Hossein Azizi - Department of Applied Mathematics, Parsabad Moghan Branch, Islamic Azad University, Parsabad Moghan, Iran
Alireza Amirteimoori - Department of Applied Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran
Sohrab Kordrostami - Department of Applied Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran

The two-stage data envelopment analysis models show the performance of individual processes and ‎thus, provide more information for decision-making compared with conventional one-stage models. ‎This article presents a set of additive models (optimistic and pessimistic) to measure inefficiency ‎slacks in which observations are shown with crisp numbers. In the concept of pessimistic efficiency, ‎DMU with balanced input and output data can be scored as efficient. Since pessimistic efficiency ‎represents the minimum efficiency that is guaranteed in any unfavorable conditions, the assessment ‎based on this efficiency is in compliance with our natural meaning, especially in risk-averse situations. ‎Therefore, pessimistic efficiency solely can play a useful role in the DMU ranking. However, it is not ‎a good idea to ignore optimistic efficiency. Hence, it is an inevitable necessity to integrate different ‎performance sizes in order to achieve an overall performance assessment for each DMU. An example ‎of resin manufacturer companies in Iran is presented to explain how to calculate the system and ‎process inefficiency slacks.‎

Data envelopment analysis, inefficiency slacks, series systems, optimistic and pessimistic viewpoints, ‎overall performance