Stochastic nonlinear optimal allocations with Weibull cost function when non-response is observed

Different cost functions, comprising of linear, quadratic and gamma cost functions, have been utilised based on their functional form and will be obsolete if additional cost is incurred. In this paper, a Weibull cost function when there is non-response is proposed for multivariate stratified sampling surveys. Hansen and Hurwitz (1946) introduced the concept of non-response by subsampling non-respondents in a more careful second attempt, and the variance function was considered to be deterministic. Furthermore, in real-life situations, population parameters are considered to be random and uncertain, and it is advisable to use a stochastic programming approach to model such problems. To optimally distribute sample sizes to strata, the problem will be modelled using the multi-objective stochastic integer nonlinear programming problem (MO-SINLPP) technique. A solution method is suggested using the D1 distance technique and fuzzy programming. The results of the comparative study showed that the compromise optimum allocations outperformed the individual optimum allocation of the different characteristics using the Weibull cost function.