Vose SoftwareModelChoice decision tree · Agriculture and food
Agricultural Irrigation
Should a 640-acre farm install centre-pivot, drip or upgraded flood irrigation, or stay rain-fed?
From the model’s decision tree
Best first decision: Center Pivot System
The expected value of each first option when every later decision is also made well (the tree rolled back).
| First decision | Expected value | |
|---|---|---|
| Center Pivot System | $6,146,600 | ✔ best |
| Drip Irrigation | $5,214,600 | |
| Flood Irrigation Upgrade | $3,725,300 | |
| Rain-Fed Only | $3,173,760 |
| Measure | Value |
|---|---|
| Expected value of the best strategy | $6,146,600 |
| Best outcome on the best strategy | $6,278,600 |
| Worst outcome on the best strategy | $6,038,600 |
S-curve (cumulative probability) of Center Pivot System from the saved simulation.
The decision
A farmer with 640 acres (one section) of cropland in the semi-arid Great Plains must decide whether to invest in an irrigation system. Current rain-fed yields are variable and declining aquifer levels make water rights increasingly valuable. The farmer must choose between:
- Center pivot system — proven technology, moderate water efficiency
- Drip irrigation — highest efficiency but highest per-acre cost
- Flood irrigation upgrade — lowest cost but least efficient
- Rain-fed only — no capital investment, accept weather risk
How the inputs are linked
The tree sheet has a parameter table above the decision tree. Crop yields, prices, water costs, and acreage are defined once and referenced by multiple branches. Changing a single parameter instantly updates all linked values.
The inputs that drive several branches at once:
- Crop Price per Bushel — revenue driver in every terminal value
- Acres to Irrigate — scales all costs and revenues across all paths
- Water Cost per AF — operating cost in all irrigation options
- Irrigated Yield — production basis for pivot, drip, and flood paths
- Rain-Fed Yield — baseline for rain-fed and partial in flood option
- Well Drilling Cost — capital cost shared by pivot and drip options
The decision tree
The tree has 1 decision, 4 chance events and 12 outcomes. The best path is open: at every decision the best choice is marked, and the expected value beside each branch counts every cash flow from the start. Open any other branch to see what follows it.
DecisionChance event+$ cash flow on the branch
Center Pivot System −$118,000expected $6,146,600 ✔ best
Chance: Rainfall (Center Pivot)- 25% Drought Year +$6,156,600payoff $6,038,600
- 50% Normal Year +$6,252,600payoff $6,134,600
- 25% Wet Year +$6,396,600payoff $6,278,600
Drip Irrigation −$801,000expected $5,214,600
Chance: Rainfall (Drip Irrigation)- 25% Drought Year +$6,005,520payoff $5,204,520
- 50% Normal Year +$6,091,920payoff $5,290,920
- 25% Wet Year +$5,873,040payoff $5,072,040
Flood Irrigation Upgrade −$23,000expected $3,725,300
Chance: Rainfall (Flood Upgrade)- 25% Drought Year +$2,399,900payoff $2,376,900
- 50% Normal Year +$4,601,500payoff $4,578,500
- 25% Wet Year +$3,390,300payoff $3,367,300
Rain-Fed Onlyexpected $3,173,760
Chance: Rainfall (Rain-Fed)- 25% Drought Year +$1,763,200payoff $1,763,200
- 50% Normal Year +$3,526,400payoff $3,526,400
- 25% Wet Year +$3,879,040payoff $3,879,040
Change the numbers. Open the workbook with ModelChoice, change a probability or a cost in the tree, and the best decision updates at once.
Key assumptions
| Assumption | Value | Notes |
|---|---|---|
| Well Drilling Cost | $25,000 | Cost to drill one irrigation well |
| Pump Cost | $8,000 | Pump and motor equipment cost |
| Water Cost per Acre-Foot | $50 | Cost of water rights or pumping per AF |
| Crop Yield - Irrigated (bu/acre) | 180 | Expected yield with full irrigation |
| Crop Yield - Rain-Fed (bu/acre) | 95 | Expected yield without irrigation |
| Crop Price per Bushel | $6 | Market price per bushel of crop |
| Acres to Irrigate | 640 | Total irrigated acreage (1 section) |
| System Maintenance Cost/Year | $4,500 | Annual maintenance and repairs |
| Center Pivot System Cost | $85,000 | Center pivot hardware and installation |
| Drip System Cost per Acre | $1,200 | Drip irrigation equipment per acre |
| Water Use - Pivot (AF/acre) | 1.50 | Water application rate for center pivot |
| Water Use - Drip (AF/acre) | 0.90 | Water application rate for drip (efficient) |
| Analysis Period | 10 | Time horizon for NPV of investment |
| Flood Upgrade Cost | $15,000 | Cost to improve existing flood system |
The figures are illustrative: the companies and numbers are invented for teaching.
Try it in ModelChoice
- Increase Crop Price. Watch irrigated options gain advantage over rain-fed
- Raise Water Cost per AF. See drip efficiency advantage grow
- Change Acres. Observe how scale affects the drip vs pivot decision
- Run Sensitivity Analysis. Tornado chart shows which parameters matter most
Find similar models
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Further reading
Download the workbook and open it with ModelChoice. The free trial opens every example.
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An illustrative example: the figures are invented for teaching. Last updated 9 October 2026.