A GOAL-PROGRAMMING METHOD OF STOCHASTIC ALLOCATIVE DATA ENVELOPMENT ANALYSIS

Allocative Data Envelopment Analysis (ADEA) is a version of Data Envel opment Analysis (DEA) which measures relative efficiency for a group o f similar operating units with known input prices. By using the actual input values, ADEA provides information to managers on the minimum co st method of operation for each unit. A major criticism of DEA methods is that they are deterministic and have no means of allowing for unce rtainty. This paper applies the goal-programming approach, introduced by Banker (1991), to allocative efficiency and develops the Stochastic ADEA model. A two-stage solution method is introduced, which is neede d because of the existence of alternate optimal solutions regarding wh ich units are found to be significantly inefficient. We propose that i dentifying the significantly inefficient units is most useful to manag ers because it best facilitates improved efficiency. The concept of a minimum frontier is introduced and used to define the significantly in efficient units. We also show how bounds can be imposed which allow th e ambiguity of the noise/inefficiency trade-off to be eliminated from the objective function. The use of bounds also allows the identificati on of the significantly inefficient unit based on the amount of uncert ainty present for each operating unit. As a result of optimizing cost, this method has the important advantage of being ideally suited for m ultiple outputs.