# Multiperiod Optimisation of Irrigated Crops under Different Conditions of Water Availability

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Multiperiod Crop Yield Function

^{−1}) are the actual and maximum crop yields, respectively. $K{y}_{i}$ is the yield response factor, which has been documented by Doorenbos and Kassam [25] for many crops at different stages and corresponds to the slope of the yield reduction due to a decrease of applied water (Figure 1a). $ET{a}_{i}$ and $ET{c}_{i}$ (both in mm) are the actual and crop evapotranspiration for the whole growing period, respectively. Later, Raes et al. [31] proposed a multiperiod crop yield equation at constant time scales smaller than growth periods.

#### 2.2. Optimisation of Irrigated Crops

^{−1}), ${A}_{i}$ is the area to be cultivated with crop i (in ha), and ${C}_{i,k}$ represents the production costs per unit area (in US$ ha

^{−1}). Some components of ${C}_{i,k}$ are [29]: labour and other costs such as seed, fertiliser and pesticides.

^{−1}), $N{L}_{i,k}$ is the labour needed per unit area (in person-day ha

^{−1}month

^{−1}), $O{C}_{i,k}$ corresponds to other costs, and $W{r}_{k}$ is the amount of water rights in month k (in m

^{3}month

^{−1}) with its respective cost $\left(Wcr\right)$ (in US$ m

^{−3}). If farmers have the possibility to buy water (to increase the area to be irrigated) and to sell water (when not using it), they can obtain higher profits. Therefore, the monthly amounts of water to buy $\left(Vw{b}_{k}\right)$ and to sell $\left(Vw{s}_{k}\right)$ are also included, with the corresponding costs to buy $\left(Wcb\right)$ and to sell $\left(Wcs\right)$ water (in US$ m

^{−3}).

- Water availability: Assuming that the farmer has the infrastructure to store water at monthly scale ($Rc$ m
^{3}of capacity), available water is defined as:$$0\le \sum _{{k}^{\prime}=1}^{k}\left(\right)open="["\; close="]">\left(\right)open="("\; close=")">W{r}_{{k}^{\prime}}+Vw{b}_{{k}^{\prime}}$$^{3}per hectare. - Land availability: This constraint defines the area to be cultivated.$$\sum _{i=1}^{n}{A}_{i}\le At$$
- Labour availability: Assuming that the labour availability can change for each month, this constraint is defined as:$$\sum _{i=1}^{n}{A}_{i}N{L}_{i,k}\le L{a}_{k},\phantom{\rule{14.22636pt}{0ex}}\forall k$$
^{−1}). - Capital availability: Assuming that farmers can save money if it is not spent, the monthly capital availability is considered as:$$\sum _{{k}^{\prime}=1}^{k}\left(\right)open="["\; close="]">\left(\right)open="("\; close=")">Wcr\xb7W{r}_{{k}^{\prime}}+Wcb\xb7Vw{b}_{{k}^{\prime}}\le \sum _{{k}^{\prime}=1}^{k}C{a}_{{k}^{\prime}},\phantom{\rule{14.22636pt}{0ex}}\forall k$$
^{−1}). - Crop area considerations: It is necessary to consider agricultural, market and productive diversity management criteria to restrict the maximum or minimum crop areas. This is due to marketing situations, rotations, or other agricultural limitations. These constraints are expressed as:$$min\phantom{\rule{2.84544pt}{0ex}}{S}_{i}\le {A}_{i}\le max\phantom{\rule{2.84544pt}{0ex}}{S}_{i},\phantom{\rule{14.22636pt}{0ex}}\forall i$$
- Complementary considerations: To force the crop water requirement to be zero when the cultivated area is also zero, the constraint is expressed as:$$Kz\xb7{A}_{i}-\sum _{k=1}^{t}ET{a}_{i,k}\ge 0,\phantom{\rule{14.22636pt}{0ex}}\forall i$$
^{−1}). In order to not apply more water than required by the crop, the following constraint is also considered:$$ET{a}_{i,k}\le ET{c}_{i,k},\phantom{\rule{14.22636pt}{0ex}}\forall i,k$$Finally, there are non-negativity constraints expressed as:$${A}_{i},ET{a}_{i,k},Vw{b}_{k},Vw{s}_{k}\ge 0$$

