Determination of the optimal blending problem of organic chemical fertilizer under uncertainty

Abstract

The advantages of organic-chemical fertilizers have been recognised by farmers, and accordingly, the demand for them has increased. An organic-chemical fertilizer, with an amount of nutrients less than that registered or as specified on the label, is considered a fake or a nonconforming fertilizer. It has been observed that nutrient compositions of samples of organic-chemical fertilizers are much greater than what is specified on the label. This research aimed to reduce the raw materials cost of organic chemical fertilizers while increasing the conformance probability of the nutrient composition. Three models have been formulated to determine the optimal organic-chemical fertilizer blend: a linear programming model (LP), a chance-constrained programming model (CCP), and a simulation optimization model. A Monte Carlo simulation was developed to determine the out-of-specification probability of the blending formula, currently in use commercially, and the blending formulas obtained from the three optimization models. The current and three proposed models were compared in terms of total raw material cost and probability of nonconformance. All blending models could save a material cost of at least 16.6% compared with the current formula. Also, the probability of producing nonconforming fertilizers is drastically reduced. On a macro level, the use of the models allows farmers to reduce the chemical residues in the soil while Thailand could reduce the import volume of chemical substances. This research may have a significant impact on manufacturers, farmers and the Thai economy.