Optimization of cold chain distribution path of fresh agricultural products under carbon tax mechanism: A case study in China

Abstract

According to the problem of large amount of carbon emissions during the cold chain distribution process, a cold chain distribution route optimization method for fresh agricultural products under the carbon tax mechanism was proposed. Firstly, with the goal of minimizing carbon emission cost and comprehensive cost, quantitative analysis of carbon tax mechanism is introduced, considering the demand quantity, demand time and unloading time constraints, a mathematical model of the problem is established. In addition, an improved quantum bacterial foraging optimization algorithm is put forward, which uses the bacterial optimization algorithm information update strategy to maintain group memory, and uses the carbon tax cost as the decision variable of the improved algorithm. Through experimental simulation, comparative analysis of the shortest distribution path, uninitialized pheromone bacterial foraging optimization algorithm and quantum bacterial foraging optimization algorithm on the last selected study model, the method proposed in this thesis can effectively optimize the distribution path, reduce carbon tax cost and comprehensive cost.

Keywords

Vehicle routing problem carbon tax quantum bacterial foraging optimization algorithm cold chain logistics

1 Introduction

Nowadays, reducing carbon emissions and lowering integrated costs have become hot research topics in cold chain logistics distribution [1]. In global carbon emissions statistics, transportation carbon emissions account for 14%, and road carbon emissions account for 70% of transportation carbon emissions [2]. In the delivery of refrigerated trucks will consume a lot of energy and a huge carbon emission, therefore, reasonable planning of cold chain logistics distribution paths to reduce carbon emissions and comprehensive costs is urgently needed to be resolved. VRP (Vehicle routing problem, VRP) initially planned the route based on the delivery distance [3]. On this basis, considering the impact of the delivery time on the route [4], the TVRP (Time vehicle routing problem, TVRP) model was established [5]. Due to the characteristics of transportation products, it is necessary to establish a JIT model [6]. JIT (Just in Time, JIT) delivery model needs to consider the customer point of working time to affect the cost of, proposed a two-time work aims model [7]. Uncertainty of demand and delivery time at the distribution point will affect the results of experiment, and the performance of the model and algorithm solution needs to be comprehensively considered [8 –10]. Secondly, the path length uncertainty will demand and delivery time and cost of the distribution points of impact [11]. In the actual transportation process, traffic congestion will increase the distribution cost and path length. For this, a multi-channel network distribution model is proposed [12]. At the same time, it is believed that disturbance events such as vehicle failures will affect the distribution plan [13, 14]. However, the refrigeration time of refrigerated trucks and energy consumption during transportation will generate a lot of carbon emissions [15], and a multi-objective optimization model for carbon emissions has been proposed [16]. Finally, by analyzing different situations of traffic congestion, a cold chain delivery model combined with time-varying networks is proposed [17]. Meanwhile, Rao Weizhen build low-carbon collaboration around the vehicle routing problem model, a two-stage algorithm for solving [18]. Ma Qizhuo proposed an optimal VRP model for urban distribution [19]. Rao Weizhen analyzed the impact of road gradient changes on carbon emissions and established a low-carbon distribution model [20]. Chen Zhi proposed a problem model considering the impact of different delivery times and driving sections on carbon emissions, and verified the effectiveness of the model [21].

Conclusively, many scholars have conducted in-depth research on different aspects of low-carbon distribution, but there are limitations. The main manifestations are as follows: (1) Existing models only consider the impact of distribution distance, capacity and time cost on carbon emissions, but carbon tax mechanisms are rarely introduced [22]. (2) Existing models have little consideration on the impact of the unloading time of refrigeration equipment and the transportation cost of different demand times on carbon emissions [23]. According to the above analysis, this article considers the impact of unloading time and different demand times on carbon emissions, introduces a carbon tax mechanism, and establishes a mathematical model of minimum comprehensive cost. Then, using the carbon tax cost as the decision variable of the algorithm, an improved quantum bacterial foraging optimization algorithm (QBFO) is put forward to solve the model. Finally, the effectiveness of the proposed model and algorithm is verified by local optimization and comparison of several algorithms.

The full text is divided into six parts, this part is the introduction, the second part is to describe the research problems and hypotheses. The third part establishes the distribution logistics model under the carbon tax mechanism. The fourth part designs an improved quantum bacterial foraging optimization algorithm for solving the model. The fifth part is to verify the validity of the algorithm for solving the model (simulation experiment of solving the model). Finally, the conclusion and prospect of the research problem are summarized.

