# A Price-Forecast-Based Irrigation Scheduling Optimization Model under the Response of Fruit Quality and Price to Water

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. EEMD-ANN for Forecasting

#### 2.2. Intergrated Evaluation Method

#### 2.2.1. Factor Analysis (FA)

- (1)
- Standardization:$${Z}_{ij}=({x}_{ij}-{\overline{x}}_{j})/{S}_{j}$$
- (2)
- Calculate the coefficient matrix R of matrix Z.
- (3)
- Calculate the eigenvalues and eigenvectors of matrix R.
- (4)
- Calculate the principal factor load and perform a varimax rotation [30].
- (5)
- Computation of factor scores for each observation ${f}_{ik}$, where K is the number of main factors.
- (6)
- Calculate the comprehensive index.$${d}_{i}^{+}=\sqrt{{\displaystyle \sum _{k=1}^{K}{w}_{k}}{\left({f}_{ik}-{f}_{k}^{+}\right)}^{2}},i=1,2,\cdots ,n$$$${d}_{i}^{-}=\sqrt{{\displaystyle \sum _{k=1}^{K}{w}_{k}}{\left({f}_{ik}-{f}_{k}^{-}\right)}^{2}},i=1,2,\cdots ,n$$$${Q}_{1i}^{\ast}=\frac{{d}_{i}^{-}}{{d}_{i}^{+}+{d}_{i}^{-}},i=1,2,\cdots ,n$$

#### 2.2.2. TOPSIS

- (1)
- Standardization.$${r}_{ij}={x}_{ij}/{\displaystyle \sum _{i=1}^{m}{x}_{ij}},i=1,\dots ,m;j=1,\dots ,n$$
- (2)
- Obtain positive ideal solution (PIS) and negative ideal solution (NIS).$$PIS={A}^{+}=\left\{{r}_{1}^{+},{r}_{2}^{+},\cdots ,{r}_{j}^{+},\cdots ,{r}_{n}^{+}\right\}=\left\{\left(\mathrm{max}{r}_{ij}|j\in {J}_{1}\right),\left(\mathrm{min}{r}_{ij}|j\in {J}_{2}\right)|i=1,2,\cdots ,m\right\}$$$$NIS={A}^{-}=\left\{{r}_{1}^{-},{r}_{2}^{-},\cdots ,{r}_{j}^{-},\cdots ,{r}_{n}^{-}\right\}=\left\{\left(\mathrm{min}{r}_{ij}|j\in {J}_{1}\right),\left(\mathrm{max}{r}_{ij}|j\in {J}_{2}\right)|i=1,2,\cdots ,m\right\}$$
- (3)
- Calculate the separation.The third step is to calculate the separation from the PIS and the NIS between alternatives. The separation values can be measured using the Euclidean distance, which is given as:$${d}_{i}^{+}=\sqrt{{\displaystyle \sum _{j=1}^{n}{w}_{j}}{\left({r}_{ij}-{r}_{j}^{+}\right)}^{2}},\hspace{1em}i=1,2,\cdots ,m$$$${d}_{i}^{-}=\sqrt{{\displaystyle \sum _{j=1}^{n}{w}_{j}}{\left({r}_{ij}-{r}_{j}^{-}\right)}^{2}},\hspace{1em}i=1,2,\cdots ,m$$
- (4)
- Similarities to the PIS$${Q}_{2i}^{\ast}=\frac{{d}_{i}^{-}}{{d}_{i}^{+}+{d}_{i}^{-}},i=1,2,\cdots ,m$$

