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Journal of Applied Mathematics
Volume 2014, Article ID 686579, 7 pages
Research Article

Estimation of Finite Population Mean in Multivariate Stratified Sampling under Cost Function Using Goal Programming

1Department of Mathematics, Comsats Institute of Information Technology, Attock 43600, Pakistan
2Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan
3Department of Statistics, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received 17 March 2014; Revised 26 May 2014; Accepted 16 July 2014; Published 14 August 2014

Academic Editor: Dongqing Wang

Copyright © 2014 Atta Ullah et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In practical utilization of stratified random sampling scheme, the investigator meets a problem to select a sample that maximizes the precision of a finite population mean under cost constraint. An allocation of sample size becomes complicated when more than one characteristic is observed from each selected unit in a sample. In many real life situations, a linear cost function of a sample size 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.