Abstract:

Although the flexible direction determination is the most characteristic advantage of the direction distance function （DDF）， the different results caused by different directions have also become the technological difficulty， which is controversial. In view of this problem， the basic principles and limitations of the existing direction determination methods in DDF are analyzed， and shadow price is introduced to clarify a new endogenous direction setting mechanism. Secondly， the improvement space of each input/output element of the decision-making unit to the maximum extent is taken as the goal to construct the optimal shadow price determination model. Sequentially， a new method for determining the optimal endogenous direction and improvement path， N-DDF method， is constructed based on the shadow price. The new method can not only get rid of the dependence on exogenous data and determine direction completely by the endogenous method， but also overcome the limitation of traditional endogenous methods that lacking economic connotation. Through theoretical expansion， it can be found that the N-DDF method is not only applicable to the hypothesis of variable returns to scale， but also applicable to others different decision scenarios， such as the hypothesis of constant returns to scale and considering undesirable outputs. Finally， an example analysis is given to illustrate the effectiveness of the N-DDF method.

Key words: data envelopment analysis, direction distance function, endogenous direction, shadow price, profit maximization