Scale directional distance function and its application to the measurement of eco-efficiency in the manufacturing sector

Directional distance function (DDF) is a recognized technique for measuring efficiency while incorporating undesirable outputs. This approach allows for desirable outputs to be expanded while undesirable outputs are contracted simultaneously. A drawback of the DDF approach is that the direction vector to the production boundary is fixed arbitrarily, which may not provide the best efficiency measure. Therefore, this study extends the previous framework of efficiency analysis to introduce a new slacks-based measure of efficiency called the scale directional distance function (SDDF) approach. This new approach determines the optimal direction to the frontier for each unit of analysis and provides dissimilar expansion and contraction factors to achieve a more reasonable eco-efficiency score. This new approach is employed to measure the eco-efficiency of the Malaysian manufacturing sector. In addition, the paper demonstrates the use of the new approach to establish target values for the reduction/expansion of outputs in order for the inefficient DMUs to achieve full eco-efficiency. The results indicate that Melaka, Pulau Pinang, Negeri Sembilan, Sabah, Sarawak and Labuan have attained full ecoefficiency while Terengganu is the least eco-efficient. The overall eco-efficiency of the manufacturing sector in Malaysia is 80.5% with wide variations across the states. Keywords Data envelopment analysis (DEA), Directional distance function (DDF), Scale directional distance function (SDDF), undesirable output, eco-efficiency Annals of Operations Research, 2013, Vol. 211(1): 381-­‐398.