Route Planning of Supermarket Delivery through Third-Party Logistics Considering Carbon Emission Cost

Abstract

China’s policies about reducing carbon emissions mainly focus on saving energy and reducing pollutant emissions. However, the carbon emissions of the logistics industry remain high. Thus, logistics companies should not only reduce distribution costs, but also consider the impact of carbon emissions when planning distribution routes. This paper studies the supermarket delivery distribution route planning problem considering carbon emissions. Aiming at the lowest economic operating cost composed of fixed cost, driving cost, and carbon emission cost, we propose a grey wolf optimized genetic algorithm to generate delivery route plans, where the social rank and hunting behavior of the grey wolf optimization algorithm are integrated into the selection operation of the genetic algorithm. Finally, a real case of a large third-party logistics enterprise in Beijing is studied. The case study results verify the effectiveness and applicability of the model and algorithm.

1. Introduction

With the increasing consumption demand of residents, supermarket distribution becomes increasingly important. Supermarket distribution refers to the logistics activities in which the distribution center delivers the goods to the designated supermarkets. The characteristics of supermarket distribution contain three aspects. First, the locations of the supermarkets are geographically dispersed; second, goods demand varies greatly among different supermarkets; and third, the delivery service time is strict [1]. As a result, the delivery cost is high, including a massive energy consumption, excessive carbon emissions, and other problems [2,3]. The Communist Party of China’s Central Committee and the State Council unveiled a guiding document on the country’s work to achieve carbon peaking and carbon neutrality goals in 2020. However, the carbon emissions of the logistics industry remain high.

Meanwhile, there are three main delivery modes, as follows: by suppliers, by supermarkets themselves, and by third-party logistics companies. The distribution efficiency of delivery by third-party logistics companies is high since the third-party logistics companies provide a joint delivery mode. The main advantage of joint delivery is that orders from different supermarkets can be delivered together. Third-party logistics companies adopt different processing strategies (i.e., splitting or merging orders) to complete delivery services. Thus, the third-party logistics delivery mode has rapidly developed in recent years [4,5]. However, the logistics companies not only need to consider reducing distribution costs, but also the impact of carbon emissions, in line with the global trend of reducing carbon emissions. It is imperative to control and reduce the carbon emissions of third-party logistics distribution under the double carbon target.

Thus, this paper proposes a grey wolf optimized genetic algorithm to plan the distribution routes between several supermarkets, from the view of the third-party logistics companies. The proposed algorithm aims to minimize the economic operating cost including the fixed cost, the driving cost, and carbon emission cost. As we know, carbon emission is high when the traffic is congested, while the traffic condition is time dependent. Thus, we further consider the correlation between the driving times, the driving velocity, and road segments. In addition, the constraint of a hard time window is also related to the requirements of strict service time. We conduct a series of experiments and analyze a real case to verify the effectiveness of the proposed model and the algorithm. Compared to the three classical genetic algorithms, our proposed grey wolf optimized genetic algorithm can reduce the economic operating cost, while considering the carbon emission cost. The convergence speed of the proposed method is faster, which can generate the high-quality supermarket distribution path plan more quickly. We also verify that the fluctuation of the carbon emission price has a great impact on the distribution scheme of supermarkets.

The rest of the paper is organized as follows: Section 2 is the literature review. We define the problem in a mathematical form in Section 3. Section 4 illustrates our proposed algorithm, which is based on the genetic algorithm optimized by the grey wolf algorithm. Section 5 is the case study. Finally, the paper is concluded in Section 6.

2. Literature Review

2.1. VRP Incorporating Carbon Emissions

Logistics will always consume a high amount energy and emit lots of carbon [6,7]. Thus, low-carbon logistics and green logistics have attracted the attention of researchers in recent years [8,9].

The existing vehicle routing problem (VRP) works to either minimize carbon emissions costs or the delivery costs, including carbon emissions. Yu et al. [10] minimized carbon emissions and used an adaptive large neighborhood search algorithm to solve gasoline–electric hybrid distribution vehicle routing. Luo et al. [11] studied vehicle route planning for agricultural products in a cold chain, which took the sum of various distribution costs including carbon emission as the goal. Meanwhile, the traffic and weather conditions are also considered. With the multi-objective optimization, Zhu et al. [12] effectively solved the transportation and distribution problems in cold chain logistics.

The carbon emissions of logistics distribution mainly arise from the fuel consumption during the distribution vehicle’s driving [13]. The factors that affect the carbon emissions of logistics distribution mainly include vehicle load, driving speed, delivery distance, road network topology, traffic, etc. Suzuki et al. [14] established a vehicle routing model with capacity restrictions and vehicle number constraints, considering the impact of real-time vehicle load on carbon emissions; an heuristic algorithm is employed. Bai et al. [15] studied the vehicle routing problem of cold chain logistics, which considered the complexity of the road network and changing traffic conditions, which helps to improve the evaluation accuracy of distribution costs and carbon emissions. Zhang et al. [16] studied the dynamic delivery vehicle routing problem, which considered the impact of distribution distance on carbon emissions through deploying virtual customer points.

In summary, existing work plans the distribution routes based on the influencing factors of carbon emissions. However, they all assume that the driving times and velocity of the vehicles are fixed. In fact, the driving times and velocity are dynamic and are affected by traffic lights and road congestion in urban traffic environments. In a different manner to the existing work, this paper takes the vehicle load, driving times, and velocities into account, and aims to minimize the distribution cost including carbon emission costs.

