Estimation of finite population mean in multivariate stratified sampling under cost function using goal programming

Abstract

In practical utilization of stratified random sampling scheme, the investigator meets a problem to select a sample that maximizes the precision of a finite populationmean under cost constraint. An allocation of sample size becomes complicated whenmore than one characteristic is observed fromeach selected unit in a sample. Inmany real life situations, a linear cost function of a sample size nh is not a good approximation to actual cost of sample survey when traveling cost between selected units in a stratum is significant. In this paper, sample allocation problem in multivariate stratified random sampling with proposed cost function is formulated in integer nonlinear multiobjective mathematical programming. A solution procedure is proposed using extended lexicographic goal programming approach. A numerical example is presented to illustrate the computational details and to compare the efficiency of proposed compromise allocation.