# Location Optimization of Fresh Agricultural Products Cold Chain Distribution Center under Carbon Emission Constraints

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Carbon Emissions from Cold Chain Logistics

#### 2.2. Location for Logistics Distribution Centers

#### 2.3. Location for Cold Chain Logistics Distribution Centers

#### 2.4. Research Framework and Summary of Ideas

- Question 1: How to build the location model of fresh agricultural products cold chain distribution center on the premise of considering carbon emissions?
- Question 2: How to design an optimization algorithm to solve the constructed model?
- Question 3: How to prove the correctness of the constructed model and algorithm through the solution of a case?

## 3. Model Formulation

#### 3.1. Descriptions and Hypotheses of Location Selection

#### 3.2. Symbols and Variables

#### 3.3. Cost Analysis of the Location Selection for Cold Chain Distribution Centers

#### 3.3.1. The Penalty Cost of Freshness

_{0}, R

_{best}, R

_{worst}represent the freshness of agricultural products when transported to a demand point, the freshness expected by the demand point and the lowest level of freshness that the demand point can accept respectively. R

_{0}> R

_{best}when the refrigerated vehicle arrives at the demand point at t

_{1}, the demand point is 100% satisfied, with a corresponding potential incentive cost β

_{2}generated. R

_{worst}< R

_{0}< R

_{best}when the refrigerated vehicle arrives at the demand point at t

_{2}, the demand point is not 100% satisfied, with a corresponding penalty cost β

_{1}generated. R

_{0}< R

_{worst}when the refrigerated vehicle arrives at the demand point at t

_{3}, the demand point is not satisfied at all, with an infinite penalty cost generated. The penalty cost of freshness (CR) is calculated as shown in Equation (1).

#### 3.3.2. The Overall Carbon Emission Costs

- (1)
- The static carbon emissions of cold chain distribution centers

_{1}is shown in Equation (2).

_{2}is calculated as shown in Equation (3).

_{s}is calculated as shown in Equation (4).

- (2)
- Dynamic carbon emissions during refrigerated vehicle transportation

_{0}= a × Q

_{0}+ b, and that of fully-loaded vehicles is VP

_{max}= a × (Q

_{0}+ Q

_{max}) + b. Based on the diesel consumption of refrigerated vehicles during transportation, the amount of carbon emissions can be calculated as follows: carbon emissions = diesel consumption × the emission per unit of diesel consumption. According to the real-time carbon emission model [43], the diesel consumption of refrigerated vehicles driving per unit distance (VP) is calculated as shown in Equation (5).

#### 3.4. Model Construction

_{1}and minimum carbon emissions MinC

_{2}, as shown in Equations (8) and (9), respectively.

_{best}) and the time of the lowest level of freshness that the demand point can accept (t

_{worst}). Constraint (15) ensures the restrictions on the values of the variables.

## 4. Model Predictions

#### 4.1. DBSCAN Spatial Clustering Algorithm for Initial Solution Clustering

#### 4.1.1. Core Point Clustering

_{c}was generated by comparison with min Pts. The equations are as follows.

_{c}. All core points in set X were set X

_{c}and the set composed of non-core points was X

_{nc}.

#### 4.1.2. Border, Standard and Noise Point Clustering

_{c}, then the point is a boundary point x

_{bd}and the constituted set is set to X

_{bd}, as shown in Equation (19); if the point is smaller than the neighbourhood range of a certain core point x

_{c}then the point is a standard point x

_{st}and the set formed is set to X

_{st}, as shown in Equation (20). If a demand point does not belong to the set of core points X

_{c}, does not belong to the set of boundary points X

_{bd}, and also does not belong to the set of standard points X

_{st}, then the point is a noise point x

_{n}, as shown in Equation (21).

#### 4.2. Improved Whale Optimization Algorithm for Iterative Solution

#### 4.2.1. The Solution Process of the Basic Whale Optimization Algorithm

- (1)
- Encircling

^{j}after being influenced by the best humpback whale X

^{*}, and k represents the number of iterations. Equation (23) represents the distance between other whales and the best whale X

^{*}before the encirclement. Equation (24) represents that A and C are the iteration matrix coefficients. r

_{1}and r

_{2}are random numbers from 0 to 1. Equation (25) represents that a is an iteration parameter that decreases linearly from 2 to 0 as the number of iterations t increases. Humpback whales obtain food by controlling the |A

_{1}| vector. When |A

_{1}| ≤ 1, the whales in other positions approach the current best one.