#### 2.2.3. FA-TOPSIS

#### 2.3. Modeling Relations of Yield and Quality with Water Deficit at Different Growth Stage

#### 2.3.1. Water–Yield Model

- (1)
- Jensen model:$$\frac{{Y}_{a}}{{Y}_{m}}={\displaystyle \prod _{i=1}^{n}{\left(\frac{{\mathrm{ET}}_{ai}}{{\mathrm{ET}}_{mi}}\right)}^{{\lambda}_{t}}},$$
- (2)
- Stewart model:$$\frac{{Y}_{a}}{{Y}_{m}}=1-{\displaystyle \sum _{i=1}^{n}{B}_{i}}\left(1-\frac{{\mathrm{ET}}_{ai}}{{\mathrm{ET}}_{mi}}\right),$$
- (3)
- Blank model:$$\frac{{Y}_{a}}{{Y}_{m}}={\displaystyle \sum _{i=1}^{n}{A}_{i}}\left(\frac{{\mathrm{ET}}_{ai}}{{\mathrm{ET}}_{mi}}\right),$$
- (4)
- Rao model:$$\frac{{Y}_{a}}{{Y}_{m}}={\displaystyle \prod _{i=1}^{n}\left(1-{\gamma}_{i}\left(1-\frac{{\mathrm{ET}}_{ai}}{{\mathrm{ET}}_{mi}}\right)\right)},$$

#### 2.3.2. Water–Fruit Quality Model

- (1)
- The multiplicative model adapted from the model by Jensen is given as$$\frac{{Q}_{a}}{{Q}_{m}}={\displaystyle \prod _{i=1}^{n}{\left(\frac{{\mathrm{ET}}_{ai}}{{\mathrm{ET}}_{mi}}\right)}^{\lambda {q}_{t}}};$$
- (2)
- The additive model adapted from the model by Stewart et al. is given as$$\frac{{Q}_{a}}{{Q}_{m}}=1+{\displaystyle \sum _{i=1}^{n}B{q}_{i}}\left(1-\frac{{\mathrm{ET}}_{ai}}{{\mathrm{ET}}_{mi}}\right);$$
- (3)
- The exponential model is given as$$\frac{{Q}_{a}}{{Q}_{m}}=\mathrm{exp}\left({\displaystyle \sum _{i=1}^{n}\psi}{q}_{i}\left(1-\frac{{\mathrm{ET}}_{ai}}{{\mathrm{ET}}_{mi}}\right)\right),$$

#### 2.3.3. Pricing by Quality

## 3. Case Study

#### 3.1. Data Collection

#### 3.1.1. Field Experimental Data Collection

_{c}) and actual crop evapotranspiration (ET

_{a}) were obtained by the field water balance principle. The design, agronomy, and other details of the 2008/2009 and 2009/2010 experiments are reported in 2013 [8] and those of the 2011 and 2012/2013 experiments are reported in 2014 [12]. The ET

_{a}and yield for different irrigation treatments are shown in Table 1.

#### 3.1.2. Other Data

#### 3.2. Irrigation Water Optimization Model

#### 3.2.1. Objective Function

^{3}); and ${W}_{i}$ is the amount of irrigation at the i-th growth stage (mm).

#### 3.2.2. Constraints

^{3}/cm

^{3}); ${\theta}_{\mathrm{w}}$ is the lower limit of volumetric water content, taken as the coefficient of wilting (cm

^{3}/cm

^{3}); and ${\theta}_{\mathrm{FC}}$ is the soil water holding capacity (cm

^{3}/cm

^{3}).

## 4. Results and Discussion

#### 4.1. The Results of Basic Price Forecasting by EEMD-ANN

#### 4.2. The Solutions of FA-TOPSIS

#### 4.3. Non-Linear Regression Results

#### 4.3.1. Water–Yield Relationships

^{2}value. Therefore, the Jensen model was selected to simulate the relationship between water consumption and yield of greenhouse tomatoes.

#### 4.3.2. Water–Fruit Quality Relationships

^{2}during simulation and verification. Among three models, the additive model had the highest R

^{2}value and performed better than the other models. Therefore, the additive model was chosen to simulate the relationship between water consumption and comprehensive quality of greenhouse tomatoes.