#### 2.3. Case Study

#### 2.3.1. Model Inputs

#### 2.3.2. Model Application

- Scenario 1: Optimisation subject to seasonal constraints. This scenario assumes that resources are available for the season, but does not consider intraseasonal variability. In this scenario, for the whole growing period, only one value of $Ky$ and $ETa$ for each crop i was considered. Water storage and water transactions were not considered.
- Scenario 2: Optimisation subject to seasonal constraints. For the whole growing period, monthly values of $Ky$ and $ETa$ for each crop i were considered. In this scenario, water storage and water transactions were not considered.
- Scenario 3: Optimisation subject to monthly constraints, i.e., water and other resources availability at a monthly scale are considered. In this scenario, water storage and water transactions were not considered.
- Scenario 4: Optimisation subject to monthly constraints with water transactions.
- Scenario 5: Optimisation subject to monthly constraints with water storage.
- Scenario 6: Optimisation subject to monthly constraints with water storage and transactions. This scenario is the most complete, considering all possible factors involved in the process.

^{−3}, and $LC$ was 20 US$ person-day

^{−1}[47]. In this study, it was considered that alfalfa, maize, and sugar beet were watered by sprinklers ($A{E}_{i}$ = 0.75) and wheat by furrow ($A{E}_{i}$ = 0.60). For scenario 1, $K{y}_{i}$ values of 1.00, 1.25, 1.15, and 1.10 were considered for alfalfa, maize, wheat, and sugar beet, respectively, according to the recommended values by Doorenbos and Kassam [25] (Figure 1a). For scenarios 2 through 6, the values considered are shown in Table 1. For scenarios where water transactions were considered (4 and 6), $Wcb$ and $Wcs$ corresponded to 0.0018 and 0.0014 US$ m

^{−3}, respectively. On the other hand, for scenarios where water storage was considered (5 and 6), $Rc$ assumed a value of 30,000 m

^{3}.

^{3}for the whole season, respectively). The analysis tested the variation in profits by changing export prices, crop area, irrigation systems, water and labour costs, labour availability and other costs, as well as capital availability.

## 3. Results and Discussion

#### 3.1. Seasonal Use of Resources and Profits

#### 3.1.1. Situation a

#### 3.1.2. Situation b

#### 3.2. Crop Allocation

#### 3.2.1. Situation a

#### 3.2.2. Situation b

#### 3.3. Monthly Limiting Resource

^{3}).

#### 3.3.1. Situation a

#### 3.3.2. Situation b

#### 3.4. Sensitivity Analysis

#### 3.4.1. Scenario 1

#### 3.4.2. Scenario 6, Situation a

#### 3.4.3. Scenario 6, Situation b

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

^{2}). Special thanks to GAMS Technical Support for all the constructive suggestions.

## Conflicts of Interest

## References

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**Figure 1.**Representation of crop yield reduction, where (

**a**) is the seasonal crop yield reduction function proposed by Doorenbos and Kassam [25] where $Ky$ is the slope; (

**b**) is the daily crop yield reduction for maize proposed by Raes et al. [31] where relative yield stays constant when the water demand is satisfied and decreases when it is not; and (

**c**) represents daily and monthly approaches for maize.

**Figure 2.**Study area location. The right-bottom panel shows available water based on streamflow records of a distribution channel.

**Figure 3.**Monthly demand and supply of resources using collated data. Deciles 1 and 9 are the driest and the wettest conditions, respectively. Distribution of labour and capital are provided by the situation a (black bar) and b (white bar). Seasonal amount of labour and capital availability is 300 person-day and 80,000 US$, respectively. See ODEPA [46], ODEPA [47], and INIA [45] for more detailed sources of information.