2.2. Typical Solutions for Vehicle Routing Problems

The vehicle routing problem (VRP) is a typical combination optimization problem, which has been proven to be NP-hard. The existing works can be divided into precise algorithms, heuristic algorithms, and hybrid algorithms. The earliest methods are precise algorithms. For example, Yang et al. [6] adopted the branch-cut-pricing algorithm, which is a precise algorithm, providing a scheme for the last kilometer distribution in rural areas. Heuristic algorithms are more suitable for solving large-scale distribution vehicle routing problems. Heuristic algorithms include annealing algorithms, genetic algorithms, search algorithms, etc. For example, Liu et al. [17] employed a simulated annealing algorithm to solve the consistent vehicle routing problem. The genetic algorithm (GA) designed by Yu et al. [7] solves the routing problem of instant delivery vehicles based on customer classification. Hybrid algorithms refer to the combination of different heuristic algorithms and precise algorithms. For example, Fatemeh et al. combined the genetic algorithm and the simulated annealing algorithm to solve the green vehicle routing problem [9].

Existing research shows that heuristic algorithms are more effective in solving large distribution vehicle routing problems. Hybrid algorithms combine different heuristic algorithms, which can complement each other. Thus, hybrid algorithms can obtain a more reasonable distribution route solution. Our work follows the line of hybrid algorithms. As a new heuristic algorithm of swarm intelligence, grey wolf optimization has the characteristics of few dependent parameters and a good optimization performance, which is suitable for solving the routing problem of distribution vehicles; however, grey wolf optimization suffers from a complex coding mode. As a classical population evolution algorithm, a genetic algorithm is easy to code and to integrate with other algorithms. Therefore, we use a genetic algorithm supported by a grey wolf heuristic to solve the problem.

3. Mathematical Model

3.1. Problem Description

The route planning of supermarket delivery through third-party logistics considering carbon emission is formalized as follows: given the supermarkets, including the number, locations, service demands, and service hours, and a distribution center of the third-party logistics enterprise, the distribution center dispatches different types of vehicles to complete the delivery service. We aim to minimize the economic operating cost, which is composed of the fixed cost for employing a vehicle, the driving cost, and the carbon emission cost.

In order to clarify the scope of the paper, we assume the following:

(1)

We only consider the one-way goods delivery procedure, which is from the distribution center to supermarkets. The pick-up procedure is not involved [18].

(2)

The number of available vehicles is not limited.

(3)

The demand of each supermarket does not exceed the maximum capacity of a vehicle.

(4)

All requirements of the supermarkets are met and each supermarket is served by one vehicle once.

(5)

All supermarkets’ windows of service hours are strict. That is, if the goods are not delivered to the supermarket within the specified service hours, the service will be refused.

(6)

The vehicles are subject to local restrictions and traffic management measures, such as vehicle type restriction. (Vehicle number and the type of restriction are measures taken by the local government to alleviate traffic congestion, reduce vehicle exhaust emissions, and achieve air quality standards. For instance, vehicle type restriction means that vehicles with limited types cannot enter the corresponding area. Violators will be fined).

Table 1. Symbols.

Symbol	Meaning
N	N = {n|n = 0, 1, 2, …, N} is the collection of the distribution center and the supermarkets. N0 = {0} is the distribution center, N′ = {1, 2, 3, …, N} are the supermarkets.
L	L = {l|l = 1, 2, …, L} is the type of delivery vehicle.
K	K = {k|k = 1, 2, …, K} is the set of delivery vehicles.
H	H = {h|h = 1, 2, …, H} is the set of road loops.
qi	Demand of the i-th supermarket.
Gijlk	Load quantity of the k-th vehicle with type l from supermarket i to supermarket j
Wl	Vehicle weight of the type l
Qkl	Maximum vehicle capacity of the k-th vehicle with type l
Qh*	Maximum vehicle capacity allowed in the h-th loop in the city
REti	Earliest service time required by the supermarket i
RLti	Latest service time required by the supermarket i
dij	Distance between the supermarket i and the supermarket j on the road network
Oijlk	Fuel consumption of the k-th vehicle with type l between supermarket i and j
Eijlk	Carbon emissions of the k-th vehicle with type l between supermarket i and j
clk	Cost of employing the k-th vehicle with type l
c0lk	Fuel price (CNY/L)
celk	Carbon emission price (CNY/kg)
tailk	The timestamp when the k-th vehicle of type l arrives at supermarket i
tsilk	Service hours of how long the k-th vehicle of type l works at supermarket i
tdilk	Timestamp when the k-th vehicle of type l leaves supermarket i
tijlk	driving times of the k-th vehicle of type l from supermarket i to j
vijlk	Driving speed of the k-th vehicle of type l from supermarket i to j
xijlk	Variable 0–1: If the vehicle arrives at supermarket j from i, the value is 1; otherwise, the value is 0
yilk	Variable 0–1: If the supermarket i is served by the vehicle, the value is 1; otherwise, the value is 0
rih	Variable 0–1: If the supermarket i is in the h-th ring of the city, the value is 1; otherwise, the value is 0

shows the symbols used in this paper.

3.2. Mathematical Model

3.2.1. Objective Function

Our algorithm aims to generate a distribution plan where all requirements of the supermarkets are met, while the economic operation cost is minimized. The economic operation cost is composed of the fixed cost for employing vehicles, the driving cost, and the carbon emission cost. The objective function is shown in Equation (1).

$$\mathit{min}Z={\sum }_{l=1}^L{\sum }_{k=1}^K{\sum }_{j=1}^N{c}^{lk}\ast x_{0j}^{lk}+c_o^{lk}\ast {\sum }_{l=1}^L{\sum }_{k=1}^K{\sum }_{i=0}^N{\sum }_{j=0}^N{O}_{ij}^{lk}+c_e^{lk}\ast {\sum }_{l=1}^L{\sum }_{k=1}^K{\sum }_{i=0}^N{\sum }_{j=0}^N{E}_{ij}^{lk}$$

(1)

where Z represents the economic operation cost of the distribution plan.

