Abstract
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.
Highlights
In sampling the precision of an estimator of the population parameters depends on the size of the sample and variability among the units of the population
The fuzzy programming approach has been described for solving the formulated Multi-Objective Geometric Programming Problem (MOGPP) and the optimum allocations of sample sizes of respondents and non respondents are obtained
This paper provides an insightful study of fuzzy programming for solving the multi-objective geometric programming problem (MOGPP)
Summary
In sampling the precision of an estimator of the population parameters depends on the size of the sample and variability among the units of the population. Varshney et al [9] formulated the multivariate stratified random sampling in the presence of non-response as a Multi-objective Integer Nonlinear Programming problem and a solution procedure is developed using lexicographic goal programming technique to determine the compromise allocation. Varshney et al [11] have considered the multivariate stratified population with unknown strata weights and an optimum sampling design is proposed in the presence of non-response to estimate the unknown population means using DSS strategy and developed a solution procedure using Goal Programming technique and obtained an integer solution directly by the optimization software LINGO. We have formulated the problem of non-response with significant travel cost where the cost is quadratic in nh in multivariate stratified sample surveys as a Multi-Objective Geometric Programming problem (MOGPP).
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