A note on optimum allocation in multivariate stratified sampling

In stratified random sampling when several characteristics are to be estimated simultaneously, an allocation that is optimum for one characteristic may be far away from optimum for others. To resolve this conflict the authors formulate the problem of determining optimum compromise allocation as a nonlinear programming problem (NLPP). The allocation obtained is optimum in the sense that it minimizes the sum of weighted variances of the estimated population means of the characteristics subject to a fixed sampling cost. The formulated NLPP is treated as multistage decision problem and solved using dynamic programming technique. A numerical example is presented to illustrate the computational details.