Chebyshev Approximate Solution to Allocation Problem in Multiple Objective Surveys with Random Costs

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DOI: 10.4236/ajcm.2011.14029   PDF   HTML     4,808 Downloads   8,402 Views   Citations

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.

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M. 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.

Conflicts of Interest

The authors declare no conflicts of interest.

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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