The first term in Equation (1) is the fixed cost for employing vehicles, which depends on the number of vehicles used in the plan. The fixed cost is equal to the product of the number of vehicles and the fixed cost of a vehicle. The second term is the driving cost. The driving cost is the product of the petrol consumption of the vehicles and the fuel price. The third term is the cost for the carbon emission of the delivery vehicles. The carbon emission cost is the product of the carbon emissions and the carbon price. The second and third terms will be described in Section 3.3 in detail.

3.2.2. Constraints

The constraints include three aspects in this paper; that is, from the view of vehicles’ operation, from the view of supermarkets’ requirements, and from the view of local restrictions and traffic management measures.

(1)

From the view of vehicles’ operation

$${\sum }_{i=1}^N{\sum }_{l=1}^L{\sum }_{k=1}^K{q}_i\ast y_i^{lk}\le Q_k^l,\forall i\in N\prime ,\forall l\in L,\forall k\in K$$

(2)

$${\sum }_{j=1}^{N\prime }{x}_{0j}^{lk}={\sum }_{i=1}^{N\prime }{x}_{i0}^{lk},\forall i\in N\prime ,\forall j\in N\prime ,\forall l\in L,\forall k\in K$$

(3)

$$t_{di}^{lk}=t_{ai}^{lk}+t_{si}^{lk},\forall i\in N,\forall j\in N,\forall l\in L,\forall k\in K$$

(4)

$$t_{aj}^{lk}=t_{di}^{lk}+t_{ij}^{lk},\forall i\in N,\forall j\in N,\forall l\in L,\forall k\in K$$

(5)

Equation (2) indicates that the total demand of the supermarkets served by each delivery vehicle cannot exceed the vehicle capacity. Equation (3) indicates that all delivery vehicles should depart from the distribution center and eventually return to the center. Equation (4) indicates that the timestamp when the vehicle leaves the supermarket i equals the time when the supermarket is served after the vehicle arrives. Equation (5) indicates that the time when the vehicle arrives at supermarket j is the time when the vehicle leaves supermarket i, as well as the driving times from i and j.

(2)

From the view of supermarkets’ requirements

$${\sum }_{i=1}^{N\prime }{\sum }_{l=1}^L{\sum }_{k=1}^K{x}_{ij}^{lk}={\sum }_{i=1}^{N\prime }{\sum }_{l=1}^L{\sum }_{k=1}^K{x}_{ji}^{lk}={\sum }_{l=1}^L{\sum }_{k=1}^K{y}_{ij}^{lk}\ge 1,\forall i\in N\prime ,\forall j\in N\prime ,\forall l\in L,\forall k\in K$$

(6)

$$RE{t}_i\le t_{ai}^{lk}\le RL{t}_i,\forall i\in N\prime ,\forall l\in L,\forall k\in K$$

(7)

Equation (6) is a constrained condition, which means that the number of vehicles reaching the supermarket equals the number of vehicles leaving the supermarket, and the same can be said for the number of vehicles serving the supermarket. Equation (7) indicates a hard time window required by the supermarket. That is, the arrival time of the delivery vehicle at the supermarket must be within the range of the required earliest service time and the latest service time.

(3)

From the view of the local restrictions traffic management measures

$${\sum }_{i=1}^{N\prime }{\sum }_{l=1}^L{\sum }_{k=1}^K{r}_i^h\ast y_i^{lk}\ge 1,Q_k^l\le Q_{h^{\prime }}^{*},\forall i\in N\prime ,\forall l\in L,\forall k\in K$$

(8)

In this paper, we only consider type restriction. Equation (8) requires that only the vehicle whose maximum capacity is not larger than the allowed maximum capacity requirement inside the h-th loop of the city can serve the supermarket.

3.3. Fuel Consumption and Carbon Emission Evaluation

We employ the widely used CMEM (Comprehensive Modal Emission Model) [19] to evaluate the fuel consumption and the carbon emissions caused by the supermarket distribution plan, which considers the effects of vehicle load, driving times, and speed. The evaluation equation is shown as follows:

$$O_{ij}^{lk}={\beta }_1{t}_{ij}^{lk}+{\beta }_2{d}_{ij}{\left(v_{ij}^{lk}\right)}^2+{\beta }_3{d}_{ij}\left(W_l+G_{ij}^{lk}\right)$$

(9)

where β₁, β₂, and β₃ are the predetermined parameters, which represent the vehicle engine coefficient, the speed coefficient, and the load coefficient, respectively; with reference to [19], the three parameters are set as 0.22, 0.036, and 0.017, respectively.

It has been proven that vehicle carbon emissions and fuel consumption hold a linear relationship. Therefore, the carbon emission of the delivery vehicle driving from supermarket i to j is shown in Equation (10):

$$E_{ij}^{lk}=O_{ij}^{lk}\ast \psi$$

(10)

where $\psi$ represents the fuel emission factor, which is set as 2.62 in this paper, as in Ref. [13].

Most scholars assume that the first two items in Equation (9), driving times $t_{ij}^{lk}$ and the driving speed $v_{ij}^{lk}$, are fixed. However, in fact, these are affected by external factors such as traffic light and road congestion in the urban traffic environment; the driving times and the driving speed of the delivery vehicles vary according to different timestamps. Therefore, in this paper, we calculate the fuel consumption and the carbon emissions of the vehicle based on the diverse driving times with respect to their different locations.

Ref. [20] verifies the lognormal distribution to be the best to fit vehicle driving times within 24 h, using 36 measured data sets. Therefore, we divide every two hours in a day into a period. Assume that the driving times $t_{ij}^{lk}$, the k-th vehicle of type l from supermarket i to j, are subject to a lognormal distribution in each period. That is, $\ln {(t}_{ij}^{lk})~\mathrm{N}\left({\mu }_{ij},{\sigma }_{ij}^2\right)$. ${\mu }_{ij}$ and ${\sigma }_{ij}^2$ are the mean and the variance of the vehicle driving times, respectively.

