Mandal, B. N.; Gupta, V. K.; Parsad, Rajender Balanced treatment incomplete block designs through integer programming. (English) Zbl 1422.62267 Commun. Stat., Theory Methods 46, No. 8, 3728-3737 (2017). Summary: 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 \(2\leq v\leq 12\), \(v+1\leq b\leq 50\), \(2\leq k\leq \min(10,v)\), \(r\leq 10\), \(r_0\leq 20\) is provided. The proposed algorithm is implemented as part of an R package. Cited in 4 Documents MSC: 62K10 Statistical block designs 90C05 Linear programming Keywords:balanced treatment incomplete block design efficiency; linear integer programming Software:ibd; lpSolve; R PDFBibTeX XMLCite \textit{B. N. Mandal} et al., Commun. Stat., Theory Methods 46, No. 8, 3728--3737 (2017; Zbl 1422.62267) Full Text: DOI References: [1] DOI: 10.1080/00401706.1981.10486236 [2] DOI: 10.1080/01621459.1988.10478620 [3] Das A., Aust. J. Comb. 32 pp 243– (2005) [4] Gupta V.K., Stat. Appl. 3 (1) pp 133– (2001) [5] DOI: 10.1214/ss/1177012767 · Zbl 0955.62616 [6] DOI: 10.1080/00401706.1984.10487989 [7] DOI: 10.1016/S0169-7161(96)13029-7 [8] DOI: 10.1080/03610918.2013.821482 · Zbl 1321.62100 [9] DOI: 10.1080/01966324.2014.901198 [10] Parsad R., Utilitas Math. 47 pp 185– (1995) [11] DOI: 10.1080/01966324.2009.10737757 · Zbl 1188.62224 [12] DOI: 10.1214/aos/1176350614 · Zbl 0629.62077 [13] DOI: 10.1016/0378-3758(88)90043-2 · Zbl 0642.62044 [14] DOI: 10.1080/00207160.2010.492869 · Zbl 1216.90062 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.