Industry: Agriculture and Food Supply Chain Product: ModelRisk Application: Optimizing Crop Rotation Strategies Under Uncertainty
A cooperative has to commit its land for the next decade: keep planting continuous corn, which the planning spreadsheet says is the highest-margin crop, or move to a diversified corn-soy-wheat rotation that the agronomists insist is "more sustainable" but harder to put a number on. The deterministic case favours monoculture — corn carries the best single-year margin, and a flat-margin projection compounds that lead into a tidy GBP 6.3k/ha of 10-year NPV. On that arithmetic, rotation looks like leaving money on the table.
Run 50,000 ten-year paths in ModelRisk and the ranking inverts. Continuous corn returns a mean NPV of just GBP 3.3k/ha — barely half the deterministic plan — because the spreadsheet ignored that monoculture degrades its own soil and bids up its own input costs year on year. Worse, continuous corn finishes in the red 24% of the time. The rotation returns a higher mean of GBP 6.2k/ha and loses money in only 1% of paths. The diversified strategy is not the sustainable-but-costly option; it is both more profitable and dramatically safer.
A deterministic rotation model fails on three counts at once, and they all push the same way. First, it freezes soil health — but a continuous-corn field loses fertility and demands more nitrogen and pesticide every season, a compounding drift a single-year margin never sees. Second, it treats each year as the same average year, when one shared regional weather season can knock down a decade of plantings together. Third, it ignores that corn, soy and wheat prices move together but not in lockstep — the entire mechanism by which diversification reduces risk.
The model addresses all three: a shared annual weather multiplier (with a drought tail) hits every crop in a given year; soil health follows a downward random walk under monoculture and a flat-to-improving one under rotation; and the three crop prices follow correlated LogNormal processes sharing a common commodity-price regime. The realised corn–soy price correlation comes out at 0.33 — positive enough to be real, loose enough for diversification to bite.
The cumulative-distribution view shows the rotation dominating exactly where it counts — the bottom of the distribution. At the 5th percentile, continuous corn returns −GBP 2.5k/ha while the rotation holds at +GBP 1.3k/ha, a GBP 3.8k/ha diversification benefit in the worst-case region. At P10 the gap is −GBP 1.6k vs +GBP 2.1k; at P25, GBP 0.1k vs GBP 3.6k. Monoculture gives up almost nothing at the top of the distribution and bleeds heavily at the bottom — the precise opposite of what a risk-bearing cooperative wants. Its coefficient of variation is 1.36 against the rotation's 0.58.
The fan chart isolates why the monoculture spreadsheet was so wrong. The naive flat-margin plan marches up to GBP 6.3k/ha, assuming year 10 is as productive as year 1. The simulated median path finishes at only GBP 2.5k/ha, with a P10 of −GBP 1.6k/ha — the cone bending below the deterministic line as soil-health decline and cost creep compound. The gap between the dashed plan and the median is the value the deterministic model quietly destroyed by holding soil fertility constant.
Ranking drivers by their quartile-to-quartile swing in rotation NPV, price dominates yield: the corn price level moves NPV ±GBP 3.1k/ha and the shared commodity-price regime ±GBP 2.8k/ha, with the soybean price adding ±GBP 2.4k/ha. Regional weather contributes ±GBP 0.9k/ha and — tellingly — the soil-health trajectory only ±GBP 0.2k/ha, because the rotation maintains its soil and so removes the very driver that wrecks the monoculture. The cooperative's residual risk is a market-price risk, which points to forward contracting, not to agronomy.
A rotation decision is not a margin comparison, it is a comparison of two NPV distributions. ModelRisk is what lets a cooperative choose the strategy that wins in the years that hurt, not just on the average year.