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Generally, stratification gives a small error and greater precision than the simple random sampling method in estimating the sample for the study. This paper aims to formulate the sampling problem as a multi-choice programming problem for determining the optimum allocation in the presence of non-response and considering a two-stage stratified Warner's randomized response model with cost constraint. But, mostly in real-life situations, the cost is not certain. Therefore, in cost constraint, the right-hand side parameter, i.e. total available budget, has been considered as multi-choice in nature. Multiple choices may exist for the fixed cost in the constraint, out of which exactly one has to be selected. The selection should make so that the combination of each choice should provide the best compromise optimum solution. The problem has been formulated as a multi-choice integer nonlinear programming problem, and an illustrative numerical example has been presented to demonstrate the proposed model.

Multi-choice stratified randomized response model with two-stage classification