Modelling Best-Practice Frontiers When There Are Multiple Outputs

Abstract

This paper presents a way of modelling relationships between multiple dependent and multiple independent variables. The method involves fitting coefficients to functions of these two sets of variables such that the resulting ‘aggregate’ functions have maximum correlation. The inclusion of constraints in the fitting procedure is also possible in order to satisfy any conditions felt to be appropriate, possibly for theoretical reasons. This approach may be described as maximum correlation modelling or constrained canonical correlation analysis.

The particular application here is to the construction of best-practice benchmark models of organisational units or branches carrying out similar activities which transform a set of inputs or resources into a set of outputs. The first stage involves identifying the non-dominated set (the efficient units) using data envelopment analysis; dominated units are then discarded from the subsequent stages. We then show how the best-practice model can be generated using a spreadsheet package which contains a constrained optimization facility. The technique is illustrated using data from university chemistry departments.