There is a necessity to optimize land allocation to enhance the productivity and sustainability of agricultural activities in areas that have limited land and water supplies, due to the uncertainty factor. The current study suggests two optimization models, taking into account six main crops, and a case study has been conducted in Uzbekistan, where the arable land constitutes less than 10 percent of the total land, and water supply to agriculture is scarce. The models are formulated based on the Markowitz and Kataoka models, which are premised on financial portfolio theory that the expected value of production is the return, and the variability of the yields is the risk. The Markowitz model reallocates arable land by adjusting different risk aversion parameters, whereas the Kataoka model redistributes land based on probabilistic production under a guarantee. The results of the Markowitz model have shown that there exists a risk-return trade-off in that a decrease in risk aversion leads to increasing values of expected production due to reallocation of land between crops, given a fixed total area. Wheat is always regarded as a stabilizing crop, and the higher-return crops increase its land share as the risk aversion is reduced. Although Kataoka's approach focuses on minimum production value, which will result in high land expansion and a less risky crop mix at a given probability. The analysis indicates that the replacement of Markowitz by Kataoka alters land-use decisions, and the interest will be in the redistribution of the available land to the development of more spaces of cultivated land at a predetermined probability. The findings can be used by policymakers in semi-arid areas since they indicate the fluctuation in the outcomes of the various optimization plans.

Keywords

Agricultural land allocation, Optimization, Risk-return trade-off, Sustainable agriculture, Decision support systems