**Figure 4.**Methodology used for this research. The six scenarios were assessed by two situations of time and resource distribution.

**Figure 5.**Interpretation of radar plots (Figures 6 and 7) showing profits and seasonal use of resources for each scenario at a situation of resource distribution. Each ring represents a resource index organised as follows (from inside to outside): Land, water, labour and capital used, and profit; each slice corresponds to a decile of water availability (DI).

**Figure 6.**Profits and seasonal use of resources obtained from the optimisation process for each scenario at situation a. Each ring represents a resource index organised as follows (from inside to outside): Land, water, labour and capital used, and profit; each slice corresponds to a decile of water availability (DI).

**Figure 7.**Profits and seasonal use of resources obtained from the optimisation process for each scenario at situation b. Each ring represents a resource index organised as follows (from inside to outside): Land, water, labour and capital used, and profit; each slice corresponds to a decile of water availability (DI).

**Figure 8.**Crop allocation as a result of the optimisation processes for each decile of water supply and for each scenario at the situation a.

**Figure 9.**Crop allocation as a result of the optimisation processes for each decile of water supply and for each scenario at the situation b.

**Figure 10.**Monthly limiting resources presented as water, labour, and capital availability for each decile of water supply (DI) and for each monthly scenario (from 3 to 6) for situation a (see Section 3.3).

**Figure 11.**Monthly limiting resources presented as water, labour, and capital availability for each decile of water supply (DI) and for each monthly scenario (from 3 to 6) for situation b (see Section 3.3).

**Table 1.**Parameters used for monthly crop yield functions based on the CROPWAT 8.0 database and the sowing date recommended by Faiguenbaum [43].

Crop | Parameter | Month | Sowing | ||||||
---|---|---|---|---|---|---|---|---|---|

