Geometric programming approach to optimum allocation in multivariate two-stage sampling design

Geometric programming provides a powerful tool for solving non-linear problems where non-linear relations can be well presented by an exponential or power function. In real life situations applications of geometric programming are found in engineering design, sampling design etc. In this paper, the problem of allocation in first stage and second stage units in multivariate two stage sampling is considered. The problem is formulated as a convex programming problem with linear objective function. A solution procedure is developed to solve the resulting mathematical programming problem by using geometric programming technique. The computational details of the procedure are illustrated through a numerical example.