Modeling efficiency in the presence of multiple partial input to output processes

Data envelopment analysis (DEA) is a methodology used to measure the relative efficiencies of peer decision-making units (DMUs). In the original model, it is assumed that in a multiple input, multiple output setting, all members of the input bundle affect the entire output bundle. There are many situations, however, where this assumption does not hold. In a manufacturing setting, for example, packaging resources (inputs) only influence the production of those products that require packaging. This is referred as partial input-to-output interactions where the DEA model is based on the view of a DMU as a business unit consisting of a set of independent subunits, such that efficiency of the DMU can be defined as a weighted average of the efficiencies of those subunits. The current paper presents an extension to that methodology to allow for efficiency measurement in situations where there exist multiple procedures or processes for generating given output bundles. The proposed model is then applied to the problem of evaluating the efficiencies of a set of steel fabrication plants.