Sep | Oct | Nov | Dec | Jan | Feb | Mar | |||

Alfalfa | $Ky$ | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 01-Sep |

$\Delta {t}^{*}$ | 30.0 | 31.0 | 30.0 | 31.0 | 31.0 | 28.0 | 15.0 | ||

${L}^{*}$ | 49.0 | 49.0 | 49.0 | 49.0 | 49.0 | 49.0 | 49.0 | ||

Maize | $Ky$ | - | - | 0.5 | 0.7 | 1.2 | 0.5 | 0.1 | 01-Nov |

$\Delta {t}^{*}$ | - | - | 30.0 | 31.0 | 31.0 | 28.0 | 5.0 | ||

${L}^{*}$ | - | - | 28.4 | 35.1 | 35.6 | 34.3 | 33.4 | ||

Wheat | $Ky$ | 0.4 | 0.6 | 0.7 | 0.5 | 0.1 | - | - | 01-Sep |

$\Delta {t}^{*}$ | 30.0 | 31.0 | 30.0 | 31.0 | 8.0 | - | - | ||

${L}^{*}$ | 30.0 | 30.9 | 32.5 | 32.6 | 8.5 | - | - | ||

Sugar beet | $Ky$ | 0.6 | 0.8 | 1.0 | 1.0 | 0.9 | 0.6 | - | 01-Sep |

$\Delta {t}^{*}$ | 30.0 | 31.0 | 30.0 | 31.0 | 31.0 | 7.0 | - | ||

${L}^{*}$ | 29.5 | 31.5 | 35.2 | 37.3 | 38.8 | 38.4 | - |

Crop | Price | Maximum Yield | Source | ||
---|---|---|---|---|---|

Value | Units | Value | Units | ||

Alfalfa | 5.1 | US$ bale^{−1} | 400 | bales ha^{−1} | INIA [45] |

Maize | 22.3 | US$ qqm^{−1} | 150 | qqm ha^{−1} | ODEPA [46] |

Wheat | 22.5 | US$ qqm^{−1} | 70 | qqm ha^{−1} | ODEPA [46] |

Sugar beet | 62.7 | US$ ton^{−1} | 100 | ton ha^{−1} | ODEPA [47] |

Function or Constraint | Equation | Scenarios |
---|---|---|

Objective | $\begin{array}{c}\hfill Max\phantom{\rule{2.84544pt}{0ex}}U=\sum _{i=1}^{n}{P}_{i}{A}_{i}Y{m}_{i}\left(\right)open="["\; close="]">1-K{y}_{i}\left(\right)open="("\; close=")">1-\frac{ET{a}_{i}}{ET{c}_{i}}& -LC\sum _{i=1}^{n}\sum _{k=1}^{t}{A}_{i}N{L}_{i,k}-\sum _{i=1}^{n}\sum _{k=1}^{t}{A}_{i}O{C}_{i,k}-Wcr\sum _{k=1}^{t}W{r}_{k}\end{array}$ | 1 |

$\begin{array}{c}\hfill Max\phantom{\rule{2.84544pt}{0ex}}U=\sum _{i=1}^{n}{P}_{i}{A}_{i}Y{m}_{i}\prod _{k=1}^{t}{\left(\right)}^{1}\Delta {t}_{i,k}^{*}/{L}_{i,k}^{*}& -LC\sum _{i=1}^{n}\sum _{k=1}^{t}{A}_{i}N{L}_{i,k}-\sum _{i=1}^{n}\sum _{k=1}^{t}{A}_{i}O{C}_{i,k}-Wcr\sum _{k=1}^{t}W{r}_{k}\end{array}$ | 2, 3, 5 | |

$\begin{array}{c}\hfill Max\phantom{\rule{2.84544pt}{0ex}}U=\sum _{i=1}^{n}{P}_{i}{A}_{i}Y{m}_{i}\prod _{k=1}^{t}{\left(\right)}^{1}\Delta {t}_{i,k}^{*}/{L}_{i,k}^{*}& -LC\sum _{i=1}^{n}\sum _{k=1}^{t}{A}_{i}N{L}_{i,k}-\sum _{i=1}^{n}\sum _{k=1}^{t}{A}_{i}O{C}_{i,k}-Wcr\sum _{k=1}^{t}W{r}_{k}-Wcb\sum _{k=1}^{t}Vw{b}_{k}+Wcs\sum _{k=1}^{t}Vw{s}_{k}\end{array}$ | 4, 6 | |

Capital | $\begin{array}{c}\hfill Wcr\sum _{k=1}^{t}W{r}_{k}+LC\sum _{i=1}^{n}\sum _{k=1}^{t}{A}_{i}N{L}_{i,k}+\sum _{i=1}^{n}\sum _{k=1}^{t}{A}_{i}O{C}_{i,k}\le \sum _{k=1}^{t}C{a}_{k}\end{array}$ | 1, 2 |

$\begin{array}{c}\hfill \sum _{{k}^{\prime}=1}^{k}\left(\right)open="["\; close="]">\left(\right)open="("\; close=")">Wcr\xb7W{r}_{{k}^{\prime}}+Wcb\xb7Vw{b}_{{k}^{\prime}}+LC\sum _{i=1}^{n}{A}_{i}N{L}_{i,{k}^{\prime}}+\sum _{i=1}^{n}{A}_{i}O{C}_{i,{k}^{\prime}}& \le \sum _{{k}^{\prime}=1}^{k}C{a}_{{k}^{\prime}},\phantom{\rule{14.22636pt}{0ex}}\forall k\end{array}$ | 3–6 | |

Water | $\begin{array}{c}\hfill 10\sum _{i=1}^{n}{A}_{i}\frac{ET{a}_{i}}{A{E}_{i}}\le \sum _{k=1}^{t}W{r}_{k}\end{array}$ | 1 |