2 Problem hypothesis and description

To issue model the following assumptions: (1) Only one distribution center. (2) The same K refrigerated trucks load capacity, and the maximum load capacity of the distribution process is not available. (3) The location of the delivery point, demand, demand time, and unloading time are known. (4) K vehicles are driving at a constant speed. (5) Each delivery point only by a delivery of refrigerated trucks, and each refrigerated truck can serve multiple delivery points.

Therefore, the cold chain logistics distribution problem refers to the analysis of the carbon emission and the degree of cargo loss of refrigerated trucks in the conventional VRP problem, and the establishment of corresponding solution strategies. The problems studied are described as follows: One delivery center transport fresh agricultural product to N delivery points. The delivery center has K refrigerated trucks, and the K vehicle models have the same fuel type and traveling speed. Each refrigerated truck serves customers which need to meet demand time, vehicle capacity and customer demand. During the transportation of these vehicles, the path selection should be rationally planned to achieve the lowest cost.

3 Mathematical model of low carbon path optimization problem

3.1 Symbol and parameter description

N: Number of delivery points;

K: Number of refrigerated vehicles;

q_i: Customer demand;

C₁: Fixed cost coefficient of refrigerated truck;

C₂: Refrigerated trucks transport cost factor;

d_ij: Customer point (i, j) transport distances;

Q_ij: Customer capacity (i, j) Vehicle capacity;

Q: The maximum capacity of the refrigerated truck;

Q_m: Product quality remaining after vehicle leaves customer point;

p₁: Unit fuel price during transportation;

p₂: Unit price of fuel oil;

P: Unit price of fresh produce;

$t_{i}^{k}$ : Time of transport vehicle to customer point i;

$t_{0}^{k}$ : Transport vehicle departure time;

T_i: Unloading time;

ω: Carbon tax factor; $\begin{matrix} x_{ijk} = \\ {\begin{matrix} 1, & If vechicle K goes from customer i to customer j \\ 0, & Else \end{matrix}; \end{matrix}$ $\begin{matrix} y_{ik} = \\ {\begin{matrix} 1, & If vechicle K symbol customer i demand \\ 0, & Else \end{matrix}; \end{matrix}$

3.2 Symbol and parameter description

This paper analyzes the impact of comprehensive vehicle transportation costs, carbon tax costs, and time penalty costs on the optimization of cold chain logistics distribution [24]. A cold chain logistics distribution optimization problem model with the minimum comprehensive cost as the goal is established as follows [25]: $\begin{matrix} min Z = Z_{1} + Z_{2} + Z_{3} = C_{1} \sum_{j = 1}^{N} \sum_{k = 1}^{N} x_{ojk} \\ + C_{2} \sum_{k = 1}^{N} \sum_{i = 0}^{N} \sum_{j = 0}^{N} d_{ij} x_{ijk} + ω \sum_{i = 0}^{N} \sum_{j = 0}^{N} {FC}_{ij} \\ + ω (C_{11} + C_{12}) + ɛ_{1} \sum_{j = 1}^{N} max {E_{j} - t_{j}, 0} \\ + ɛ_{2} \sum_{j = 1}^{N} max {t_{j} - L_{j}, 0} \end{matrix}$ (1) The corresponding constraints are as follows: $\sum_{i = 1}^{N} q_{i} y_{ik} \leq Q, \forall K$ (2) $\sum_{k = 1}^{K} y_{ik} = 1, \forall I$ (3) $\sum_{i = 0}^{N} x_{ijk} = y_{ik}, \forall j, K$ (4) $\sum_{j = 0}^{N} x_{ijk} = y_{ik}, \forall j, K$ (5) $\sum_{i, j \in S \times S} x_{ijk} \leq | S | - 1, S \subseteq {1, 2 \dots N}$ (6) $t_{j} = t_{i} + t_{ij}$ (7)

Equation (2) express transportation vehicles in transit cannot exceed the maximum capacity. Equation (3) indicates that every customer point served by only one transportation vehicle. Equations (4) and (5) indicate that the vehicle is allowed to depart and arrive only once for any customer. Equation (6) represents the elimination of the sub-loop conditions. Equation (7) indicates that vehicle transportation is continuous during the distribution process.

