(5) Carbon Emissions Cost

This cost is mainly related to carbon emissions and the price of carbon trading. Carbon emissions mainly come from two sources: one is generated by energy consumption during transportation, and the other is generated by refrigeration equipment.

#### 1. Carbon emissions caused by driving

The amount of CO2 produced by a vehicle while transporting products is not only related to the distance, but also to the load capacity of the whole process. The fuel consumption per unit distance is different at full load and at no load. The carbon emissions of the travel process from node *i* to *j* were given:

$$G\_1 = \varepsilon d\_{ij} [\rho\_0 + (\rho^\* - \rho\_0) \frac{Q\_{ij}}{Q}] \tag{16}$$

#### 2. Carbon emissions from refrigeration

In order to maintain freshness, we used refrigeration equipment in the distribution process. The cumulative carbon emissions from refrigeration between nodes *i* and *j* were as follows:

$$G\_2 = qd\_{ij}Q\_{ij} \tag{17}$$

As a result, the total amount of carbon emitted in the whole distribution process was (*G*<sup>1</sup> + *G*2). Due to current carbon trading policies, there are regional variations and significant fluctuations in the price of carbon trading. According to spatial and temporal distribution characteristics of the "carbon K-line", the CV-GVRP calculated the carbon cost through random variables. The price per carbon transaction was *ω* ∼ (*ω* − *ω*ˆ , *ω* + *ω*ˆ), and the probability of taking any value in this range was equal.

The carbon emission cost could be expressed as:

$$Z\_5 = \omega \sum\_{k=1}^{m} \sum\_{i=0}^{u} \sum\_{j=0}^{u} X\_{ij}^k d\_{ij} \{ \varepsilon [\rho\_0 + (\rho^\* - \rho\_0) \frac{Q\_{ij}}{Q}] + \varphi Q\_{ij} \} \tag{18}$$

#### 2.2.2. Customer Value Measurement Method

The CV-GVRP considered the customer value in two parts: the current value and the potential value. The current customer value depends on the customer demand, and the two are positively correlated. The calculation method was as follows: *gi* = *qi <sup>u</sup>* ∑ *qi qiR*2.

*i*=1 The potential value is primarily related to the company's reputation, business strength, technological innovation and other factors, while the quality of the distribution has a more pronounced effect on the company's image. When the distribution is properly optimized, the freshness of the food can improve and customer satisfaction can increase. This motivates more potential consumers and, then, the company gains more potential customer value.

The potential value was calculated using *pi* = *WiniqiR*2. Customer satisfaction in the CV-GVRP was computed based on the time windows, and the expected time window *ET<sup>α</sup> <sup>i</sup>* , *LT<sup>β</sup> i* was set to be within the specified time window (*ETi*, *LTi*). Figure 1 shows the customer satisfaction function curve of the model.

**Figure 1.** Customer satisfaction curve.

Based on this, the linear change trend of customer satisfaction over time could be expressed with the fuzzy membership function. The time satisfaction function of a customer *i* was as follows:

$$\mathcal{W}\_{i}(t\_{i}) = \begin{cases} \frac{(t\_{i} - ET\_{i})}{(ET\_{i}^{\alpha} - ET\_{i})} & t\_{i} \in [ET\_{i}, ET\_{i}^{\alpha}] \\ \frac{(LT\_{i} - t\_{i})}{(LT\_{i} - LT\_{i}^{\beta})} & t\_{i} \in [LT\_{i}^{\mathcal{G}}, LT\_{i}] \\ 1 & t\_{i} \in [ET\_{i}^{\alpha}, LT\_{i}^{\mathcal{G}}] \\ 0 & t\_{i} \notin [ET\_{i}^{\alpha}, LT\_{i}^{\mathcal{G}}] \end{cases} \tag{19}$$

The calculation of the value of a single customer could be expressed as *λi*(*gi* + *pi*). Giving service priority to customers with high weights *λ<sup>i</sup>* can increase customer satisfaction and customer value, which is helpful for long-term business growth. The value of total customers was as follows:

$$V = \sum\_{i=1}^{u\_c} \lambda\_i (g\_i + p\_i) \tag{20}$$