$\begin{array}{c}\hfill 10\sum _{i=1}^{n}\sum _{k=1}^{t}{A}_{i}\frac{ET{a}_{i,k}}{A{E}_{i}}\le \sum _{k=1}^{t}W{r}_{k}\end{array}$ | 2 | |

$\begin{array}{c}\hfill 10\sum _{i=1}^{n}{A}_{i}\frac{ET{a}_{i,k}}{A{E}_{i}}\le W{r}_{k},\phantom{\rule{14.22636pt}{0ex}}\forall k\end{array}$ | 3 | |

$\begin{array}{c}\hfill 10\sum _{i=1}^{n}{A}_{i}\frac{ET{a}_{i,k}}{A{E}_{i}}+Vw{s}_{k}\le W{r}_{k}+Vw{b}_{k},\phantom{\rule{14.22636pt}{0ex}}\forall k\end{array}$ | 4 | |

$\begin{array}{c}\hfill 0\le \sum _{{k}^{\prime}=1}^{k}\left(\right)open="["\; close="]">W{r}_{{k}^{\prime}}-10\sum _{i=1}^{n}{A}_{i}\frac{ET{a}_{i,{k}^{\prime}}}{A{E}_{i}}\le Rc,\phantom{\rule{14.22636pt}{0ex}}\forall k\end{array}$ | 5 | |

$\begin{array}{c}\hfill 0\le \sum _{{k}^{\prime}=1}^{k}\left(\right)open="["\; close="]">\left(\right)open="("\; close=")">W{r}_{{k}^{\prime}}+Vw{b}_{{k}^{\prime}}-\left(\right)open="("\; close=")">10\sum _{i=1}^{n}{A}_{i}\frac{ET{a}_{i,{k}^{\prime}}}{A{E}_{i}}+Vw{s}_{{k}^{\prime}}\\ \le Rc,\phantom{\rule{14.22636pt}{0ex}}\forall k\end{array}$ | 6 |

Crop Allocation | Use of Resources | ||||||||
---|---|---|---|---|---|---|---|---|---|

Alfalfa | Maize | Wheat | Sugar Beet | Land | Water | Labor | Capital | Profits | |

(ha) | (ha) | (m^{3}) | (Person-d) | (US$) | (US$) | ||||

1. Optimum cropping pattern | 0 | 0 | 0 | 20 | 20 | 167,477 | 120 | 80,000 | 45,917 |

2. Export prices | |||||||||

2.1 Decrease in 50% for sugar beet | 0 | 25 | 0 | 0 | 25 | 172,417 | 267 | 57,114 | 26,671 |

2.2 Decrease in 50% for maize | 0 | 0 | 0 | 20 | 20 | 167,477 | 120 | 80,000 | 45,917 |

2.3 Increase in 50% for alfalfa | 8 | 0 | 0 | 17 | 25 | 201,623 | 192 | 80,000 | 51,708 |

2.4 Increase in 50% for wheat | 0 | 0 | 0 | 20 | 20 | 167,477 | 120 | 80,000 | 45,917 |

3. Agronomic management | |||||||||

3.1 Minimum area to be sowed corresponds to 3 ha | 3 | 3 | 3 | 16 | 25 | 196,754 | 178 | 79,578 | 41,695 |

4. Application efficiency of the irrigation system | |||||||||

4.1 Sugar beet is irrigated by furrow ($AE=0.60$) and | |||||||||

wheat by sprinkler ($AE=0.75$) | 0 | 0 | 0 | 20 | 20 | 209,346 | 120 | 80,000 | 45,917 |