#### 4.4. Optimal Results and Discussion

#### 4.4.1. Optimization MODEL

#### 4.4.2. Optimal Solution of WYQ

^{4}Yuan/ha, respectively. At this point, the difference between the highest and lowest net benefits were 13.56 × 10

^{4}Yuan/ha, accounting for 25% of the highest. Obviously, the basic price has a direct and important impact on farmers’ income from planting tomato. Therefore, the use of more accurate price forecasting methods, such as EEMD-ANN, can provide effective advice for farmers to arrange greenhouse-tomato planting scale and planting date, thereby increasing farmers’ economic income.

^{4}Yuan/ha. This is because $\u2206d$ characterizes the price difference due to changes in tomato quality. When $\u2206d$ is larger, it indicates that the market price difference caused by the same quality change of tomato is larger. There was a negative correlation between the water requirement of tomato and the comprehensive quality index. Therefore, when the price of the tomato market is more affected by the quality, the WYQ model tends to reduce the water distribution to obtain better quality and thus obtain higher returns. Less water brings higher benefits, which suggests that it is necessary to consider the water–quality–benefit relationship at this time. This also provides irrigation advice to farmers: Full irrigation does not bring the highest benefits when the market price is more sensitive to tomato quality. Local farmers should appropriately reduce the amount of irrigation especially in Stage I, in order to improve the quality of tomatoes and thus obtain higher economic benefits at this time.

#### 4.4.3. Discussion

## 5. Conclusions

- (1)
- For the monthly forecast of tomato price, the EEMD-ANN model can significantly improve forecast accuracy compared with ANN method.
- (2)
- In the WYQ model, it can be found that Stages II and III of tomato are more important than Stage I, and meeting their water requirement should be a priority.
- (3)
- Considering the economic mechanism of market price changes with fruit quality, the irrigation scheduling optimization model can achieve the purposes of saving water resources, improving net benefit, increasing quality, and improving water-use efficiency.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**The forecast results of each intrinsic mode functions (IMF) and the residue by the artificial neural network (ANN) model.

**Figure 4.**The forecast results of tomato price using the EEMD-ANN (2009–2019) and ANN (2009–2018) models.

**Figure 5.**Actual crop evapotranspiration (ETa) and total benefits under different ${P}_{0}$ and $\u2206d$ of the water–yield–quality–benefit optimization (WYQ) model.

**Table 1.**Actual crop evapotranspiration (ET

_{a}) and yield for different irrigation treatments in four growing seasons [12].

Cropping Season | Treatment | ETa (mm) | Yield (t/ha) | |||
---|---|---|---|---|---|---|

