Generation of Dissimilar Alternative Product Formulations Using Graphs

Abstract

In this work, alternative product formulations are represented as a bipartite graph, and mixed-integer programming is used to find a graph partitioning that identifies the most dissimilar formulations within a potentially large design space. This involves fully integrating available models for product properties and known heuristic rules for product formulation. The set of dissimilar alternative formulations thus found constitutes the best exploratory plan of experiments in the face of the available knowledge. Also in this work, a cosmetic emulsion example is explored, where some ingredients (in a non-specified number) have to be chosen from a pool of 32 possible. The number of possible combinations of ingredients is around half a million. With the new tools proposed herein, one is able to identify small sets of alternative formulations that adhere to available models and known heuristics rules, have maximum dissimilarity, and are optimal regarding a specific product design objective (cost or other), in a few minutes of computational time.