Generating optimal order-of-addition designs with flexible run sizes

A series of optimal designs with flexible run sizes is proposed in this paper for designing order-of-addition experiments. Because the full design can be partitioned into several isotopic Latin squares, a fractional design can be obtained by juxtaposing some selected Latin squares according to a particular optimality criterion. A computer-assisted search procedure is first implemented to generate optimal designs with small to moderate run sizes. Based on the computer-generated designs, a recursive method is then used to construct optimal designs with large run sizes. In addition, two practical techniques are introduced to obtain new optimal or near-optimal designs via existing optimal designs. The proposed designs are compared with competing designs generated by conventional software. The results show that the proposed designs are often more efficient for estimating the unknown parameters. A catalogue of optimal designs and near-optimal designs is provided as a reference for future work. ? 2021 The Author(s)