A dimensional decomposition approach to identifying efficient units in large-scale DEA models

In this paper, we propose the use of a dimensional decomposition procedure together with lexicographic parametric programming to reduce computational burden when identifying the efficient decision making units in data envelopment analysis (DEA). The use of lexicographic parametric programming makes it possible to develop an efficient algorithm for the problems with few inputs and outputs. Based on this we propose the procedure which first partitions the original problem dimensionally into sub-problems and then identifies the efficient units of the sub-problems. Since those units are a subset of the weakly efficient solutions of the original problem, they are used as an initial approximation for the efficient units of the original problem. The efficiency of the approach is illustrated by numerical results.