Identification of optimal organic fertilizer subsidy policies under dual uncertainty via a self-calibrated fuzzy-boundary interval programming method

The effective design of organic fertilizer subsidy policies requires a precise understanding of their socio-economic and environmental impacts under uncertainty. However, previous methods face challenges in accurately simulating policy impacts due to the lack of a calibration process for observations and their inability to handle the dual uncertainty, where intervals and fuzziness coexist within a parameter. To fill such gap, a fuzzy-boundary interval positive mathematical programming (FIPMP) model was proposed. FIPMP improves upon previous positive mathematical programming (PMP) by handling dual uncertainties expressed as fuzzy-boundary intervals in both the objective function and constraints. FIPMP can also calibrate to observed values and address constraint-violation issues. This study further integrated the inventory analysis (IA) method into the FIPMP framework (IA-FIPMP), which enabled the impact analysis of organic fertilizer subsidy policies on TN and TP loads. Applied to a case study in Chengde City, Northern China, IA-FIPMP simulated the effects of various subsidy policies, prioritizing profit maximization and considering water resources and environmental constraints. The recommended optimal subsidy levels ranged from 350-600 yuan/ton, depending on the water availability and pollution discharge permits. The recommended subsidy levels could lead to a maximum reduction of 140,000 kg in TN loads and 9000 kg in TP loads, as well as a maximum increase of 3.3 times in the organic fertilizer use area. The study further reveals that quality-based subsidy policies outperform area-based subsidy policies in promoting organic fertilizer utilization and increasing farmer income. Compared to interval PMP and interval credibility-constrained PMP, FIPMP expands the capability of uncertainty treatment by handling dual uncertainties and enhances model robustness by balancing system benefits and violation risks. FIPMP can be used to simulate the impacts of other types of policies.