Abstract: When studying the relationship between the order of a set of components and a measured response in an order-of-addition experiment, the number of components may exceed the number of available positions. In this case, there is an added layer of complexity, in which the experimenter is tasked with locating both the best combination of components and its corresponding best order. Akin to the standard order-of-addition setup, the number of possible sequences grows quickly with the number of components, rendering a brute force approach unfeasible. This necessitates the development of parsimonious designs for such experiments. We present a framework for constructing optimal and near-optimal screening designs under adapted versions of two prominent order-of-addition models. We apply our order-of-addition screening designs to job scheduling problems with job rejection penalties in the context of both a single-shot experiment and an active learning framework for sequential experimentation. The proposed designs not only offer precise effect estimation and accurate predictions, but also facilitate quick convergence to the optimal ordering in sequential experiments.

Key words and phrases: Active learning, experimental design, job scheduling, optimal design, orthogonal array, screening experiment.