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An Integer Programming Formulation Applied to Optimum Allocation in Multivariate Stratified Sampling

The problem of optimal allocation of samples in surveys using a stratified sampling plan was first discussed by Neyman in 1934. Since then, many researchers have studied the problem of the sample allocation in multivariate surveys and several methods have been proposed. Basically, these methods are divided into two class: The first involves forming a weighted average of the stratum variances and finding the optimal allocation for the average variance. The second class is associated with methods that require that an acceptable coefficient of variation for each of the variables on which the allocation is to be done. Particularly, this paper proposes a new optimization approach to the second problem. This approach is based on an integer programming formulation. Several experiments showed that the proposed approach is efficient way to solve this problem, considering a comparison of this approach with the other approach from the literature.