DEA multiplier analytic center sensitivity with an illustrative application to independent oil companies

The set E of extreme points which are also efficient are of basic importance in defining the efficiency frontier, from which the observations for all other DMUs are evaluated in DEA. A significant question which we address is ''What variations in the data can be tolerated before the membership in E is changed?'' This topic is explored using (1) a simple illustrative example, and (2) production data for 30 independent oil companies during the period 1983-1985. Data were allowed to vary simultaneously for all observations and in different subsets determined by random drawings of data for points both in E and not in E. The results were found to be robust in this study, thereby lending further support to earlier studies which also found these classifications into efficient and inefficient performers to be robust in DEA. Technical developments for these new methods of sensitivity analysis are supplied. These developments feature an application of analytic center (interior point) algorithms which ensure that the Strong Complementary Slackness Condition (SCSC) is fulfilled. The solutions satisfy a mathematical condition called ''centrality''. Generally, the solutions are at interior points called analytic centers. At these interior points, continuity of the input-output ratios ensures that DMUs in E remain in E for at least small relative variations in the data, while empirically these properties have been found to extend to much larger variations in the data sets.