Nonlinear Stochastic Multiobjective Optimization Problem in Multivariate Stratified Sampling Design

Decision-making in survey sampling planning is a tricky situation; sometimes it involves multiple objectives, with various decision variables emanating from heterogeneous and homogeneous populations. Dealing with the entire population under study and its uncertain nature becomes a challenging issue for researchers and policymakers. Hence, an appropriate sampling design and optimization methodology are imperative. The study presents a useful discussion on stochastic multiobjective multivariate stratified sampling (MSS) models theoretically, and the concepts are illustrated with numerical examples. Also, it has been found that the linearization of sampling variance in survey sampling does not help determine the optimal sampling allocation problem with minimum variability. Optimal allocation problems under the weighted goal programming, stochastic goal programming, and Chebyshev goal programming methods are also discussed with numerical examples. Finally, the study discussed the linear approximation of the MSS problem with examples. The study is a conceptual and theoretical framework for MSS under a stochastic environment. The numerical data is simulated using the stratifyR package.