Balanced treatment incomplete block designs through integer programming

ABSTRACT

An algorithm is presented to construct balanced treatment incomplete block (BTIB) designs using a linear integer programming approach. Construction of BTIB designs using the proposed approach is illustrated with an example. A list of efficient BTIB designs for 2 ⩽ v ⩽ 12, v + 1 ⩽ b ⩽ 50, 2 ⩽ k ⩽ min(10, v), r ⩽ 10, r₀ ⩽ 20 is provided. The proposed algorithm is implemented as part of an R package.

KEYWORDS:

• Balanced treatment incomplete block design efficiency
• Linear integer programming.

Acknowledgments

We thank the reviewer for very useful and constructive suggestions which have improved the presentation of the article.