Interval two-stage stochastic programming model under uncertainty for planning emission rights trading in the Yellow River basin of China

Abstract

As a critical way to realize the optimal allocation of water environment capacity resources in the basin, emission rights trading faces multiple uncertainties, making it extremely hard and challenging to formulate appropriate decisions and plans. Therefore, this study uses interval two-stage stochastic programming (ITSP) method to model the emission rights trading process with multiple uncertainties. It can promote the secondary optimal allocation of the emission rights between the demander and the supplier after the initial allocation. Externalities caused by environmental problems are internalized through the form of emission rights trading, thereby reducing the transaction costs and promoting the coordination and integrity of water pollution control among governments in a basin. Finally, the Yellow River basin is taken as an example for case analysis. The results show that the net revenue of emission rights system in the transaction status is better than that in the non-transaction status, and the average gap of net income reaches [171.031, 193.056] billion yuan. Under different reduction policies, the average water pollutant emission reduction in transaction status is [451.15, 628.34] thousand tons, which is generally less than [516.57, 670.05] thousand tons in non-transaction status. As policies get stricter and assimilative capacity of water bodies dwindles, reduction shrinks, leading to higher risks and economic loss from being unable to meet the discharge demand. When reduction policies are relatively loose and assimilative capacity is high, emission rights trading volume peaks. At this time, the trading volume of COD reached [29.05, 40.76] thousand tons, and that of NH₃-N reached [3.74, 4.31] thousand tons. All these findings will offer insights for decision-makers on how to strike a balance between economic benefits and emission rights trading plans in the Yellow River basin.

Appendix

The assimilative capacity of the basin is closely related to the AWI and changes in the DARL of major pollutants in the past years. In detail, the assimilative capacity of water body is positively correlated with its water quantity and distribution, while negatively correlated with DARL. The probability distribution value ${p}_{dh}$ of the assimilative capacity for pollutant d is determined as follows:

• (1) Determining the probability ${p}_{h}(AWI)$ of AWI of different years

This study discretizes AWI of the past years to obtain ${p}_{h}(AWI)$. $\sum\limits_{h=1}^{H}{p}_{h}(AWI)=1$ with $h=\mathrm{1,2},\cdots ,H$. When $h=1$, there is low AWI in the planning year, resulting in low assimilative capacity. When $h=2$, there is medium AWI in the planning year, resulting in medium assimilative capacity. When $h=H$, there is high AWI in the planning year, resulting in high assimilative capacity.

• (2) Determining the probability distribution value ${p}_{dh}(DARL)$ of DARL

This study discretizes DARL of pollutant d in the past years to obtain the probability ${p}_{dh}(DARL)$ of DARL of pollutant d. $\sum\limits_{h=1}^{H}{p}_{dh}(DARL)=1$ and $h=\mathrm{1,2},\cdots ,H$. When $h=1$, there is low DARL in the planning year, resulting in high assimilative capacity. When $h=2$, there is medium DARL in the planning year, resulting in medium assimilative capacity. When $h=H$, there is high AWI in the planning year, resulting in low assimilative capacity.

• (3) Determining the ${p}_{dh}$ of assimilative capacity of water bodies in the region

As the assimilative capacity is positively influenced by AWI while negatively influenced by DARL, ${p}_{h}(AWI)$ and ${p}_{dh}(DARL)$ can be combined with their influences unified. Therefore, ${p}_{dh}$ is set as ${p}_{dh}\text{=}\xi {p}_{h}(AI)+(1-\xi ){p}_{d(H+1-h)}(DARL)$. $\sum\limits_{h=1}^{H}{p}_{dh}\text{=}1$, and $0\le \xi \le 1$, $d=\mathrm{1,2},\cdots ,D$, and $h=\mathrm{1,2},\cdots ,H$. $\xi$ is denoted according to the status quo of the water environment and water resource endowment of the region. If $\xi$ is close to 0, it means ${p}_{dh}$ is more influenced by DARL. If $\xi \text{=}0.5$, ${p}_{dh}$ is nearly equally influenced by DARL and AWI. If $\xi$ is close to 1, ${p}_{dh}$ is more influenced by AWI.

This study treats the AWI and emission amount of pollutant d in the Yellow River basin as discrete functions and obtains ${p}_{h}(AWI)$—the probability of AWI, and ${p}_{dh}(DARL)$—the value of probability distribution of pollutant d in the past years, as shown in Table 6. When $h=1$, there is low AWI in the planning year, resulting in low assimilative capacity. When $h=2$, there is medium AWI in the planning year, resulting in medium assimilative capacity. When $h=3$, there is high AWI in the planning year, resulting in high assimilative capacity.

Table 6 Value of probability distribution under different assimilative capacities

According to $\sum\limits_{h=1}^{3}{p}_{dh}=\sum\limits_{h=1}^{3}(\xi {p}_{h}(AWI)+(1-\xi ){p}_{d(4-h)}(DARL))\text{=}1,d=\mathrm{1,2}$, the assimilative capacity of water bodies in the planning year 2030 is affected by inflow and closely correlated with pollutant discharge in the past years; this study denotes $\xi \text{=}0.4$ and obtains the value of probability distribution of pollutant d under different assimilative capacities: ${({p}_{dh})}_{2\times 3}=[\begin{array}{ccc}0.354& 0.446& 0.200\\ 0.446& 0.400& 0.154\end{array}]$.