Abstract
Farmland management and irrigation scheduling are vital to a productive agricultural economy. A multistage stochastic programming model is proposed to maximize farmers’ annual profit under uncertainty. The uncertainties considered include crop prices, irrigation water availability, and precipitation. During the first stage, pre-season decisions including seed type and plant density are made, while determinations of when to irrigate and how much water to be used for each irrigation are made in the later stages. The presented case study, based on a farm in Nebraska, U.S.A., showed that a 10% profit increase could be achieved by taking the corn price and irrigation water availability uncertainties into consideration using two-stage stochastic programming. An additional 13% profit increase could be achieved by taking precipitation uncertainty into consideration using multistage stochastic programming. The stochastic model outperforms the deterministic model, especially when there are limited water supplies. These results indicate that multistage stochastic programming is a promising method for farm-scale irrigation management and can increase farm profitability.
Highlights
As the world population increases and the amount of arable land decreases, it becomes vital to improve the productivity of available farmland
The objective value of two-stage stochastic programming ðvTf SÞ is $13,367, which yields a value of the stochastic solution (VSS) of $1,239 and a relative values of two-stage stochastic programming (RVSS) of 10%. These results show that a 10% profit increase could be achieved by taking corn price and total water limit uncertainties into consideration when making pre-season decisions of seed type selection and plant population selection
The uncertainties under investigation include the corn price, irrigation water limits, and precipitation amount. Their distributions are carefully defined based on a detailed derivation process, and the sample average approximation method is used to generate scenarios
Summary
As the world population increases and the amount of arable land decreases, it becomes vital to improve the productivity of available farmland. The advent of diesel and electric motors has led to systems that can pump groundwater out of major aquifers and help increase crop productivity. Concerns have been raised regarding the permanent loss of aquifer capacity, declining surface and groundwater supplies, and increased pumping costs [1, 2]. Irrigation management practices under limited water supplies are critical for sustainable agriculture and food security
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