A goal-programming method of stochastic allocative data envelopment analysis

Allocative Data Envelopment Analysis (ADEA) is a version of Data Envelopment Analysis (DEA) which measures relative efficiency for a group of similar operating units with known input prices. By using the actual input values, ADEA provides information to managers on the minimum cost method of operation for each unit. A major criticism of DEA methods is that they are deterministic and have no means of allowing for uncertainty. This paper applies the goal-programming approach, introduced by Banker, to allocative efficiency and develops the Stochastic ADEA model. A two-stage solution method is introduced, which is needed because of the existence of alternate optimal solutions regarding which units are found to be significantly inefficient. The authors propose that identifying the significantly inefficient units is most useful to managers because it best facilitates improved efficiency. The concept of a minimum frontier is introduced and used to define the significantly inefficient units. The authors also show how bounds can be imposed which allow the ambiguity of the noise/inefficiency trade-off to be eliminated from the objective function. The use of bounds also allows the identification of the significantly inefficient unit based on the amount of uncertainty present for each operating unit. As a result of optimizing cost, this method has the important advantage of being ideally suited for multiple outputs.