**2. Problem Description and Model Formulation**

#### *2.1. Problem Description*

Fresh cold chain logistics show that distribution networks consist of multiple customer points and distribution centers. After the goods are packed and sorted in the distribution center, they are distributed using multiple refrigerated trucks. In cases where the vehicle speed changes constantly due to traffic conditions, the optimal vehicle travel path can be planned, considering both the delivery cost and customer value, and the delivery service can be provided within the time window specified by the customer.

In order to ensure the feasibility of the model, this paper assumed the following: (1) That all vehicles depart from the same distribution center and return to the distribution center after completing the delivery. (2) The refrigerated vehicles used are the same type and are sufficient to complete the delivery task. (3) The location of the customer, the amount of demand, the time window and their importance, as well as the temperature of the refrigerated vehicle at the opening and closing of the door, are known. (4) The demand at each customer point does not exceed the maximum capacity of the refrigerated vehicle, and each customer is delivered to using only one vehicle. (5) The quality of the fresh products transported is the same and the requirements for the refrigerated temperature are the same. (6) The preservation period and deterioration rate of fresh products are the same and known. (7) The speed of the vehicle in each period is only related to the delay factor of traffic congestion in that period. (8) Positive publicity is given to the enterprise when customer satisfaction is positive.

### *2.2. Problem Formulation*

In this paper, some corresponding parameters and variables were used to construct the model. The variables and definitions are listed in Table 1.


**Table 1.** Symbols and definitions.


**Table 1.** *Cont.*

With the previous comprehensive analysis, the CV-GVRP multiobjective optimization model with a minimum total cost and maximum customer value was formulated. The calculations for *Z*1, *Z*2, *Z*3, *Z*<sup>4</sup> and *Z*<sup>5</sup> were explained in the following section. The objective function was as follows:

$$\text{max}V = \sum\_{i=1}^{u} \lambda\_i (\mathcal{g}\_i + p\_i) \tag{1}$$

$$\begin{aligned} \min Z &= Z\_1 + Z\_2 + Z\_3 + Z\_4 + Z\_5 \\ &= \mathbb{C}\_0 \sum\_{k=1}^k \sum\_{i=1}^u X\_{0i}^k + \sum\_{k=1}^u \sum\_{i=0}^u \sum\_{j=0}^u d\_{ij} \mathbb{C}\_p X\_{ij}^k \\ &+ \sum\_{i=0}^u \sum\_{k=1}^m Y\_{ik} [q\_i (1 - K\_1 e^{-\theta\_i}) + Q\_{i0} (1 - K\_2 e^{-\theta \frac{Q\_i}{\pi k}})] R\_1 \\ &+ \gamma\_1 \sum\_{i=1}^u \max\{ET\_i - t\_i, 0\} + \gamma\_2 \sum\_{i=1}^u \max\{t\_i - LT\_i, 0\} \\ &+ \omega \sum\_{k=1}^m \sum\_{i=0}^u \sum\_{j=0}^u X\_{ij}^k d\_{ij} \{\varepsilon [\rho\_0 + (\rho \ast - \rho\_0) \frac{Q\_{ij}}{Q'}] + \varphi Q\_{ij}\} \end{aligned} \tag{2}$$

subject to:

$$\sum\_{k=1}^{m} q\_i Y\_{ik} \le Q\_i \land = 1,2,3\cdots\mu, k = 1,2,3\cdots m \tag{3}$$

$$\sum\_{k=1}^{m} \sum\_{j=1}^{u} X\_{ij}^{k} \le m\_{\prime} i = 0 \tag{4}$$

$$\sum\_{k=1}^{m} \sum\_{j=1}^{n} X\_{ij}^{k} = 1, i \neq j, i = 0, 1, 2 \cdot \cdots \cdot u \tag{5}$$

$$\sum\_{k=1}^{m} \sum\_{i=0}^{n} X\_{ij}^{k} = 1, i \neq j, j = 1, 2, 3 \cdots \mu \tag{6}$$

$$\sum\_{k=1}^{m} Y\_{ik} = 1, i = 1, 2, 3 \cdots m \tag{7}$$

$$\sum\_{j=0}^{u} X\_{ij}^{k} = \sum\_{j=0}^{u} X\_{ji}^{k} \le 1, i = 0, k = 1, 2, 3, \cdots \cdot m \tag{8}$$

$$t\_j = t\_i + S\_i + t\_{ij}, i = 1,2,3 \cdots \\\cdot u, j = 1,2,3 \cdots \\\cdot u \tag{9}$$

Equations (1) and (2) indicate that the objective functions of the model minimized the total distribution cost and maximized the customer value. Under the constraint of Equation (3), the total order demand assigned to the K-th vehicle could not exceed the loading capacity of the distribution vehicle. Constraint (4) indicated that the number of vehicles involved in the distribution could not exceed the total number of refrigerated vehicles. Each customer point was allowed to be served using only one refrigerated vehicle for one delivery, which was realized with constraints (5) and (6). Constraint (7) indicated that each customer point was served using only one delivery vehicle. Constraint (8) indicated that the refrigerated vehicle departed from the distribution center and returned to the distribution center after completing the transportation task. The time relationship through constraint (9) indicated that the whole distribution process was continuous.

Under a time-dependent road network, the objective function of the CV-GVRP based on the variable price of carbon trading and customer value was to minimize the total cost and maximize the customer value. The total cost contained five components: the vehicle fixed cost, transportation cost, loss cost, penalty cost and carbon emission cost, which were as follows:
