Integrating Suppliers into the Simultaneous Process and Product Design of Formulated Products

In this work, we present an extended pooling problem for the design of formulated detergents that includes process and product design and supplier's selection. It was a multiobjective, multiperiod and multiscale optimization product. The integrated problem presented was highly non-linear and non-convex. To address the problem, two different mathematical formulations have been compared. A traditional MINLP and a reformulation of the problem using a decision vector and the definition of penalties reducing the need for binary variables. To present the problem, a case study in Europe was formulated considering several ingredients, suppliers and price policies. The traditional formulation takes days to converge if it converges at all, while the reformulation, in spite of the larger problem size, achieves solution in 20 hours. Furthermore, it was demonstrated that when considering a multiobjective optimization (profit and environmental impact), the model can reduce the CO2 emissions by 40% in the design of a set of detergents, maintaining the benefit within 1.39% of the maximum by selecting the detergent composition and the suppliers.