Stage I | Stage II | Stage III | Whole Season | |||

2008–2009 | V_{1/3} | 56.1 | 61.8 | 141.5 | 259.4 | 118.2 |

V_{2/3} | 42.1 | 83.9 | 144.5 | 270.5 | 119.2 | |

F_{1/3} | 52.2 | 40.2 | 134.9 | 227.3 | 103.6 | |

F_{2/3} | 58.3 | 64.7 | 139.9 | 262.9 | 109.6 | |

R_{1/3} | 53.0 | 74.1 | 74.1 | 201.2 | 102.2 | |

R_{2/3} | 71.7 | 59.4 | 100.7 | 231.8 | 106.5 | |

CK | 65.2 | 63.4 | 140.0 | 268.6 | 113.8 | |

2009–2010 | F_{1/3} | 68.8 | 39.8 | 126.8 | 235.4 | 114.7 |

F_{2/3} | 67.9 | 66.6 | 134.0 | 268.6 | 121.5 | |

R_{1/3} | 69.3 | 82.2 | 61.0 | 212.5 | 111.0 | |

R_{2/3} | 71.2 | 80.1 | 94.4 | 245.2 | 120.7 | |

CK | 68.4 | 82.1 | 134.0 | 284.5 | 128.1 | |

2011 | F_{8/9}R_{8/9} | 26.1 | 85.3 | 189.8 | 301.2 | 136.9 |

F_{7/9}R_{7/9} | 28.8 | 80.1 | 185.1 | 294.0 | 119.4 | |

F_{6/9}R_{6/9} | 27.0 | 76.5 | 158.4 | 261.8 | 110.3 | |

F_{5/9}R_{5/9} | 26.3 | 67.0 | 125.7 | 218.9 | 97.5 | |

F_{4/9}R_{4/9} | 26.9 | 61.7 | 103.5 | 192.0 | 88.2 | |

CK | 28.9 | 95.9 | 205.0 | 329.9 | 138.0 | |

2012–2013 | F_{1/3} | 58.8 | 62.2 | 140.9 | 262.0 | 84.2 |

F_{2/3} | 52.6 | 78.2 | 146.6 | 277.4 | 95.2 | |

R_{1/3} | 57.8 | 98.7 | 66.1 | 222.7 | 75.6 | |

R_{2/3} | 51.6 | 97.3 | 114.4 | 263.3 | 92.2 | |

F_{2/3}R_{2/3} | 59.6 | 74.1 | 98.4 | 232.0 | 84.6 | |

F_{2/3}R_{1/3} | 59.4 | 74.8 | 80.4 | 214.6 | 80.6 | |

F_{1/3}R_{2/3} | 54.6 | 57.2 | 100.3 | 212.2 | 81.4 | |

F_{1/3}R_{1/3} | 56.8 | 53.8 | 60.8 | 171.3 | 64.6 | |

CK | 58.3 | 98.2 | 146.6 | 303.1 | 96.9 |

_{1/3}: 1/3 full irrigation at Stage I, F

_{8/9}R

_{8/9}: 8/9 full irrigation at Stage II, and 8/9 full irrigation at Stage III. The explanation of the symbols is the same as below.

**Table 2.**Tomato quality parameters for different irrigation treatments in four growing seasons [12] (TSS, total soluble solids; RS, reducing sugars; OA, organic acids; SAR, sugar/acid content ratio; VC, vitamin C; Fn, fruit firmness; CI, color index).

Cropping Season | Treatment | TSS (°rix) | RS (g 100 g/FW) | OA (g 100 g/FW) | SAR | VC (mg kg/FW) | Fn (kg/m^{2}) | CI |
---|---|---|---|---|---|---|---|---|