We also use the case of Sinotrans Beijing Distribution Center, whose detailed information can be found in Section 5, to test whether the driving times of delivery vehicles are subject to a lognormal distribution in each period using the K–S test. First, the driving times between the distribution center and the designated 20 supermarkets are retrieved every 15 min between 6:00 and 22:00 for 15 consecutive days using Baidu map API. The unit of driving time is minutes. Then, each day from 6:00 to 22:00 is divided into eight periods, every two hours. The retrieved driving times and driving speeds are split into each period. After that, the frequency distribution histogram of the logarithmic driving times of the vehicles is drawn. Taking the ordinary period (10:00~12:00) and the peak period (18:00~20:00) as examples, the histogram of vehicle driving times after taking logarithm are shown in Figure 1. The K–S test results are shown in

Table 2. Hypothesis test summary using K–S test.

Null Hypothesis	Test	Sig.	Decision Maker
1—The distribution of travel time log from 10 o’clock to 12 o’clock is normal, the mean value is 7.38, and the standard deviation is 0.05	One sample Kolmogorov–Smirnov Test	0.716	Preserve the null hypothesis
2—The distribution of travel time log from 18 to 20 is normal, with a mean of 7.67 and a standard deviation of 0.03	One sample Kolmogorov–Smirnov Test	0.486	Preserve the null hypothesis

The significance level is 0.05.

.

According to the density curve of the frequency distribution histogram in Figure 1, the logarithm of the driving times approximately and intuitively follows a normal distribution. In Table 2, the p-values of the two periods were 0.716 and 0.486, respectively. The null hypothesis is accepted. Therefore, the driving times of the vehicles in the two periods approximately followed the lognormal distribution. That is, during 10:00~12:00, $\ln {(t}_{ij}^{lk})~\mathrm{N}\left(7.38,{0.05}^2\right)$ and during 18:00 to 20:00, $\ln {(t}_{ij}^{lk})~\mathrm{N}\left(7.62,{0.03}^2\right)$.

Table 3. Distribution of vehicle driving times between two locations at different times.

Time Period	Distribution (Mean, Standard Deviation)	Significance p-Value
6:00~8:00	(7.66, 0.05)	0.681
8:00~10:00	(7.46, 0.07)	0.740
10:00~12:00	(7.38, 0.05)	0.716
12:00~14:00	(7.55, 0.04)	0.327
14:00~16:00	(7.40, 0.07)	0.708
16:00~18:00	(7.46, 0.06)	0.651
18:00~20:00	(7.67, 0.03)	0.486
20:00~22:00	(7.51, 0.02)	0.958

shows the K–S test results of vehicle driving times’ distribution at different periods between two locations. We use the mean of the driving times to compute driving speed, v_ij^lk, as shown in Equation (11):

$$v_{ij}^{lk}=\frac{d_{ij}}{{\mu }_{ij}}$$

(11)

In Equation (11), $d_{ij}$ is the road network distance between supermarket i and supermarket j, and ${\mu }_{ij}$ is the average vehicle driving times between the two locations at different periods.

4. Grey Wolf Optimized Genetic Algorithm

As we know, the number of supermarkets served by third-party logistics enterprises is large. Their locations are sparse and their demands are quite diverse. Therefore, we propose a grey wolf optimized genetic algorithm to solve the supermarket distribution route plan problem of third-party logistics enterprises. The grey wolf optimized genetic algorithm is a hybrid heuristic algorithm combining the genetic algorithm and the grey wolf optimization idea. The genetic algorithm is simple and easy to combine with other algorithms. At the same time, the grey wolf optimization algorithm is less dependent on parameters and has a good optimization performance. Thus, we propose to integrate the social rank and hunting behavior in the grey wolf optimization algorithm into the selection operation of the genetic algorithm, which is suitable for solving complex distribution path problems. For ease of understanding,

Table 4. Term description.

Term	Meaning		Meaning Description
A grey wolf/chromosome	A candidate solution.		A supermarket distribution route plan.
Gene	Components of a grey wolf/chromosome, component in the candidate solution.		Distribution centers and supermarket stores.
Grey wolf population	A group of grey wolves, a collection of candidate solutions.		A collection of supermarket distribution route plans.
Population size	The number of grey wolves in the population and the number of candidate solutions in the set.		The number of supermarket distribution route plans generated each time.
Fitness	Measurement for the superiority and inferiority of the grey wolf population to carry out social classification.		The index to judge the best distribution route plan of supermarkets according to the objective function
Social hierarchy of the grey wolf	α Wolf	The best solution in the current candidate solutions.	The best solution in the set of supermarket distribution route plans.
	β Wolf	The second best solution in the current candidate solutions.	The second best solution in the set of supermarket distribution route plans.
	δ Wolf	The third best solution in the current candidate solutions.	The third best solution in the set of supermarket distribution route plans.
	ω Wolf	The remaining solutions in the current candidate solution set.	Other solutions in the set of supermarket distribution route plans.
Prey	The best solution.		The best supermarket distribution route plan.
Hunting behavior of the grey wolf	Surround	The distance between individual grey wolves and prey is calculated for grey wolf location update.	Calculate the difference between the fitness value of each supermarket distribution path scheme and the fitness value of the global best scheme.
	Hunt	ω wolves update the locations based on α, β, and δ wolves’ locations.	The top three solutions are assumed to be the current best solutions and the target fitness of the other solutions is calculated.
Evolve	The process of creating a new generation of grey Wolf populations.		The process of obtaining a new set of distribution solutions for supermarkets.
Genetic operator	Select	Selection acts on the grey wolf population to achieve genetic purposes and to prepare for crossover and mutation.	The selection operation is carried out according to the law of grey wolf hunting behavior.
	Crossover	Crossover acts on a grey wolf population to produce new individuals in the population.	The crossover operation is carried out using the sequential crossover method.
	Mutation	Mutation acts on a grey wolf population to produce new individuals in the population.	The mutation operation was carried out using the binary mutation method.

gives the common terms and the correspondence meanings in our proposed new algorithm.

