Exact I-Optimal Constrained Order-of-Addition Experiments

In the chemical, pharmaceutical, and food industries, sometimes the order of adding a set of components has an impact on the final product. These are instances of the order-of-addition (OofA) problem, which aims to find the optimal sequence of the components. Extensive research on this topic has been conducted, but almost all designs are found by optimizing the D−optimality criterion. However, when prediction of the response is important, there is still a need for I−optimal designs, especially if there are constraints on components’ order or interactions among triplets of components. Several algorithms are used to find I−efficient designs under the popular pairwise ordering (PWO) model. Simulations show that the proposed algorithms find highly efficient subsets under the I−optimality criterion. Finally, two examples are shown to illustrate the effectiveness of the proposed designs at identifying optimal orders in scenarios with block constraints on the order of addition and interaction effects between pairwise orders of components.