |

${\varphi}_{1}$ | The cost factor for product cooling during distribution; | |

$T$ | High and low temperatures in the carriage; | |

${t}_{j}^{k}$ | Length of time required for the vehicle $k$ to load and unload at the distribution point $j$; | |

${\varphi}_{2}$ | The cost factor for product cooling during loading and unloading; | |

$\Delta T$ | The existence of temperature differences between the inside and outside of the carriage; | |

$Q$ | The load limit of the vehicle; | |

${q}_{i}$ | Customer demand $i$; | |

${Q}_{ij}$ | Vehicle shipment from customer $i$ to customer $j$; | |

${p}_{c}$ | Unit carbon tax price; | |

$e$ | Carbon dioxide emission factor; | |

${\lambda}_{i}$ | The actual time the delivery vehicle arrives at the customer demand point; | |

${C}_{e}$ | Waiting cost per unit time advance service; | |

${C}_{l}$ | Penalty cost per unit of time delayed service; | |

Collection variable | $[e{t}_{i},l{t}_{i}]$ | Optimal service time for the client $i$; |

$[E{T}_{i},L{T}_{i}]$ | A soft time window limit for the client $i$; | |

Decision variable | ${x}_{ij}^{k}\left\{\begin{array}{l}1,\mathrm{Distribution}k\mathrm{vehicles}\mathrm{travels}\mathrm{from}\mathrm{customer}i\mathrm{to}\mathrm{customer}j\hfill \\ 0,\mathrm{Other}\hfill \end{array}\right.$ |

Customer Number | Longitude (E) | Latitude (N) | Demand (t) | Service Time (h) | ET | et | lt | LT |
---|---|---|---|---|---|---|---|---|

