Interval integrated data envelopment analysis for simultaneously measuring both efficiency and effectiveness

Abstract

Relative efficiency of decision making units producing homogeneous outputs can be estimated by data envelopment analysis (DEA) which is a non-parametric technique. Sometimes, different types of efficiencies such as technical (relative) efficiency and effectiveness of services in transport services, or other commodities which cannot be stored, need to be measured simultaneously to fully capture these services’ overall efficiency because of different dimensions of these two measurements. The integrated data envelopment analysis (IDEA) approach simultaneously measures these two efficiency measurements. But can deterministic models be developed to solve the problems that have a different level of uncertainty? The extension of the IDEA approach from deterministic to uncertain situations, where interval numbers illustrate observations, has been proposed in this study. The extension principle is utilised to develop a pair of two-level mathematical programs to compute the upper and lower bounds of the interval service effectiveness (SE) and technical efficiency (TE). The example of intercity bus companies in Iran is applied to illustrate how to calculate the TE, SE, technical effectiveness (TET), and how to derive their relationship when the data is interval.