Slack- based Measures of Efficiency in Two-stage Process: An Approach Based on Data Envelopment Analysis with Double Frontiers

Data envelopment Analysis (DEA) is a mathematical technique for evaluating the relative efficiency of Decision Making Units (DMUs) that convert multiple inputs to multiple outputs. DEA is considered to find optimistic efficient performers in most favorable scenario while giving most favorable weights to inputs and outputs of every DMU. The obtained efficient DMUs construct an optimistic efficient (best-practice) frontier. On the other hand for the purpose of identifying bad performers in most unfavorable scenario, pessimistic DEA model has been proposed, which measures the efficiency with the set of most unfavorable weights. The obtained pessimistic efficient DMUs construct pessimistic (worst-practice) frontier. In many real life situations, DMUs may have a two-stage structure where the first stage uses inputs to produce outputs (called Intermediate) then in second stage that intermediate measures are taken as inputs to produce the final outputs. Assuming this type of structure of production process we used a Slack-based Model (SBM) for obtaining Optimistic and Pessimistic DEA models for stage one, stage two and for overall system in order to measure optimistic and pessimistic efficiencies. An example of non-life insurance industry of Taiwan is selected for supporting our model.