The cost of surveying and the precision of estimation are opposing survey components. Therefore, carefully allocating sample sizes is crucial to obtain efficient estimates. The problem, known as optimal allocation, was first discussed by Tschuprow and Neyman in the context of a stratified survey design. Since their approach oversimplifies most practical use cases, a more general strategy is needed, especially in the presence of multiple survey purposes. In this talk, we will outline the fundamental structure of optimal allocation problems and specify efficient algorithmic strategies for different variants of the problem formulation. The hyperbolic structure of the variance functional allows for a conic quadratic reformulation to account for precision and sample size restrictions at various subpopulation levels. We will see how the conic reformulation provides access to a sensitivity analysis for balancing multiple survey purposes. In addition, we will address the problem of uncertain input data, as the variation in the population is often estimated from pilot studies, historical data, or correlated supplementary information.