Determination of Sample Size Selecting from Strata Under Nonlinear Cost Constraint by Using Goal Programming and Kuhn-Tucker Methods

Although sampling methods are various, most frequently used method is Stratified Random Sampling in practice, especially, in case of heterogeneous population structure. One of the most important points, which should be considered, in the use of stratified random sampling method is how many units of samples should be selected from which stratum. Determination of optimum sample size to be selected from strata allows the sample to represent the population properly and increases precision of the obtained estimations. Kuhn-Tucker Method, which is accepted as a basic method for determination of sample sizes to be selected from strata in stratified random sampling, and the goal programming method, which can take into consideration the researcher’s multi-objectives, will be used in this study. It will be tried to minimize variance of sample mean statistics by using these methods under the non-linear cost constraint and superiorities of these methods over each other will be discussed under the light of the results obtained from the conducted simulation study.