Under the fierce market competition and the demand of low-carbon economy, the freshness of fresh products directly determines the degree of customer satisfaction. Cold chain logistics companies must pay attention to the freshness and carbon emissions of fresh products to obtain better service development. In the cold chain logistics path optimization problem, considering the cost, product freshness and carbon emission environmental factors at the same time, based on the cost-benefit idea, a comprehensive cold chain vehicle routing problem optimization model is proposed to minimize the unit cost of product freshness and the carbon trading mechanism for calculating the cost of carbon emissions. The improved adaptive chaotic ant colony algorithm is used to perform calculation experiments on the model, and the feasibility and effectiveness of the model are analyzed through classic examples and actual cases, which proves the feasibility of the model and the effectiveness of the algorithm. This model enriches the logistics and distribution of cold chain optimization studies, and the research results supplement the impact of carbon prices on carbon emissions, emissions and customer satisfaction. Finally, there are some practical enlightenments for the provision of business management and government services.

With the continuous improvement of people’s happiness in life, the safety and quality of food have received more and more attention from consumers [

The cold chain logistics transportation problem is essentially the Vehicle Routing Problem (VRP), which was proposed in 1959 by Dantzing et al. [

There are two main problems in the existing research on vehicle path optimization of cold chain logistics distribution: (1) For the problem of cold chain logistics path optimization, on the one hand, many scholars study vehicle path optimization under static networks. On the other hand, many scholars focused on the optimization of carbon emissions in the distribution process, and they studied how to minimize the total cost of distribution as the goal in a theoretical scenario to rationally arrange the delivery route and loading sequence of vehicles, using heuristic algorithms, precise algorithms, and meta-heuristic algorithms solve similar path optimization problems. (2) ACO (ant colony optimization) is widely used to solve the VRP due to its good robustness and parallel characteristics. However, the global search ability of ACO is poor, in the initial stage of the algorithm, it is easy to fall into the local optimum due to the lack of path pheromone. As a result, the solution of the VRP can be further optimized and improved.

Aiming at the above two problems, based on the perspectives of economic cost and environmental cost, this research constructs a cost-benefit optimal mathematical model aiming at minimizing the average freshness cost. The model not only considers the decline of freshness of fresh agricultural products over time, but also introduces the measurement function of freshness of agricultural products and the measurement function of carbon emission rate. When using the algorithm to solve this problem, chaos theory is introduced, and an improved ant colony algorithm is designed which integrates the dynamic probability selection strategy and the pheromone update strategy. The effective information recorded in the iteration is used to guide subsequent operations, and based on multiple sets of experimental cases and traditional ant colony algorithms. The group algorithm is compared to verify the solving performance of the algorithm.

A distribution center needs to deliver fresh products to different customers. Each customer’s location and needs are different. All trucks must depart from the distribution center and return to the distribution center after serving customers. In the distribution process, not only the various costs must be considered, but also the carbon emissions and the freshness of the products delivered to the customers. The design of the distribution plan is carried out under the constraints of these restrictions and objectives.

There are a certain number of refrigerated trucks in the distribution center to serve customers, and the types of refrigerated trucks, refrigerating conditions, and load limits are all the same.

Data such as the number of customers, location, demand, service time for unloading at the door, and delivery time window are known quantities.

The same customer is distributed by only one refrigerated truck. A refrigerated truck can serve multiple customers under the condition of ensuring that the load limit is not exceeded. Only one vehicle is allowed to depart and arrive at each customer point.

The maintenance of the internal temperature of each refrigerated vehicle is only related to the refrigerant and has nothing to do with fuel consumption and carbon emissions.

Each customer has a fixed delivery time window. If the delivery vehicle does not deliver within the specified time window, a certain penalty fee must be paid.

The product maintains the maximum freshness in the distribution center. The freshness of the product begins to decrease by a certain percentage at the moment of departure of the delivery vehicle.

The model [

When the vehicle k drives directly from the customer point i to the customer point j, that is, when the vehicle passes through the path (i, j),

Fixed costs generally include driver wages, vehicle maintenance costs, depreciation costs etc. and are only related to the number of vehicles used, which can be represented by

The cost of maintaining temperature refers to the refrigerant consumption in the refrigerated vehicle to keep the temperature in the compartment at a certain level. The rate of refrigerant consumption during the vehicle driving process and the waiting time is the same, which is lower than the rate of refrigerant consumption when the door is opened and unloaded. The maintenance cost can be represented by

The customer will agree on a time window (

From the literature [

The fuel consumption rate per unit distance for normal driving is

Among them, c is the oil price;

It can be seen from the literature that the freshness of a unit product during the distribution process can be represented by

Among them, T is the shelf life of the delivered product,

The objective function of the model is expressed by

The vehicle routing problem studied in this paper is an N-P hard problem, which is usually solved by a heuristic algorithm. As a heuristic algorithm, ACO has positive feedback and strong robustness, but it has shortcomings such as long search time and prone to local optimization. In this paper, the distribution cost and product loss are taken as heuristic factors, and the adaptive function is given to calculate the transition probability, and finally the chaotic system is introduced to update the pheromone. In this way, the shortcomings of the ant colony algorithm can be overcome, so that the vehicle can reduce the cost during the transportation process, ensure the freshness of the fresh products, and better achieve the optimal cost and benefit.

