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

Yıl 2011, Cilt: 24 Sayı: 2, 249 - 262, 05.04.2011

S. Tuğba Şahin Sinem Sahin

Öz

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.

 

 
 

Keywords: Goal programming, Kuhn-Tucker Method, nonlinear cost function, stratified random sampling.

 

 

Anahtar Kelimeler

Goal programming Kuhn-Tucker Method nonlinear cost function stratified random sampling.

Kaynakça

  • Neyman, J., “On the two different aspects of the representative methods: The method stratified sampling and the method of purposive selection”, Royal Statistical Society, 97: 558-606 (1934).
  • Bretthauer, K. M., Ross, A., Shetty , B., “Nonlinear integer programming for optimal allocation in stratified sampling”, European Journal of Operational Research, 116: 667-680 (1999).
  • Cochran, W.G., “Sampling techniques”, 3rd Ed., John Wiley and Sons Inc., New York, 89-111 (1977).
  • Chernyak, A., “Optimal allocation in stratified and double random sampling with a nonlinear cost function”, Journal of Mathematical Sciences, 103 (4): 525-528 (2001).
  • Diaz-Garcia, J. A., “Optimum allocation in multivariate stratified sampling:Multi-objective programming”, I-06-07(PE), 1-22 (2006).
  • Judez, L., Chaya, C., Miguel, J. M., Bru, R., “Stratification and sample size of data sources for agricultural mathematical programming models”, Mathematical and Computer Modelling, 43: 530- 535 (2006).
  • Diaz-Garcia, J. A., Garay-Tapia M. M., “Optimum allocation in stratified surveys”, I-05-14(PE), 1-16 (2005).
  • Bosch, V., Wildner, R., “Optimum allocation of stratified random samples designed for multiple mean estimates and multiple observed variables”, Communications in Statistics, 32 (10): 1897-1909 (2003).
  • Khan, M. G. M., Ahsan, M. J., “A note on optimum allocation in multivariate stratified sampling”, S. Pac. J. Nat. Sci., 21: 91-95 (2003).
  • Khan, M. G. M., Khan, E. A., Ahsan, M. J., “An optimal multivariate stratified sampling design using dynamic programming”, Australian&New Zeland Journal of Statistics, 45 (1): 107-113 (2003).
  • Clark, R. G., Steel, D. G., “Optimum allocation of sample to strata and stages with simple additional constraints”, The Statistician, 49 (2): 197-207 (2000).
  • Green, J. L., “Mathematical programming for sample design and allocation problems”, American Statistical Association Proceedings of the Section on Survey Research Methods, 688-692 (2000).
  • Mulvey, J. M., Rush, R., Mitchell, J. E. And Willemain, T. R., “Stratified filtered sampling in stochastic optimization”, Journal of Applied Mathematics and Decision Sciences, 4 (1): 17-38 (2000).
  • Bretthauer, K. M., Shetty , B., “The nonlinear resource allocation problem”, Operations Research, 43 (4): 670-683 (1995).
  • Charnes, A., Cooper, W. W., “Management models and industrial applications of linear programming”, John Wiley & Sons, New York, 44-72 (1961).
  • Carrizosa, E., Morales, D. R., “A biobjective method for sample allocation in stratified sampling”, European Journal of Operational Research, 177: 1074-1089 (2007).
  • Reyes, P. M., Frazier G. V., “Goal programming model for grocery shelf space allocation”, European Journal of Operational Research, 181: 634-644 (2007).
  • Wei, Y., Hu, Q., Fan, Y., “Mathematical model for the optimization of the allocation of nonferrous raw materials in China”, Computers & Industrial Engineering, 46: 293-303 (2004).
  • Oliveira, F., Volpi, N. M. P. And Sanquetta, C. R., “Goal programming in a planning problem”, Applied Mathematics and Computation, 140: 165- 178 (2003).
  • Blake, J. T., Carter, M. W., “A goal programming approach to strategic resource allocation in acute care hospitals”, European Journal of Operational Research, 140: 541-561 (2002).
  • Yahya, S., Kingsman, B., “Modelling a multi- objective allocation problem in a government sponsored entrepreneur development programme”, European Journal of Operational Research, 136: 430-448 (2002).
  • El-Gayar, O. F. And Leung, P., “A multiple criteria decision making framework for regional aquaculture development”, European Journal of Operational Research, 133: 462-482 (2001).
  • Ogryczak, W., “Comments properties of the minmax solutions in goal programming”, European Journal of Operational Research, 132: 17-21 (2001).
  • Wise, K., Perushek, D. E., “Goal programming as a solution technique for the acquisitions allocation problem”, Library & Information Science Research, 22: 165-183 (2000).
  • Baki, M. F., Fraser, N. M., “Error noted in a case study on fund allocation using goal programming”, European Journal of Operational Research, 97: 213-214 (1997).
  • Ignizio, J. P., “Goal programming and extension”, Lexington Books, Lexington, 1-263 (1976).
  • Griffith, R. E. And Stewart R. A., “A nonlinear programming tecnique for the optimization of continious processing systems”, Management Science, 7: 379-392 (1961).
  • Cooper, L. And Steinberg, D., “Introduction to methods of optimization”, Philadelphia:W. B. Saunders, 103-152 (1970).