2008–2009 | V_{1/3} | 4.57 | 3.44 | 0.432 | 7.96 | 73.60 | 5.25 | 32.3 |

V_{2/3} | 4.50 | 3.47 | 0.436 | 7.96 | 73.60 | 5.36 | 33.9 | |

F_{1/3} | 5.06 | 4.08 | 0.486 | 8.40 | 85.80 | 5.93 | 35.0 | |

F_{2/3} | 4.64 | 3.60 | 0.449 | 8.02 | 78.10 | 5.62 | 34.3 | |

R_{1/3} | 4.98 | 4.07 | 0.482 | 8.44 | 101.10 | 6.19 | 36.5 | |

R_{2/3} | 4.88 | 3.67 | 0.454 | 8.06 | 86.80 | 5.64 | 35.9 | |

CK | 4.66 | 3.38 | 0.438 | 7.72 | 72.80 | 5.23 | 30.2 | |

2009–2010 | F_{1/3} | 6.02 | 2.91 | 0.311 | 9.36 | 183.60 | 8.26 | 35.8 |

F_{2/3} | 5.44 | 2.55 | 0.273 | 9.34 | 176.40 | 7.90 | 33.5 | |

R_{1/3} | 6.16 | 3.29 | 0.300 | 10.99 | 217.40 | 8.37 | 35.4 | |

R_{2/3} | 5.91 | 2.82 | 0.285 | 9.91 | 199.20 | 7.96 | 33.8 | |

CK | 5.55 | 2.60 | 0.283 | 9.20 | 163.20 | 7.39 | 31.3 | |

2011 | F_{8/9}R_{8/9} | 4.86 | 2.45 | 0.374 | 6.53 | 167.50 | 5.45 | 33.4 |

F_{7/9}R_{7/9} | 5.51 | 2.59 | 0.398 | 6.52 | 179.10 | 5.84 | 35.8 | |

F_{6/9}R_{6/9} | 5.67 | 2.86 | 0.407 | 7.01 | 185.50 | 5.94 | 36.3 | |

F_{5/9}R_{5/9} | 5.76 | 3.17 | 0.423 | 7.50 | 198.70 | 5.92 | 36.7 | |

F_{4/9}R_{4/9} | 6.11 | 3.64 | 0.440 | 8.27 | 204.90 | 6.05 | 37.4 | |

CK | 4.99 | 2.46 | 0.376 | 6.55 | 166.40 | 5.43 | 32.5 | |

2012–2013 | F_{1/3} | 5.70 | 3.76 | 0.452 | 8.32 | 143.60 | 4.58 | 37.8 |

F_{2/3} | 5.33 | 3.39 | 0.417 | 8.15 | 120.70 | 4.27 | 36.5 | |

R_{1/3} | 6.33 | 4.63 | 0.435 | 10.24 | 150.20 | 4.71 | 41.1 | |

R_{2/3} | 5.28 | 3.44 | 0.400 | 8.58 | 136.40 | 4.00 | 36.4 | |

F_{2/3}R_{2/3} | 5.90 | 3.83 | 0.431 | 8.89 | 141.10 | 4.16 | 39.1 | |

F_{2/3}R_{1/3} | 5.78 | 4.20 | 0.457 | 9.48 | 150.60 | 4.75 | 38.9 | |

F_{1/3}R_{2/3} | 6.22 | 4.42 | 0.445 | 9.93 | 148.40 | 4.49 | 39.1 | |

F_{1/3}R_{1/3} | 6.63 | 4.79 | 0.452 | 10.59 | 151.70 | 4.91 | 40.1 | |

CK | 5.22 | 3.34 | 0.402 | 7.98 | 117.60 | 3.95 |

Soil Water Holding Capacity | (cm^{3}/cm^{3}) | 0.36 | Fixed cost | (Yuan/ha) | 30,420.4 |

Initial Soil Moisture Content | (cm^{3}/cm^{3}) | 0.29 | Basic water price | (Yuan/ha) | 30.0 |

Lower Limit of Volumetric Water Content | (cm^{3}/cm^{3}) | 0.16 | Metered water price | (Yuan/m^{3}) | 0.157 |

Planned Wet Layer Depth | (m) | 0.5 |

Model | RMSE (Yuan/kg) | MARE (%) | R | NSEC |
---|---|---|---|---|

ANN | 0.491 | 10.36 | 0.856 | 0.732 |

EEMD-ANN | 0.224 | 4.40 | 0.972 | 0.944 |

Variable | Factor 1 | Factor 2 | Factor 3 |
---|---|---|---|

TSS | 0.214 | 0.402 | −0.380 |

RS | 0.542 | 0.100 | −0.450 |

OA | −0.432 | 1.233 | −0.489 |

SAR | 0.914 | −0.479 | −0.309 |

VC | 0.259 | −0.368 | 0.363 |

Fn | −0.434 | 0.248 | 0.549 |

CI | −0.416 | −0.524 | 1.319 |

Percent of variance (%) | 38.130 | 29.748 | 27.423 |

Cumulative percent of variance (%) | 38.130 | 67.878 | 95.301 |

**Table 6.**Tomato comprehensive quality scores for different irrigation treatments by factor analysis (FA), technique for order of preference by similarity to ideal solution (TOPSIS), and FA-TOPSIS methods.

