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 AJCM  Vol.1 No.4 , December 2011
Chebyshev Approximate Solution to Allocation Problem in Multiple Objective Surveys with Random Costs
Abstract: In this paper, we consider an allocation problem in multivariate surveys as a convex programming problem with non-linear objective functions and a single stochastic cost constraint. The stochastic constraint is converted into an equivalent deterministic one by using chance constrained programming. The resulting multi-objective convex programming problem is then solved by Chebyshev approximation technique. A numerical example is presented to illustrate the computational procedure.
Cite this paper: nullM. khan, I. Ali and Q. Ahmad, "Chebyshev Approximate Solution to Allocation Problem in Multiple Objective Surveys with Random Costs," American Journal of Computational Mathematics, Vol. 1 No. 4, 2011, pp. 247-251. doi: 10.4236/ajcm.2011.14029.
References

[1]   A. R. Kokan and S. Khan, “Optimum Allocation in Multivariate Surveys: An Analytical Solution,” Journal of the Royal Statistical Society. Series B, Vol. 29, No. 1, 1967, pp. 115-125.

[2]   S. Chatterjee, “Multivariate Stratified Surveys,” Journal of the American Statistical Association, Vol. 63, No. 322, 1968, pp. 530-534.

[3]   H. F. Huddlesto, et al., “Optimal Sample Allocation to Strata Using Convex Programming,” Journal of the Royal Statistical Society. Series C, Vol. 19, No. 3, 1970, pp. 273-278.

[4]   J. Bethel, “An Optimum Allocation Algorithm for Multivariate Survey,” Proceeding of the Survey Research Section, American Statistical Association, 1985, pp. 204- 212.

[5]   J. R. Chromy, “Design Optimization with Multiple Ob- jectives,” Proceeding of the Survey Research Section, American Statistical Association, 1987, pp. 194-199.

[6]   J. A. Diaz-Garcia and M. M. Garay-Tapia, “Optimum al- location in Stratified surveys: Stochastic Programming,” Computational Statistics and Data Analysis, Vol. 51, No. 6, 2007, pp. 3016-3026. doi:10.1016/j.csda.2006.01.016

[7]   S. Javed, Z. H. Bakhshi and M. M. Khalid, “Optimum allocation in Stratified Sampling with random costs,” International Review of Pure and Applied Mathematics, Vol. 5, No. 2, 2009, pp. 363-370.

[8]   Z. H. Bakhshi, M. F. Khan and Q. S. Ahmad, “Optimal Sample Numbers in Multivariate Stratified Sampling with a Probabilistic Cost Constraint,” International journal of Mathematics and Applied Statistics, Vol. 1, No. 2, 2010, pp. 111-120.

[9]   P. V. Sukhatme, B. V. Sukhatme, S. Sukhatme and C. Asok, “Sampling Theory of Surveys with Applications,” 3rd Edi- tion, Iowa State University Press, Ames, 1984.

[10]   W. G. Cochran, “Sampling Techniques,” 3rd Edition, John Wiley and Sons, New York, 1977.

 
 
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