Cyclic circular balanced and strongly balanced cross over designs through integer programming.

Abstract

This article proposes a new linear integer programming approach to obtain cyclic circular balanced and strongly balanced crossover designs for a given number of treatments v, number of periods p, and number of units n. The linear integer programming approach has been used for generating a sequence of treatments to be assigned to the units. Using this approach, cyclic circular balanced and strongly balanced crossover designs for v < 30, p < 5, and λ ⩽ 4 or λ* ⩽ 4 have been generated, where λ (λ*) refers to the number of times each treatment is preceded by every other treatment excluding itself (including itself) depending on whether it is circular balanced or circular strongly balanced. The designs obtained are uniform over periods. A catalogue of designs for v < 30, p < 5, λ ⩽ 4 or λ* ⩽ 4, p < v with n ⩽ 100 is given. The designs obtained are universally optimal over the class of all connected designs with a fixed number of treatments, number of periods, and number of sequences.