A fuzzy goal programming approach in stochastic multivariate stratified sample surveys (original) (raw)
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INTERACTIVE FUZZY GOAL PROGRAMMING APPROACH IN MULTI-RESPONSE STRATIFIED SAMPLE SURVEYS
In this paper, we applied an Interactive Fuzzy Goal Programming (IFGP) approach with linear, exponential and hyperbolic membership functions, which focuses on maximizing the minimum membership values to determine the preferred compromise solution for the multi-response stratified surveys problem, formulated as a Multi- Objective Non Linear Programming Problem (MONLPP), and by linearizing the nonlinear objective functions at their individual optimum solution, the problem is approximated to an Integer Linear Programming Problem (ILPP). A numerical example based on real data is given, and comparison with some existing allocations viz. Cochran’s compromise allocation, Chatterjee’s compromise allocation and Khowaja’s compromise allocation is made to demonstrate the utility of the approach.
Journal of Applied Mathematics, 2014
In practical utilization of stratified random sampling scheme, the investigator meets a problem to select a sample that maximizes the precision of a finite population mean under cost constraint. An allocation of sample size becomes complicated when more than one characteristic is observed from each selected unit in a sample. In many real life situations, a linear cost function of a sample sizenhis not a good approximation to actual cost of sample survey when traveling cost between selected units in a stratum is significant. In this paper, sample allocation problem in multivariate stratified random sampling with proposed cost function is formulated in integer nonlinear multiobjective mathematical programming. A solution procedure is proposed using extended lexicographic goal programming approach. A numerical example is presented to illustrate the computational details and to compare the efficiency of proposed compromise allocation.
Journal of Statistical Computation and Simulation, 2014
In multivariate cases, usually the minimization of sampling variances is considered as an objective under a cost constraint. Since the variances are not unit free, it is more logical to consider the minimization of the squared coefficients of variation as an objective. In this paper, the problem of optimum compromise allocation in multivariate stratified sampling in the case of non-response as a multi-objective all-integer nonlinear programming problem is described. A solution procedure using four different approaches is considered, namely the value function, goal programming, ∈-constraint and distance based, to obtain the compromise allocation for non-response. A numerical example is also presented to illustrate the computational details.
2014
Optimal allocation of sample size among various strata is an important step to get the precise estimates for population parameters and to reduce the cost of the survey. A reasonable criterion for optimal allocation is the minimization of the variances of the estimates for a specified cost or to minimize the cost of survey for desired precision of the estimates. The total cost of survey is a function of sample sizes allocated to various strata and the unitary cost of collecting information/measurement associated to particular stratum. The measurement cost h c which vary from stratum to stratum and affected by some factors such as nature of climate, weather conditions which occurs randomly is considered as fuzzy random variable (FRV). The survey is taken as multivariate in which we want to study more than one characteristic. Thus, in this paper the problem of optimum allocation in multivariate stratified sampling is formulated as a multiobjective fuzzy chance constrained programming (...
An Optimal Chance Constraint Multivariate Stratified Sampling Design Using Auxiliary Information
Journal of Mathematical Modelling and Algorithms in Operations Research, 2013
When we are dealing with multivariate problem then we need an allocation which is optimal for all the characteristics in some sense because the individual optimum allocations usually differ widely unless the characteristics are highly correlated. So an allocation called "Compromise allocation" is to be worked out suggested by Cochran. When auxiliary information is also available, it is customary to use it to increase the precision of the estimates. Moreover, for practical implementation of an allocation, we need integer values of the sample sizes. In the present paper the problem is to determine the integer optimum compromise allocation when the population means of various characteristics are of interest and auxiliary information is available for the separate and combined ratio and regression estimates. This paper considers the optimum compromise allocation in multivariate stratified sampling with non-linear objective function and probabilistic non-linear cost constraint. The probabilistic non-linear cost constraint is converted into equivalent deterministic one by using Chance Constrained programming. The formulated multi-objective nonlinear programming problem is solved by Fuzzy Goal programming approach and Chebyshev approximation. Numerical illustration is also given to show the practical utility of the approaches.
Journal of Mathematical Modelling and Algorithms in Operations Research, 2015
In this paper, we have formulated the problem of non-response in multivariate stratified sample surveys as a Multi-Objective Geometric Programming problem (MOGPP). The fuzzy programming approach has described for solving the formulated MOGPP. The formulated MOGPP has been solved and the solution is obtained. The obtained solution is the dual solution corresponding to the multi-objective multivariate stratified sample surveys in presence of non-response. Afterward with the help of dual solution of formulated MOGPP and primal-dual relationship theorem the optimum allocation of sample sizes of respondents and non respondents are obtained. A numerical example is given to illustrate the procedure.
Allocation in Multivariate Stratified Surveys with Non-Linear Random Cost Function
American Journal of Operations Research, 2012
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.
American Journal of Operations Research, 2014
In this paper, the problem of non-response with significant travel costs in multivariate stratified sample surveys has been formulated of as a Multi-Objective Geometric Programming Problem (MOGPP). The fuzzy programming approach has been described for solving the formulated MOGPP. The formulated MOGPP has been solved with the help of LINGO Software and the dual solution is obtained. The optimum allocations of sample sizes of respondents and non respondents are obtained with the help of dual solutions and primal-dual relationship theorem. A numerical example is given to illustrate the procedure.