A Fuzzy Chance Constraint Programming Approach for Optimal Allocation in Multivariate Stratified Surveys: A Compromise Solution

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 (MOFCCP) problem with measurement cost h c as a normally distributed FRV. Compromise solution of its deterministic equivalent is obtained by goal programming technique. In addition, an illustrative example is also given to demonstrate the correctness of the proposed approach.