Yıl 2011, Cilt: 24 Sayı: 2, 249 - 262, 05.04.2011

S. Tuğba Şahin Sinem Sahin

Öz

Kaynakça

  • Neyman, J., “On the two different aspects of the representative methods: The method stratified sampling and the method of purposive selection”, Royal Statistical Society, 97: 558-606 (1934).
  • Bretthauer, K. M., Ross, A., Shetty , B., “Nonlinear integer programming for optimal allocation in stratified sampling”, European Journal of Operational Research, 116: 667-680 (1999).
  • Cochran, W.G., “Sampling techniques”, 3rd Ed., John Wiley and Sons Inc., New York, 89-111 (1977).
  • Chernyak, A., “Optimal allocation in stratified and double random sampling with a nonlinear cost function”, Journal of Mathematical Sciences, 103 (4): 525-528 (2001).
  • Diaz-Garcia, J. A., “Optimum allocation in multivariate stratified sampling:Multi-objective programming”, I-06-07(PE), 1-22 (2006).
  • Judez, L., Chaya, C., Miguel, J. M., Bru, R., “Stratification and sample size of data sources for agricultural mathematical programming models”, Mathematical and Computer Modelling, 43: 530- 535 (2006).
  • Diaz-Garcia, J. A., Garay-Tapia M. M., “Optimum allocation in stratified surveys”, I-05-14(PE), 1-16 (2005).
  • Bosch, V., Wildner, R., “Optimum allocation of stratified random samples designed for multiple mean estimates and multiple observed variables”, Communications in Statistics, 32 (10): 1897-1909 (2003).
  • Khan, M. G. M., Ahsan, M. J., “A note on optimum allocation in multivariate stratified sampling”, S. Pac. J. Nat. Sci., 21: 91-95 (2003).
  • Khan, M. G. M., Khan, E. A., Ahsan, M. J., “An optimal multivariate stratified sampling design using dynamic programming”, Australian&New Zeland Journal of Statistics, 45 (1): 107-113 (2003).
  • Clark, R. G., Steel, D. G., “Optimum allocation of sample to strata and stages with simple additional constraints”, The Statistician, 49 (2): 197-207 (2000).
  • Green, J. L., “Mathematical programming for sample design and allocation problems”, American Statistical Association Proceedings of the Section on Survey Research Methods, 688-692 (2000).
  • Mulvey, J. M., Rush, R., Mitchell, J. E. And Willemain, T. R., “Stratified filtered sampling in stochastic optimization”, Journal of Applied Mathematics and Decision Sciences, 4 (1): 17-38 (2000).
  • Bretthauer, K. M., Shetty , B., “The nonlinear resource allocation problem”, Operations Research, 43 (4): 670-683 (1995).
  • Charnes, A., Cooper, W. W., “Management models and industrial applications of linear programming”, John Wiley & Sons, New York, 44-72 (1961).
  • Carrizosa, E., Morales, D. R., “A biobjective method for sample allocation in stratified sampling”, European Journal of Operational Research, 177: 1074-1089 (2007).
  • Reyes, P. M., Frazier G. V., “Goal programming model for grocery shelf space allocation”, European Journal of Operational Research, 181: 634-644 (2007).
  • Wei, Y., Hu, Q., Fan, Y., “Mathematical model for the optimization of the allocation of nonferrous raw materials in China”, Computers & Industrial Engineering, 46: 293-303 (2004).
  • Oliveira, F., Volpi, N. M. P. And Sanquetta, C. R., “Goal programming in a planning problem”, Applied Mathematics and Computation, 140: 165- 178 (2003).
  • Blake, J. T., Carter, M. W., “A goal programming approach to strategic resource allocation in acute care hospitals”, European Journal of Operational Research, 140: 541-561 (2002).
  • Yahya, S., Kingsman, B., “Modelling a multi- objective allocation problem in a government sponsored entrepreneur development programme”, European Journal of Operational Research, 136: 430-448 (2002).
  • El-Gayar, O. F. And Leung, P., “A multiple criteria decision making framework for regional aquaculture development”, European Journal of Operational Research, 133: 462-482 (2001).
  • Ogryczak, W., “Comments properties of the minmax solutions in goal programming”, European Journal of Operational Research, 132: 17-21 (2001).
  • Wise, K., Perushek, D. E., “Goal programming as a solution technique for the acquisitions allocation problem”, Library & Information Science Research, 22: 165-183 (2000).
  • Baki, M. F., Fraser, N. M., “Error noted in a case study on fund allocation using goal programming”, European Journal of Operational Research, 97: 213-214 (1997).
  • Ignizio, J. P., “Goal programming and extension”, Lexington Books, Lexington, 1-263 (1976).
  • Griffith, R. E. And Stewart R. A., “A nonlinear programming tecnique for the optimization of continious processing systems”, Management Science, 7: 379-392 (1961).
  • Cooper, L. And Steinberg, D., “Introduction to methods of optimization”, Philadelphia:W. B. Saunders, 103-152 (1970).
Toplam 28 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Statistics
Yazarlar

