A large number of mathematical models were developed for supporting agricultural production structure optimization decisions; however, few of them can address various uncertainties existing in many factors (e.g., eco-social benefit maximization, food security, employment stability and ecosystem balance). In this study, an interval-probabilistic agricultural production structure optimization model (IPAPSOM) is formulated for tackling uncertainty presented as discrete intervals and/or probability distribution. The developed model improves upon the existing probabilistic programming and inexact optimization approaches. The IPAPSOM considers not only food security policy constraints, but also involves rural households'income increase and eco-environmental conversation, which can effectively reflect various interrelations among different aspects in an agricultural production structure optimization system. Moreover, it can also help examine the reliability of satisfying (or risk of violating) system constraints under uncertainty. The model is applied to a real case of long-term agricultural production structure optimization in Dancheng County, which is located in Henan Province of Central China as one of the major grain producing areas. Interval solutions associated with different risk levels of constraint violation are obtained. The results are useful for generating a range of decision alternatives under various system benefit conditions, and thus helping decision makers to identify the desired agricultural production structure optimization strategy under uncertainty.
