How can we measure and compare the relative performance of production units? If input and output variables are one dimensional, then the simplest way is to compute efficiency by calculating and comparing the ratio of output and input for each production unit. This idea is inappropriate though, when multiple inputs or multiple outputs are observed. Consider a bank, for example, with three branches A, B, and C. The branches take the number of staff as the input, and measures outputs such as the number of transactions on personal and business accounts. Assume that the following statistics are observed: Branch A: 60000 personal transactions, 50000 business transactions, 25 people on staff, Branch B: 50000 personal transactions, 25000 business transactions, 15 people on staff, Branch C: 45000 personal transactions, 15000 business transactions, 10 people on staff. We observe that Branch C performed best in terms of personal transactions per staff, whereas Branch A has the highest ratio of business transactions per staff. By contrast Branch B performed better than Branch A in terms of personal transactions per staff, and better than Branch C in terms of business transactions per staff. How can we compare these business units in a fair way? Moreover, can we possibly create a virtual branch that reflects the input/output mechanism and thus creates a scale for the real branches? Productivity analysis provides a systematic approach to these problems. We review the basic concepts of productivity analysis and two popular methods DEA and FDH, which are given in Sections 12.1 and 12.2, respectively. Sections 12.3 and 12.4 contain illustrative examples with real data.