3.3 Cold chain logistics distribution cost analysis

In Equation (1), $Z_{1} = C_{1} \sum_{j = 1}^{N} \sum_{k = 1}^{N} x_{0 ik} + C_{2} \sum_{k = 1}^{N} \sum_{i = 0}^{N} \sum_{j = 0}^{N} d_{i, j} x_{ijk}$ represents the comprehensive transportation Vehicle cost, which is composed of transportation costs and fixed costs of vehicle the vehicle. $C_{1} \sum_{j = 1}^{N} \sum_{k = 1}^{N} x_{0 jk}$ stands for vehicle fixed cost, which is set by the enterprise. $C_{2} \sum_{k = 1}^{N} \sum_{i = 0}^{N} \sum_{j = 0}^{N} d_{i, j} x_{ijk}$ represents the transportation cost of the vehicle, and usually has a linear relationship with the distribution distance in the distribution process.

The problem studied in this article is fresh produce. Considering the impact of product consumption on transportation refrigeration and unloading refrigeration costs, a carbon tax coefficient ω was introduced to quantitatively analyze carbon emissions. In Equation (1), the carbon tax cost Z₂ is as follow: $Z_{2} = ω \sum_{i = 0}^{N} \sum_{j = 0}^{N} {FC}_{ij} + ω C_{11} + ω C_{12}$ (8)

This article introduces the method of calculating carbon emission costs [26]. ρ₀ is the oil consumption per unit distance with zero load capacity, and ρ^* is the oil consumption per unit with Maximum capacity. In Equation (8), when the vehicle capacity is Q_ij, the carbon emission cost FC_ij of the customer node (i, j) is as follows: ${FC}_{ij} = p_{1} \cdot [ρ_{0} + \frac{ρ^{*} - ρ_{0}}{Q} Q_{ij}] \cdot d_{ij}$ (9)

This paper introduces the freshness decay function of fresh produce [27]. ∂₁ is the fresh attenuation coefficient of the product during transportation, ∂₂ is the fresh attenuation coefficient of the product during unloading, and ∂₁ < ∂₂ [28]. $C_{11} = \sum_{k = 1}^{K} \sum_{i = 0}^{N} y_{ik} {Pq}_{i} (1 - e^{- \partial_{1} (t_{i}^{k} - t_{o}^{k})})$ represents the cost of transportation refrigeration, and $C_{12} = \sum_{k = 1}^{K} \sum_{i = 0}^{N} y_{ik} {PQ}_{m} (1 - e^{- \partial_{2} T_{i}})$ represents the cost of unloading refrigeration [29].

This paper considers the time demand window (E_j, L_j), which indicates the time range of the earliest and latest time points when the customer can accept the transportation vehicle. ɛ₁ is the time penalty coefficient for customers who arrive early, and ɛ₂ is the time penalty coefficient for customers who arrive late. In Equation (1), the time penalty cost Z₃ is as follows: $\begin{matrix} Z_{3} = ɛ_{1} \sum_{j = 1}^{N} max {E_{j} - t_{j}, 0} \\ + ɛ_{2} \sum_{j = 1}^{N} max {t_{j} - L_{j}, 0} \end{matrix}$ (10)

4 Improved quantum bacteria foraging algorithm

4.1 Common BFO

The common bacteria foraging optimization algorithm (BFO) [16] is a kind of algorithm based on global random search, and its main operations include chemotaxis, Reproduction and Elimination. The chemotaxis is the core of BFO, including Tumbling and Swimming. When the bacterial individual is to search nutrients, it will turn to search better fitness value until it reaches the maximum number of chemotaxis or meets worse solutions. Then a half of individual with weak ability of foraging will be eliminated according to fitness value of all individuals in a cycle, meanwhile, the other half ones will be replicated to keep the number of bacteria. Elimination is to create new bacteria individuals to keep the total number of bacteria, due to some individual may die in the searching process, which is conductive for chemotax is to jump out of the local optimization. If the elimination reaches enough iteration, the algorithm will end.

4.2 Improved QBFO

It is known that the short step results in the lack of effective information sharing among individuals during the evolution process, which is not conductive to the diversity of the population. If the step is too short, the possibility of premature convergence will be highly, otherwise, the convergence will reduce too greatly to obtain the optimal solution [19]. Considering the quantum theory can make the individual appear in any position of the whole feasible search space with strong global search performance and population randomness [30], the QBFO is proposed in this paper.

