Solving bi-objective bi-item solid transportation problem with fuzzy stochastic constraints involving normal distribution

In today's competitive world, entrepreneurs cannot argue for transporting a single product. It does not provide much profit to the entrepreneur. Due to this reason, multiple products need to be transported from various origins to destinations through various types of conveyances. Real-world decision-making problems are typically phrased as multi-objective optimization problems because they may be effectively described with numerous competing objectives. Many real-life problems have uncertain objective functions and constraints due to incomplete or uncertain information. Such uncertainties are dealt with in fuzzy/interval/stochastic programming. This study explored a novel integrated model bi-objective bi-item solid transportation problem with fuzzy stochastic inequality constraints following a normal distribution. The entrepreneur's objectives are minimizing the transportation cost and duration of transit while maximizing the profit subject to constraints. The chance-constrained technique is applied to transform the uncertainty problem into its equivalent deterministic problem. The deterministic problem is then solved with the proposed method, namely, the global weighted sum method (GWSM), to find the optimal compromise solution. A numerical example is provided to test the efficacy of the method and then is solved using the Lingo 18.0 software. To highlight the proposed method, comparisons of the solution with the existing solution methods are performed. Finally, to understand the sensitivity of parameters in the proposed model, sensitivity analysis (SA) is conducted

Origin of silica in rice plants and contribution of diatom Earth fertilization : insights from isotopic Si mass balance in a paddy field

International audienceBackground and aims: The benefits of Si for crops is well evidenced but the biogeochemical cycle of Si in agriculture remains poorly documented. This study aims at identifying and quantifying the Si sources (primary and secondary soil minerals, amorphous silica, irrigation, Si-fertilizer) to rice plants.Method: Field experiments were carried out with and without application of diatomaceous earth (DE) under rice and bare conditions to determine the water and dissolved mass balance in paddy fields (Karnataka, Southern India). The fate of the Si brought by irrigation (DSi) (uptake by rice, uptake by diatoms, adsorption) was assessed through a solute mass balance combined with silicon isotopic signatures.Results: Above the ground-surface, about one third of the DSi flux brought by borewell irrigation (545 mmol Si.m−2) to bare plots and half of DSi in rice plots were removed from solution within minutes or hours following irrigation. Such rate is consistent with the rate of DSi adsorption onto Fe-oxyhydroxides but not with diatom blooms. In rice and rice + DE experiments, the isotopic fractionation factor (30ε) between bore well and stagnant water compositions is close to −1 ‰, i.e. the isotopic fractionation factor known for rice, indicating that above-ground DSi removal would be dominated by plant uptake upon adsorption. Within the soil layer, pore water DSi decreases much faster in rice experiments than in bare ones, demonstrating the efficiency of DSi rice uptake upon adsorption. Total irrigation-DSi to plant-Si would then represent 24 to 36% in rice experiments (over 1460 ± 270 mmol Si m−2 in biomass) and 15 to 23% in rice + DE ones (over 2250 ± 180 mmol Si m−2). The δ30Si signature of whole plants was significantly different in the rice + DE plot analyzed, 0.99 ± 0.07 ‰, than in the rice one, 1.29 ± 0.07 ‰. According to these δ30Si signatures, the main Si source from the soil would be the amorphous silica pool (ASi). A slight contribution of DE to the rice plant could be detected from the Si isotopic signature of rice.Conclusions: The δ30Si signatures of the various soil-plant compartments, when associated to Si mass balance at soil-plant scale, constitute a reliable proxy of the Si sources in paddy fields. The solute Si balance is controlled by rice uptake in rice plots and by adsorption in bare ones. The main Si sources for the rice plants were soil ASi, irrigation Si and to a lesser extent Si fertilizer when it was applied