Abstract
Improving efficiency has long been a focal challenge in sampling literature. However, simultaneously enhancing estimator efficacy and optimizing survey costs is a practical necessity across various fields such as medicine, agriculture, and transportation. In this study, we present a comprehensive family of generalized exponential estimators specifically designed for estimating population means within stratified sampling frameworks. Optimizing the survey cost is one the major challenges in the stratified sampling because the cost of the survey is fixed and decided before the survey. To optimize survey costs, we employ integer programming and Lagrange multipliers. We have carefully derived the Mean Square Error (MSE) of the proposed estimators and addressed this as an optimization problem to further refine estimator performance in light of cost constraints and optimal sample sizes. The results have been rigorously validated using real-world datasets, and both theoretical and empirical evaluations show that the proposed estimators significantly outperform existing alternatives. These findings underscore the estimators' practical relevance and theoretical robustness.