International E-publication: Publish Projects, Dissertation, Theses, Books, Souvenir, Conference Proceeding with ISBN.  International E-Bulletin: Information/News regarding: Academics and Research

Linear / Non Linear Plus Fractional Goal Programming (L/NLPFGP) Approach in stratified sampling design

    , , ,

Author Affiliations

  • 1Division of Agri-stat SKUAST-K, Salimar, Srinagar, INDIA
  • 2Division of Agri-stat SKUAST-K, Salimar, Srinagar, INDIA
  • 3Division of Agri-stat SKUAST-K, Salimar, Srinagar, INDIA
  • 4Division of Agri-stat SKUAST-K, Salimar, Srinagar, INDIA

Res. J. Mathematical & Statistical Sci., Volume 3, Issue (12), Pages 1-5, December,12 (2015)

Abstract

This article deals with the problem of finding an integer optimal allocation of sample sizes in stratified sampling design as a problem of multi-objective optimization. In this paper tertiary objective stratified sampling design is converted into linear/non linear plus fractional goal programming. Then a fuzzy goal programming approach is used to solve the converted problem through LINGO. When a non integer solution is obtained then Branch and Bound method is used to obtain the integer solution. Numerical illustration is also given for the demonstration of proposed approach.

References

  1. Neyman J., On the two Different aspects of therepresentative method: The method of stratifiedsampling and the method of purposive selection, Journalof Royal Statistical Society .,97(4), 558-625 (1934)
  2. Ghosh S.P., A note on stratified random sampling withmultiple characters, Calcutta Statistical Bulletin, 8, 81-89 (1958)
  3. Yates F., Sampling Methods for Censuses and Surveys, 3rd ed. London: Charles Griffin, (1960)
  4. Hartley H.O., Multiple purpose optimum allocation instratified sampling, Proc. Amer. Statist. Assoc., SocialStatist., 258-261 (1965)
  5. Folks J.K. and Antle C.E., Optimum allocation ofsampling units to the strata when there are R responsesof interest, Journal of American Statistical Association.,60, 225-233(1965)
  6. Aoyama H., Stratified Random Sampling with OptimumAllocation for Multivariate Populations, Annals of theinstitute of statistical Mathematics., 14, 251–258 (1963)
  7. Gren J., Some Application of Non-linear Programmingin Sampling Methods, Przeglad Statystyczny, 13:203–217 (in polish) (1966)
  8. Kokan A.R. and Khan S.U., Optimum allocation inmultivariate surveys: An analytical solution, Journal ofRoyal Statistical Society, B, 29, 115-125 (1967)
  9. Chatterjee S., A study of optimum allocation inmultivariate stratified surveys, SkandinaviskActuarietidskrift , 55, 73-80 (1972)
  10. Bethel J., Sample Allocation in Multivariate Surveys, Survey Methodology, 15, 40-57 (1989)
  11. Kreienbrock L., Generalized measures of dispersion tosolve the allocation problem in multivariate stratifiedrandom sampling, Cmmunication in Statistics: Theoryand methods, 22(1), 219-239 (1993)
  12. Khan M.G.M., Ahsan M.J. and Jahan N., Compromiseallocation in multivariate stratified sampling : An integersolution, Naval Research Logistics, 44, 69-79 (1997)
  13. Ahsan M.J., Najmussehar and Khan M. G.M., Mixedallocation in stratified sampling, Aligrah Journal ofStatistics sciences, 25, 87-97 (2005)
  14. Kozok M., On sample allocation in multivariatesurveys, Communication in Statistics-Simulation andComputation, 35, 901-910 (2006)
  15. Ansari A.H., Najmussehar and Ahsan M.J., On MultipleResponse Stratified Random Sampling Design, International Journal of Statistical Sciences, 1(1), 45-54(2009)
  16. Hirche J., A note on programming problems with linearplus linear fractional objective functions, EuropeanJournal of Operation Research, 26(1-2), 49-64 (1984)
  17. Chadha S.S., Dual of the sum of linear and linearfractional program, European Journal of OperationResearch, 67,136-139 (1993)
  18. Jain S. and lachhwani K., Sum of linear and fractionalmultiobjective programming problem under Fuzzy rulesconstraints, Australian journal of basic and AppliedScience, 4(2), 105-108 (2008)
  19. Schaible S., A note on the sum of linear and linearfractional functions, Naval Research LogisticQuarterly,24, 961-963 (1977)
  20. Sukhatme et al., Sampling theory of Surveys withApplications, Iowa State University Press, Iowa, U. S. A.and Indian Society of Agricultural Statistics, New Delhi,India, (1984)
  21. Arthanari T.S. and Dodge Y., Mathematicalprogramming in statistics, New York: John Willy, (1993)
  22. LINGO, LINGO User’s Guide, LINDO SystemsInc.,1415, North Dayton Street, Chicago, Illinois, 60622,USA (2013)