<p>In many practical survey situations, researchers need to estimate several population characteristics simultaneously while operating under limited resources. The motivation of this study arises from the need to obtain efficient estimates for multiple variables in stratified sampling while accounting for differences in measurement costs. In practice, the cost of measuring different variables may vary considerably, but many existing allocation methods do not adequately incorporate these variations, which may result in inefficient sampling designs. To address this issue, this study proposes a new multivariate stratified random sampling technique based on a family of estimators for compromise allocation. The proposed approach aims to improve the accuracy and efficiency of population mean estimation while controlling the overall measurement cost. The problem is formulated as an integer nonlinear multivariate stratified sampling model within a multi-objective mathematical programming framework using the proposed cost functions. The developed procedure is based on integer programming, and the resulting coefficients of variation are compared with those obtained from some existing compromise allocation methods. Numerical illustrations demonstrate that the proposed allocation technique provides improved efficiency. The proposed method is particularly useful in practical survey designs where budget, time, and effort must be carefully balanced with the requirement of achieving reliable statistical estimates.</p>