An inexact robust two-stage mixed-integer linear programming approach for crop area planning under uncertainty

Abstract

This study presents an inexact robust two-stage mixed-integer linear programming (IRTMLP) approach for crop area planning under uncertainty. The approach is developed by incorporating the techniques of interval parameter programming, robust optimization method, and mixed-integer linear programming within a two-stage stochastic programming optimization framework. In the IRTMLP, uncertainties presented in terms of probability distributions and discrete intervals can be reflected. Moreover, the approach improves upon the previous stochastic programming method and thus has the following four major advantages. First, the IRTMLP approach can incorporate pre-defined irrigation water policies directly into its optimization framework, and second, it can readily facilitate dynamic analysis of water-saving irrigation pattern planning for irrigation water management. Third, it can explicitly account for the variability of the second-stage variables within a conventional two-stage stochastic programming context. Fourth, it can generate more flexible solutions under different robustness levels. The IRTMLP approach is applied to a case study of crop area planning in the middle reaches of the Heihe River Basin, northwest China. Therefore, a variety of decision alternatives for binary and continuous variables can be generated by giving different robustness levels, which will demonstrate how the developed approach can provide desired and stable solutions. In addition, the results can support in-depth analysis of the interrelationships among system benefits, robustness levels and the system-failure risk levels. These results can provide more reliable scientific basis for supporting irrigation water management under arid and semiarid environments.