Interval Economic Efficiency Measures in Data Envelopment Analysis

One of the most essential pieces of information given by DEA models is the cost efficiency of decision-making units (DMUs). Cost efficiency (CE) is defined as the ratio of minimum costs to current costs and in fact, evaluates the ability to produce current outputs at a minimal cost. While the traditional cost efficiency models require the values for all data to be known exactly, in real-world problems the exact values of input prices are unknown, and only the maximum and minimum bounds of input prices can be estimated for each DMU. Hence, the main aim of the current paper is to develop a pair of two-level mathematical programming problems, whose optimal values represent the optimistic and pessimistic cost efficiency measures. The two-level nonlinear program for the optimistic cost efficiency measure is then transformed into a one-level linear program. In this regard, we provide an explicit formula for measuring the pessimistic CE measure.