Cropping Season | Treatment | Factor Score | ${\mathit{Q}}_{1\mathit{i}}^{\ast}$ | Ranking | ${\mathit{Q}}_{2\mathit{i}}^{\ast}$ | Ranking | ${\mathit{Q}}_{\mathit{i}}$ | Ranking | ||
---|---|---|---|---|---|---|---|---|---|---|

Factor 1 | Factor 2 | Factor 3 | ||||||||

2008–2009 | V_{1/3} | −0.066 | −1.030 | −0.581 | 0.372 | 6 | 0.105 | 6 | 0.239 | 6 |

V_{2/3} | −0.631 | −1.249 | 0.618 | 0.401 | 5 | 0.156 | 5 | 0.278 | 5 | |

F_{1/3} | 1.154 | 1.863 | −1.087 | 0.660 | 2 | 0.455 | 2 | 0.557 | 2 | |

F_{2/3} | −0.567 | −0.351 | 0.607 | 0.465 | 4 | 0.233 | 4 | 0.349 | 4 | |

R_{1/3} | 1.052 | 0.610 | 1.084 | 0.732 | 1 | 0.569 | 1 | 0.651 | 1 | |

R_{2/3} | −0.250 | −0.357 | 1.264 | 0.532 | 3 | 0.354 | 3 | 0.443 | 3 | |

CK | −0.693 | 0.514 | −1.905 | 0.365 | 7 | 0.054 | 7 | 0.209 | 7 | |

2009–2010 | F_{1/3} | −1.713 | 2.085 | 0.872 | 0.539 | 2 | 0.336 | 3 | 0.438 | 2 |

F_{2/3} | −0.797 | −1.544 | 1.052 | 0.406 | 4 | 0.146 | 4 | 0.276 | 4 | |

R_{1/3} | 2.020 | −0.096 | 0.205 | 0.675 | 1 | 0.616 | 1 | 0.645 | 1 | |

R_{2/3} | 0.611 | −0.620 | 0.076 | 0.518 | 3 | 0.342 | 2 | 0.430 | 3 | |

CK | −0.121 | 0.175 | −2.206 | 0.372 | 5 | 0.054 | 5 | 0.213 | 5 | |

2011 | F_{8/9}R_{8/9} | −0.303 | −1.093 | −0.726 | 0.332 | 6 | 0.052 | 6 | 0.192 | 6 |

F_{7/9}R_{7/9} | −1.280 | 0.154 | 0.969 | 0.468 | 4 | 0.245 | 4 | 0.356 | 4 | |

F_{6/9}R_{6/9} | −0.534 | 0.258 | 0.885 | 0.531 | 3 | 0.368 | 3 | 0.450 | 3 | |

F_{5/9}R_{5/9} | 0.454 | 0.403 | 0.509 | 0.621 | 2 | 0.544 | 2 | 0.582 | 2 | |

F_{4/9}R_{4/9} | 1.679 | 0.901 | −0.025 | 0.735 | 1 | 0.745 | 1 | 0.740 | 1 | |

CK | −0.016 | −0.624 | −1.613 | 0.341 | 5 | 0.054 | 5 | 0.197 | 5 | |

2012–2013 | F_{1/3} | −1.549 | 1.607 | 0.147 | 0.496 | 5 | 0.401 | 6 | 0.448 | 6 |

F_{2/3} | −1.310 | 0.023 | −0.487 | 0.356 | 8 | 0.143 | 8 | 0.249 | 8 | |

R_{1/3} | 1.157 | −0.779 | 1.443 | 0.619 | 2 | 0.780 | 2 | 0.699 | 2 | |

R_{2/3} | 0.234 | −1.921 | −0.287 | 0.375 | 7 | 0.234 | 7 | 0.305 | 7 | |

F_{2/3}R_{2/3} | −0.152 | −0.399 | 0.389 | 0.484 | 6 | 0.416 | 5 | 0.450 | 5 | |

F_{2/3}R_{1/3} | −0.319 | 1.050 | 0.480 | 0.586 | 4 | 0.611 | 4 | 0.599 | 4 | |

F_{1/3}R_{2/3} | 1.076 | 0.317 | −0.295 | 0.617 | 3 | 0.674 | 3 | 0.646 | 3 | |

F_{1/3}R_{1/3} | 1.446 | 0.747 | 0.194 | 0.724 | 1 | 0.842 | 1 | 0.783 | 1 | |

CK | −0.583 | −0.646 | −1.585 | 0.277 | 9 | 0.054 | 9 | 0.165 | 9 |

Model | $\mathbf{Sensitivity}\mathbf{Index}({\mathit{\lambda}}_{\mathit{i}}$$/{\mathit{B}}_{\mathit{i}}$$/{\mathit{A}}_{\mathit{i}}$$/{\mathit{\gamma}}_{\mathit{i}})$ | ${\mathbf{R}}^{2}$ | |||
---|---|---|---|---|---|

