On optimal design of multi-survey questionnaires

In the paper we model the problem of optimal assignment of respondents to internet questionnaires. The task is taken from a leading online survey company in Central and Eastern Europe which runs several dozen of surveys in parallel. Each survey has a unique respondent inclusion criteria based on their socio-demographic data and target number of times it has to be collected. Company has data on distribution of socio-demographic characteristics in general population under survey. In the paper we propose a mathematical programming model that allows us to find an optimal decision making scheme allowing to assign respondents to surveys so as to minimize expected number of questions asked subject to survey inclusion criteria and their target number of respondents.