Figure 2 shows the flow chart of the proposed algorithm. At the beginning of the algorithm, the distribution center and the supermarkets are coded based on the chromosome coding. As a result, the distribution centers and supermarkets are mapped to genes. This is the basis for the following steps. The chromosome, i.e., a grey Wolf, is a supermarket distribution path plan. The chromosome is composed of genes (which are the distribution center and supermarkets). This paper uses integer coding to encode genes in chromosomes, where “0” represents distribution centers and “1, 2, …, N” are supermarkets. After encoding, the initial grey wolf population is generated. That is, several supermarket distribution path plans are generated randomly. The specific procedure will be described in detail in Section 4.1.

Secondly, the fitness of each grey wolf in the population was calculated. Fitness is computed using the objective function; that is, the economic operating cost of the plan. The distribution route plans are checked based on the fitness, such that the social classifications of the grey wolves are classified. Then, the grey wolves start to hunt. In the first generation, all grey wolves (i.e., supermarket distribution path plans) regard the first three wolves with the highest social rank (i.e., the first three distribution route plans with the lowest economic operating cost) as the target to update locations. Through hunting behavior, it is possible to renew the location of the target for grey wolves. The two grey wolves closest to the target are found and the subsequent selection operations are conducted. The specific social hierarchy criteria and hunting behavior rules of the grey wolf will be described in detail in Section 4.2.

After that, through the genetic operators such as selection, crossover, and mutation, the population are evolved. That is, a new supermarket distribution route plan is generated. In order to improve the local search ability, the genetic operator operation of the proposed algorithm is based on the hunting behavior rule of the grey wolf. The specific operation will be described in detail in Section 4.3.

Finally, the termination condition is tested. The termination condition is the number of evolutionary generations (i.e., number of iterations). If the termination condition is not met, the above steps are repeated. Otherwise, the best individual in the last generation of the grey wolf population is output; that is, the best supermarket distribution route plan.

4.1. Population Generation Initialization

The initial population must meet the maximum vehicle capacity constraint and the service time window requirement of the supermarket.

First, supermarket visiting sequences are generated randomly. Then, the time of arrival and departure of delivery vehicles at each supermarket in the sequence and the load of delivery vehicles during the service procedure are calculated. After that, route segmentation is carried out for the supermarkets. The constraints of the route segmentation are the maximum capacity constraint of delivery vehicles and the service time window requirements of supermarkets. For each supermarket in the sequence, if the two conditions are met, the supermarket will be assigned a distribution vehicle. The route segmentation procedure is stopped until all supermarkets are served. The initial grey wolf population is obtained (i.e., sets of supermarket distribution route plans).

4.2. Grey Wolf Social Hierarchy and Hunting Behavior Rules

The social classification of grey wolves includes α, β, δ, and ω levels, according to the fitness. Each grey wolf is classified as one kind of wolf. There is only one α-wolf, one β-wolf, and one δ-wolf. The α-wolf, the β-wolf, and the δ-wolf correspond to the first, second, and third supermarket distribution route plans ranked by the fitness. ω-wolves correspond to the other supermarket distribution route plans.

The traditional hunting behavior of grey wolves includes surrounding, hunting, attacking, and searching. We adapt two activities, i.e., surrounding and hunting. The hunting behavior of the grey wolves depends on the social hierarchy. ω wolves take α, β, and δ wolves as targets to update locations. The specific behavior is as follows:

(1)

Surrounding

Surrounding is the way in which grey wolves approach their prey when the prey’s location is known. In our problem, surrounding means that in a generation population (i.e., sets of supermarket distribution route plans), a route plan is selected as the prey (i.e., the best supermarket distribution route plan) and other plans are adjusted as the best one. The adjustment method is as follows:

$$D=\left|2r_2{Z}_p\left(t\right)-Z\left(t\right)\right|$$

(12)

$$Z\left(t+1\right)=Z_p\left(t\right)-\left(2a{r}_1-a\right)D$$

(13)

Z(t) is fitness of the current grey wolf; Z_p(t) is the fitness of the prey; and t is the iteration number. D is the fitness gap between grey wolves and their prey. Formula (13) is the fitness after updating locations, while 2ar₁ − a and 2r₂ are the coefficient vectors. The coefficient vectors help to avoid falling into the local optimal solution [21]. In Equation (13), a is the convergence factor, which decreases linearly from 2 to 0; r₁ and r₂ are random numbers between [0, 1].

(2)

Hunting

We assume that α, β, and δ wolves know more about their prey, and the ω wolf pursues prey based on the fitness of these three wolves. The hunting method is as follows:

$$\left\{\begin{array}{c}{D}_{\alpha }=\left|C_1{Z}_{\alpha }-Z\right|\\ D_{\beta }=\left|C_2{Z}_{\beta }-Z\right|\\ D_{\delta }=\left|C_3{Z}_{\delta }-Z\right|\end{array}\right.$$

(14)

$$\left\{\begin{array}{c}{Z}_1=Z_{\alpha }-A_1{D}_{\alpha }\\ Z_2=Z_{\beta }-A_2{D}_{\beta }\\ Z_3=Z_{\delta }-A_3{D}_{\delta }\end{array}\right.$$

(15)

$$Z\left(t+1\right)=\frac{Z_1+Z_2+Z_3}{3}$$

(16)

A₁(C₁), A₂(C₂), and A₃(C₃) are the coefficient vectors for α, β, and δ wolves, respectively. As in Equations (12) and (13), A = $2a{r}_1-a$, and C = 2r₂, as in Equation (13). In Equations (14)–(16), the current best top three supermarket distribution route plans are regarded as prey. The plan is adjusted according to the adjustment method in the surrounding. Equation (16) means that the average fitness value is taken as the adjustment target for the fitness of the remaining route plans.

