Optimum allocation of sample to strata and stages with simple additional constraints

The optimum allocation of a sample to strata and stages in a stratified two-stage design for a simple cost function is well known. In practice there may be reasons to impose simple additional constraints. It is shown how the theory for optimum allocation can be generalized to account for such constraints. A simple way of assessing the effect that each constraint has on the efficiency of the sample design is developed. This general approach allows several additional constraints that are used in practice to be applied. Data from the 1996 redesign of the Australian Monthly Labour Force Survey are used to illustrate how the inefficiencies arising from different constraints can be calculated.