A fuzzy fractional programming model for optimizing water footprint of crop planting and trading in the Hai River Basin, China

Abstract

This study integrates water footprint theory, fuzzy chance-constrained programming (FCCP) and fractional programming (FP) into a general optimization framework to help seek the optimal crop planting patterns for the agricultural water management (AWM) system. The modeling framework can not only address the system objective as output-input ratios and tackles uncertainties by using fuzzy sets, but also help support the cleaner production of crops by controlling the portion of green, blue and grey water footprint. It also considers the efficiency of system’s economic water productivity, water footprint components control, water-food nexus, balance of crop trade benefit and water footprint loss of trading crops. This framework is applied to agricultural water planning and management in Hai River Basin, China. The study results indicated that more rice, sorghum and millet are desired in the central districts, the south-central districts and almost all districts, while wheat and maize need to be reduced over most districts. This optimal crop planting pattern (under γ=0.75) would reduce blue and grey water in the central and southeastern, and almost all districts, respectively, improve the basin’s economic water productivity by 139%, and increase the trade benefit by 0.35 × 109 $ and reduce the total water footprint loss by 1.38 × 109 m3. When the credibility level increased from 0.55 to 0.95, the optimal economic water productivity would decrease from 0.1280 to 0.1127 $/m3 associated with decreasing grey and blue water footprints, increasing trade benefit and decreasing footprint loss. It appeared that a higher credibility level would lead to a stricter control requirement for the fuzzy chance constrains and a greater drag on searching a better objective. Thus, the proposed modelling framework could help obtain a series of crop planting patterns under various credibility levels and ensure to optimize the water footprint of crop planting and trading under uncertainties.