As an important part of transition probability, heuristic factor is an crucial factor influencing the transfer of ants from one point to another. The research problem of this paper focuses on product quality and distribution cost, so two heuristic factors are designed to make the selection of the next point of ants affected by the total cost of movement and the damage of product quality during the movement. The heuristic factorial design is shown in

Among them,

The pheromone concentration and the two heuristic factors are assigned different degrees of importance

The transition probability of the traditional ACO is easy to make the algorithm generate a local optimum. In order to solve this difficulty, this study introduces a random number

Among them,

As the number of iterations continues to increase, the pheromone concentration and the importance of the two heuristic factors also change. If

Among them,

Due to the positive feedback characteristic of the ACO, it can quickly find the approximate optimal solution, but it also makes it easier to fall into the local optimal solution and fail to jump out. The usual method is to combine the ACO with the local search algorithm. After the global solution is obtained, the optimized solution is searched locally, and the pheromone is updated according to the newly obtained optimized solution. In this way, the algorithm can move again near the optimized solution, which increases the probability that the algorithm searches for the global optimal solution. The chaotic disturbance is to use the random characteristics of the pure system to generate a pseudorandom variable within a range. Adding this random variable to the update of the pheromone can make it avoid the local optimum when looking for the optimal solution in the search process, which can improve algorithm search performance. To explore a more suitable delivery route, after all ants have gone through an iteration, the established route should be updated with pheromone. The pheromone update adopts the ant week model, and the pheromone change is the pheromone update constant divided by the total distance when the optimal goal is reached. The specific formula is shown in

Among them,

Among them,

Step 1 Initialize the parameters. The parameters mainly include customer demand, distance, time window, total number of ants, and maximum number of iterations.

Step 2 Each ant selects and sorts all customer points in turn. Under the condition that the vehicle load limit is met, the state transition probability of each ant is obtained according to the formula, and the next access node is selected in turn until all nodes are traversed.

Step 3 Analyze the existing path of the ant and find the set of transferable customer points that meet the time window constraint and the load capacity constraint.

Step 4 Calculate the transition probability of the ant moving from the current position to each point in the set of transferable customer points, and determine the calculation formula of the transition probability according to the selection of random numbers.

Step 5 Find the next point according to the transition probability until all customer points are traversed. During the traversal process, if the time window or load capacity constraint is not met, return to the starting point and start again.

Step 6 After each ant has traversed all the points, calculate the total cost of this traversal, and compare the route of the optimal ant.

Step 7 Update pheromone. Update the pheromone concentration according to the improved pheromone update strategy.

Step 8 The algorithm ends the judgment. After the number of iterations reaches the specified maximum number of iterations, the iteration is terminated and the corresponding delivery route is output.

The flow chart of the improved ant colony algorithm is shown in

In order to verify the feasibility of the model, this paper uses the classic C101 example C101 in the VRPTW database for testing. Assuming that the number of ants is 10, the maximum load of the vehicle is 200 tons, the driving speed of the vehicle is 40 km/h, the fixed cost of each refrigerated truck is 200 yuan/day, and the maintenance cost of the transportation and loading and unloading process is 5 and 12 yuan/h, the penalty costs for early and late arrivals are 5 and 10 yuan/h, respectively. The fuel consumption rate when the vehicle is empty and fully loaded are 0.18 and 0.41 l/km, respectively. It is 5.41 yuan/l, the environmental cost coefficient is 0.008 yuan/l, and the shelf life of the product is 24 h. In order to effectively balance the relationship between the algorithm effect and the convergence speed [

It can be seen from

In order to verify the universality and effectiveness of the model and algorithm in this paper, the model and algorithm are used to solve different customer distribution examples. The test parameter design is the same as the previous section. C102, C104, C106, R102, R104, R106, RC102, RC104, RC106 nine examples of computer operation test 10 times, and the best results of all examples are recorded, the data test results are shown in

Case | Number of vehicles | Total cost | Green cost | Maintenance cost | Penalty cost | Freshness cost | Freshness ratio |
---|---|---|---|---|---|---|---|