- (2)
- Bubble-net attacking

^{*}to encircle the prey, they not only contract the encirclement but also follow a logarithmic spiral towards the prey. To synchronize the algorithmic operations of encircling the prey and swimming up the spiral, it was assumed that encircling is selected with 50% probability p and swimming in a spiral with 50% probability 1 − p. Equation (26) shows the mathematical model.

- (3)
- Spiral-shaped hunting

_{1}| > 1. At this time, other humpback whales randomly select individuals in the group to approach, which facilitates the algorithm to obtain the overall optimal solution. From this, the position iteration mechanism of the WOA algorithm under the influence of |A

_{1}| can be obtained, as shown in Figure 4.

^{rand}and the location of the whale to swim as X

^{j}. The mathematical model of the behaviour of spiral-shaped hunting is shown in Equations (27) and (28).

#### 4.2.2. Using Sort Matrices to Calculate the Overall Fitness of the Bi-objective Function

_{c}of the location selection for cold chain distribution centers was calculated, and the performance comparison sort of the sort matrices was carried out, which was further transformed into the overall fitness of the alternative locations. Assuming that the total costs of the location selection and the total carbon emissions during the warehousing and distribution process are Obj

_{1}and Obj

_{2}. Their ranking numbers are OR

_{1}and OR

_{2}in ascending order, and the values of fitness are f1 and f2, as shown in Table 3.

_{j}(i) stands for the results of comparison sort. M is the total number of alternative locations. Equation (30) represents the overall fitness of alternative locations. K is a variable within the range of 1 to 2, which is used to increase the fitness of the optimal individual.

#### 4.2.3. Adopting the Mutation-Induced Perturbation of the Cauchy Distribution

^{−1}represents the inverse cumulative distribution function of the Cauchy distribution. X

_{mn}is the nth location of the mth humpback whale between the Cauchy mutation. γ = A. p is uniformly distributed within the range of 0 to 1.

#### 4.2.4. Introducing Sine and Cosine Inertia Weights

_{1}| vector to move closer or farther away from the best humpback whales so as to realize the three stages of encircling, bubble-net attacking and spiral-shaped hunting. In other words, the WOA controls the search capability through the |A

_{1}| vector. The key iteration parameter a in the |A

_{1}| vector decreases linearly as the number of iterations increases. The law of the linear decreasing leads to a reduction in the convergence range in the early iterations that require a larger search range, while causing a slowdown in the rate of convergence in the later iterations that require a smaller search range, thus affecting the overall quality of convergence of the algorithm. This paper, based on the characteristics of sine and cosine curves, introduced non-linear sine and cosine inertia weights to the iteration parameter a. The search range was expanded by the sine inertia weights and the rate of convergence was enhanced by the cosine inertia weights, in order to improve the quality of convergence and population diversity of the algorithm [51,52,53]. The formulas of sine and cosine inertia weights are shown in Equations (33) and (34).

_{3}represents a random number in the range of 0 to 2, which is used to control the influence of the relative positions of the random humpback whales and the optimal humpback whale. The random parameter rand represents a random number in the range of 0 to 1, which is used to improve the population diversity of the algorithm. t is the current number of iterations and T is the total number of iterations, and the division of the two makes the iteration parameter a somewhat adaptive. Specifically, in the early iterations of the algorithm, the value of t/T is small and the inertia weight w is large; in the later iterations of the algorithm, t gradually converges to T, so the value of t/T is large and the inertia weight w is small. Equation (32) can be therefore improved to Equation (35).

_{1}| vector under sine and cosine inertia weights on the global search and local convergence of the hunting of the humpback whales in different iteration cycles of the one-dimensional hunting space.

^{rand}of the population. A global search is carried out before the stage of spiral-shaped hunting, reducing the blind spot of the small local convergence range of the cosine inertia weights and avoiding the situation where the potential optimal solution is missed. The dotted line represents the situation of shunting under the influence of cosine inertia weights. The target humpback whale moves in a cosine logarithmic spiral trajectory guided by the best humpback whale X*. A local convergence takes place at the late stage of spiral-shaped hunting, which compensates for the slow convergence of the global search of sine inertia weights and improves the operation efficiency of the algorithm.

