Imprecise data envelopment analysis – envelopment and multiplier model approaches

When multiple outputs and multiple inputs are imprecise data such as bounded data, ordinal data or ratio bound data, the standard linear data envelopment analysis (DEA) model becomes nonlinear and is called imprecise DEA (IDEA) which can either be converted into a linear program by scale transformations and variable alternations, or solved using the standard DEA model by converting imprecise data into a set of exact data. The current paper investigates the working mechanism of IDEA and shows alternative ways to convert ordinal data into a set of exact data. It is shown that (i) the original IDEA, multiplier IDEA (MIDEA) which is developed from the multiplier DEA model presents the best efficiency scenario, and (ii) the primal IDEA (PIDEA) which is developed from the primal DEA model presents the worst efficiency scenario. The nonlinear PIDEA can also be easily executed by the standard linear DEA models based upon a set of derived exact data whereas it cannot be converted into a linear program via scale transformations and variable alternations.