A hierarchical multi-level model for compromise allocation in multivariate stratified sample surveys with non-response problem

Abstract

Stratified sampling, a widely-applicable probabilistic technique, is especially suited for large and heterogeneously distributed populations. This paper studies optimal allocation of sampling units to minimize variances and cost. Given that not all strata hold equal importance in survey projects, we propose a hierarchical multi-level programming model for compromise allocation in stratified sampling. The model considers multiple objectives across hierarchical levels and addresses the issue of non-response by dividing strata into respondent and non-respondent groups. The survey budget restriction is considered as a constraint in our model. We employ a fuzzy concept-based solution methodology to solve the multi-level allocation problem. A literature-based numerical example describes the model’s applicability and efficiency. Comparative analysis shows our model’s superior efficiency over existing models due to its optimization of allocation across varied strata, non-response consideration, and budget constraint integration. The proposed model promotes flexibility, enhancing representativeness and cost-effectiveness of large-scale surveys, thereby improving decision-making in research and industry settings.