The state and the position of the individual bacteria are uncertain in the quantum space, and they are determined by wave function of ψ (Y, t). The probability density function of the individual position is represented as |ψ|². The attractive potential based on the Delta potential well model is established on each dimension of the attractor. The potential energy function can be expressed as follow: $V (Y) = - γ δ (Y)$

Where, Y = x_id - P_d is the distance between the individual position of x_id and the attractor. It is introduced into Schrodinger (Equation 11) to obtain ψ (Y, t) (Equation 12) and Q (Y) (Equation 13) in each dimension, in which L represents the feature length of Delta. $jh \frac{\partial}{\partial t} ψ (Y, t) = [- \frac{h^{2}}{2 m} \nabla^{2} + V (Y)] ψ (Y, t)$ (11) $ψ (Y) = \frac{1}{\sqrt{L}} e^{- | Y | / - L}$ (12) $Q (Y) = | ψ (Y) |^{2} = | ψ (x_{id} - P_{d}) |^{2} = \frac{1}{L} e^{- 2 | x_{id} - P_{d} | / - L}$ (13)

The motion of the individual in the potential field follows the above |ψ|², and its position is uncertain. But in the practical application, the individual bacteria must have a certain position in any time, so the individual motion equation will be got through the Monte Carlo simulation in this paper. Take the random number of u in (0, 1), and u = e^{-2|x_id-P_d|/-L}, then the position update equation of the d dimension variable of individual i is shown in Equation 14: $x_{id} = P_{d} \pm \frac{L}{2} ln (1 / u), u \sim U (0, 1)$ (14) $L = 2 β \cdot | mbest - x_{id} (t) |$ (15)

In Equation 15, β is contraction expansion coefficient, and β <1.782 is to ensure the convergence of the algorithm [31]. The method is to change β₁ into β₂ linearly following the evolutionary algebra (Equation 16), and mbest is the average value of the best position vector in the population (shown in Equation 17). $β = \frac{(β_{1} - β_{2}) \times (MAXIER - t)}{MAXIER} + β_{2}$ (16) $\begin{matrix} mbest = \sum_{i = 1}^{M} P_{i} / M = [\sum_{i = 1}^{M} P_{i 1} / M, \sum_{i = 1}^{M} P_{i 2} / M, \\ \dots, \sum_{i = 1}^{M} P_{iD} / M]^{T} \end{matrix}$ (17)

Considering the disadvantages of the fixed step, a dynamic indentation control strategy is proposed here to expand the search space under the premise of the convergence.

The implementation steps of QBFO are as follows:

Initialize the parameters. Including the number of individual bacteria of s, migration times of N_ed, reproductive times of N_re, chemotaxis times of N_c, swimming times of N_s and migration probability of P_ed.

Initialize population. Generate s individual bacterial vector of x_i randomly in the solution space.

Calculate the fitness function J of each individual bacteria.

Start to cycle. Transfer cycle l = 1:N_ed; reproductive cycle k = 1:N_re; chemotaxis cycle j = 1:N_c.

Start to chemotaxis. The following operation is performed for each bacteria i:

Turning: generate a random vector of Δ ∈ Rⁿ to adjust the direction, and each element in vector Δ is a random number in [–1, 1]. Update the position of the individual bacterial x_id (d = 1, 2, …, D), and the rest D-1 variables remain unchanged. $x_{id} (j + 1, k, l) = x_{id} (j, k, l) + C (i, j) φ (i)$ (18) $C (i, 0) = x_max_{d} - x_min_{d}$ (19) $φ (i) = \frac{Δ (i)}{\sqrt{Δ^{T} (i) Δ (i)}}$ (20) Where, C(i,j) represents the step size of the forward swimming, φ (i) represents the random direction after rotation.

Swimming: evaluate the fitness of x_i (j + 1, k, l), if the fitness is superior to x_i (j, k, l), x_i (j, k, l) will be replaced with x_i (j + 1, k, l) and swim in accordance with the direction of the move until the fitness value is no longer improve or reach the maximum number of steps.

Make d = d+1, if d = D, then go to step 5(d), otherwise go to step 5(a) to continue to operate the next variable.

