Agricultural Water Management under Uncertainty Using Minimax Relative Regret Analysis Method

In this study, an inexact minimax relative regret analysis (IMRA) method is proposed for planning the agricultural water management under uncertainty. The IMRA incorporates interval-parameter programming (IPP) and minimax relative regret analysis (MRA) within an integer programming framework. IMRA can deal with uncertainties expressed as both interval values and random variables; it is capable of seeking an optimal strategy through analyzing all possible scenarios without any assumption on their probabilities. The IMRA method is then applied to a real case of agricultural water management in the Zhangweinan River Basin, one of the main food and cotton producing regions in North China and facing severe water shortage. An interval relative regret matrix is obtained based on a matrix of interval-element system benefit, and it is helpful for decision makers to identify the optimal irrigation strategy with the maximum system benefit and the minimum worst relative regret.