Abstract Reasoned fertilization, which is a major concern for sustainable and efficient agriculture, consists of applying customized fertilizers which requires a very large increase in the number of fertilizer formulae, involving increasing costs due to the multiplication of production batch, of storage areas and of transportation constraints. An alternative solution is given by adopting a Reverse Blending approach, which is a new Blending Problem where inputs are non-pre-existing composite materials that need to be defined in both number and composition, simultaneously with the quantities to be used in the blending process, such as to meet the specifications of a wide variety of outputs, while keeping their number as small as possible. This would replace the production of a large variety of small batches of fertilizers by few large batches of new composite materials whose blending may be performed close to end-users (delayed differentiation), delivering substantial production and logistics cost savings, well in excess of remote blending costs. Reverse Blending presents some analogies with the Pooling Problem which is a two-stage Blending Problem where primary inputs are existing raw materials. An adapted version of this problem may be used to facilitate the design of new composite materials used by Reverse Blending. This paper presents the Reverse Blending approach, whose modelling is based on a quadratic programming formulation, and a large case study to demonstrate its feasibility. Reverse Blending, therefore, may be a disruptive approach to successfully reengineer not only the fertilizer supply chain but any other industry operating in blending contexts to meet a great diversity.

中文翻译：

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反向混合：一种经济有效的方法来应对肥料大规模定制的挑战

摘要 合理施肥是可持续和高效农业的主要关注点，包括施用定制肥料，这需要大量增加肥料配方的数量，由于生产批次、存储区域和运输的增加而导致成本增加。约束。通过采用反向混合方法给出了另一种解决方案，这是一个新的混合问题，其中输入是非预先存在的复合材料，需要在数量和组成方面进行定义，同时还要定义混合过程中使用的数量，例如满足各种输出的规格，同时保持它们的数量尽可能少。这将用少数大批量的新型复合材料代替大量小批量肥料的生产，这些复合材料的混合可以在靠近最终用户的地方进行（延迟差异化），显着节省生产和物流成本，远远超过远程混合成本。反向混合提供了与混合问题的一些类比，混合问题是一个两阶段混合问题，其中主要输入是现有原材料。此问题的改编版本可用于促进反向混合使用的新复合材料的设计。本文介绍了反向混合方法，其建模基于二次规划公式，并通过一个大型案例研究来证明其可行性。反向混合，因此，