Make j = j+1, and change the swimming step of individual bacteria according to the dynamic indentation strategy in Equation 21, where A is dynamic indentation coefficient. $C (i, j + 1) = A \cdot C (i, j)$ (21)

Reproduction based on quantum behavior. After a complete chemotaxis cycle, the current individual best position and the global optimal position are to update. Calculate the average best position mbest of the population according to Equation 17 and update its position according to Equation 14.

Migration. Sort all the bacteria according to the energy, and migrate the bacteria (s, Ped) whose fitness is low according to random initialization.

Judge whether the cycle is complete.

The flow chart of the Improved Quantum Bacterial Optimization Algorithm (QBFO) is shown in Fig. 1.

Fig.1

Flow chart of QBFO.

5 Experimental solution and analysis

5.1 Experimental parameters

This paper selects literature data and 13 supermarket stores with centralized logistics distribution as service points [15]. The refrigerated transport truck has a maximum load of 10 tons, and the unit price of fresh vegetables is 3,500 yuan/ton. Transportation vehicles are delivered from the transportation center at 5 am. The fixed transportation cost of each refrigerated truck is 80 yuan, the fuel type is diesel, and the uniform speed is 45 km/h. The fuel consumption per unit of refrigerated transport truck is 17.5 l/km, and the fuel consumption per unit is 22.5 l/100 km. The unit cooling cost per unit of time for vehicle transportation is 2 yuan/h, the unit cooling cost per unit of unloading is 6 yuan/h, the carbon emission is 2.5 kg/l, and the carbon tax cost is 142.63 yuan/ton. The number of the transportation center is 0, and the number of each supermarket customer point is 1,2,3...12,13. The detailed demand information of the supermarket customer points is shown in Table 1.

Table 1
Supermarket customer point detailed demand information

Number Customer point coordinates (KM) Customer demand (T) Demand Time Unloading time (min)

0 (75,95) / / /

1 (56,136) 2.5 (6 : 30 - 9 : 30) 15

2 (28,112) 1.5 (5 : 30 - 9 : 30) 12

3 (41,38) 3.3 (6 : 30 - 10 : 00) 23

4 (50,98) 6.0 (6 : 30 – 9 : 30) 30

5 (45,132) 3.0 (6 : 30 – 10 : 00) 20

6 (89,146) 2.5 (7 : 00 – 9 : 30) 18

7 (82,77) 4.5 (5 : 30 – 10 : 00) 24

8 (91,121) 4.6 (6 : 00 – 9 : 30) 28

9 (97,179) 6.2 (6 : 30 – 9 : 30) 33

10 (46,158) 6.1 (6 : 30 – 10 : 00) 31

11 (23,51) 3.4 (7 : 00 – 10 : 00) 21

12 (105,36) 5.0 (6 : 00 – 10 : 30) 27

13 (124,92) 5.1 (5 : 30 – 10 : 00) 26

Number	Customer point coordinates (KM)	Customer demand (T)	Demand Time	Unloading time (min)
0	(75,95)	/	/	/
1	(56,136)	2.5	(6 : 30 - 9 : 30)	15
2	(28,112)	1.5	(5 : 30 - 9 : 30)	12
3	(41,38)	3.3	(6 : 30 - 10 : 00)	23
4	(50,98)	6.0	(6 : 30 – 9 : 30)	30
5	(45,132)	3.0	(6 : 30 – 10 : 00)	20
6	(89,146)	2.5	(7 : 00 – 9 : 30)	18
7	(82,77)	4.5	(5 : 30 – 10 : 00)	24
8	(91,121)	4.6	(6 : 00 – 9 : 30)	28
9	(97,179)	6.2	(6 : 30 – 9 : 30)	33
10	(46,158)	6.1	(6 : 30 – 10 : 00)	31
11	(23,51)	3.4	(7 : 00 – 10 : 00)	21
12	(105,36)	5.0	(6 : 00 – 10 : 30)	27
13	(124,92)	5.1	(5 : 30 – 10 : 00)	26

5.2 Comparison and analysis of carbon tax costs

According to the algorithm and case data, seeking answers to the cold chain logistics distribution model. The number of population is 40, the coefficient of contraction-expansion=1,=0.5, the migration probability is 0.25, the number of migration = 3, the number of reproduction = 5, the number of chemotaxis = 20, the number of swimming = 4 and the coefficient of dynamic indentation A = 0.7. Then the total number of chemotaxis iteration MAXIER = 300 and the maximum number of iterations QBFO is 150 generations. The test running environment of this article is: MATLAB R2010a was used to run the computer with 2.8 GHz Intel Core I5 CPU and 4GB RAM to generate the initial schedule. Considering the lowest carbon tax cost and the shortest distribution route, the optimal distribution route for 10 transportation runs is shown in Fig. 2:

Fig.2

The lowest carbon tax and the shortest distribution route.

