An optimal multivariate cluster sampling design

This article presents a problem of determining optimum cluster size and sampling units in multivariate surveys. When a cluster sampling design is to be used and more than one characteristic is under study, it is usually not advisable to use the individual optimum cluster size and sampling unit for one reason or the other. In such situations, some criterion is needed to work out an acceptable cluster size and sampling unit which are optimum for all characteristics in some sense. Moreover, for practical implementation of sample size, we need integer values of the cluster size and sampling unit. Therefore, the present article addresses the problem of determining integer optimum compromise cluster size and sampling unit when the population means of the various characteristics are of interest. Formulating the problem as an All Integer Nonlinear Programing Problem (AINLPP), the article develops a solution procedure using a Genetic algorithm. The compromise solution discussed is the optimal in the sense that it minimizes a weighted sum of the variances of the cluster sample means of various characteristics under study. Two numerical examples illustrate the practical application of the solution procedure. The results show that the proposed technique can be efficiently applied in determining the sample size in multivariate cluster sampling design.