Multi-objective geometric programming approach in multivariate stratified sample survey with quadratic cost function

ABSTRACT

The problem of optimum allocation in multivariate stratified sample surveys where the total cost ($C$) of the survey is quadratic in $\sqrt{n_h}$ with significant travel cost has been formulated of as a Multi-Objective Geometric Programming Problem (MOGPP). The fuzzy programming approach has been described for converting the (MOGPP) into Single Objective Geometric Programming Problem (SOGPP) with the use of the membership function. The formulated SOGPP has been solved with the help of LINGO [LINGO User's Guide. Published by Lindo Systems Inc., 1415 North Dayton Street, Chicago, Illinois-60622; 2013.] Software and the dual solution is obtained. The optimum allocations of sample sizes are obtained with the help of dual solutions and the primal–dual relationship theorem. A numerical example is given to illustrate the procedure.

KEYWORDS:

• Multi-objective
• fuzzy programming
• geometric programming
• multivariate stratified sample surveys
• optimum allocations

Disclosure statement

No potential conflict of interest was reported by the authors.