S. Tuğba Şahin Bu kişi benim

Sinem Sahin

Yayımlanma Tarihi 5 Nisan 2011
Yayımlandığı Sayı Yıl 2011 Cilt: 24 Sayı: 2

Kaynak Göster

APA Şahin, S. T., & Sahin, S. (2011). Determination of Sample Size Selecting from Strata Under Nonlinear Cost Constraint by Using Goal Programming and Kuhn-Tucker Methods. Gazi University Journal of Science, 24(2), 249-262.
AMA Şahin ST, Sahin S. Determination of Sample Size Selecting from Strata Under Nonlinear Cost Constraint by Using Goal Programming and Kuhn-Tucker Methods. Gazi University Journal of Science. Nisan 2011;24(2):249-262.
Chicago Şahin, S. Tuğba, ve Sinem Sahin. “Determination of Sample Size Selecting from Strata Under Nonlinear Cost Constraint by Using Goal Programming and Kuhn-Tucker Methods”. Gazi University Journal of Science 24, sy. 2 (Nisan 2011): 249-62.
EndNote Şahin ST, Sahin S (01 Nisan 2011) Determination of Sample Size Selecting from Strata Under Nonlinear Cost Constraint by Using Goal Programming and Kuhn-Tucker Methods. Gazi University Journal of Science 24 2 249–262.
IEEE S. T. Şahin ve S. Sahin, “Determination of Sample Size Selecting from Strata Under Nonlinear Cost Constraint by Using Goal Programming and Kuhn-Tucker Methods”, Gazi University Journal of Science, c. 24, sy. 2, ss. 249–262, 2011.
ISNAD Şahin, S. Tuğba - Sahin, Sinem. “Determination of Sample Size Selecting from Strata Under Nonlinear Cost Constraint by Using Goal Programming and Kuhn-Tucker Methods”. Gazi University Journal of Science 24/2 (Nisan 2011), 249-262.
JAMA Şahin ST, Sahin S. Determination of Sample Size Selecting from Strata Under Nonlinear Cost Constraint by Using Goal Programming and Kuhn-Tucker Methods. Gazi University Journal of Science. 2011;24:249–262.
MLA Şahin, S. Tuğba ve Sinem Sahin. “Determination of Sample Size Selecting from Strata Under Nonlinear Cost Constraint by Using Goal Programming and Kuhn-Tucker Methods”. Gazi University Journal of Science, c. 24, sy. 2, 2011, ss. 249-62.
Vancouver Şahin ST, Sahin S. Determination of Sample Size Selecting from Strata Under Nonlinear Cost Constraint by Using Goal Programming and Kuhn-Tucker Methods. Gazi University Journal of Science. 2011;24(2):249-62.