#### 4.3. Solving Steps of Two-Stage Heuristic Algorithm

Algorithm 1 First stage |

Import the necessary class library files Define key variables and parameters BEGIN Click the Start button Sign () function marks all objects as unvisited The random function Random () determines an alternative point as x Assign the x attribute to visited X = visited Calculate N demand points in x field If (N>=M) { Create solution set X X. add (x) Computational heuristic information Cluster() clustering algorithm marks demand points If (still target object unvisited) { Execute random function Random() module }else { Output all initial solution sets X } }else { Re-execute the random function Random() module } END |

Algorithm 2 Second stage |

Import the necessary class library files Define key variables and parameters BEGIN According to the solution set X of the previous algorithm Calculate() calculate the overall fitness of the bi-objective function If (iteration termination condition satisfied) { Output program results } Else { The MAX() function selects the initial solution set with the highest fitness The Random() function randomly selects the corresponding probability P If (probability P<0.5) { Carry out spiral-shaped swimming Determine whether the iteration termination condition is satisfied Perform corresponding operations } Else { If (|A|<=1) { Apply the Cauchy mutation Determine whether the iteration termination condition is satisfied Perform corresponding operations } Else { Introduce the sine and cosine inertia weights Determine whether the iteration termination condition is satisfied Perform corresponding operations } } } END |

## 5. Case Description and Data Acquisition

_{ij}from the alternative location i of a cold chain distribution center to the target demand point j, this paper used the ArcGIS software to convert the latitude and longitude coordinate data into plane coordinate data, as shown in Figure 7.

_{2}). Therefore, this paper assumes that the current cost per unit of carbon emissions in Zhejiang Province is 0.03 dollar/kg·CO

_{2}. Based on relevant data, the values of other constants are assumed as shown in Table 7.

## 6. Results and Discussion

#### 6.1. Contrastive Analysis of the Case Study

#### 6.2. Sensitivity Analysis Based on the Cost per Unit of Carbon Emissions

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 5.**The solution mechanism of WOA algorithm under sin-cos inertial weight in one-dimensional space.

**Figure 7.**The Plane cartesian coordinate system based on latitude and longitude of Y enterprise’s demand points.

**Figure 8.**The effect pictures of location selection and iterative convergence curves of the THA algorithm.

**Figure 9.**The effect pictures of location selection and iterative convergence curves of the WOA algorithm.

**Figure 10.**The effect pictures of location selection and iterative convergence curves of the PSO algorithm.

Hypothetical Situations | Content |
---|---|

Supply and Demand | (1) the inventory of a single distribution center can satisfy the demand of covering demand points, and the inventory is equal to the sum of the demand of all demand points (2) the demand for fresh agricultural products at each demand point is fixed and will not fluctuate greatly in the short term |

Transportation | (1) alternative locations are equipped with sufficient refrigerated vehicles for transport, regardless of shipping batches and fixed costs of vehicles (2) refrigerated vehicles travel at a constant speed, regardless of service time window constraints and vehicles routing |

Carbon Emissions | (1) the site selection process involves static carbon emissions from distribution centers and dynamic carbon emissions from refrigerated vehicle transportation (2) carbon emissions from product decay are not considered |

Freshness | (1) the freshness of fresh agricultural products is only related to the transportation time (2) the effect of temperature change on freshness is not considered |

Parameters and Symbols | Meaning |
---|---|

n | the number of demand points of fresh agricultural products |

m | the number of alternative locations for distribution centers |

h | the number of distribution centers to be established |

f_{i} | the fixed reconstruction costs of the alternative location i for distribution centers |

q_{ij} | the quantity of products provided by i to the demand point j |

D_{j} | the quantity of products that j needs to provide |

c_{i} | the storage cost per unit of goods stored in i |

d_{ij} | the straight-line distance between i and j |

c_{o} | the fuel cost per unit distance during transportation |

λ | the cost per unit of carbon emissions |

EC_{i} | the electric energy consumed by i |

e_{1} | carbon emission factor per unit of electricity consumed |

e_{2} | carbon emission factor per unit of diesel consumed |

OP_{i} | the amount of diesel consumed in daily storage operations in i |

δ_{1} | the low calorific value of diesel |

δ_{2} | carbon content per unit calorific value of diesel |

δ_{3} | the carbon oxidation factor of diesel |

VP | the diesel consumption per unit distance travelled by a refrigerated vehicle |

