Interval And Ordinal Data

Abstract

The standard Data Envelopment Analysis (DEA) method requires that the values for all inputs and outputs are known exactly. When some inputs and output are imprecise data, such as interval or bounded data, ordinal data, and ratio bounded data, the resulting DEA model becomes a non-linear programming problem. Such a DEA model is called imprecise DEA (IDEA) in the literature. There are two approaches in dealing with such imprecise inputs and outputs. One approach uses scale transformations and variable alternations to convert the non-linear IDEA model into a linear program. The other identifies a set of exact data from the imprecise inputs and outputs and then uses the standard linear DEA model. This chapter focuses on the latter IDEA approach that uses the standard DEA model. This chapter shows that different results are obtained depending on whether the imprecise data are introduced directly into the multiplier or envelopment DEA model. Because the presence of imprecise data invalidates the linear duality between the multiplier and envelopment DEA models. The multiplier IDEA (MIDEA), developed based upon the multiplier DEA model, presents the best efficiency scenario whereas the envelopment IDEA (EIDEA), developed based upon the envelopment DEA model, presents the worst efficiency scenario. Weight restrictions are often redundant if they are added into MIDEA. Alternative optimal solutions on the imprecise data can be determined using the recent sensitivity analysis approach. The approaches are illustrated with both numerical and real world data sets.