4.3. Genetic Operator Operation

4.3.1. Selection

The purpose of selection is to select the distribution route plan with the highest fitness during each evolution, which is the basis for crossover and mutation. We selected the plan based on the social classification and hunting behavior rules of grey wolves. It mainly consists of two steps. First, the grey wolf, which pass down to the next generation (a supermarket distribution route plan) directly, is selected. Second, the grey wolves that are crossed and mutated are selected.

The specific steps are as follows: First, the α, β, and δ wolves are inherited by the next generation directly. That is, the top three route plans with the best fitness in the current generation are retained. Then, based on the fitness adjustment target of grey wolf hunting behaviors, the two grey wolves closest to the target fitness, i.e., the two supermarket distribution route plans with the closest economic cost, were selected for local adjustment.

4.3.2. Crossover

The aim of crossover is to generate a new supermarket distribution route plan. Typical crossover operators include partial matching crossover, sequential crossover, cyclic crossover, etc. This paper adopts a sequential crossover strategy to carry out crossover operations.

The basic steps are as follows: First, two grey wolves (i.e., supermarket distribution route plans) generated from the previous selection operation are chosen as parents. Then, several genes in one parent are left unchanged and the remaining genes are crossed with the genes in the other parent, in order. The filial generation is obtained. In other words, the service order of some supermarkets in a route plan are kept unchanged and the service order of other supermarkets changes according to the service order in another route plan. The process diagram of sequential crossing is shown in Figure 3. Each crossover will produce two children (i.e., the new supermarket distribution route plans).

4.3.3. Mutation

Mutation generates new supermarket distribution route plans as well, whose function is to expand the search range and avoid falling into the local best solution. In a different manner to the traditional mutation only requiring one operator, we adopt a binary mutation strategy to carry out mutation operations. That is, we require two supermarket distribution route plans to participate.

The basic steps are as follows: First, two grey wolves generated from the previous selection operation are chosen as parents. Second, a different gene (i.e., a supermarket) from the two grey wolves was selected randomly. Then, the locations of the two selected genes exchange. That is, the service order of the different selected supermarkets is exchanged, such that two new supermarket distribution route plans are generated. The process of a mutation operation is shown in Figure 4. Similarly to crossover, the process of each binary mutation will produce new supermarket distribution route plans.

5. Case Study

5.1. Data Analysis

We use the data from Sinotrans (https://www.sinotrans.com/), a pioneer in China’s third-party logistics industry, as the studying case. The delivery demands of the supermarkets on one day in Beijing were used to verify the model and the algorithm. The distribution center is marked as a star and 20 supermarkets are marked as small red and blue balls. The distances between the distribution center and the supermarkets are retrieved using Baidu map API. The distances are drawn as a hot map, as Figure 5 shows. From Figure 5, the distances between the distribution center and each supermarket varies from 0 to 80 km. More than half of the supermarkets are within 50 km of each other. That is because most of the supermarkets served by Sinotrans are in the sixth loops, which are near the shopping malls with large passenger flow in Beijing. A small number of supermarkets are located in the suburbs outside the sixth loop.

The specific locations of the distribution and the supermarkets and their orders’ demands are shown in

Table 5. Distribution center and supermarket stores information.

ID	Longitude	Latitude	Demand (pcs)	Earliest Service Time/Minute	Latest Service Time/Minute	Service Times/Minute
0	116.58435483	39.76564835	—	—	—	—
1	116.72296721	40.04770537	537	480	960	15
2	116.60640356	39.84275063	160	420	1020	15
3	116.58343134	39.91597776	20	420	960	15
4	116.47129544	39.87113725	35	420	1020	15
5	116.27829385	39.95056627	158	420	1440	15
6	116.45388693	39.95338014	30	420	1020	15
7	116.46123122	39.81952399	42	480	960	15
8	116.21766119	39.72757056	233	480	1020	15
9	116.59090317	40.14284996	83	480	720	15
10	116.59999842	40.21791566	723	420	960	15
11	116.5297555	40.00940921	1604	480	660	15
12	116.34543029	39.79611328	30	540	1020	15
13	116.27520364	40.12902854	1049	480	600	15
14	116.39710449	39.98650819	13	480	1440	15
15	116.47384384	40.01701514	45	480	1440	15
16	116.61448348	40.11253296	80	600	1020	15
17	116.68277809	39.71844609	649	480	660	15
18	116.799908	39.78599117	72	540	1020	15
19	116.70618928	39.9238797	30	480	960	15
20	116.73954121	39.68472682	442	480	1020	15

. The demand of each supermarket varies from [13, 1604] pieces. The demands of all supermarkets are quite different. The available vehicle types are listed in

Table 6. Distribution center vehicle types.

Vehicle Type	Maximum Vehicle Capacity (pcs)	Use Fixed Cost	Fuel Price	Carbon Emissions Price
6.8 t	250	CNY 450	CNY 6.5 per liter	CNY 0.5 per kilogram
9.6 t	350	CNY 850	CNY 6.5 per liter	CNY 0.5 per kilogram

. The traffic restriction policy claims that trucks larger than 8 t are prohibited within the Fifth Ring Road of Beijing. Thus, we divide the 20 supermarkets into two groups, as follows: Group 1, i.e., the supermarkets within the Fifth Ring Road, includes supermarkets 4, 5, 6, 7, 12, 14, and 15; Group 2, i.e., the supermarkets outside the Fifth Ring Road, includes the rest of the supermarkets. Considering the restrictions on vehicle types, the first group of supermarkets can only have a delivery from 6.8 t vehicles. For the second group, the 9.6 t vehicle is guaranteed to be fully loaded and the 9.6 t or 6.8 t model will be randomly selected for the remaining demand.

