Multi-objective mathematical programming approach for multivariate compromise allocation for stratified random sampling

Abstract

The optimal allocation of stratified sample in multivariate surveys faces two main challenges. First, optimization of the conflicting objectives of the variation of the estimates and survey cost, that minimizing one of them results in an increase in the other. Second, the optimal allocation for one characteristic may result in a loss of the precision of the estimates of the other characteristics. In this paper, a multivariate optimal compromise allocation is proposed using a multi-objective mathematical programming model that aims at simultaneously minimizing the total survey cost and the variation of the overall stratified mean of all of the characteristics of interest. The proportional increase in the variance of the estimator due to minimizing the variance of the estimates from the variance of the estimator under optimum cost is set as a constraint and is upper-bounded by a pre-determined quantity. Weighted Goal Programming is adopted as a solution technique. Simulation-based comparative study is conducted to assess the performance of the proposed allocation versus other optimal allocation techniques selected from the literature, and the results show the superiority of the proposed allocation in obtaining efficient estimators.