The transportation strategy with the lowest carbon tax cost is: 5 vehicles departing from the transportation center, and the first vehicle path is 0-1-10-5-4-0. The second vehicle path is 0-7-12-13-0. The third vehicle path is 0-11-3-0. The fourth car has a path of 0-9-8-0, and the fifth car has a path of 0-2-6-0. The shortest path under this strategy is 1989KM, the comprehensive cost is 4456 yuan, and the carbon tax cost is 4009 yuan.

The shortest transportation strategy for the distribution route is: 4 vehicles from the transportation center, and the first vehicle route is 0-1-10-5-4-0. The second vehicle path is 0-2-11-3-0. The third vehicle path is 0-6-8-9-0, and the fourth vehicle path is 0-13-7-12-0. The shortest path under this strategy is 1896 km, the comprehensive cost is 4537 yuan, and the carbon tax cost is 4186 yuan.

The results of two different experiments are shown in Table 2. From the analysis in Table 2, it can be known that the shortest distribution path may not necessarily reduce the carbon tax cost and comprehensive cost. Experimental results show that although the distribution path under the carbon tax model is increased by about 0.49%, the overall cost is reduced by 1.7% and the carbon tax cost is decreased by 4.2%, which verifies the effectiveness of the model.

Table 2

Comparison of carbon tax cost results in different situations

	Delivery distance (km)	Comprehensive cost (yuan)	Carbon tax cost (yuan)
Lowest cost	1989	4456	4009
Shortest path	1896	4537	4186

5.3 Comparison of different algorithms

In order to test the performance of QBFO and its improved strategy for solving low carbon cold chain distribution, and to compare with the performance of the popular classical quantum, simulation experiment is run in this section. On the basis of the above testing, the classical Solomon [32] examples are used to compare QBFO with other variations of algorithm. There are 6 kinds of examples in Solomon, and one standard problem from each kind of examples is selected and executed for 20 times using QBFO. The efficiency will be verified through the comparison with existing QPSO (Quantum particle swarm optimization) [33], QACO (Quantum ant colony optimization) [24], IBFO (Improved bacterial optimization) [18] and BFO.

The maximum iteration is 100 and the convergence curve of the optimal solution of the five algorithms can be shown in Fig. 3. It can be seen from Fig. 3 that the convergence speed of the proposed QBFO is faster than the other four algorithms obviously, and it has also better global optimization capability.

Fig.3

The fitness convergence curve of 5 algorithms.

Moreover, in order to further proof the validity of the algorithm, the above experimental parameters were selected, and comparative analysis of the proposed QBFO with QACO and BFO. Besides, the experiment was run randomly for 20 times. The combined cost and carbon tax cost results of different algorithms are shown in Fig. 4.

Fig.4

Comparison of comprehensive cost and carbon tax cost.

Derived from the experimental results in Fig. 4, for the problem of cold chain logistics distribution path optimization under the carbon tax mechanism studied, the experimental results of its algorithm are compared with the basic BFO in this paper: the minimum comprehensive cost is reduced by about 3.4%, and the carbon tax cost is reduced by about 8.3%. Similarly, compared with the QACO, the minimum comprehensive cost is reduced by about 2.7%, and the carbon tax cost is reduced by about 4.5%.

6 Conclusion and prospect

6.1 Conclusion

(1) Consider carbon tax costs. By comparing and analyzing the shortest distribution path and the smallest distribution cost, the experimental results show that the shortest distribution path cannot effectively reduce the carbon tax cost and the comprehensive cost.

(2) Local optimization analysis. Through comparative analysis of different situations of initializing pheromone, the experiment results show that the proposed QBFO makes the algorithm jump out of the problem of local optimization. In addition, the carbon tax cost and comprehensive cost during transportation are also reduced. Choosing different values for the algorithm’s data for analysis has little effect on the experiment results, verifying the effectiveness and stability of the proposed algorithm.