5.2. Analysis of Results

We use the proposed grey wolf optimized genetic algorithm to solve the above practical distribution route problem. Python 3.8 was used to implement the algorithm. This paper verifies the effectiveness of the model and algorithm from the following three aspects: the influence of different parameters, the comparison of different algorithms, and the change in carbon emission price.

5.2.1. Impact Analysis of Different Algorithm Parameters

The parameter setting has an important effect on the overall performance. With reference to the parameter setting experience of previous genetic algorithms, the crossover probability was set to 0.8 and the mutation probability was set to 0.2. The population size was 50, 75, 100, 125, and 150, and the number of iterations was 50, 100, 150, 200, and 250, respectively. The economic operation cost of the supermarket distribution scheme under different parameter combinations is shown in

Table 7. Economic operation cost under different parameter combinations.

	#Iterations	50	100	150	200	250
Population Size
50		5566.8	4670.0	4202.6	4202.1	4202.1
75		5539.6	4667.2	4202.1	4202.1	4198.8
100		5539.2	4209.9	4175.7	4142.1	4142.1
125		5074.2	4193.4	4188.7	4142.1	4142.1
150		4209.3	4166.8	4165.6	4142.1	4142.1

. From Table 7, when the population size is 100 and the iteration number is 200, the economic operation cost is minimized.

Through our proposed grey wolf optimized genetic algorithm, a distribution route plan is obtained, as shown in

Table 8. Supermarket distribution route scheme.

Vehicle Serial Number	Vehicle Type	Vehicle Route	Delivery Time
1	9.6 t	0-19-16-8-0	(522.0, 522.0)-(548, 563.0)-(600.0, 615.0)-(636.0, 651.0)-(1229.0, 1229.0)
2	9.6 t	0-18-9-3-2-0	(279.0, 279.0)-(540.0, 555.0)-(575.0, 590.0)-(612.0, 627.0)-(647.0, 662.0)-(1072.0, 1072.0)
3	9.6 t	0-20-1-13-10-11-17-0	(537.0, 537.0)-(551, 566.0)-(587.0, 602.0)-(622.0, 637.0)-(656.0, 671.0)-(691.0, 706.0)-(725.0, 740.0)-(858.0, 858.0)
4	6.8 t	0-6-0	(738.0, 738.0)-(755, 770.0)-(1525.0, 1525.0)
5	6.8 t	0-7-4-0	(464.0, 464.0)-(490, 505.0)-(784.0, 799.0)-(1483.0, 1483.0)
6	6.8 t	0-12-15-14-5-0	(1062.0, 1062.0)-(1094, 1109.0)-(1129.0, 1144.0)-(1330.0, 1345.0)-(1401.0, 1416.0)-(1484.0, 1484.0)

. The two numbers in the brackets under the column “delivery time” represent the time of arrival at or departure from the distribution center or supermarkets, respectively. In order to visualize the delivery routes, we transformed the latitudes and longitudes into the coordinates in the Cartesian coordinate system. Then, the distribution vehicle routes are shown in Figure 6. Each line with one color is a vehicle route.

From Table 8 and Figure 6, a total of 6 vehicles are needed to complete the distribution demand of 20 supermarkets, including 3 vehicles of 9.6 t and 6.8 t, respectively. The number of supermarkets a delivery vehicle serves for varies greatly. The difference mainly comes from the strict service window requirements. In order to ensure the provision of a distribution service within the required time window, the distribution vehicles cannot be fully loaded, resulting in the waste of distribution resources. This shows that the time window requirement of supermarket stores is an important factor affecting the distribution route plan of supermarket stores.

5.2.2. Comparative Analysis with the Genetic Algorithm

In order to verify its effectiveness, the proposed method is compared with the classical genetic algorithm. The difference between the proposed method and the classical genetic algorithm mainly lies in the selection operation. The classical genetic selection operators include roulette selection, binary tournament selection, linear sorting selection, etc. Therefore, we compare the genetic algorithm with the above classical genetic selection operators with our proposed methods under the same parameter settings. The comparison results are shown in

Table 9. Comparison of results of different solutions.

Solution Method	Fixed Cost (CNY)	Vehicle Driving Cost (CNY)	Carbon Emission Cost (CNY)	Economic Operating Cost (CNY)
Grey wolf optimized genetic algorithm	3900	201.5	40.6	4142.1
Genetic algorithm with roulette selection	3900	283.4	57.1	4240.5
Genetic algorithm with binary tournament selection	3900	228.5	46.0	4174.5
Genetic algorithm with linear sorting selection	3900	269.8	54.4	4224.2

and the population evolution trend of the four algorithms is shown in Figure 7.

Table 9 shows that the fixed cost of the vehicles used in different methods is the same, but the total economic operating cost is different. Among the four solutions, the economic operating cost obtained by our proposed method is the lowest. The economic operating cost obtained by other algorithms is about CNY 30 to CNY 100 higher than our method. The difference mainly lies in driving cost and carbon emission cost. The fuel consumption and carbon emission of delivery vehicles are related to their driving route and driving times. The grey wolf optimized genetic algorithm can reduce the driving cost and carbon emission cost on the premise of ensuring the service demand of supermarkets. As a result, the cost of economic operation is reduced.

From Figure 7, the economic operating costs of different methods decrease with the increase in iteration number. By observing the evolution trends of different methods, the convergence speed of the grey wolf optimized genetic algorithm is fastest, while the economic operation cost is lowest. This is because the grey wolf optimized genetic algorithm is based on the position update rule of grey wolf hunting behavior. In addition, the grey wolf optimized genetic algorithm selects the top three grey wolves with the best fitness each time, which is more than the traditional genetic algorithm does. This can improve the local search ability. Therefore, the supermarket distribution route plan with the lowest economic operation cost can be obtained in less evolutionary time.