Q_{0} | the weight of a refrigerated vehicle |

Q_{max} | the maximum load of a refrigerated vehicle |

β_{1} | the penalty cost for fresh agricultural products that do not meet the freshness requirements of the demand points |

β_{2} | the negative penalty cost for fresh agricultural products that meet the freshness requirements of the demand points |

R | the freshness of fresh agricultural products when delivered to the demand points |

Φ | the sensitivity coefficient of freshness to time |

Δt | the time needed for the transportation of fresh agricultural products to the point of demand |

y_{i} | a 0/1 variable. If a cold chain distribution center is established on i, y _{i} is 1, otherwise, it is 0 |

x_{ij} | a 0/1 variable. If i serves j, x_{ij} is 1, otherwise, it is 0 |

a&b | the linear parameters |

Object | Alternative | ||||
---|---|---|---|---|---|

Al(1) | Al(2) | Al(3) | ⋯ | Al(M) | |

Obj1 | OR1(1) | OR1(2) | OR1(3) | ⋯ | OR1(M) |

Obj2 | OR2(1) | OR2(2) | OR2(3) | ⋯ | OR2(M) |

**Table 4.**Y enterprise’s demand points for fresh agricultural products and the corresponding demands.

Demand Points | Longitude and Latitude Coordinates | Demanded Quantity/t | Demand Points | Longitude and Latitude Coordinates | Demanded Quantity/t |
---|---|---|---|---|---|

1 Yuhang District | (120.30, 30.42) | 82 | 19 Anji County | (119.68, 30.63) | 39 |

2 Fuyang District | (119.95, 30.05) | 53 | 20 Pinghu City | (121.02, 30.70) | 77 |

3 Linan District | (119.72, 30.23) | 38 | 21 Haining City | (120.68, 30.53) | 36 |

4 Linping District | (120.30, 30.43) | 80 | 22 Tongxiang City | (120.57, 30.63) | 87 |

5 Qiantang District | (120.22, 30.26) | 59 | 23 Lanxi City | (119.45, 29.22) | 57 |

6 Jiande City | (119.28, 29.48) | 46 | 24 YiwuCity | (120.07, 29.30) | 61 |

7 Tonglu County | (119.67, 29.80) | 60 | 25 Wuyi County | (119.82, 28.90) | 93 |

8 Beilun District | (121.85, 29.93) | 70 | 26 Pujiang County | (119.88, 29.45) | 84 |

9 Zhenhai District | (121.72, 29.95) | 75 | 27 Pan’an County | (120.43, 29.05) | 88 |

10 Fenghua District | (121.40, 29.65) | 40 | 28 Huangyan District | (121.27, 28.65) | 76 |

11 Yuyao City | (121.15, 30.03) | 81 | 29 LInhai City | (121.12, 28.85) | 59 |

12 Cixi City | (121.23, 30.17) | 39 | 30 WenLingCity | (121.37, 28.37) | 30 |

13 Ninghai County | (121.43, 29.28) | 82 | 31 Sanmen County | (121.38, 29.12) | 57 |

14 Keqiao District | (120.50, 30.08) | 58 | 32 Tiantai County | (121.03, 29.13) | 32 |

15 Shangyu District | (120.87, 30.03) | 84 | 33 Xianju County | (120.73, 28.87) | 91 |

16 Zhuji City | (120.23, 29.72) | 39 | 34 Jinyun County | (120.07, 28.65) | 83 |

17 Nanxun City | (120.43, 30.88) | 39 | 35 Suichang County | (119.27, 28.60) | 70 |

18 Deqing County | (119.97, 30.53) | 91 | 36 Songyang County | (119.48, 28.45) | 48 |

Alternative Location | Storage Cost per Unit of Goods ci/Dollar | Fixed Reconstruction Costs fi/10,000 Dollar | Electric Energy Consumption ECi/kw×h | Diesel Consumption OPi/kg |
---|---|---|---|---|

