Optimum allocation in multivariate stratified random sampling with overhead cost

The problem of allocating the sample numbers to the strata in multivariate stratified surveys, where, apart from the cost involved in enumerating the selected individuals in the sample, there is an overhead cost associated with each stratum, has been formulated as a non-linear programming problem. The variances of the posterior distributions of the means of various characters are put to restraints and the total cost is minimized. The main problem is broken into subproblems for each of which the objective function turns out to be convex. When the number of subproblems happens to be large an approach has been indicated for obtaining an approximate solution by solving only a small number of subproblems.