C102 | 12 | 9455 | 2148 | 2370 | 2537 | 9588 | 0.9861 |

C104 | 11 | 6811 | 1836 | 2226 | 549 | 6896 | 0.9878 |

C106 | 13 | 10162 | 2092 | 2506 | 2964 | 10327 | 0.984 |

R102 | 24 | 8352 | 2412 | 633 | 507 | 8435 | 0.9901 |

R104 | 18 | 6375 | 2061 | 505 | 209 | 6432 | 0.9911 |

R106 | 22 | 7539 | 2239 | 553 | 347 | 7613 | 0.9902 |

RC102 | 23 | 8411 | 2799 | 613 | 399 | 8516 | 0.9877 |

RC104 | 19 | 7032 | 2577 | 524 | 131 | 7112 | 0.9887 |

RC106 | 22 | 8083 | 2697 | 572 | 414 | 8180 | 0.9881 |

It can be seen from the test results that this model and algorithm can effectively solve different customer distribution examples and get their respective vehicle path planning. (1) It can be seen from

In order to further verify the practicability and effectiveness of the algorithm, this article uses examples for research and analysis. A distribution center provides distribution services to 26 customers in its vicinity. The location coordinates of the distribution center and each customer, the service time window, and the product demand and service duration of each customer are shown in

Number | Abscissa | Ordinate | Demand | Left time window | Right time window | Service hours |
---|---|---|---|---|---|---|

0 | 56 | 56 | 0 | 0 | 480 | 0 |

1 | 56 | 78 | 17 | 0 | 120 | 102 |

2 | 88 | 27 | 8 | 210 | 300 | 48 |

3 | 50 | 72 | 4 | 270 | 450 | 24 |

4 | 30 | 38 | 6 | 270 | 360 | 36 |

5 | 16 | 80 | 13 | 90 | 330 | 78 |

6 | 88 | 69 | 5 | 120 | 390 | 30 |

7 | 48 | 96 | 5 | 240 | 330 | 30 |

8 | 48 | 96 | 3 | 90 | 390 | 18 |

9 | 32 | 104 | 13 | 150 | 300 | 78 |

10 | 68 | 48 | 10 | 0 | 60 | 60 |

11 | 24 | 16 | 11 | 180 | 420 | 66 |

12 | 16 | 32 | 4 | 210 | 300 | 24 |

13 | 8 | 48 | 3 | 180 | 330 | 18 |

14 | 32 | 64 | 4 | 60 | 450 | 24 |

15 | 24 | 96 | 9 | 180 | 270 | 54 |

16 | 72 | 104 | 13 | 150 | 240 | 78 |

17 | 72 | 32 | 16 | 30 | 120 | 96 |

18 | 72 | 16 | 8 | 120 | 390 | 48 |

19 | 88 | 25 | 8 | 90 | 450 | 48 |

20 | 104 | 56 | 5 | 270 | 390 | 30 |

21 | 104 | 32 | 11 | 180 | 300 | 66 |

22 | 83 | 45 | 14 | 90 | 360 | 84 |

23 | 32 | 40 | 12 | 90 | 390 | 72 |

24 | 57 | 43 | 10 | 0 | 390 | 60 |

25 | 65 | 65 | 10 | 0 | 390 | 60 |

26 | 48 | 72 | 11 | 0 | 60 | 66 |

27 | 42 | 55 | 9 | 0 | 60 | 54 |

Assuming that the number of ants is 10, the maximum load of the vehicle is 50 tons, the driving speed of the vehicle is 40 km/h, the fixed cost of each refrigerated truck is 200 yuan/day, and the maintenance cost of the transportation and loading and unloading process is 5 and 12 yuan/h, the penalty costs for early and late arrivals are 50 and 100 yuan/h, respectively. The fuel consumption rate when the vehicle is empty and fully loaded are 0.18 l/km and 0.41 l/km, respectively. It is 5.41 yuan/l, the environmental cost coefficient is 0.008 yuan/l, and the shelf life of the product is 24 h. In order to effectively balance the relationship between the algorithm effect and the convergence speed [

Improved ACO | Traditional ACO | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

