OPTIMIZATION OF RESOURCE ALLOCATION USING INTEGER PROGRAMMING OF IMPROVED RATIO ESTIMATOR UNDER STRATIFIED RANDOM SAMPLING

This paper provides a case study that illustrates how integer programming may be used to optimize resource allocation. With the known population median of the study variable acting as auxiliary data, an exponential ratio estimator is shown for estimating the finite population mean under stratified random sampling. The objective is to minimize a cost function within specific bounds. Using integer programming techniques and the Lagrange multiplier approach, we transform the proposed problem into an optimization problem with a linear cost function. This allows us to propose an optimal way for minimizing total costs while maintaining desired accuracy levels. We found that the suggested estimator performed better than methods involving stratified random sampling. Additionally, a numerical example is given to verify the theoretical conclusions for real-world applications. We go over how the problem was formulated, how to use LINGO software to solve it, and the results. It is advised to choose the estimator with the lowest MSE in real-world stratified random sampling situations. The strategy shows significant cost savings and efficient use of resources. The effectiveness of the recommended approach is demonstrated by testing the methodology on both simulated and real-world datasets.