5.2.3. Analysis of Carbon Emission Price

With the continuous expansion of the scale of the carbon emission trading market, the carbon emission price shows a certain degree of volatility. In addition, the carbon emission price varies greatly between different countries. Therefore, this paper analyzes the impact of carbon emission price changes on supermarket distribution route plans, which can provide feasible suggestions for the third-party logistics enterprises responsible for supermarket distribution under the market environment of carbon emission price changing.

Taking the carbon emission price of various countries as a reference, we set the carbon emission price between 0 and 7.0 CNY/kg and the increasing step was 0.5. In total, 15 groups of experiments were conducted under different carbon emission prices, respectively. The comparison results between different carbon emissions prices are shown in

Table 10. Comparison between different carbon emissions prices.

Carbon Emissions Price (CNY/kg)	Vehicle Number	Fuel Consumption (L)	Carbon Emission (Kg)	Fixed Cost (CNY)	Driving Cost (CNY)	Carbon Emission Cost (CNY)	Economic Operating Cost (CNY)
0	6	33.5	87.8	3900	217.8	0.0	4117.8
0.5	6	31.0	81.2	3900	201.5	40.6	4142.1
1.0	6	31.0	81.2	3900	201.5	81.2	4182.7
1.5	6	31.0	81.2	3900	201.5	121.8	4223.3
2.0	6	31.0	81.2	3900	201.5	162.4	4263.9
2.5	6	29.8	78.1	3900	193.7	195.3	4289.0
3.0	6	28.3	74.1	3900	184.0	222.3	4306.3
3.5	6	27.6	72.3	3900	179.4	253.1	4332.5
4.0	6	27.2	71.3	3900	176.8	285.2	4362.0
4.5	6	26.5	69.4	3900	172.3	312.3	4384.6
5.0	6	26.3	68.9	3900	171.0	344.5	4415.5
5.5	7	26.0	68.1	4750	169.0	374.6	5293.6
6.0	7	26.0	68.1	4750	169.0	408.6	5327.6
6.5	7	26.0	68.1	4750	169.0	442.7	5361.7
7.0	7	26.0	68.1	4750	169.0	476.7	5395.7

. Different carbon emission prices have an impact on the supermarket distribution route plan.

Obviously, the cost of carbon emissions increases linearly with the increase in carbon prices in Figure 8e. With the increase in carbon emission price, fuel consumption, carbon emission, and driving cost show the same trends as shown in Figure 8a,b,d. The three variations decrease first and then stabilize as the carbon emission price is larger than 5. From Table 9, we observe that the vehicle number increases by 1 with the price of carbon emissions increasing in order to serve all customers. As a result, fuel consumption is reduced since more vehicles can improve the service efficiency, while the fixed cost increases. Thus, the helpfulness of increasing vehicle numbers is limited.

From Figure 8c, with the price of carbon emissions increases, the fixed cost of vehicle use shows a “step-like” increasing trend. This is because the fixed cost is related to the number of vehicles. When the carbon emission price changes at [0, 5.0] CNY/kg, the number of vehicles used remains unchanged, so the fixed cost remains unchanged. When the carbon emission price continues to increase, in order to reduce carbon emission costs, companies increase the number of vehicles used, resulting in a sharp increase in the fixed costs of vehicle use.

With the increase in carbon emission price, the economic operating cost of the supermarket distribution scheme shows an increasing trend, as shown in Figure 8f. When the carbon emission price changes in the range of [0, 5.0] and [5.5, 7.0] CNY/kg, the change in trend of economic operating cost is only slight, which is mainly affected by the driving cost and carbon emission cost. The trend changes sharply when the carbon emission price is in the range of [5.0, 5.5] CNY/kg, due to the fixed cost of vehicle use sharply increasing.

From the above analysis, carbon emission price has a great impact on the supermarket distribution route plan. Third-party logistics enterprises should formulate reasonable supermarket distribution route schemes according to different carbon emission prices. When the carbon emission price is in the range of [0, 2.0] CNY/kg, the enterprises should give priority to reducing the fixed cost and driving cost, because the carbon emission cost accounts for a relatively small proportion of the economic operation cost, about 1% to 4%. When the carbon emission price is in the range of [2.0, 5.0] CNY/kg, the carbon emission cost accounts for a relatively large part of the economic operation cost. As a result, fuel consumption and carbon emission have significant changes. Therefore, the enterprises should focus on reducing the carbon emission cost. When the carbon emission price is in the range of [5.0, 7.0] CNY/kg, the enterprises should balance the fixed cost, driving cost, and carbon emission cost to ensure the lowest economic operating cost.

6. Conclusions

Through analyzing the characteristics of the route planning of supermarket deliveries through third-party logistics, this paper proposes a grey wolf optimized genetic algorithm for supermarkets distribution route planning, considering carbon emission cost. The main conclusions are as follows:

(1)

When building the supermarket distribution route planning model, carbon emissions are calculated based on dynamic driving times on the road networks. The route planning can reduce the fuel consumption and carbon emissions of the supermarket distribution service.

(2)

Compared with the three classical genetic algorithms, the proposed grey wolf optimized genetic algorithm reduces the economic operating cost of CNY 98.4, CNY 32.4, and CNY 82.1, respectively. The convergence speed is faster, which can reach the high-quality supermarket distribution path plan more quickly.

(3)

The fluctuation of carbon emission price has a great impact on the distribution scheme of supermarkets. Therefore, it is suggested that third-party logistics enterprises develop supermarket distribution route schemes applicable to different carbon emission prices, so as to reduce carbon emissions and improve profit margins.

This paper only considers the delivery problem with one single distribution center, without time constraints. In the future, we will expand the study on the distribution path of supermarkets with multiple distribution centers for simultaneous pickup and delivery with time constraints and the order of vehicles selection on the different route planning of supermarket delivery.