Multiobjective land–water allocation model for sustainable agriculture with predictive stochastic yield response

Abstract Consider an agricultural land–water resource allocation problem in which yields are spatial dependent and stochastically correlated. To achieve sustainability, we formulate a multiobjective (MO) optimization problem, in which the decision maker determines the cultivation areas and the supplemental irrigation water levels at different locations, with social, economic, and environmental goals in mind. For the social goal, we minimize the root mean squared difference of incomes among locations. For the economic goal, we minimize the production risk. We show that minimizing production risk is equivalent to maximizing the service level, when demand is normally distributed. For the environmental goal, we minimize the resource utilization. Assume that the yield vector at different locations follows a multivariate normal distribution. We formulate the MO optimization problem using a weight global criterion method, and we provide a sufficient condition for convex quadratic programming. We demonstrate the applicability of our proposed framework in the case study of sugarcane production in Thailand. To capture yield response to water, we propose several models including linear and nonlinear regressions, and we obtain the closed‐form expression for the linear and probit yield response models. The numerical experiment reveals that our solution significantly improves the social and economic goals, compared to the current policy. Finally, we illustrate how to apply our model to quantify the monetary value from reducing yield variability, which could be resulted from smart irrigation or precision agriculture.