0 | 108.677091 | 34.266719 | - | - | - | - | - | - |

1 | 108.834904 | 34.298973 | 0.9 | 0.36 | 123 | 168 | 192 | 224 |

2 | 108.351339 | 34.457663 | 1.2 | 0.48 | 111 | 159 | 181 | 193 |

3 | 108.659804 | 34.335292 | 0.6 | 0.24 | 24 | 57 | 92 | 114 |

4 | 108.401643 | 34.201826 | 1 | 0.4 | 15 | 36 | 54 | 121 |

5 | 108.431812 | 34.426692 | 0.5 | 0.2 | 113 | 142 | 154 | 171 |

6 | 108.686791 | 34.458481 | 1 | 0.4 | 96 | 133 | 170 | 208 |

7 | 108.534434 | 34.336947 | 0.5 | 0.2 | 50 | 78 | 96 | 113 |

8 | 108.733897 | 34.315858 | 0.7 | 0.28 | 85 | 115 | 148 | 193 |

9 | 108.810638 | 34.422681 | 0.6 | 0.24 | 12 | 45 | 89 | 121 |

10 | 108.163187 | 34.358199 | 1.3 | 0.52 | 102 | 144 | 195 | 238 |

11 | 108.613462 | 34.124683 | 1.1 | 0.44 | 23 | 69 | 194 | 114 |

12 | 108.917593 | 34.157497 | 0.6 | 0.24 | 15 | 42 | 68 | 92 |

13 | 108.411762 | 34.306202 | 0.7 | 0.28 | 18 | 33 | 50 | 68 |

14 | 108.342154 | 34.367553 | 0.7 | 0.28 | 103 | 136 | 158 | 169 |

15 | 108.194996 | 34.259948 | 0.9 | 0.36 | 46 | 87 | 137 | 162 |

16 | 108.939718 | 34.202915 | 0.8 | 0.32 | 24 | 53 | 88 | 105 |

17 | 108.833701 | 34.251392 | 0.6 | 0.24 | 124 | 149 | 183 | 207 |

18 | 108.977323 | 34.398478 | 0.8 | 0.32 | 117 | 132 | 156 | 172 |

19 | 108.601433 | 34.395234 | 0.7 | 0.28 | 52 | 78 | 95 | 112 |

20 | 108.957505 | 34.346586 | 0.5 | 0.2 | 21 | 45 | 92 | 135 |

21 | 108.453489 | 34.154947 | 0.6 | 0.24 | 18 | 26 | 35 | 42 |

22 | 108.904797 | 34.360362 | 0.7 | 0.28 | 124 | 159 | 180 | 208 |

23 | 108.760642 | 34.507643 | 0.5 | 0.2 | 16 | 32 | 68 | 135 |

24 | 108.615176 | 34.532539 | 0.7 | 0.28 | 45 | 87 | 106 | 182 |

25 | 109.021785 | 34.273477 | 0.7 | 0.28 | 42 | 93 | 149 | 181 |

26 | 108.339864 | 34.218985 | 1.3 | 0.52 | 18 | 25 | 47 | 60 |

27 | 108.234023 | 34.146337 | 0.8 | 0.32 | 21 | 36 | 59 | 113 |

28 | 108.961859 | 34.267609 | 0.6 | 0.24 | 58 | 97 | 142 | 173 |

29 | 108.023154 | 34.131234 | 0.7 | 0.28 | 54 | 72 | 103 | 124 |

30 | 108.580261 | 34.458556 | 0.5 | 0.2 | 58 | 94 | 139 | 192 |

31 | 108.726415 | 34.356136 | 1.1 | 0.44 | 21 | 32 | 48 | 64 |

32 | 108.281024 | 34.328557 | 0.6 | 0.24 | 23 | 42 | 61 | 83 |

33 | 108.079304 | 34.282961 | 1.1 | 0.44 | 26 | 47 | 68 | 107 |

34 | 108.904597 | 34.446687 | 0.7 | 0.28 | 48 | 98 | 148 | 174 |

35 | 109.010218 | 34.444346 | 1.2 | 0.48 | 26 | 63 | 91 | 142 |

36 | 108.077109 | 34.246373 | 0.5 | 0.2 | 169 | 184 | 207 | 256 |

37 | 108.136842 | 34.526286 | 0.7 | 0.28 | 108 | 121 | 147 | 163 |

38 | 108.885776 | 34.523326 | 0.6 | 0.24 | 21 | 68 | 91 | 115 |

39 | 109.010997 | 34.185556 | 0.7 | 0.28 | 18 | 25 | 59 | 96 |

40 | 109.056321 | 34.246891 | 1 | 0.4 | 76 | 98 | 135 | 164 |

41 | 109.137439 | 34.356827 | 0.6 | 0.24 | 23 | 48 | 89 | 154 |

42 | 108.718379 | 34.126482 | 0.8 | 0.32 | 113 | 143 | 165 | 201 |

43 | 108.107532 | 34.415861 | 0.9 | 0.36 | 91 | 105 | 134 | 148 |

Immediate Demand Type | Customer Number | Receiving Moment | Longitude (E) | Latitude (N) | Demand (t) | Service Time (h) | ET | et | lt | LT |
---|---|---|---|---|---|---|---|---|---|---|

0 | 44 | 3:54 | 108.613742 | 34.426692 | 0.8 | 0.32 | 84 | 125 | 153 | 201 |

0 | 45 | 4:12 | 108.709566 | 34.245249 | 0.6 | 0.24 | 149 | 172 | 196 | 256 |

1 | 22 | 5:13 | 108.904797 | 34.360362 | 0.7 | 0.28 | 35 | 35 | 50 | 50 |

1 | 18 | 5:18 | 108.977323 | 34.398478 | 0.8 | 0.32 | 137 | 137 | 148 | 148 |

Vehicle | Route | Vehicle Load (t) | Vehicle Full Load Ratio |
---|---|---|---|

1 | 0-26-4-11-42-0 | 4.2 | 84% |

2 | 0-20-41-35-34-18-22-0 | 4.5 | 90% |

3 | 0-12-39-16-40-25-28-0 | 4.4 | 88% |

4 | 0-13-32-7-3-8-17-1-0 | 4.6 | 92% |

5 | 0-33-43-37-2-0 | 3.9 | 78% |

6 | 0-31-19-5-14-10-0 | 4.3 | 86% |

7 | 0-9-38-23-24-30-6-0 | 3.9 | 78% |

8 | 0-21-27-29-15-36-0 | 3.5 | 70% |

Vehicles | Vehicle Fixed Costs | Vehicle Transportation Costs | Temperature Costs | Carbon Costs | Time Window Penalty Costs | Total Customer | Dissatisfaction |
---|---|---|---|---|---|---|---|

1 | 350 | 685.36 | 139.98 | 184.66 | 58.5 | 1417.49 | 24.54% |

2 | 350 | 871.60 | 158.95 | 259.58 | 0 | 1640.14 | 12.26% |

3 | 350 | 689.12 | 143.53 | 187.99 | 0 | 1370.64 | 16.86% |

4 | 350 | 887.68 | 162.25 | 284.09 | 166.5 | 1850.52 | 22.10% |

5 | 350 | 1123.57 | 164.61 | 283.91 | 0 | 1922.09 | 15.29% |

6 | 350 | 916.35 | 157.98 | 160.03 | 0 | 1584.36 | 19.44% |

7 | 350 | 797.08 | 140.80 | 195.84 | 0 | 1483.72 | 13.69% |

8 | 350 | 1210.74 | 162.48 | 208.09 | 91 | 2022.32 | 24.87% |

Immediate Demand Type | Customer Number | Receiving Moment | Vehicle | Distribution Cost (yuan) | Adjusted Distribution Path |
---|---|---|---|---|---|

0 | 44 | 3:54 | 7 | 1576.46 | 0-9-38-23-24-30-44-6-0 |

0 | 45 | 4:12 | 1 | 1472.39 | 0-26-4-11-42-45-0 |

1 | 22 | 5:13 | 2 | 1897.15 | 0-20-22-41-35-18-34-0 |

1 | 18 | 5:18 | 2 | 1897.15 | 0-20-22-41-35-18-34-0 |

Vehicle 1 | Vehicle 2 | Vehicle 3 | Vehicle 4 | Vehicle 5 | Vehicle 6 | Vehicle 7 | Vehicle 8 | |
---|---|---|---|---|---|---|---|---|

Total load rate of distribution vehicles under initial demand | 84% | 90% | 88% | 92% | 78% | 86% | 78% | 70% |

Total load rate of delivery vehicles under immediate customer demand | 96% | 90% | 88% | 92% | 78% | 86% | 94% | 70% |

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## Share and Cite

**MDPI and ACS Style**

Ma, Z.; Zhang, J.; Wang, H.; Gao, S. Optimization of Sustainable Bi-Objective Cold-Chain Logistics Route Considering Carbon Emissions and Customers’ Immediate Demands in China. *Sustainability* **2023**, *15*, 5946.
https://doi.org/10.3390/su15075946

**AMA Style**

Ma Z, Zhang J, Wang H, Gao S. Optimization of Sustainable Bi-Objective Cold-Chain Logistics Route Considering Carbon Emissions and Customers’ Immediate Demands in China. *Sustainability*. 2023; 15(7):5946.
https://doi.org/10.3390/su15075946

**Chicago/Turabian Style**

Ma, Zhichao, Jie Zhang, Huanhuan Wang, and Shaochan Gao. 2023. "Optimization of Sustainable Bi-Objective Cold-Chain Logistics Route Considering Carbon Emissions and Customers’ Immediate Demands in China" *Sustainability* 15, no. 7: 5946.
https://doi.org/10.3390/su15075946