Water-Saving Revenue Guarantee Optimization in Water Saving Management Contract Based on Simulation Method

Abstract

Water saving management contract (WSMC) is an innovative water saving strategy based on market mechanism. As the minimum annual project water-saving revenue agreed with water saving service company (WSSC) and water user, water-saving revenue guarantee (WRG) is one of the key elements in WSMC projects. This paper attempted to establish a model to determine the optimal WRG based on simulation method. First, a nonlinear relationship between water-saving amount and initial investment was built by industry standards. Then, the quantitative influence of water-saving awareness on water-saving amount was built based on Markov chain. Next, a random process with decreasing variance over time was used to describe the fluctuation. Next, the failure maintenance cost in water-saving system was described by renewal function. After that, an unconstraint WRG optimization model of the WSMC was constructed with the WSSC total profit difference net present value (NPV) as the objective function and a solution algorithm was designed. Then, the sensitivity analysis was performed on fluctuation coefficient, estimated model parameters and project original variables. Next, the validities analysis on water-saving revenue and water-saving cost was provided. Finally, a WSMC project case in China was studied and the solutions were compared with traditional model. The results showed that the optimized WRG in this paper was 17% higher than the original one, and the WSSC total profit difference NPV was reduced by about 1200000 yuan. Reducing appropriate initial investment and increasing assistance to water user, like enhancing its water-saving awareness, are efficient methods to improve WRG for WSSC.

Appendices

Appendix A

When the annual realized water saving income exceeds the guaranteed value, the excess is shared between WSSC and the water user; When the annual realized water savings revenue does not reach the guaranteed value, WSSC is required to compensate for the shortfall. The profit difference of each participant can be calculated from the profit difference of the project.

When the realized water saving revenue exceeds the guaranteed value of water saving revenue, we have

Water user Profit difference

$$\begin{aligned}&=\text{Water user actual profit}-\text{Water user expected profit}\\&=\left(\text{Water-saving revenue guarantee}\times \text{Water user's share ratio}+\text{Extra water-saving}\right.\\&\left.\quad\text{revenue}\times \text{Water user's share ratio}-\text{Water user actual cost}\right)\\&\;\;\,-\left(\text{Water-saving revenue guarantee}\times \text{Water user's share ratio}-\text{Water user} \right.\\&\left.\quad\text{expected cost}\right)\\&=\text{ Extra water-saving revenue} \times \text{water users' share ratio} \end{aligned}$$

$$\begin{aligned}&\text{ WSSC profit difference}=\text{WSSC actual profit}-\text{WSSC expected profit}\\&=(\text{Water-saving revenue guarantee}\times \text{WSSC's share ratio}+\text{Extra water-saving}\\&\quad\;\text{revenue}\times \text{WSSC's share ratio}-\text{WSSC actual cost})\\&\quad-(\text{Water-saving revenue guarantee}\times \text{WSSC's share ratio }-\text{WSSC expected}\\&\text{ cost)}\\&=\text{Extra water-saving revenue}\times \text{WSSC share ratio}-\text{Actual project cos}\\&\quad+\text{Expected project cost}\end{aligned}$$

When the realized water-saving revenue is less than the water-saving revenue guarantee,

$$\begin{aligned}&\text{ Water user profit difference}=\text{Water user actual profit}-\text{Water user expected profit}\\&=\left(\text{Water-saving revenue guarantee}\times \text{Water user's share ratio}-\text{Water user actual}\right.\\&\left.\text{ cost}\right)-\left(\text{Water-saving revenue guarantee}\times \text{Water user's share ratio}-\text{Water user} \right.\\&\left. \text{ expected cost}\right)\\&=0\end{aligned}$$

$$\begin{aligned}&\text{ WSSC profit difference}=\text{WSSC actual profit}-\text{WSSC expected profit}\\&=(\text{Actual water-saving revenue}\times \text{WSSC's share ratio}-\text{Insufficient water-saving}\\&\text{ revenue}\times \text{Water user's share ratio}-\text{WSSC actual cost})-(\text{Water-saving revenue} \\&\text{ guarantee}\times \text{WSSC's share ratio}-\text{WSSC expected cost})\\&=\text{Actual water-saving revenue}-\text{Water-saving revenue guarantee}-\text{Actual project}\\&\text{ cost }+\text{Expected project cost}\end{aligned}$$

Appendix B

Fig. 4

Uncertainty with fluctuation coefficient: a Water-saving amount with adjusted fluctuation coefficient. b Total profit difference NPV of WSSC with adjusted fluctuation coefficient. c Optimal WRG with adjusted fluctuation coefficient

Fig. 5

Sensitivity analysis of water-saving amount and water-saving cost: a Water-saving amount with adjusted potential water-saving coefficient. b Water-saving amount with adjusted transition probability. c Water-saving cost with adjusted cost coefficient. d Water-saving cost with adjusted growth rate

Fig. 6

Sensitivity analysis of WSSC total profit difference NPV: a With adjusted potential water-saving coefficient. b With adjusted transition probability. c With adjusted cost coefficient. d With adjusted growth rate

Appendix C

Table 3 Sensitivity analysis results