A sample allocation method for two-phase survey designs

Motivated by a business survey design at Statistics Canada, we formulate the problem of sample allocation for a general two-phase survey design as a constrained nonlinear programming problem. By exploiting its mathematical structure, we propose a solution method that consists of iterations between two subproblems that are computationally much simpler. Using an approximate solution as a starting value, the proposed method works very well in an empirical study.