Computer-Aided Blocking of Factorial and Response-Surface Designs

We consider the problem of blocking response-surface and factorial designs when block sizes are prespecified, often rendering standard approaches inapplicable. A generalization of Harville's (1974) algorithm is given for generating nearly D-optimal block designs and is applied in a number of representative settings. The algorithm is time and space efficient and can be used in conjunction with qualitative treatments for generating many of the classical designs—balanced and partially balanced incomplete block designs, for example.