Allocation in Multivariate Stratified Surveys with  Non-Linear Random Cost Function

Abdul Bari,Yashpal Singh Raghav,Irfan Ali,Mohammed Faisal Khan

doi:10.4236/ajor.2012.21012

Abstract

In this paper, we consider an allocation problem in multivariate surveys with non-linear costs of enumeration as a problem of non-linear stochastic programming with multiple objective functions. The solution is obtained through Chance Constrained programming. A different formulation of the problem is also presented in which the non-linear cost function is minimised under the precision constraints on estimates of various characters. The solution is then obtained by using Modified E-model. A numerical example is solved for both the formulations.

Highlights

In multivariate stratified sampling where more than one characteristic are to be estimated, an allocation which is optimum for one characteristic may not be optimum for other characteristics
If the budget of the survey is fixed in advance, say, C, the multivariate allocation problem is stated to minimize the variances for various characters for a desired precision as the following p convex programming problems; Min
In a survey the costs for enumerating a character in various strata are not known exactly, rather these are being estimated from sample costs. As such the formulated allocation problem should be considered as stochastic programming problem

Summary

Introduction

In multivariate stratified sampling where more than one characteristic are to be estimated, an allocation which is optimum for one characteristic may not be optimum for other characteristics. Kokan and Khan [7] formulated the minimization of the cost of the survey for desired precisions on various characters as the following convex programming problem; L. characters to be estimated in the survey and ci , aij , k j and Ni are all positive constants. If the budget of the survey is fixed in advance, say, C, the multivariate allocation problem is stated to minimize the variances for various characters for a desired precision as the following p convex programming problems; Min. V. In a survey the costs for enumerating a character in various strata are not known exactly, rather these are being estimated from sample costs As such the formulated allocation problem should be considered as stochastic programming problem.

Problem Formulation

E V f f t t

Modified E-Model

Numerical Illustration

Minimization of the Variances Subject to the Non-Linear Cost Function

Conclusion