Efficient Incomplete Block Designs Through Linear Integer Programming

SYNOPTIC ABSTRACT

The purpose of this paper is to present a linear integer programming approach to construct efficient binary incomplete block designs for any given number of treatments v, number of blocks b, with common block-size k, and with a nearly balanced concurrence matrix. The proposed approach is illustrated by constructing an efficient incomplete block design. A-efficient and D-efficient incomplete block designs have been constructed and catalogued using the proposed algorithm for a restricted range of parameters 3 ⩽ v ⩽ 20, b ⩾ v, and 2 ⩽ k ⩽ min(10, v − 1), with vb⩽1, 000. An R package is developed to implement the proposed approach.

Key Words and Phrases::

• incomplete block design
• linear integer programming
• A-efficiency
• D-efficiency
• algorithm.

Acknowledgments

The authors are grateful to two anonymous reviewers and the Associate Editor for making valuable suggestions that have improved the presentation of this article.

Notes

http://iasri.res.in/design/ibd/ibd.htm

cran.r-project.org/web/packages/ibd/index.html

http://iasri.res.in/design/ibd/ibd.htm