5. Water costs | |||||||||

5.1 Costs of water rights increase to 0.05 US$/m^{3} | 0 | 0 | 0 | 16 | 16 | 131,010 | 94 | 80,000 | 18,500 |

6. Labour | |||||||||

6.1 Costs increase to 30 US$/person-d | 0 | 0 | 0 | 20 | 20 | 164,974 | 119 | 80,000 | 44,036 |

6.2 Availability decreases to 100 person-d | 0 | 0 | 0 | 17 | 17 | 139,015 | 100 | 66,502 | 38,017 |

7. Other costs | |||||||||

7.1 Increase in 50% for sugar beet | 0 | 25 | 0 | 0 | 25 | 172,417 | 267 | 57,114 | 26,671 |

7.2 Increase in 50% for maize | 0 | 0 | 0 | 20 | 20 | 167,477 | 120 | 80,000 | 45,917 |

7.3 Decrease in 50% for alfalfa | 6 | 0 | 0 | 19 | 25 | 203,014 | 184 | 80,000 | 50,321 |

7.4 Decrease in 50% for wheat | 0 | 0 | 6 | 19 | 25 | 198,643 | 146 | 80,000 | 47,781 |

8. Capital | |||||||||

8.1 Availability decreases to 50% | 0 | 0 | 0 | 10 | 10 | 83,136 | 60 | 40,000 | 22,506 |

Crop Allocation | Use of Resources | ||||||||
---|---|---|---|---|---|---|---|---|---|

Alfalfa | Maize | Wheat | Sugar Beet | Land | Water | Labor | Capital | Profits | |

(ha) | (ha) | (m^{3}) | (Person-d) | (US$) | (US$) | ||||

1. Optimum cropping pattern | 3 | 4 | 0 | 6 | 13 | 96,212 | 109 | 36,000 | 18,754 |

2. Export prices | |||||||||

2.1 Decrease in 50% for sugar beet | 5 | 0 | 0 | 0 | 5 | 37,995 | 58 | 8098 | 2805 |

2.2 Decrease in 50% for maize | 5 | 0 | 0 | 6 | 11 | 89,835 | 95 | 32,687 | 17,122 |

2.3 Increase in 50% for alfalfa | 5 | 0 | 0 | 6 | 11 | 89,835 | 95 | 32,687 | 22,349 |

2.4 Increase in 50% for wheat | 3 | 4 | 5 | 4 | 16 | 114,625 | 125 | 36,687 | 19,046 |

3. Agronomic management | |||||||||

3.1 Minimum area to be sowed corresponds to 3 ha | 3 | 4 | 3 | 5 | 14 | 107,854 | 119 | 36,434 | 16,578 |

4. Application efficiency of the irrigation system | |||||||||

4.1 Sugar beet is irrigated by furrow ($AE=0.60$) and | |||||||||

wheat by sprinkler ($AE=0.75$) | 3 | 4 | 0 | 6 | 13 | 108,040 | 109 | 36,000 | 18,737 |

5. Water costs | |||||||||

5.1 Costs of water rights increase to 0.05 US$/m^{3} | 3 | 4 | 0 | 6 | 13 | 96,212 | 109 | 53,350 | 12,505 |

6. Labour | |||||||||

6.1 Costs increase to 30 US$/person-d | 3 | 4 | 0 | 6 | 13 | 96,212 | 109 | 37,091 | 17,662 |

6.2 Availability decreases to 100 person-d | 1 | 1 | 0 | 2 | 4 | 32,071 | 36 | 12,380 | 6204 |

7. Other costs | |||||||||

7.1 Increase in 50% for sugar beet | 0 | 10 | 2 | 0 | 12 | 81,744 | 115 | 25,683 | 10,416 |

7.2 Increase in 50% for maize | 5 | 0 | 0 | 6 | 11 | 89,835 | 95 | 32,687 | 17,122 |

7.3 Decrease in 50% for alfalfa | 3 | 4 | 0 | 6 | 13 | 96,212 | 109 | 34,032 | 20,722 |

7.4 Decrease in 50% for wheat | 3 | 4 | 0 | 6 | 13 | 96,212 | 109 | 36,000 | 18,754 |

8. Capital | |||||||||

8.1 Availability decreases to 50% | 3 | 0 | 0 | 6 | 10 | 79,035 | 78 | 30,922 | 16,577 |

Crop Allocation | Use of Resources | ||||||||
---|---|---|---|---|---|---|---|---|---|

