Linear integer programming approach to construct distance balanced sampling plans

Abstract

Distance balanced sampling plans (DBSP) area a class of sampling plans in which second order inclusion probabilities are non-decreasing function of the distance between the population units. DBSP were introduced by Mandal et al. (2009) as a generalization of balanced sampling plans excluding adjacent units. In this article, a general w-point DBSP w = 1, 2, ..., (N/2), were N is the population size and (x) denotes largest integer contained in x is introduced and a method of construction of w-point DBSP using linear integer programming is proposed. The method is general in nature and two-point, three-point, (N/2)-point, many other DBSPs, simple random sampling without replacement, balanced sampling plans excluding contiguous units (Hedayat et al., 1988) and balanced sampling without excluding adjacent units (Stufken, 1993) fall out as a particular case. A list of (N/2)-point DBSP for sample size three is obtained for population size N 100, where N is odd