An inexact left-hand-side chance-constrained programming (ILCCP) was proposed and applied to a nonpoint-source water quality management problem within an agricultural system. The ILCCP model can reflect uncertainties presented as interval parameters (manure mass balance, crop nutrient balances, energy and digestible protein requirements, pollutant losses, water quantity constraints, technical constraints, and so on) and left-hand-side random variables (nitrogen requirement of crop i) at the same time. A non-equivalent linearization form of ILCCP was deduced and proved intuitively, which can help handle the left-hand-side random parameters in the constraints. The decision schemes through ILCCP were analyzed under scenarios at different individual probabilities (p ᵢ , denotes the admissible probability of violating the constraint i). The performance of ILCCP was also compared with the corresponding interval linear programming model. A representative nonpoint-source water quality management case was employed to facilitate the analysis and the comparison. The optimization results indicated that the net system benefit in the water quality management case would decrease with increasing probability levels on the whole. This was because that the higher constraint satisfaction of probability would lead to stricter decision space. The optimal scheme shows an obvious downtrend in the application amount of manure as the violation probability levels decreasing from scenarios 1 to 3 (p ᵢ = 0.1, 0.05 and 0.01). This demonstrates that the application amount of manure would be reduced effectively by adjusting strictness of the constraints. This study is the first application of the ILCCP model to water quality management, which indicates that the ILCCP is applicable to other environmental problems under uncertainties.

This study explored the effects of supplemental dietary extra virgin olive oil (EVOO), gallic acid (GA), or lemongrass essential oil (LGEO) on growth performance, nutrient digestibility, carcass traits, lipid peroxidation, hematological, and antioxidative status in growing rabbits under heat stress conditions. A total of 48 male growing New Zealand White rabbits were randomly divided into four equal groups, which received a basal diet without any supplementation or supplemented with 15 g EVOO, 500 mg GA, or 400 mg LGEO/kg of diet, for eight consecutive weeks. Results revealed that the overall mean of temperature humidity index was 84.67 ± 0.35, reflecting a state of severe heat stress. Moreover, dietary supplementation with EVOO, GA, or LGEO significantly increased live body weight and daily body weight gain but decreased both feed conversion ratio and daily water consumption. Additionally, a significant increase in both organic matter and crude protein digestibility besides a remarkable elevation in the nutritive values of digestible crude protein, total digestible nutrients, and digestible energy, as well as an increase in the numbers of WBCs, lymphocytes, and heterophils was significant in EVOO-supplemented rabbits. Supplementation with EVOO, GA, or LGEO in the heat-stressed growing rabbit’s diet enhanced catalase activity and reduced glutathione content, whereas EVOO-treated rabbits had the highest values. Also, malondialdehyde activity was reduced in response to all tested additives. In conclusion, these findings suggested that addition of EVOO, GA, or LGEO in growing rabbit’s diet could be used effectively to alleviate negative impacts of heat stress load on performance, nutrient digestibility, oxidative status, and hemato-biochemical features. Furthermore, among these additives, EVOO achieved the best effects.