Alfalfa | Maize | Wheat | Sugar Beet | Land | Water | Labor | Capital | Profits | |

(ha) | (ha) | (m^{3}) | (Person-d) | (US$) | (US$) | ||||

1. Optimum cropping pattern | 0 | 0 | 0 | 20 | 20 | 167,460 | 120 | 80,000 | 46,177 |

2. Export prices | |||||||||

2.1 Decrease in 50% for sugar beet | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 572 | −71 |

2.2 Decrease in 50% for maize | 0 | 0 | 0 | 20 | 20 | 167,460 | 120 | 80,000 | 46,177 |

2.3 Increase in 50% for alfalfa | 0 | 0 | 0 | 20 | 20 | 167,739 | 121 | 80,000 | 46,224 |

2.4 Increase in 50% for wheat | 0 | 0 | 0 | 20 | 20 | 167,760 | 121 | 79,958 | 46,135 |

3. Agronomic management | |||||||||

3.1 Minimum area to be sowed corresponds to 3 ha | 3 | 3 | 3 | 5 | 14 | 101,803 | 113 | 36,395 | 7464 |

4. Application efficiency of the irrigation system | |||||||||

4.1 Sugar beet is irrigated by furrow ($AE=0.60$) and | |||||||||

wheat by sprinkler ($AE=0.75$) | 0 | 0 | 0 | 20 | 20 | 209,292 | 120 | 80,000 | 46,108 |

5. Water costs | |||||||||

5.1 Costs of water rights increase to 0.05 US$/m^{3} | 0 | 0 | 0 | 17 | 17 | 143,133 | 103 | 77,493 | 32,014 |

6. Labour | |||||||||

6.1 Costs increase to 30 US$/person-d | 0 | 0 | 0 | 20 | 20 | 163,870 | 118 | 79,363 | 43,920 |

6.2 Availability decreases to 100 person-d | 0 | 0 | 0 | 16 | 16 | 137,558 | 99 | 65,815 | 37,919 |

7. Other costs | |||||||||

7.1 Increase in 50% for sugar beet | 0 | 0 | 0 | 13 | 14 | 112,451 | 82 | 79,277 | 5221 |

7.2 Increase in 50% for maize | 0 | 0 | 0 | 20 | 20 | 167,433 | 121 | 79,988 | 46,074 |

7.3 Decrease in 50% for alfalfa | 0 | 0 | 0 | 20 | 20 | 168,256 | 122 | 79,980 | 46,268 |

7.4 Decrease in 50% for wheat | 0 | 0 | 0 | 20 | 20 | 168,256 | 122 | 79,980 | 46,268 |

8. Capital | |||||||||

8.1 Availability decreases to 50% | 0 | 0 | 0 | 10 | 10 | 83,074 | 60 | 39,972 | 22,872 |

© 2018 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**

Kuschel-Otárola, M.; Rivera, D.; Holzapfel, E.; Palma, C.D.; Godoy-Faúndez, A.
Multiperiod Optimisation of Irrigated Crops under Different Conditions of Water Availability. *Water* **2018**, *10*, 1434.
https://doi.org/10.3390/w10101434

**AMA Style**

Kuschel-Otárola M, Rivera D, Holzapfel E, Palma CD, Godoy-Faúndez A.
Multiperiod Optimisation of Irrigated Crops under Different Conditions of Water Availability. *Water*. 2018; 10(10):1434.
https://doi.org/10.3390/w10101434

**Chicago/Turabian Style**

Kuschel-Otárola, Mathias, Diego Rivera, Eduardo Holzapfel, Cristian D. Palma, and Alex Godoy-Faúndez.
2018. "Multiperiod Optimisation of Irrigated Crops under Different Conditions of Water Availability" *Water* 10, no. 10: 1434.
https://doi.org/10.3390/w10101434