(3) From the method based on mathematical model and experimental data, compare the proposed QBFO, QACQ and basic BFO, it proves that the method proposed in this study can effectively decrease the carbon tax cost and comprehensive cost in the cold chain transportation process, which further shows that the model and algorithm proposed are effective.

6.2 Future directions

Except the methods used in the paper, some of the most representative computational intelligence algorithms can be used to solve the problems, like monarch butterfly optimization (MBO) [34], earthworm optimization algorithm (EWA) [24], elephant herding optimization (EHO) [35], moth search algorithm(MSO) [36].

Based on this article, additionally, the occurrence of uncertain interference events such as traffic congestion and vehicle failure during vehicle transportation will affect the overall cost and carbon tax cost. Therefore, how to reduce the impact of uncertain interference events on costs is the direction of this paper’s next research.

Declaration of competing interest

None. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Footnotes

Acknowledgments

Foundation items-Project supported by Liaoning Provincial Natural Science Foundation (20180550499, 2019-ZD-0109), the Fundamental Research Funds for the Central Universities (110084) and Education Department Project of Liaoning Province (JDL2019022, L2020006).

References

Chuanmin

Shuai

and Yukun

Zhang

, Difference analysis of chinese consumers willingness to pay for low-carbon products–scenario experimental data based on carbon labels, China Soft Science 7 (2013), 61–70.

Piecyk

M.I.

and Mckinnon

A.C.

, Forecasting the carbon foot-print of road freight transport in, International Journal of Production Economics 128(1) (2010), 31–42.

Solomon

M.M.

and Desrosiers

, Time window constraint routing and scheduling problems, Transportation Science 22(1) (1988), 1–13.

Dantzing

G.B.

and Ramser

J.H.

, The truck dispatching problem, Management Science 6(1) (1959), 80–91.

Jabali

, Leus

, Van Woensel

, et al., Self-imposed time windows in vehicle routing problems, OR Spectrum 37(2) (2015), 331–352.

Haining

and Xing

, Research on material distribution path optimization based on improved ant colony algorithm, Machinery Design and Manufacturing 08 (2017), 265–268.

Yangkun

Xia

and Zhuo

, Distribution vehicle routing problem in supermarket chains with soft time windows, Information and Control 47(05) (2018), 599–605.

Franceschette

, Honhon

, Woensel

T.V.

, et al., The time-depend pollution-routing problem, Transportation Research Part B(Methodological). 56 (2013), 265–293.

Xiao

and Konak

, The heterogeneous green vehicle routing and scheduling problem with time-varying traffic congestion, Transportation Research Part E (Logistics and Transportation Review) 88 (2016), 146–166.

10.

Wen

, Catay

and Eglese

, Finding a minimum cost path between a pair of nodes in a time-varying road network with a congestion charge, European Journal of Operational Research 236 (2014), 915–923.

11.

Houming

Fan

, Jiaxin

, Jing

Geng

, et al., Vehicle routing problem with fuzzy demand and time window and hybrid genetic algorithm solution, Journal of Systems Management 29(01) (2020), 107–118.

12.

Shunyong

, Bin

Dan

and Xianlong

, Low carbon vehicle routing optimization model and algorithm in multi-channel time-varying network, Computer Integrated Manufacturing System 25(2) (2019), 454–468.

13.

Tao

Ning

, Xuping

Wang

and Xiangpei

, Interference management decision model for delivery vehicle scheduling under driving delay, System Engineering Theory and Practice 39(5) (2019a), 1236–1245.

14.

Ning

and Wang

X.P.

, Study on disruption management strategy of job-shop scheduling problem based on prospect theory, Journal of Cleaner Production 194 (2018), 174–178.

15.

Kai

Kang

, Jie

Han

, Wei

and Yanfang

, Optimization of low-carbon distribution path for cold chain logistics of fresh agricultural products, Computer Engineering and Applications 55(2) (2019), 259–265.

16.

Wenting

Fang

, Zhongzhong

, Qing

Wang

, et al., Research on cold chain logistics distribution path optimization based on hybrid ant colony algorithm, China Management Science 27(11) (2019), 107–115.

17.

Zhixue

Zhao

, Xiamiao

, Xiancheng

Zhou

and Changshi

Liu

, GVRP research on cold chain logistics city distribution considering traffic congestion, Computer Engineering and Applications 56(01) (2020), 224–231.