N | TC | AFC | GC | R | N | TC | AFC | GC | R | ||

1 | 7 | 3491 | 3533 | 993 | 98.81% | 9 | 4874 | 4945 | 1410 | 98.56% | |

2 | 8 | 3852 | 3901 | 1053 | 98.73% | 9 | 4571 | 4638 | 1377 | 98.56% | |

3 | 7 | 3712 | 3758 | 1017 | 98.72% | 9 | 4791 | 4857 | 1536 | 98.65% | |

4 | 7 | 3551 | 3595 | 1069 | 98.75% | 8 | 4277 | 4335 | 1353 | 98.67% | |

5 | 7 | 3277 | 3318 | 1016 | 98.77% | 9 | 4661 | 4728 | 1483 | 98.58% | |

6 | 7 | 3402 | 3444 | 1038 | 98.78% | 9 | 4817 | 4883 | 1381 | 98.64% | |

7 | 8 | 3498 | 3540 | 1053 | 98.83% | 9 | 4787 | 4855 | 1394 | 98.58% | |

8 | 7 | 3441 | 3483 | 1077 | 98.79% | 9 | 4965 | 5038 | 1422 | 98.54% |

From the experimental results, for the cold chain logistics problem with the goal of minimizing the average freshness cost, the improved ACO proposed in this paper has better operating results than the traditional ACO. (1) It can be seen from

Goal | Improved ACO | Traditional ACO |
---|---|---|

Number of vehicles | 7 | 8 |

Route planning | 0-27-14-6-19-12-23-4-0-24-10-2-18-19-0-26-8-15-9-0-25-1-7-3-20-0-5-16-0-11-22-0-17-21-0 | 0-6-15-12-0-10-19-1-25-0-27-5-2-4-24-0-26-18-7-0-22-16-8-0-21-20-3-0-17-23-11-0-9-13-14-0 |

Average freshness cost | 3318 | 4334 |

Total cost | 3277 | 4335 |

Green cost | 1016 | 1352 |

Freshness ratio | 98.77% | 98.67% |

Common vehicle path planning problems are often studied based on the total distance traveled by the vehicle. Therefore, the goal of the minimum freshness cost and the minimum total travel distance proposed in this paper are compared and analyzed. The test parameters are consistent with the parameters used in the comparison of different algorithms in the previous section. Using the example data in

Aim to minimize average freshness cost | Aim to minimize total distance | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

N | TC | AFC | GC | TD | N | TC | AFC | GC | TD | ||

1 | 7 | 3299 | 3335 | 1051 | 981 | 7 | 5701 | 5779 | 1221 | 874 | |

2 | 8 | 3636 | 3683 | 1125 | 1049 | 8 | 4970 | 5038 | 1178 | 868 | |

3 | 8 | 3658 | 3705 | 1204 | 1122 | 7 | 5042 | 5111 | 1248 | 900 | |

4 | 7 | 3438 | 3479 | 961 | 893 | 8 | 5882 | 5963 | 1200 | 872 | |

5 | 7 | 3389 | 3429 | 1101 | 1037 | 7 | 5553 | 5633 | 1157 | 823 | |

6 | 7 | 3497 | 3540 | 1015 | 942 | 7 | 3780 | 3825 | 1229 | 894 | |

7 | 7 | 3264 | 3302 | 1059 | 988 | 8 | 4623 | 4691 | 1160 | 864 | |

8 | 8 | 3781 | 3835 | 1107 | 1037 | 7 | 4929 | 4991 | 1232 | 871 |

Judging from the experimental results, the algorithm in this paper can solve the models of different targets and obtain satisfactory results. (1) It can be seen from

This paper conducts four different simulation experiments on the model by improving the ant colony algorithm, including the feasibility analysis, different customer distribution analysis, algorithm comparison analysis and different target analysis. The results of the simulation experiments show that:

The improved ant colony algorithm proposed in this paper can effectively reduce the cost of distribution, reduce the cost of carbon emissions, and reduce the use of vehicles.

The improved ant colony algorithm proposed in this paper can effectively solve the vehicle routing problem of different customer distributions of C type, R type and RC type.

The model proposed in this paper aiming at the minimum average freshness cost can effectively solve the vehicle routing problem under different objectives for fresh cold chain logistics enterprises.

With the continuous improvement of living standards, consumers’ demand for fresh products will continue to increase, and the effective way for fresh food companies to increase customer stickiness and enhance their own competitiveness is to improve the freshness of fresh products. From the perspective of environmental issues, this paper combines the minimization of enterprise operating costs and the maximization of the average freshness of delivered products, and proposes to model the cold chain logistics distribution path of fresh products with the goal of minimizing the unit freshness cost, which make companies guarantee greater product freshness at less cost. In order to better solve the model, this research improves the traditional ACO, takes the total cost and the loss of product freshness as heuristic factors, and randomizes the transition probability of ants, so that the algorithm effectively proposes a local optimum. The feasibility of the model and the effectiveness of the algorithm are verified through the classic VRPTW example. Finally, an actual case is used to compare the experimental results of different algorithms and different targets, and it is concluded that the model and target proposed in this article are superior to other models and targets.