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.

Delayed differentiation, one of the key techniques of mass customization, has proven to be a high-performance strategy in the discrete industry. In the process industry, however, it remains poorly explored, especially when differentiation relates to product composition rather than form. Reverse Blending is a new OR blending problem based on a quadratic formulation, where output requirements are similar to those of classical blending, but here inputs are not preexisting and must be defined simultaneously with their use in the blending process while exactly meeting output requirements. These may then be used to obtain a wide variety of custom fertilizers (outputs) from a small number of Canonical Basis Inputs that can be blended outside the chemical plant, close to the endusers. This would avoid production of a wide variety of small batches of final products through a small number of large batches of intermediate products, resulting in valuable logistical streamlining and substantial cost savings. Accordingly, our paper investigates the potential benefits of implementing Reverse Blending in the fertilizer industry.