An integrated DP-MIP model for optimal crop mix selection with deficit irrigation

We consider a region suffering from irrigation water scarcity. Candidate crops differ widely in their growth cycles, economic values and water consumption. We develop an integrated dynamic programming-mixed integer programming model to solve for optimal land exploitation over a one year horizon for multiple crops. The model applies deficit irrigation in order to increase the irrigated area at the expense of reducing crop yield per unit area. The dynamic program (DP) guarantees that deficit irrigation is only considered when it is economically efficient. Moreover, it provides optimal combinations of irrigation levels for each growth stage of candidate crops, accounting for the varying impact of water stress over time and the seasonal supply of irrigation water. The output of the DP serves as input to the mixed integer program (MIP). The MIP selects the most profitable crops in the right sequence to benefit the most from the crop-yield dependence on crop predecessor and allocates water and land optimally to maximize total profit. The objective function accounts for the attitude of the decision-maker toward risk by incorporating in its expression a risk-aversion coefficient.