Stage I | Stage II | Stage III | Simulation | Verification | |

Jenson | 0.058 | 0.257 | 0.286 | 0.764 | 0.878 |

Stewart | 0.108 | 0.287 | 0.344 | 0.810 | 0.808 |

Blank | 0.281 | 0.349 | 0.402 | 0.809 | 0.727 |

Rao | 0.107 | 0.295 | 0.347 | 0.783 | 0.838 |

**Table 8.**The water deficit sensitivity indexes of tomato comprehensive quality and the ${\mathrm{R}}^{2}$.

Model | $\mathbf{Sensitivity}\mathbf{Index}(\mathit{\lambda}{\mathit{q}}_{\mathit{i}}/\mathit{B}{\mathit{q}}_{\mathit{i}}/\mathit{\psi}{\mathit{q}}_{\mathit{i}})$ | ${\mathbf{R}}^{2}$ | |||
---|---|---|---|---|---|

Stage I | Stage II | Stage III | Simulate | Verify | |

Multiplication | −1.507 | −0.806 | −1.392 | 0.838 | 0.547 |

Additive | 2.643 | 1.629 | 3.793 | 0.914 | 0.713 |

Exponential | 1.709 | 0.880 | 1.947 | 0.852 | 0.645 |

**Table 9.**Comparison of optimal results from the water–yield–benefit optimization (WY) and WYQ ($\u2206d=0.5$ and $\u2206d=1.0$) models.

Models | Optimal Irrigation Water in the Whole Season (mm) | Net Benefits (10^{4} Yuan) | Water Use Efficiency (Yuan/m^{3}) | ||||||
---|---|---|---|---|---|---|---|---|---|

P0_{1} | P0_{2} | P0_{3} | P0_{1} | P0_{2} | P0_{3} | P0_{1} | P0_{2} | P0_{3} | |

WY | 238.1 | 238.1 | 238.1 | 55.3 | 49.1 | 41.7 | 232.5 | 206.4 | 175.1 |

WYQ (Δd = 0.5) | 237.0 | 231.3 | 224.4 | 55.3 | 49.2 | 41.8 | 233.5 | 212.6 | 186.2 |

WYQ (Δd = 1.0) | 210.0 | 209.0 | 209.0 | 56.4 | 50.4 | 43.2 | 268.3 | 241.2 | 206.9 |

_{1}= 6.03 Yuan/kg, P0

_{2}= 5.39 Yuan/kg, P0

_{3}= 4.62 Yuan/kg.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Shan, B.; Guo, P.; Guo, S.; Li, Z. A Price-Forecast-Based Irrigation Scheduling Optimization Model under the Response of Fruit Quality and Price to Water. *Sustainability* **2019**, *11*, 2124.
https://doi.org/10.3390/su11072124

**AMA Style**

Shan B, Guo P, Guo S, Li Z. A Price-Forecast-Based Irrigation Scheduling Optimization Model under the Response of Fruit Quality and Price to Water. *Sustainability*. 2019; 11(7):2124.
https://doi.org/10.3390/su11072124

**Chicago/Turabian Style**

Shan, Baoying, Ping Guo, Shanshan Guo, and Zhong Li. 2019. "A Price-Forecast-Based Irrigation Scheduling Optimization Model under the Response of Fruit Quality and Price to Water" *Sustainability* 11, no. 7: 2124.
https://doi.org/10.3390/su11072124