Multi-objective nonlinear programming problem approach in multivariate stratified sample surveys in the case of non-response

Abstract

In multivariate cases, usually the minimization of sampling variances is considered as an objective under a cost constraint. Since the variances are not unit free, it is more logical to consider the minimization of the squared coefficients of variation as an objective. In this paper, the problem of optimum compromise allocation in multivariate stratified sampling in the case of non-response as a multi-objective all-integer nonlinear programming problem is described. A solution procedure using four different approaches is considered, namely the value function, goal programming,∈-constraint and distance based, to obtain the compromise allocation for non-response. A numerical example is also presented to illustrate the computational details.