Abstract: The problem of allocating experimental units to treatment groups when variance heterogeneity over treatment groups is present is considered. A_A- and D_A-optimal allocations are derived for estimation of linear combinations of treatment means. Explicit expressions for the design weights are provided for the A_A-optimal design. The minimax strategy is introduced as an approach to handle unknown variances. Efficiencies of minimax allocations are evaluated.

Key words and phrases: A-optimality, D-optimality, minimax designs, factorial experiments.