1 Yuhang District | 137.22 | 5.40 | 2324 | 28 |

5 Qiantang District | 145.46 | 5.70 | 2033 | 36 |

7 Tonglu County | 110.97 | 7.50 | 2204 | 32 |

10 Fenghua District | 134.22 | 4.05 | 2341 | 34 |

11 Yuyao City | 130.47 | 3.15 | 2063 | 34 |

22 Tongxiang City | 138.72 | 6.15 | 2191 | 21 |

26 Pujiang County | 122.97 | 6.90 | 2304 | 35 |

29 LInhai City | 117.72 | 5.25 | 2100 | 21 |

32 Tiantai County | 127.47 | 4.65 | 2075 | 30 |

34 Jinyun County | 119.22 | 6.15 | 2394 | 39 |

Variable | Value | Unit |
---|---|---|

the fuel cost per unit distance during transportation co | 0.27 | dollar/km |

the speed of the vehicle v | 40 | km·h^{−1} |

the diesel consumption of empty vehicles VP0 | 0.14 | kg·km^{−1} |

the diesel consumption of fully-loaded vehicles VPmax | 0.16 | kg·km^{−1} |

the weight of a refrigerated vehicle Q0 | 32,000 | kg |

the maximum load of a refrigerated vehicle Qmax | 50,000 | kg |

Constant | Value | Unit |
---|---|---|

carbon emission factor per unit of electricity consumed e_{1} | 0.5810 | tCO_{2}·MW·h^{−1} |

carbon emission factor per unit of diesel consumed e_{2} | 3.0959 | kg-CO_{2}·kg^{−1} |

the low calorific value of diesel δ_{1} | 42652 | kJ·kg^{−1} |

carbon content per unit calorific value of diesel δ_{2} | 20.20 | t-C·TJ^{−1} |

the carbon oxidation factor of diesel δ_{3} | 0.98 | unitless |

the cost per unit of carbon emissions λ | 0.03 | dollar/kg·CO_{2} |

the penalty cost when the freshness requirements are not met β_{1} | 119.97 | dollar |

the negative penalty cost when the freshness requirements are met β_{2} | 119.97 | dollar |

the sensitivity coefficient of freshness to time φ | 1.60 | unitless |

Algorithm | THA | WOA | PSO |
---|---|---|---|

the location of the cold chain distribution center | (1, 11, 22, 26, 29, 34) | (1, 5, 10, 26, 29, 34) | (5, 7, 11, 22, 29, 34) |

storage cost/dollar | 139,086.58 | 147,940.42 | 153,955.45 |

transport costs/dollar | 33,929.22 | 38,137.20 | 42,663.09 |

penalty costs of freshness/dollar | 10,805.16 | 12,938.69 | 14,041.38 |

overall carbon emission/kg | 154,921 | 172,573 | 180,400 |

overall carbon emission costs/dollar | 4414.17 | 4917.15 | 5140.15 |

total costs of the location selection/dollar | 188,235.14 | 203,933.46 | 215,800.07 |

the number of iterations | 32 | 57 | 78 |

operation time/second | 17.4 | 35.2 | 48.6 |

the Cost per Unit of Carbon Emissions λ/(Dollar/kg) | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 |
---|---|---|---|---|---|

overall carbon emission costs/dollar | 4066.11 | 4414.17 | 4622.77 | 5420.58 | 5776.74 |

the total costs of location selection/dollar | 183,987.13 | 188,235.14 | 183,944.84 | 188,871.58 | 189,597.71 |

the difference in the total costs of location selection/dollar | −4248.01 | 0 | 4290.30 | 636.44 | 1362.57 |

the proportion of the overall carbon emission costs in the total costs | 2.21% | 2.35% | 2.51% | 2.87% | 3.05% |

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## Share and Cite

**MDPI and ACS Style**

Wang, H.; Ran, H.; Dang, X.
Location Optimization of Fresh Agricultural Products Cold Chain Distribution Center under Carbon Emission Constraints. *Sustainability* **2022**, *14*, 6726.
https://doi.org/10.3390/su14116726

**AMA Style**

Wang H, Ran H, Dang X.
Location Optimization of Fresh Agricultural Products Cold Chain Distribution Center under Carbon Emission Constraints. *Sustainability*. 2022; 14(11):6726.
https://doi.org/10.3390/su14116726

**Chicago/Turabian Style**

Wang, Hongzhi, Haojie Ran, and Xiaohong Dang.
2022. "Location Optimization of Fresh Agricultural Products Cold Chain Distribution Center under Carbon Emission Constraints" *Sustainability* 14, no. 11: 6726.
https://doi.org/10.3390/su14116726