Behavior of Mathematical Goal Programming For Determining Optimum Stratum Boundaries

S. Abo- El.Hassan, Fatma; Hamid, Ramadan; A. Ismail, Elham; M. Ezzat, Safia

doi:10.21608/jsfc.2021.248609

Behavior of Mathematical Goal Programming For Determining Optimum Stratum Boundaries

نوع المستند : المقالة الأصلية

المؤلفون

¹ Faculty of Commerce, Al-Azhar University (Girls’ Branch Cairo) ,Egypt

² Faculty of Economics and Political Science, Cairo University, Egypt .

10.21608/jsfc.2021.248609

المستخلص

Stratified random sampling is an effective sampling technique for estimating the population characteristics. The determination of strata boundaries and the allocation of sample size to the strata is one of the most critical factors in maximizing the precision of the estimates. Most surveys are conducted in an environment of severe budget constraints and a specific time is required to finish the survey. So cost and time are especially very important objectives of most surveys thus they are necessitating to be under consideration. The study suggested Mathematical goal programming model for determining optimum stratum boundaries for an exponential study variable under multiple objectives model when cost and time are under consideration. To evaluate the performance for the suggested model for the exponential distribution a numerical example is presented. The results of the suggested mathematical goal programming are satisfying.

الكلمات الرئيسية

المراجع

Danish, F., Rizvi, S.E.H., Jeelani, M.I. and Reashi, J.A. (2017)"Obtaining strata boundaries under proportional allocation with varying cost of every unit". Pakistan Journal of Statistics and Operation Research, 13(3), 567-574.
Danish, F., Rizvi, S.E.H (2019)" Optimum Stratification by Two Stratifiction Variables Using Mathematical Programming" Pakistan Journal of Statistics Vol. 35(1), 11-24.
Fanolahi, A.V. and Khan, M.G.M. (2014)" Determing the optimum strata boundaries with constant cost factor". Conference: IEEE Asia-Pacific World Congress on Computer Science and Engineering (APWC), At PlantationIsland, Fij.
Khan, M. G. M., Nand, N., & Ahmad, N. (2008). "Determining the optimum strata boundary points using dynamic programming". Survey Methodology, 34(2), 205-214.
Khan, M. G. M., Ahmad, N. and Khan, Sabiha (2009)."Determining the optimum stratum boundaries using mathematical programming". J. Math. Model. Algorithms, Springer, Netherland, 8(4): 409- 423.
Khan, E.A., Khan, M.G.M. and Ahsan, M.J. (2002). "Optimum stratification: A mathematical programming approach". Culcutta Statistical Association Bulletin, 52 (special), 205-208.
Khan, M.G.M., Sehar, N. , and Ahsan, M.J. (2005). "Optimum stratification for exponential study variable under Neyman allocation". Journal of Indian Society of Agricultural Statistics, 59(2), 146-150.
Rao, D.K. , Khan, M.G.M. and Reddy, K.G. (2014)."Optimum stratification of a skewed population". International journal of mathematical, computational, natural and physical engineering, 8(3):497-500.
Reddy, K. G., M. G. Khan, and D. Rao (2016). "A procedure for computing optimal stratum boundaries and sample sizes for multivariate surveys". JSW 11(8), 816–832.
Reddy K.G., Khan M.G.M., Khan S. (2018) "Optimum strata boundaries and sample sizes in health surveys using auxiliary variables". PLoS ONE 13(4): e0194787.
Reddy KG and Khan MGM (2020)" stratifyR: An R Package for optimal stratification and sample allocation for univariate populations " Australian & New Zealand Journal of Statistics 62 (3), 383-405