18.

Weizhen

Rao

, Zhongfei

Duan

, Bingcheng

Wang

and Yan

, Research on the theoretical boundary of distance and energy saving of cooperative vehicle routing problem, Journal of System Management 28(04) (2019), 697–707.

19.

Qizhuo

, Jian

Wang

and Haiqing

Song

, Small-area low-carbon multi-vehicle low-carbon VRP in urban areas: A case study of Zhuhai Express Co, Ltd.’s regional receiving network, Journal of Management Engineering 30(04) (2016), 153–159.

20.

Weizhen

Rao

, Chun

Jin

, Xinhua

Wang

and Feng

Liu

, Low carbon VRP problem model and solution strategy considering road slope factor, System Engineering Theory and Practice 34(08) (2014), 2092–2105.

21.

Zhi

Chen

, Zhijie

Jiang

and Yao

Liu

, Optimization of low carbon logistics paths in different links based on improved ant colony algorithm, Eco-economics 35(12) (2019), 53–59+66.

22.

Goodarzian

Fariba

and Hosseini-Nasab

Hassan

, Applying a fuzzy multi-objective model for a production- distribution network design problem by using a novel self-adaptive evolutionary algorithm, International Journal of Systems Science: Operations & Logistics 14 (2019), 1–22.

23.

Khalid

Asma

, Khan

Ilyas

and Khan

Arshad

, Unsteady MHD free convection flow of Casson fluid past over an oscillating vertical plate embedded in a porous medium, Engineering Science and Technology, an International Journal 18(3) (2015), 309–317.

24.

Ning

Tao

, Wang

, Zhang

Peng

, et al., Integrated optimization of disruption management and scheduling for reducing carbon emission in manufacturing, Journal of Cleaner Production 263 (2020), 1–8.

25.

Garg

Harish

, A hybrid GSA-GA algorithm for constrained optimization problems, Information Sciences 478 (2019), 499–523.

26.

Yiyong

Xiao

, Qiuhong

Zhao

, Kaku

, et al., Development of a fuel consumption optimization model for the capacitated vehicle routing problem, Computer & Operations Research 39(7) (2012), 1419–1431.

27.

Lin

, Xiujun

Fan

, Comparative study on pricing strategies of fresh agricultural product supply chains dominated by retailers, China Management Science 23(12) (2015), 113–123.

28.

Osvald

and Stirn

L.Z.

, A vehicle routing algorithm for the distribution of fresh vegetables and similar perishable food, Journal of Food Engineering 85(2) (2008), 285–295.

29.

Montanari

, Cold chain tracking: a managerial perspective[J], Trends in Food ence & Technology 19(8) (2008), 425–431.

30.

Tao

Ning

, Xuping

Wang

and Xiangpei

, Research on the management method of terminal logistics interference based on prospect theory, System Engineering Theory and Practice 39(3) (2019b), 673–681.

31.

Tao

Ning

, Tao

Gou

and Peng

Zhang

, Disruption management strategy of terminal logistics under accidental travel time delay based on prospect theory, Journal of Intelligent & Fuzzy Systems 37(6) (2019c), 8371–8379.

32.

Piroozfard

Hamed

, Wong

Kuan Yew

and Wong

Wai Peng

, Minimizing total carbon footprint and total late work criterion in flexible job shop scheduling by using an improved multi-objective genetic algorithm, Resources, Conservation & Recycling 128 (2018), 267–283.

33.

Deguang

, Taihua

Zhang

and Weiping

, Prediction and analysis of workpiece surface roughness based on QGA-SVR, Machine Too & Hydraulics 15 (2020), 103–108.

34.

Dorgham

O.M.

, Alweshah

Mohammed

, Ryalat

M.H.

, et al., Monarch butterfly optimization algorithm for computed tomography image segmentation, Multimedia Tools and Applications (2021), 1–34.

35.

Fathy

Ahmed

, Abd Elaziz

Mohamed

, Sayed

Enas Taha

, et al., Optimal parameter identification of triple-junction photovoltaic panel based on enhanced moth search algorithm, Energy 188(1) (2019), 1–14.

36.

Shouqiang

Sun

, Yumei

, Chengbo

Yin

, et al. Optimal parameters estimation of PEMFCs model using Converged Moth Search Algorithm, 6 (2020), 1501–1509.