Models for Order-of-Addition Screening Experiments

In many physical and engineering experiments, the order in which a process is executed or components are added can have a marked impact on the response.Due to constraints on resources or feasibility, there are situations where only a subset of the components can be administered in practice and experimenters encounter a complicated task with the selection of components and the corresponding best order.We present a series of models for such order-of-addition screening experiments and study their properties.We develop theoretical results on the corresponding optimal designs and illustrate these models on job scheduling problems with job rejection penalties.